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KICD GERMAN SYLLABUS FREE PDF

October 5, 2025 Hillary Kangwana Leave a comment

502 – GERMAN SYLLABUS

GENERAL OBJECTIVES OF GERMAN LANGUAGE IN KENYAN SECONDARY
SCHOOLS

The learner’s language skills should be developed to a level that enables him/her to comprehend
simple spoken German, take part in a basic conversation with a native speaker, read simple
authentic texts with understanding and communicate in simple written German.

By the end of the course the learner should be able to:
1.   communicate through speaking and writing;
2.   express his/her intentions adequately and appropriately in specific communicative situations.
These  communicative  abilities  can  be  applied  in  monologic,  dialogic  and  polylogic
encounters with German-speakers; such as:
a.   individual and class-correspondence with German-speakers
b.   basic mediating and interpreting processes
c.   real-life conversation in German-speaking countries
d.   simple presentations and discussions, contrasting for instance Kenya and
Germany;
3.   appreciate closer cultural, political and economic links between Kenya and the German-
speaking countries;
4.   show creative use of the language;
5.   display basic standard German necessary for further studies of the language in institutions
of higher learning;
6.   demonstrate basic communicative skills;
7.   read and listen to authentic oral and written material in German;
8.   show understanding of the German way of life and thus enhance the understanding and
appreciation of the learner‟s own culture;
9.   show appreciation of the German culture, its values and views with respect and tolerance;
10. show appreciation of such benefits of traveling as broadening one‟s horizons and varying
one‟s outlook;
11. develop critical and rational thinking on his/her environment;
12. display  a  responsible  attitude  and  behaviour  with  regard  to  life,   nature  and  its
conservation;
13. develop a future-oriented outlook towards industrial and technological development of the nation;
14. develop social skills;
15. develop skills and strategies to locate and retrieve information from
print and electronic media on subject-relevant topics;
16. demonstrate knowledge of the implications of pertinent national and global topical
issues at the individual and societal levels;
17. appreciate the importance of global peace through the understanding and appreciation of
other people‟s cultures.

THE FOUR LANGUAGE SKILLS

1. Listening Comprehension
Listening is an integral part of communication and the understanding of what is heard forms
the basis of the resultant response. Its significance in academic and general life cannot
therefore be over-emphasized. Listening comprehension entails detailed, extensive and
selective listening either singly or in combination

By the end of the course, the learner should be able to:
a)   display a detailed understanding of  questions, instructions and statements and respond
accordingly.
b)  display a detailed and extensive understanding of fictional and non-fictional narrated or
recorded listening texts.
c)   display an understanding of prosodic elements and interpret the intentions and the
emotional state of the speaker in different simply-structured communicative situations,
and develop the ability to decode the emotional state of the speakers.2. Speaking
Speech production is the most widespread means of communication between people of the
same  language  system.  Lack  of  accuracy  in  expression  can  lead  to  misunderstanding;
therefore all aspects of speech production need special attention for the learner of a foreign
language.

By the end of the course, the learner should be able to:

a)   read out – with correct pronunciation, clearly and fluently – unknown texts with new words
and word combinations;
b)  make and respond to requests;
c)   issue and follow instructions;
d)  formulate and ask questions on written texts and give answers based on the texts;
e)   use and respond appropriately to prosodic elements and some few stylistic devices;
f)   formulate observations and rules on linguistic structures and their functions;
g)  engage in role plays on conflict resolution;
h)  play out situations which call for an interpreter;
i)   present talks about themselves and their  immediate environment;
j)   engage in guided discussions on topics taken from the Kenyan socio-cultural background.
k)  present prepared short talks on topics within the Kenyan background and express opinions
on some aspects of the Kenyan reality;
l)   engage in discussions on similar or contrasting socio-cultural aspects in Kenya and
Germany;
m) present prepared free talks on topics from the Kenyan and German realities within a given
time limit;
n)  sing songs or recite texts, e.g. poems, with basically familiar linguistic elements and
present them with appropriate gestures;
o)  present texts, e.g. short plays,  with predominantly familiar linguistic elements, and
perform these appropriately;
p)  extract simple information from maps on geographical and political features of Germany,
Austria and Switzerland;
q)  evaluate some similarities and differences between Kenyan and German geographical and
political features e.g. climate, seasons, federal states;
r)   put pictures in sequence and verbalise the content with the help of given expressions
revealing a plot, characters and settings.
Reading Comprehension

Reading enhances retrieval of information from different types of printed media. This makes
reading an indispensable skill for effective functioning in the modern world.

By the end of the course, the learner should be able to:
a)   read aloud texts with correct pronunciation and intonation;
b)  carry out skimming and scanning strategies in texts;
c)   display a detailed and extensive understanding of  texts, i.e. topical or narrative,
descriptive and argumentative texts, chosen from within or without  the learners’ cultural
background with some unknown words whose meaning can be inferred from the context;
d)  display a fine understanding of written questions, instructions and explanations, e.g. in a
questionnaire for an au-pair job application, on a German visa application form etc.
e)   display an understanding of linguistic terminology;
f)   utilise reading skills to support listening comprehension (through the use of worksheets);
g)  deduce the meaning of new words in a text e.g. narratives;
h)  recognise the structure of German texts through the structural and linguistic signals learnt;
i.e. paragraphs, reference words, additional cohesives,  connectors, and transitional
devices.

Writing

Writing is an expressive language skill that requires a high degree of organisation. It affects to
a large extent our way of thinking and of acquiring knowledge and is a cornerstone of
academic success. This skill is required by the learner in order to express his/her own ideas in
written form.

By the end of the course, the learner should be able to:

a)   write unknown German graphemes and typical German letter combinations, e.g. “ß”,”sch”, “ö” ;
b)  write answers to questions on texts or topics;
c)   complete open  ended fictional texts directed by questions or other guidelines e.g.
pictures;
d)  fill in a detailed questionnaire, e.g. an application form for an au-pair job (functional
writing);
e)   utilise the structural and linguistic devices e.g. paragraphs, connectors for main and
subordinate clauses, transitional devices and  reference words  for own creative writing;
f)   express in writing personal position/stand  and judgement on topical issues;
g)  transform texts by changing the perspective (tense, subjects, location), e.g. from a
program of events to an invitation, or from a fairy tale to a  skit;
h)  write openings or endings to short fictional and non-fictional texts;
i)   plan, organise and write texts on opinions/ conflicts/contrasting aspects of the Kenyan and
German realities using the writing skills developed throughout the course (formal,
informal letters, articles for a school magazine);
j)   write short simply-structured more creative texts directed by questions or stimulated by
pictures e.g. long dialogues, short narrative and descriptive texts on own experiences,
informal letters, formal letters e.t.c.
Content and intercultural topics
The topics to be covered in the learning of German from Form 1 to Form 4 are
– greeting friends   and  adults
– making contacts,  introducing oneself  and others
– school/school items
– family life
– friends
– hobbies, leisure  activities
– likes and dislikes
– career wishes
– alphabet
– cardinal numbers
– food and shopping
– telling time
– daily (school) routine
– describing rooms and places
– holiday activities
– ordinal numbers
– health and health conditions
– describing people/characters
– making appointments and dates, exchanging presents
– visiting people and places
– giving directions
– geography of Kenya
– agricultural and other typical produce of Kenya
– Kenyan/German fables
– biographies, curriculum vitae
– tourism in Kenya
– basic geography of Germany
– travelling in Germany
– family life in Germany
– leisure activities in Germany
– school system, school routine in Germany
– youth and their varied lifestyles
– job opportunities and job training
– environmental awareness
– political life in Germany
– role and impact of media and technological innovation on society.

Grammar

The grammar requirements define the basics for mastering a multitude of communicative
situations. The list below shows the required grammar items for the 4-year course.
– question words
– prepositions “in ” and “au s” follow ed by info rmation  without  article
– countable nouns and their plural forms
– nominative case: definite, indefinite articles (singular and  plural)
– nominative case: possessive articles (singular and  plural)
– simple questions with and  without question words
– subject pronouns/ nominative case
– conjugation of regular and some irregular verbs in the present tense
– auxiliary verbs “kö nn en ”, “w o llen ”, “m ög en ” (p resent tense)
– negation of verbs and questions
– word order in simple sentences (main clauses)
– main clause conjunctions “aber”, “und ”, “oder” an d “denn ”
– some adjectives (in predicative use)
– equal and unequal  comparisons of the adjective: positive/ comparative/ superlative
(in predicative use)
– countable and uncountable nouns
– nominative case: negative article
– accusative case: definite, indefinite, negative and possessive articles
– dative case: definite article/singular and plural after prepositions
– prepositions governing the accusative
and dative cases (wechselpräposition)
– prepositions governed by accusative case “ohne”, “durch ”, “für” and “gegen ”
– formation of the present perfect tense, using the auxiliary verbs  “hab en ” and “sein ”
– verbs with separable prefixes (present tense and present perfect tense)
– auxiliary verbs “m üssen ”, “(nicht) dürfen ” (presen t tense)
– imperative mood of the verb in main clauses (regular and irregular verbs)
– articles as pronouns in the nominative and accusative cases
– word order in subordinate clauses
– m ain clause conjunctions “dann ”, “danach ”, “so ndern ”
– the conjunctions “w eil”, “dass” (subo rdinate clauses)
– subject and object pronouns (nominative and accusative cases)
– descriptive adjectives (in predicative use)
– dative objects (all articles/ singular and plural)
– prepositions of direction, location and m eans  “n ach ” ,”zu ” ,“von ”, “b ei”, “aus”, ”m it”
and “seit” governed by the dative case
– conjugation of the verb in the simple past tense (regular and irregular forms)
– infinitive constructions w ith “zu ”
– verbs followed by the dative case
– the auxiliary verb “sollen ”
– all auxiliary verbs (past tense)
– imperative mood in the reported speech (subordinate clauses)
– the temporal conjunction s, e.g. “nachd em ”, “seitdem ”, “bevo r”, “solange”, “bis”,
“als”, “w enn ”, “obw ohl” and “w äh rend ” (subordin ate clauses)
– the conjunctions “um ….zu ”, “ohne..zu ” (infinitive construction), “dam it”, “ohne dass”
(subordinate clauses)
– the question w ord “w elch -” (all cases, singular an d plural)
– reported speech (questions) w ith the conjunctions “dass”, “ob ” and all question words
– object pronoun in the dative case
– reflexive and reciprocal pronouns
– adjectives (attributive) in combination with the definite, indefinite, negative and
possessive articles (nominative and accusative cases)
– sequencing of the syntactical elements, e.g. objects, dative and accusative pronouns,
– adverbial qualifiers
– some nouns with special declension
– nom inative, accusative and dative cases o f the dem onstrative articles, e.g. “dies-”
– the genitive case (all articles, singular and plural)
– the genitive attribute
– prepositions governed by the genitive case, e.g. “trotz”, “w egen ”, “w äh rend ”
– verbs w ith prepositions governed by the d ative an d accusative cases, e.g. “w arten au f
(acc.)”, and the correspo nding question w ords, e.g. “w orau f”
– special negation forms, e.g. “niemand”, “kein-“, “nie(m als)”, “nirgendw o”, “un -“, “-
los”
– subordinate clauses with a relative pronoun (nominative, dative and accusative  cases)
– adjectives (attributive) in combination with the definite, indefinite, negative and
possessive articles (dative and genitive cases)
– adjectives (attributive) in combination with nouns without articles
– unequal  comparisons of the  adjective (attributive) comparative / superlative
– receptive command of the passive voice

Pronunciation and intonation

The pronunciation norm underlying the German course is that of Standard High German. By
the end of the course the learners should be able to:
· recognise and pronounce typical German sounds, e.g. the Umlaute and the different
“ch”-sounds

·   differentiate  between  relevant  phonological  characteristics,  e.g.  voiced  –  voiceless,
short -long, stressed – unstressed
·   recognise and articulate patterns of intonation in questions and answers
·   understand the meaning and functions of rhythm, stress and emphasis and use prosodic
elements appropriately according to the communicative situations.

Orthography

The syllabus recommends the use of the orthography of Standard High German. The correct
spelling is a prerequisite for successful written communication. The practice of spelling is of
significance – especially in areas where the German orthography deviates from English and or
Kiswahili orthographic rules – and where the pronunciation differs from the spelling.

Teachers' Resources

KCSE HOME SCIENCE JOINT EXAMS (QUESTIONS AND ANSWERS)

October 5, 2025 Hillary Kangwana Leave a comment

DISTRICTS SAMPLED AND COMPILED

NDHIWA
SOTIK
KAKAMEGA CENTRAL
NYAMIRA
HOMABAY
RACHUONYO
MIGORI
UGENYA/UGUNJA
KISUMU WEST
MATUNGU
BUTERE
KAKAMEGA EAST
NYATIKE
KHWISERO
TRANS NZOIA WEST
TRANSMARA
KAKAMEGA NORTH
MUMIAS

HOME SCIENCE

PAPER ONE

*KSM*

Explain the role of sweat glands in the soiling of the body (2mks)
Identify any four main causes of accidents in the house (2mks)
State any two characteristics of clothes made of fabric that develop static electricity (2mks)
Explain how living a relatively sedentary lifestyle can lead to obesity (1mk)
State two qualities that make the run and fell (machine fell) seam suitable for making night dress
Explain two precautionary measures to be taken when cleaning a painted wall
Give two reasons why low heeled shoes are recommended for a pregnant woman (2mks)
Give four uses of fat in flour mixture (2mks)
State the two main roles of garnishing in food presentation (2mks)
Identify linen using burning test (3mks)
Give reasons for using the following processes during garment construction (2mks)

(a) Basting

(b) Trimming

Identify any six factors that may affect normal foetal development (3mks)
Define the term food fortification (1mk)
State any two dangers of misusing drugs (1mk)
State any two factors that affect the efficiency of a detergent (2mks)
Define the term ‘hue’ as used in colour (1mk)
State any function of riboflavin (2mks)
What are two disadvantages of credit buying (2mks)
Mention any two preparations to be made before carrying out a family wash (1mk)
Suggest two reasons for using smoking in garment construction (2mks)
Give two reasons for having a plan for spending the money available to a family (2mks)
What are the two forms of “malnutrition” (1mk)
You have visited your aunt who is sick

(a) Wash and treat her loose coloured cotton bed sheets (10mks)

(b) Clean a pair of stainless steel cutlery she will use (5mks)

(a) State five factors that affect individual nutrient requirement (5mks)

(b) State five factors to consider when packing meals (5mks)

(d) Suggest for advantage of blending wool with nylon (4mks)

(a) Giving four examples explain why some nutritional disorders are referred to as

lifestyle related (4mks)

(b) Discuss five precautionary measures to take when using frying as a method of cooking (5mks)

(d) With the aid of diagram explain the procedure of working out wide tucks (5mks)

(a) State five factors to consider when choosing fastenings (5mks)

(b) State five precautions to take when using kerosene as a fuel (5mks)

(d) State five qualities of a well constructed piece of furniture (5mks)

*MGN*

Explain why dump dusting is better than dry dusting in a sick room
Mention any two results of lack of vitamin C in the diet
Give any two factors to consider when making a choice of accessories for an evening

Part

State two disadvantages of concealed drainage system
Mention two uses of (dhania) coriander leaves in cookery
What is the reason for giving a teething baby a hard object to bite on
State two qualities of a good soup
Give two areas in a garment where top stitching is done
Mention one way in which each of the following articles is given special treatment

(i) Tray cloth

(ii) Baby Napkin

Mention two advantages of blending cotton and nylon fibres
Give two methods of credit buying
Outline three points to consider when choosing a work surface in the kitchen
Give one reason for kneading yeast dough
Write down any two reasons why it’s important to eat raw carrots
State three qualities to look for in a pair of cutting out scissors
Give two ways in which a mother can infect her new born baby with HIV/AIDS virus
Outline two reasons for snipping curved seams
Name three types of immunization given to children before their first birthday
Give two reasons for disposing of waste properly
(a) Explain the procedure of sweeping a cemented floor

(b) Give the procedure of cleaning an enamel plate

(a) Describe any three types of meal service

(b) Supporting your answer with four reasons, give a most suitable fabric for an institutions

bed linen

(d) With two specific examples, give three uses of permanent stitches

(a) Give the systematic order of placing bedding items when preparing a baby’s cot

(b) Explain three desirable qualities of ironing board

(d) Your house is experiencing frequent black outs. Explain how you would clean a hurricane

lamp in readiness

(a) Breast milk is the best option for any new baby. In which ways would a lactating mother

improve supply of breast milk to her baby? (Give five points)

(b) State five points to consider when giving general care to all the clothes

(d) Discuss five factors that influence consumer buying

*KKC*

Outline three forms of food service (3 marks)
State three reasons for interfacing collars (3 marks)
State two properties which make asbestos suitable for theatre curtains and protective clothing
State two factors that influence choice of a method of controlling fullness (2 marks)
State three characteristics of a good French seam (3 marks)
List down four methods of neatening an open seam (2 marks)
Mention three positive effects of advertisements to a consumer (3 marks)
State two important rules to observe when darning (2 marks)
Give three factors determining the choice of color in a sitting room (3 marks)
Explain three rules to observe during stain removal (3 marks)
Mention four points to observe when packing meals (4 marks)
State three principles of wise buying (3 marks)
Identify three dangers of weaning the baby when it is too late (3 marks)
Give two reasons why common salt is iodized (3 marks)
State four disadvantages of using charcoal when cooking (2 marks)
a) Launder cotton blood stained sheet (7 marks)
b) Describe how to occasionally clean a gas lamp (4 marks)
c) Give the procedure for cleaning two Aluminium cups (5 marks)
d) Explain briefly how you can carry out spotting on a woolen skirt (4 marks)

a) Describe how run and fell seam is made on the side of a cotton skirt (8 marks)
b) State four functions of tucks in garment construction (4 marks)
c) With the aid of a diagram, describe the making of gathers before attaching to the waist band

a) Explain points to consider when choosing flowers for flower arrangement (5 marks)
b) Describe the procedure of cleaning a wooden polished table surface (7 marks)
c) List four ways of enhancing personal appearance (4 marks)
d) Explain four ways of encouraging a child to play (4 marks)

a) State six points to consider when choosing and preparing weaning foods (6 marks)
b) Give three desired qualities of a deep frying pan (3 marks)
c) State five reasons for preserving foods (5 marks)
d) Explain six dietary needs of an elderly person (6 marks)

*MAT*

List four fat soluble vitamins
State two possible causes of anaemia
Give two points to look for when buying spinach
State two effects of strong heat on proteins
State two disadvantages of suing left over foods
State two forms in which laundry soap is found in the market
Give the steps of removing chewing gum stain from a garment
Mention the three areas (centres of work that make up the work triangle in a kitchen
Suggest two measures to take immediately nose bleeding occurs
List two improvised abrasives in the home
Identify three tacks that are carried out only during special cleaning of a bedroom
Mention two dangers of heavy smoking during pregnancy
Give four methods of advertising
State two reasons why cotton fabrics are popular for the table linen
Give two reasons why silk is expensive
State three qualities of a good tape measure
Give three reasons for a needle freaking during machining
Give two reasons why press studs are not suitable for use in children’s garments

(a) You are arranging dinner for your two friends, describe how to carryout the listed chores.

(i) Thoroughly clean a stained melamine cup you will use

(ii) Starch a previously laundered cotton tray cloth using boiling water starch

(iii) Thorough cleaning the terrazzo kitchen floor

(a) Mention four ways of improving maize meal porridge

(b) Explain three precautions to take when using an oven to bake cakes

(d) Explain four uses of carrot in cookery

(a) Identify two fibers in each case wet the properties listed below;

(i) Stronger when wet

(ii) weaker when wet

(iii) elastic

(iv) luctious

(iv) Flakes with a yellow flame

(b) Describe the procedure of taking the following body measurements

(i) hips

(ii) Inside arm length

(iii) Couch

ready for attachment

(a) Discuss four desirable qualities of a good clothes line

(b) Explain five ways of disposing of refuse in the home

(d) Giving a reason in each case, state three factors to consider when wearing a baby

(a) Explain three preparations to make on a sewing machine in readiness to stitching

(b) Describe the procedure of making a single pointed dart

*MUM*

Mention any three classes of stain removers used in laundry work
State two uses of facings in garment construction
State three uses of eggs in flour mixtures
Give any two precautions measures to take when using dry cleaning fluid
What is the cause of swelling of body tissues that is symptomatic of kwashiorkor
Name any four common groups of people that are usually affected by anaemia
List three functions of water in the bodies of human beings
Define the term essential Amino acids correctly
Why are there more than usual numbers of Tuberculosis victims in today’s

societies than in the past (i.e. after the 80’s than before)

What is the work of a thermostat in an electric iron box
What are the following parts of an enclosed drainage system ?
a) Water closet:
b) Man hole
c) Septic tanks
State three general causes of poor sanitation
Give two advantages of frying as a method of cooking
State any two common problems that may afflict a pregnancy before its full term
Give two reasons why the double stitched seam is commonly used on children’s

garments

Explain two methods or ways in which the body can gain immunity to help resist

disease attacks

Give two advantages of using carpets in the home
State two reasons why wooden surfaces in the home need finishing
List four points to look for when buying cabbages
State two measures to take in order to control the incidence of bed sores in bed

ridden invalids

Your friend is celebrating her seventeenth birthday and you are to help in the preparations.

Describe how you would:

a) Launder her loose coloured cotton dress that she is going to wear that afternoon
b) Explain how you will thoroughly clean the cemented floor in the living room to be used
a) A doctor diagnosed pellagra in a foreign student. Briefly describe two symptoms he might

have noticed that were affecting his patient

b) Explain any two common faults often encountered in the making of yeast based mixture

products

c) Explain one disadvantage of advertising
d) With aid of a labeled illustration describe how to make an overlaid seam
a) Explain three causes of dental caries
b) Explain one main difference between inter facing and interlining
c) With the aid of clearly labeled diagrams describe how to work and make a box pleat
d) Explain four factors to consider before choosing a method for mending a tear in the

fabric of an item to be laundered

a) Explain four points to consider when weaning a baby
b) Explain two types of play to which growing children are normally exposed AND

mention one benefit and one demerit in each case

c) State four reasons or ways in which a consumer needs protection from negative market

effects

d) Draw a simple illustration and state the main function of each of the following

tacking stitches

i) Tailors tacking:
ii) Fishbone tacking:

iii) Basting:

*KKC*

Outline three forms of food service (3 marks)
State three reasons for interfacing collars (3 marks)
State two properties which make asbestos suitable for theatre curtains and protective clothing
State two factors that influence choice of a method of controlling fullness (2 marks)
State three characteristics of a good French seam (3 marks)
List down four methods of neatening an open seam (2 marks)
Mention three positive effects of advertisements to a consumer (3 marks)
State two important rules to observe when darning (2 marks)
Give three factors determining the choice of color in a sitting room (3 marks)
Explain three rules to observe during stain removal (3 marks)
Mention four points to observe when packing meals (4 marks)
State three principles of wise buying (3 marks)
Identify three dangers of weaning the baby when it is too late (3 marks)
Give two reasons why common salt is iodized (3 marks)
State four disadvantages of using charcoal when cooking (2 marks)
a) Launder cotton blood stained sheet (7 marks)
b) Describe how to occasionally clean a gas lamp (4 marks)
c) Give the procedure for cleaning two Aluminium cups (5 marks)
d) Explain briefly how you can carry out spotting on a woolen skirt (4 marks)
a) Describe how run and fell seam is made on the side of a cotton skirt (8 marks)
b) State four functions of tucks in garment construction (4 marks)
c) With the aid of a diagram, describe the making of gathers before attaching to the waist band
a) Explain points to consider when choosing flowers for flower arrangement (5 marks)
b) Describe the procedure of cleaning a wooden polished table surface (7 marks)
c) List four ways of enhancing personal appearance (4 marks)
d) Explain four ways of encouraging a child to play (4 marks)
a) State six points to consider when choosing and preparing weaning foods (6 marks)
b) Give three desired qualities of a deep frying pan (3 marks)
c) State five reasons for preserving foods (5 marks)
d) Explain six dietary needs of an elderly person (6 marks)

*TNW*

Why is figure type an important factor to consider in choice of your clothes? (2mks)
What is the importance of learning first aid? (2mks)
Which laundry processes are carried out before washing a fast- coloured cotton shirt? (2mks)
Differentiate between tear and wear (2mks)
Give two reasons as to why steel wool is not suitable for cleaning plastics (2mks)
Name two main methods of purchasing goods and services in Kenya (2mks)
What are the advantages of dry cleaning? (2mks)
State two ways of minimizing wastage of detergents when washing (2mks)
Give any two uses of running stitches (2mks)
How can one identify the warp thread in the absence of the selvedge? (2mks)
Which factors make meat dry and tough after roasting (2mks)
State three points to bear in mind when making seams on under wears (3mks)
Define the following terms as applied to meal??????
Give one flavouring that is suitable for salads (1mk)
State two points to consider when selecting the baby’s layette (2mks)
Differentiate between complementary and supplementary feeding (2mks)
Why is management of fullness important (3mks)
Give two uses of vinegar in cooking (1mk)
Your father is to facilitate a very important seminar. Explain how to:
a) Dry clean his tie (5mks)
b) Finish his cotton shirt (5mks)
c) Clean the leather bag be will use (5mks)
d) Clean a pair of shipper he will use (5mks)
a) Giving examples in e ach case explain three changes that take place in a dough

during the frying of mandazi (6mks)

b) Give four faults that could occur in cooking of mandazi (4mks)
c) Explain four nutritional needs of an adolescent (8mks)
d) Explain four qualities of a well made vegetable salad (2mks)
a) Explain three points to consider when using a sewing machine (6mks)
b) Mention six stitches used during the blouse/shirt construction from cutting to readiness (3mks)
c) Explain the procedure followed in preparation of around patch pocket ready for attaching (6mks)

a) Explain two positive and two negative effects of advertisements on the consumer (4mks)
b) What precautions would one take when using kerosene (4mks)
c) Explain five advantages of breast feeding (5mks)
d) What five problems could result to a baby during weaning (5mks)
e) Give two reasons for labelling products (2mks)

*NDW*

State the importance of sebaceous glands in relation to a healthy skin (1mk)
State two qualities that make aluminium popular for household utensils (2mks)
Give a reason why nylon is unsuitable for sports wears (1mk)
Mention two uses of dhania (coriander) leaves in cookery (2mks)
Mention two advantages of blending cotton and nylon fibers (2mks)
State any two reasons why a child’s growth monitoring is important (2mks)
List four laundry processes that are harmful to woolen fibres and in each case state the

harm caused

State three ways of providing variety in meal planning and management (3mks)
State two factors to consider when choosing where to buy vegetables (2mks)
Give two qualities of a good advertisement (2mks)
Explain three ways of economizing fuel when using electricity for cooking (3mks)
Explain two reasons for using interfacing during garment construction (2mks)
Identify three methods of finishing the edges of sleeves other than using a cuff (3mks)
State three reasons for labeling products in a factory (3mks)
State two precautions to be taken to prevent bed sores when taking care of the sick persons

at home

List two uses of lamp shades (2mks)
State two factors to consider when planning lighting for various rooms in the home (2mks)
Differentiate between advancing and receeding colours (2mks)
Give two reasons why most women in the rural areas are less groomed (2mks)

20 a) Describe the correct procedure of laundering nylon dress (8mks)

b) Describe the correct procedure of cleaning white canvas shoes without shoe laces (7mks)
c) Give the correct procedure of cleaning two aluminium cups (5mks)

21 a) Mention two uses of butter in the home (2mks)

b) Identify four major nutrients found in butter (4mks)

c)i)Describe four changes that takes place when heating butter (4mks)

ii) Name four main groups of fats giving an example for each (4mks)
d) Explain three considerations to make when selecting a storage facility for butter (6mks)
a)Outline four tests undertaken at the clinic to an expectant mother in the first month of

pregnancy (4mks)

b) Describe two supplementary foods for a baby (2mks)
c) Explain two benefits of supplementary food (4mks)

d)i)Explain four reasons why a mother may be unable to breast feed

ii) Explain four points on care of play items (2mks)
a) Explain four properties of viscose rayon which are undesirable (8mks)
b) Suggest four features that can be used to finish a nigh dress decoratively (4mks)
c) Give three reasons for ironing a night dress during construction (3mks)
d) Explain five desirable qualities of an iron box (5mks)

*RCH*

State the importance of sebaceous glands in relation to a healthy skin (1mk)
State two qualities that make aluminium popular for household utensils (2mks)
Give a reason why nylon is unsuitable for sports wears (1mk)
Mention two uses of dhania (coriander) leaves in cookery (2mks)
Mention two advantages of blending cotton and nylon fibers (2mks)
State any two reasons why a child’s growth monitoring is important (2mks)
List four laundry processes that are harmful to woolen fibres and in each case state

the harm caused (2mks)

State three ways of providing variety in meal planning and management (3mks)
State two factors to consider when choosing where to buy vegetables (2mks)
Give two qualities of a good advertisement (2mks)
Explain three ways of economizing fuel when using electricity for cooking (3mks)
Explain two reasons for using interfacing during garment construction (2mks)
Identify three methods of finishing the edges of sleeves other than using a cuff (3mks)
State three reasons for labeling products in a factory (3mks)

State two precautions to be taken to prevent bed sores when taking care of the sick persons

at home (2mks)

List two uses of lamp shades (2mks)
State two factors to consider when planning lighting for various rooms in the home (2mks)
Differentiate between advancing and receeding colours (2mks)
Give two reasons why most women in the rural areas are less groomed (2mks)
a) Describe the correct procedure of laundering nylon dress (8mks)
b) Describe the correct procedure of cleaning white canvas shoes without shoe laces (7mks)
c) Give the correct procedure of cleaning two aluminium cups (5mks)
a) Mention two uses of butter in the home (2mks)
b) Identify four major nutrients found in butter (4mks)

c)i)Describe four changes that takes place when heating butter (4mks)

ii) Name four main groups of fats giving an example for each (4mks)
d) Explain three considerations to make when selecting a storage facility for butter (6mks)
a)Outline four tests undertaken at the clinic to an expectant mother in the first month

of pregnancy (4mks)

b) Describe two supplementary foods for a baby (2mks)
c) Explain two benefits of supplementary food (4mks)

d)i)Explain four reasons why a mother may be unable to breast feed

ii) Explain four points on care of play items (2mks)

23 . a) Explain four properties of viscose rayon which are undesirable (8mks)

b) Suggest four features that can be used to finish a nigh dress decoratively (4mks)
c) Give three reasons for ironing a night dress during construction (3mks)
d) Explain five desirable qualities of an iron box (5mks)

*KKE*

Why is comfort an important factor to consider during the choice of cosmetics (2mks)
What observation should you make when cleaning a house? (2mks)
What is the difference between drainage and refuse disposal (2mks)
Green vegetables should be blanched before freezing. Give three reasons why (3mks)
State any two vaccines that every child should receive (2mks)
State ways of preventing insect bites and stings in an environment (2mks)
Give three uses of facing in garment construction (3mks)
Which factors influence the rise of prices of commodities in the market? (2mks)
Which precautionary measures should one take to prevent food spoilage during storage? (2mks)
Identify two kitchen equipment that occupy small space and are easy to store (2mks)
Explain two functions of water in the body (2mks)
Suggest two points to ob serve when cooking beef (2mks)
State two nutritional needs of adolescents (2mks)
State two reasons why bicarbonate of soda is not popular used in flour mixtures (2mks)
Explain how food can be preserved at home without refrigerator (2mks)
List three classes of convenience foods (2mks)
State the effects of insufficient/light pressure exerted by the pressure foot during stitching (2mks)
Give properties that make linen suitable for making kitchen clothes
State two qualities of a well made patch pocket (2mks)
In the space provided, sketch two pattern marking that will assist in laying of pattern (2mks)
You are taking care of an aunt who is recovering from n infection disease:
a) Explain how you could launder a white cotton bed sheet (14 mks)
b) Describe how you would clean a plastic basin she has used in the room (6mks)
a)Mention three methods used to coat before frying(3mks)
b) State 4 ways of improving appetite when presenting food at the table (4mks)
c) Discuss general points to observe when drying meat (3mks)
d) Discuss five important points to observe when planning meals for the elderly (10mks)
a)State three ways of transferring pattern markings(5mks)
b) State five advantages of home based care of the sick (5mks)
c) Giving reasons, explain 5 rules to observe when removing stains (10mks)
a) explain three roles of play in child development (3mks)
b) Give five qualities of a well made cuff (5mks)
c) With the aid of a well labeled diagram, describe how to make machine fell seam (7mks)
d) Describe how you would clean your wooden locker (5mks)

*STK*

1 Define the term hue as used in home science (1mk)

Give two Ways in which the studying of home science benefits an individual (2mks)
Give two functions of a colander as kitchen equipment
Sate four basic instructions on the use of medicine (2mks)
Name two types of accidents that can cause fractures (2mks)
State two points to consider when choosing a toilet brush. (2mks)
Why are clothes dampened before ironing? (1mk)
Give three precautions to take when cleaning wooden surfaces (3mks)
State three qualities to look for when buying a sauce pan (3mks)
Give three uses of eggs in flour mixtures (3mks)
Give two different methods of identifying linen as a textile fibre (2mks)
List four decorative methods of disposing off fullness in a toddlers dress (2mks)
Give two causes of needle breaking when machine stitching (2mks)
Suggest two reasons why a French seam is suitable for fraying fabrics (2mks)
Give two points on the importance of consumer education to a consumer . (2mks)
State three factors that will affect the efficiency of a laundry soap (3mks)
(a) State two reasons for using tucks on children’s clothing (2mks)

(b) Identify any four factors that may affect normal foetal development (2mks)

Explain two advantages of home-based care of the sick. (2mks)
You are taking care of your sister who is recovering from an infectious skin disease

(a) Giving reasons in each case, explain the procedural steps you would take to launder her

woolen shawl (10mks)

(b) Thoroughly clean her white canvas shoes with laces (6mks)

(a) Discuss five danger signs of pregnancy 10mks)

(b) Explain four points to consider when buying hand sewing needles (4mks)

(i) A coarse open texture in rubbed –in cakes (2mks)

(ii) Heavy and close texture in creamed cakes (2mks)

(iii) Hard and tough pastry (2mks)

(a) With the aid of three clearly labeled diagrams, explain the working of a lapped seam (8mks)

(b) Explain the functions of each of the following:-

(i) Balance wheel (1mk)

(ii) Bobbin case (1mk)

(iii) Pressure foot lifter (1mk)

(d) (i) Explain three points of importance of care labels (3mks)

(ii) Give two undesirable properties of nylon (2mks)

(a) Explain five changes that occur when cooking ugali using maize flour (10mks)

(b) Define the following terms as used in home science. Give an example in each case:-

(i) Food fortification (2mks)

(ii) Food vehicle (2mks)

(iii) Food supplements (2mks)

*STK²*

Give two economical ways of disposing refuse. (2mks)
Define the term descaling as used in home science (1mk)
Using an example in each case list three types of drainage (7mks)
Give two use of a mangle (2mks)
Name the three categories under which clothes should be sorted out in laundry work (3mks)
Name two inexpensive sponging solutions (2mks)
Define the term natural immunization (2mks)
Give two major functions of vitamin K (phylloquinone) (2mks)
Explain two effects of cooking on vitamin C (ascorbic acid) (2mks)
Give two differences between weaning and supplementary feeding (2mks)
Define the term medicine as used in home science (2mks)
State two precautions to take when using grease solvents (2mks)
(a) What is valeting in home science?

(b) Explain it’s importance (1mk)

List three processes through which sodium s lost in the body (3mks)
List three methods of neatening an overlaid seam (3mks)
Give two reasons why consumer education is caught in schools (2mks)
(i) Which is the most important meal for the day? (1mk)

(ii) Give a reason for your answer (1mk)

You’re preparing to entertain visitors in our birthday party.

(a) Sponge your aunties woolen coat to be worn on the day (10mks)

(b) Launder your white cotton blouse with chewing gum stain (6mks)

(a) Explain four principles of conserving nutrients while preparing vegetables (8mks)

(b) Explain five major functions of advertisements (5mks)

(d) Give two uses of salt in the house (2mks)

(a) Describe how to make a machine fell seam at the shoulders of a blouse (8mks)

(b) Mention four ways of watering an open seam (2mks)

listed above (6mks)

(a) Explain five social needs of an expectant mother (10mks)

(b) Explain five points to consider when choosing personal clothes (10mks)

PAPER TWO

*NYR*

A pattern of a child’s dress is provided. You are advised to study the sketch and the layout before you begin the test.

MATERIALS PROVIDED

PATTERN PIECES:-

A Dress Front

B Dress Back

C Sleeve

D Sleeve binding and ties

E Sleeve opening facing

F Front neck facing

G Back neck facing

Plain light weight fabric 60cm long by 91cm wide.
Sewing thread to match the fabric colour
One large envelope

THE TEST

Using the materials provided, cut out and make the LEFT HALF of the child’s dress to show the following:-

The joining of the front to back bodice at the shoulder line using a neatened open seam.
Making a French seam at the sides of the front and the back
Joining the front and back neck facing with a neatened open seam
Neatening the outer edge of the joined neck-facing
Using the prepared facing to neaten the neck-line of the dress bodice
Preparation of the sleeve opening facing
preparation of the faced slit opening on the sleeve
Attachment of the binding sleeve ties onto the sleeve
Making of the French seam on the sleeve
Attaching the sleeve on the bodice. DO NOT NEATEN THE SEAM.

At the end of the examination, firmly sew onto your work, on a single fabric, a label bearing your name and the index number. Remove the needle and pins from your work. Then fold and place it

in the envelope provided. Do not put scraps of material in the envelope.

VIEWS

*MGN*

A pattern of a girl’s blouse is provided. You are advised to study the sketches, instructions and layout carefully before you begin the test. *MGN*

MATERIALS PROVIDED

Pattern pieces for the blouse *MGN*

– BODICE FRONT
– BODICE BACK
– BACK NECK FACING
– ARM HOLE BINDING STRIP

Light weight plain cotton fabric 45cm long by 90cm wide.
Sewing thread to match the fabric
One large envelope

THE TEST

Using the materials provided, cut out and make the LEFT HALF of the blouse to show the following processes;

Working of the front bodice double dart
Making a French seam at the shoulder
Making a neated open seam on the side of the blouse
Joining the back neck facing to the front facing and neatening the free edge
Attachment of the facing to the neckline and under stitch
Neatening the armhole using a binding strip
Cutting the marked tear on the back bodice and repairing it with hand darning

*KSM*

A pattern of a child’s blouse is provided. You are advised to study the sketches instructions and the layout carefully before you begin the test.

Materials provided:-

1 pattern pieces

A. – bodice front
B. – bodice back
C. – sleeve
D. – cuff
E. – front facing
F. – back facing
G. – patch
H. – straight strip
Plain lightweight cotton fabric 45cm long by 90cm wide.
Cotton sewing thread to match the fabric.
One button (shirt) with to holes
One envelope.

THE TEST

Using the material provided cut out and make the left half of the blouse to show the following processes:

(a) Making of the waist dart

(b) Working of the calico patch

(d) Making the side seam using an open seam.

(e) Working of continuous wrap opening

(f) Preparing an attaching the cuff on sleeves

(g) Preparing and fixing the neckline facing

(h) Attaching the sleeves on to bodice

(i) Slip hemming the back bodice lower hem

(j) Working of buttonhole and attaching of the shirt button.

LAYOUT NOT DRAWN TO SCALE

N/B: X represents the hole to be patched.

*KKC*

A pattern of a child’s dress is provided. You are advised to study the sketches, instructions and the layout carefully before you begin the test. *KKC*

MATERIALS PROVIDED

Pattern pieces for the dress

A – Dress front

B – Dress back

C – Pocket

D – Front facing

E – Back facing

Plain light weight cotton fabric 55cm long by 90cm wide
Sewing thread to match the fabric
One large envelope

THE TEST

Using material provided, cut out and make the LEFT HALF of a child’s dress to show the following

Working of a shoulder dart
The joining of the shoulder seam using a French seam
The joining of the side seam using a plain seam
The preparation of the patch pocket
Fixing of the patch pocket on to the garment
The joining of the front and the back facings at the shoulder. Neatening the outer edge of the facing
Attaching of the facing at the neckline of the dress. Understitching the seams
Hem the lower Bodice using slip hemming stitches

At the end of the examination, firmly sew onto your work, on a single fabric a label bearing your name and index number. Remove the needle and pins from your work, then fold your work neatly and place it in the envelope provided. Do not put scraps of fabric in the envelope.

*RCH*

MATERIALS PROVIDED

– Skirt front
– Skirt back
– Front yoke
– Back yoke
– Collar
– Front neck facing
– Back neck facing
– Frill

N.B Interfacing for collar is cut with pieces from the same fabric

Light weight cotton fabric 70cm by 91 cm wide
Sewing cotton thread to match the fabric
An envelope

THE TEST

Using the materials provided, cut out and make the left half of a child’s dress as shown in the sketch below to give the following;

The attachment of the back yoke to the back skirt using an overlaid/ seam
The attachment of front yoke to front skirt using an overlaid seam
The working of a open seam at the shoulder
The preparation of an interfaced collar
The neatening of the free edge of the facings
The attaching of the collar using the facings
The making of a French seam at the side of the dress
The preparation of the frill. Use inverted pleats
The attaching of the frill to the skirt front only using neatened open seam ( use loop stitches)

At the end of the test, remove all the pins, loose hanging threads and attach your name, index number on a single layer of fabric. Fold your work neatly with the label on the top most and put them inside the envelope provided.

*MUM*

A pattern of girls skirt is provided. You are advised to study the sketches the question paper and the layout carefully before you begin the test

MATERIALS PROVIDED

Pattern pieces:-
Skirt front
Skirt back
Pocket
Pocket facing
Front waist band
Back waist band
Light weight plain cotton fabric 60cm long by 90cm wide
Zip (13 cm long)
Sewing threads match the fabric
One large envelope

THE TEST*MUM*

Using the materials provided cut out and make the RIGHT HALF of the skirt below to show

the following processes:

Making the back dart
Facing of the pocket mouth
Preparation and attachment of the pocket
The preparation of the gathers on the skirt front piece
The making of a neatened open seam at the side – below the opening
The attachment of the zip using concealed method
The preparation of un-interfaced waist bands
The attachment of the waist band to the skirt pieces and preparation of the tie ends
Edge stitching the hem and holding down using running stitches (do not hem)

At the end of the examination firmly sew onto your work, on a single fabric, a label bearing your name and index number. Remove the needle and pins from your work, then fold your work carefully and place it in the envelope provided. Do not put scraps of fabric in the envelope.

*KKE*

A pattern of a girls dress is provided. You are advised to study the question paper, sketches, instructions and layout carefully before you begin the test.

MATERIALS PROVIDED

Pattern pieces for the dress:

A -Dress front

B -Dress back

C -Sleeve

D -Sleeve binding and ties

E -Sleeve opening

F -Front neck facing

G -Back neck facing

H -The collar

Plain light weight cotton fabric 80cm long by 90cm wide
Sewing thread to match
One large envelope

THE TEST

Using the materials provided, cut out and make up the right half of a child’s dress to show the following

a) The making of a French seam at the shoulder
b) The making of a neatened open seam at side
c) The preparation of the sleeve opening
d) The joining of the underarm seam using a neatened open seam
e) The preparation of the interfaced collar
f) The preparation of the front and back facing.
g) The joining of the collar to the neckline using the facings.
h) The binding of the lower edge of the sleeve and preparation of the tie ends
i) The preparation and attachment of the sleeve.

N/B Do not trim or neatened the armhole seam allowance.

*NDW*

A pattern of a boy’s pair of shorts is provided. You are advised to study the sketches, the question paper and the layout before you begin the test.

MATERIALS PROVIDED
A. Shorts front
B. Shorts back
C. Waist band
D. Fly and opening facing
E. Fly binding.

Light weight cotton fabric of 70cm long by 90cm wide
Cotton sewing thread to match the fabric
One large envelope

THE TEST

Using the provided materials cut out and make up the LEFT LEG of the shorts to show the following:

The making of the back dart
The facing of the short
The preparation of the fly
The lining of the prepared fly with the attached facing
The neatening of the raw edges if the fly together with the facing using the bias binding
The fixing of the fly in position by top stitching.
The joining of the side seam using a plain seam (not open) and neatening half of it
The joining of the inner-leg seam using a neatened open seam.
The preparation and attachment of an interfaced waist band
The preparation and slip-hemming of half of the hem (i.e. from side seam to inner leg only)

At the end of the examination, firm sew on to your work, on single fabric a label bearing your name and index number. Remove the needle and pins from your work. Then fold your work carefully and place it in the envelope provided. Do not put scraps of materials in the envelope.

BOY’ S SHORT

*STK*

A pattern of a girl’s blouse is provided. You are advised to study the sketches, instructions and layout carefully before you begin the test.

MATERIALS PROVIDED

Pattern pieces for the blouse

BODICE FRONT
BODICE BACK
BACK NECK FACING
ARM HOLE BINDING STRIP

Light weight plain cotton fabric 45cm long by 90cm wide.
Sewing thread to match the fabric
One large envelope

THE TEST

Using the materials provided, cut out and make the LEFT HALF of the blouse to show the following processes;

Working of the front bodice double dart
Making a French seam at the shoulder
Making a neated open seam on the side of the blouse
Joining the back neck facing to the front facing and neatening the free edge
Attachment of the facing to the neckline and under stitch
Neatening the armhole using a binding strip
Cutting the marked tear on the back bodice and repairing it with hand darning

PAPER THREE

*KKC*

THE TEST *KKC*

Your parents are away on a journey and you are expected to make breakfast for yourself and two visitors who have just arrived in the wee hours of the morning

Use the foods given below to come up with a balanced breakfast

INGREDIENTS

Wheat flour
Eggs
Baking powder
Sugar
Milk
Maize flour/ millet flour
Oranges
Salt
Fat

*NYR*

INSTRUCTIONS TO CANDIDATES

Read the test carefully
You are advised to spend not more than thirty minutes for planning
Recipe books may be used for planning

THE TEST

You are getting ready to go back to school after the December, holidays. Using the ingredients provided prepare cook and serve:

A one-course lunch for you and a friend
A baked tea item to carry to school

PLANNING SESSION

Make a rough order of work to include:

List of dishes
List of food stuff and equipment you would require

Order to work

LIST OF INGREDIENTS

Meat/chicken/peas
Rice
Cabbage/sukuma wiki
Tomatoes
Onions
Sugar
Salt
Self rising flour/flour + Raising Agent
Carrots
Cooking oil/fat

*KSM*

Your younger sister is celebrating her 10^th birthday and your mother has asked you to help her in some preparation for the party. using the ingredient listed below, prepare and serve one sweet and one savoury item suitable for passing round in addition include a suitable beverage

Eggs
Fruits in season
Sugar
Sausages
Self raising flour
Margarine
Fat/oil
Milk
Salt
Sultanas/mixed peel/grated rind of lemon

PLANNING SESSION (30MINUTES)

PRACTICALS 1 ¼ HOURS)

Read the test carefully and proceed as follows:-

Write the ingredient and recipes your shopping list, your list of requirements on separate sheet of paper using carbon paper to form duplicate copies.
Write a time plan to guide your work in duplicate copies.
Text books and recipes may be used but constant reference to them during practical and planning

session should be avoided

Write your name and index number on your plan and your entire list. After planning assemble your

duplicates and originals separately remove shopping list from duplicate to be used to purchase your

requirement.

At the end of the examination hand in both your question paper. Original and duplicate time plans with separate shopping list to the examiner

*MGN*

THE TEST

You are left with our brother at home. Using the ingredients listed below, cook and present a two course breakfast for the two of you

Ingredients

Fruit in season
Margarine
Tea leaves
Bread
Eggs
Sugar
Tomatoes
Milk
Fat
Seasoning

PLANNING SESSION: 30 MINUTES

Use separate sheets of paper for each task listed below and use carbon paper to make duplicate copies then proceed as follows:-

Identify the dishes, then write down their recipes

Write down you order of work

Make a list of the food stuffs and equipment you will require

*NDW*

TEST

Your cousin is visiting you over the weekend for an overnight stay. Using the ingredients listed below prepare, cook and server a complete breakfast for the two of you.

Ingredients

Margarine
Tomatoes
Eggs
Fruits in season
Finger millet/sorghum flour
Fat/oil
Salt
Tea leaves
Milk
Bread

PLANNING SESSION (30MINUTES)

Use separate sheets of paper for each task listed below and use carbon paper to make duplicate copies then proceed as follows:

Identify the breakfast then write the recipes
Write down your order of work
Make a list of the food stuff and equipments you will require.

*MAT*

THE TEST

Your parents are coming for lunch, using the ingredients listed below, prepare cook and present a two course meal for two.

Rice (spaghetti/ macaroni/ wheat flour/potatoes
Fat/oil
Salt
Tomatoes
Vegetables
Fruits

PLANNING SESSION

Use separate sheets of paper for each task listed below:

Make duplicate copies then proceeds as follows;

Identify the dishes (write down their recipes)
Write down your order of work
Make a list of the foodstuffs and equipment you will require.

*RCH*

THE TEST

Your elder brother has just recovered from severe malaria attack. Your mother has asked you look after him while she is away.

Using the ingredients listed below, prepare, cook and serve a two course lunch for both of you. Include a nutritious drink

INGREDIENTS

Beef/ Eggs

Onions

Tomatoes

Cooking fat/ oil

Sugar

Fruit in season

Salt

Rice/ Wheat flour/ maize flour

Milk

Green leafy vegetables

PLANNING SESSION

Use a separate sheet of paper for each task listed below and use carbon paper to make duplicate copies then proceed as follows;

Identify the dishes and write down their recipes
Write down your plan/ order of work
Write a shopping list of the food stuff that you will require and a list of equipment

*KKE*

THE TEST

You are a day scholar who stays with your grandmother and you carry packed lunches to school. Using the ingredients provided, prepare, cook and serve.

i) One course supper for both of you.
ii) Include a nutritious drink.

Liver/beef/green grams
Green bananas/rice
Green leafy vegetables
Tomatoes
Onions
Cooking fat/oil
Salt
Garlic
Sweet pepper
Corrianda
Spices
Oranges
Pineapples
Mangoes

PLANNING SESSION 30 MINUTES

Use separate sheets of paper for each task listed below and a carbon paper to make duplicate copier.

Then proceed as follows:

1) Identify the dishes and write down their recipes.

2) Write down your order of work.

3) Make a list of the food stuffs and equipment you will require.

*MUM*

THE TEST

You are traveling to a neighbouring province to visit your friend during the holidays. Using the ingredients listed below, prepare, cook and pack a suitable snack for two to be eaten on the journey. Omit baking method

Ground nuts/eggs
Fruits in session
Baking powder
Wheat flour
Milk/water
Eggs
Sugar
Salt
Margarine
Oil/fat
Carrots

Planning session – 30minutes

Use separate sheets of paper for each task listed below and a carbon paper to make duplicate copies.

Then proceed as follows:

Identify the food items used and write down their recipes.
Write down your order of work.
Make a list of the food stuffs, material and equipment you will require.

*STK*

You are expecting your friend for lunch. Using the ingredients listed below, prepare cook and present a one course lunch and a nutritious drink for the two of you.

Ingredients

Plain wheat flour

Beef

Green leafy vegetables

Fruit in season

Salt

Cooking fat

Tomatoes

Onions

Capsicum

Sugar

Rice/macaroni/spaghetti

PLANING SESSION (30 MINUTES)

Use separate sheets of paper for each task listed below and use a carbon paper to

make duplicate copies then proceed as follows:-

Identify the dishes then write down their recipes
write down your order of work
make a list of foodstuff, equipment and materials that you will require

*TNW*

THE TEST

You are expecting your friend for lunch. Using the ingredients listed below, prepare, cook and present a one lunch and a nutritious drink for the two of you.

Ingredients

Plain wheat flour/rice
Beef
Green leafy vegetables
Fruit in season
Salt
Cooking fat
Tomatoes
Onions
Capsicum
Sugar
Milk

PLANNING SESSION (30 MINUTES)

Use separate sheets of paper for each task listed below and use a carbon paper to make duplicate copies then proceed as follows:-

Identify the dishes then write down their recipes
Write down your order of work
Make a list of food stuff, equipment and materials that you will require.

*STK2*

THE TEST

You are hosting your two friends who came on an overnight stay in your home. Using the ingredients listed below, prepare, cook and present a well balanced full breakfast for the three of you.

Ingredients:-

Baking flour
Baking powder
Eggs/liver/kidney
Cooking fat/oil /margarine
Bread/sweet potatoes/arrow roots
Lettuce/cucumber/tomatoes/onions
Drinking chocolates/tea/coca
Sugar
Milk
Salt

PLANNING SESSION- 30MINUTES

Use a separate sheet of paper for each task listed below. Use carbon paper to make duplicate copies.

Identify the dishes and write down their recipes
Write down your order of work
Make a list of foodstuff and equipment you will require

*STK 3*

PLANNING SESSION – (30 MINS)

You are taking care of your 10yr old nephew who is recovering from malaria. Using the ingredients listed below, prepare, cook and present;

A one course lunch for both of you.
Include of refreshing drink.

Ingredients

Meat/eggs
Rice/spaghetti/macaroni
Cabbage/kales/spinach
Passion/orange/pineapple fruit
Sugar
Salt
Cooking fat/oil
Tomatoes
Potatoes
Onions
Capsicum
Carrots
Dhania
Royco

Planning session (30mins)
Use separate sheets of paper for each task listed below and use carbon paper to make duplicate copies then proceed as follows;

Identify the menu, then write down the recipes.
Write down the order of work.

Make a list of the equipment and foodstuff you will require to carry out the practical

ANSWERS

PAPER ONE

*KSM*

*MGN*

-To avoid blowing dust into the air.

To prevent cross infection.
So that dust particles in the air cannot spread germs.

– Swollen gums with weak capillaries that bleed easily.

Blood in he stool and urine due to ruptured capillaries.
Unhealthy skin.
Slow healing of wounds.
General weakness of the body.

-The style.

The colour.
– Material i.e. metal, shiny etc.

-Can only be used where there is supply of piped water.

Are expensive to install.
Maintenance may be expensive if carelessly used especially when plumbers have to be

engaged in unblocking sinks and drains or replacing broken fitting.

-Decorative purposes.

Adding flavour.

– Strengthen the teeth as they come out.

Exercise the jaws.
To ease discomfort.

-Should have skin on the surface.

Right in consistency.
Well flavoured.
Not oily on the surface.

-Waist band.

Hem

i) Tray cloth

By starching.

(ii) Baby Napkin

– By boiling or disinfecting. (2 x 1 = 2 mks)

Mention two advantages of blending cotton and nylon fibres. *MGN*

Fabric made is:-

Light in weight.
Crease resistant.
Becomes absorbent.
Not attacked by moth.
Does not attract static electricity. (2 x 1 = 2mks)

Give two methods of credit buying. *MGN*

Hire-purchase.
Use of credit cards.
– Simple non-installment credit. (2 x 1 = 2mks)

– Height

Smoothness
Source of light

-Kneading divided\s the gluten strands and spreads them evenly through the mixture, holding carbon dioxide produced during the fermentation process.
–Exercise the teeth.

Get all the nutrients it contains because cooking destroys some. (2 x 1 = 2mks)

-Should be made of stainless steel / Rustless.

Should be sharp.
Firmly fixed or hinged.
One blade should be pointed.
One end should be curved.
Comfortable handles with one hole large enough for two or more fingers. (2 x 1= 2mks)

-Through breast feeding.

When giving birth.

-To smoothen the edge.

For shaping the curve.

-BCG. – Given at birth.

DPT – Given at 6, 10 14 weeks respectively.

Yellow Fever and Measles – Given at 9 months .

Vitamin A capsule – Given from age 6 – 9 months.

Give two reasons for disposing of waste properly. *MGN*

To prevent thee environment degradation.
To prevent breeding of disease causing organisms.
To prevent the spread of communicable diseases.
To prevent environmental pollution.

(a)-Collect necessary equipment and material. (1)

Move all the moveable furniture to one side. (1)
Close all the windows and doors (1)
Sweep from the furthest and to the door. (1)
Keep head of broom down and stand behind the broom. (1)
Sweep methodically. (½)
Gather all the dust together and collect and dispose. (1)
Rearrange the furniture and open the window and door. (½ )
Dust all the surfaces. (½ )
Clean used equipment (½ )

(b)Procedure of cleaning an enamel plate.

Use warm soapy water. (1)
Clean using sponge or soft cloth/ sisal fibre. (1)
Rinse thoroughly (½) in warm water (½ )
To remove dirt and soap traces. (1)
Dry completely (½ ) before storage to avoid rusting. (½ ) (5 mks)

(c)Methods of dry cleaning a polyester tie.

Work in a well ventilated place away from flames. (1)
Shake the article to be dry cleaned. Thoroughly to remove loose dirt. (1)
Pour an adequate amount of dry – cleaning liquid in a small basin. (1)
Immerse the tie, knead and squeeze until clean. (1)
Squeeze out as much of the liquid as possible. (1)
Hang the tie to dry in an airy place. (1)
When the sediments have settled out the bottom of the basin holding the sediment, pour back in the storage can. (½ )
Press the tie. (½ )

(a)Describing any three types of meal service. *MGN*

Blue plate service.

Food served on an individual plate and the family member can eat anywhere.

Self Service

Different dishes are cooked and placed on the table and the diners serves themselves and eat while either seated at the table or standing.

Family Service

Cooked dishes placed on the table and people serve themselves what they want to eat while seated.

Buffet Service

Food served on a large table and plates and cutlery are neatly arranged at one end.

(b)Supporting your answer with your reasons, give a most suitable fabric for an institutions bed

linen.

COTTON FABRIC

Its absorbent, cool and comfortable, light and durable.
Withstands high temperatures, cheap, attractive. (2 x 2 = 4 mks)

(c)Give your ways in which scarcity of time would affect a consumer.

Deprives consumer from comparative shopping.
Prevent consumer from setting the right goals or commodity.
–
Prevents the consumer from purchasing items. (4 mks)

(d)With two specific examples give three uses of permanent stitches.

-To join two or more pieces of fabric together e.g. Running stitches Back stitches, oversewing and others.

To neaten raw edges to prevent them from fraying and make edges look smart e.g. items, over casting, loop stitches.
Decorative stitches meant to add beauty to design e.g loop stitch, chain stitch etc.

(a) Give the systematic order of placing bedding items when preparing a baby’s cot. *MGN*

Place the under blanket R.S. up & wide hem towards head side.
Place markin tosh in the middle.
Place under bed sheet R.S up to cover markin tosh & tuck.
Place top blanket R.S down.
Place down the sheet over the blanket & tuck both sides.
Put the bed spread (bed cover).

(b)Five desirable qualities of ironing board.

Height can be adjusted.
Board is padded, making ironing easy and comfortable.
Ironing board has a heat proof mat attached for placing iron.
Most of them are sold with sleeve board for ironing sleeves and children’s garment.
Stand steadily on their own.
Can be folded easening storage.

(c)Five characteristics of a well made dart.

Should taper gradually to a point.
Should be of correct length and width.
The stitching line should be straight.
Should be firmly secured at the point.
– Should be pressed towards the right direction. (5 mks)

(d)Cleaning a hurricane lamp.

Protect the working surface.
Remove glass and wipe gently with a soft cloth/ tissue.
Weep the inside of the metal chimney to remove soot.
Trim the wick if necessary.
Wipe the burner and other metal parts.
Refill the reservoir with enough oil.
Wipe off any split paraffin.
Replace the glass and keep the lamp ready for use.

(a)Ways in which a lactating mother would improve supply of breast milk to her baby. *MGN*

Mother taking in nutritious and adequate fluids for milk production.
Eating a well balanced diet but rich in calcium, energy and protein.
Adopt a positive attitude towards breast feeding the baby in a relaxed and free atmosphere.
Massage and clean breasts with warm water to stimulate milk production.
– Avoid stress and stressful situations when feeding the baby. (5 mks)

(b)Five points to consider when giving general care to all the clothes.

Make fastening secure before they become loose.
Strengthen openings at the base so that they do not tear readily.
Neaten raw edges if a seam is likely to fray.
Sew hanging loops onto jackets, coats and skirts.
Keep clothing clean and free from dust e.g. regular washing and dusting.
Brush outer garments before putting them away and mend if necessary.
Press clothes regularly.
Use hangers whenever possible.
Remove brooches and other ornaments before putting away clothes.
Do not allow perfumes and deodorants harmful to clothes to come into conduct. (5 mks)

(c)Five rules to observe when fixing fastenings.

Must be sewn on double fabric for support and strength.
They must be sufficiently distributed.
Should be evenly spaced to avoid gaping.
Many are sewn on after the opening has been made and pressed.
Must be well aligned so that the opening can lie flat when closed.
Buttons should not protrude beyond edge of the opening.

(d)Five factors that influence consumer buying.

Income limitation

If income is low, it is a serious struggle to meet basic necessities without proper planning.

Prices

When prices change, the various allocations in a budget are affected.

Substitute goods

g. use of butter and margarine interchangeably in order to cut down on cost.

Complementary products.

Where one needs to be used with another e.g. a shoe polish and shoe, sugar and bread etc.
Limitation of time and energy.
Availability of a product within a given time.
Availability of product with urban and rural and vice versa.
Age of the family.
Change in customs and traditions.
Social status.

*KKC*

Food service. (3 mks)

– Plate

– Buffet

– Family table service.

– Tray / trolley service.

Interfacing collars. (3 mks)

– Stiffen.

– Prevent stretching or sagging.

– Give body or shape,

– Increase crease resistance.

– Obtain a good knife – edge.

Asbestos suitable. (2 mks)

– Non- inflammable

– Resistant to chemicals, insects and microbes.

Choice of controlling fullness.

– Effect desired.

– Type of fabric.

– Body figure – figure type of person.

Characteristics of a good French Seam. (3 mks)

– All raw edges closed.

– Straight stitches.

– Seam allowance width uniform.

Neatening an open seam. (4 x ½ = 2 mks)

– Overcastting stitches.

– Using over lock.

– Using pinking hears zig zag cuts.

– Using loop stitches.

Effects of Advertising to a customer. (3 mks)

– Entertaining

– Creates employment of advertising .

– Creates competition among producers.

– Information – creates awareness of goods and services to customers.

Darning (2 mks)

-Use darning needle for the fabric being darned.

– Darn on the wrong side.

– Avoid stretching or pulling fabric while working.

– Loops of threads should be left.

Choice of colour in a sitting room.

– Size of room.

– Effect desired.

– Personal taste.

– Orientation of the room.

Rules to observe during stain removal.

– Removed when still fresh.

– Identify the kind of stain and type of fabric to get suitable stain remover.

– For unknown stain start with milder stain removals.

– Rinse the article well to remove traces of reagent.

– Work outside towards inside – prevent spreading

Packing meals.

– Each type of food packed separately.

– Each soups and hot drinks in flasks.

– Pack fruit juices in plastic bottles.

– Salads be packed in polythene bags and plastic containers.

– Put all foods for the packed meals in a large container such as a bag or plastic basket.

Principles of wise buying.

– Set goals and priorities.

– Prepare budget.

– Suitability of item.

– Durability of item.

– Versability of item

– Attractive in colour and design.

– Shopping list preparation.

– Interpret advertisement.

Dangers of late weaning.

– Child becomes malnourished.

– Child refuse to accept new foods.

– Deficiencies due to lack of extra nutrients.

– Baby growth slow and development.

Salt iodized.

– Avoid deficiencies

– Supply iodine not food in other foods.

Disadvantages of using charcoal.

– Dirty

– Not properly burned produce smoke.

– Not readily available in some areas.

(a) Cotton blood stained sheet.

– Soak the sheet in cold water (1) to remove the blood stain.

– Wash it thoroughly using friction method in cold water. (1)

Procedure for washing

Soak in cold water (½) for less than 12 hours.
Wash in hot water. (½)

Using friction method. (½)

Rinse in hot water. (½)
Final rinse in cold water. (½)
Add jik to the final rinse or laundry blue to brighten the garment or boil it. (1)
Iron while still damp with a hot iron.
Air (½)
Fold and store. (½) (8 mks)
Use of curtains.

– To filter light. 1mk for each

– For privacy

– Decorative purposes.

– For comfort

– For screening widows at night or during the day.

(c) Give the correct procedure – Aluminium.

– Soak in jik to remove stains. (1 mk)

– Wash them using a scoring pad in warm water. (½)

– Rinse in warm (½)water one at a time (½)

– Final rinse in cold water. (1)

– Drip them. (1).

– Dry with a piece of clothe. (1).

– Store it well (½) (5 mks) (d) SPOTTING – WO

– Use warm water. (1)

– Use a piece of cloth as pad. (1)

– Dip in clean soapy water and rub on the stained are hem to remove dirt and other

areas. (1)

– Work on all areas with stain (1)

– Air (4 mks)

(a) Run and fell seam

– Place the fabric together wrong sides facing and fitting matching. Pin and tack along

fitting line. (1 mk)

Remove pins and machine along the fitting line. (½)
Remove tacking and press. (½)
Trim back turning to 6 mm and front to 12mm. (½)
Fold over the front over to the back to form the fell. (1).
Press the fall to lie on the back of the garment. (½)
Tack and machine close to the fold through the three layers. (1)
Remove tacking and press the completed seam. (½)

(b) Functions of tucks.

– Decorative.

Serve as styles feature.
Used on blouses, night dresses and mothers wear.
Children’s garment to give room and take extra lengths on children garment.
Reduce fullness. (4 mks)

(c) Making of Gathers

– Working by Hand Running stitches. (1)

– Begin with Hand knot to secure the thread then work first row running stitches. (1)

– Work second row running stitches, 6 mm from the fitting line. 1 mk

– Leave the thread hangings at the end of the row of running stitches. (1)

– Work second row of running stitches and leave the thread hangings at the end. 1mk.

– Pull both the thread ends together to draw up the fabric until the required size is achieved. 1 mk.

– Wind the Hanging threads round a pin, forming a figure 8 and secure the gathers. 1

a)Choosing flowers.

Choose fresh flowers. (1)

Make sure the foliage is clean. (1)

Avoid choosing flowers in bloom. (1)

Avoid choosing scented plants (1) because people may be allergic (1).

Choose a mixture of feat and pointed. (1) (5 mks)

Wooden polished table surface. (7 mks)

Dust surface table thoroughly.

Clean with cloth wrung out (1) warm soapy water with cloth wrung out of clean water. (1)

Apply polish sparingly on the surface and old piece of cloth. (½)

Rub in circular movement that overlap. (1). Ensure that it is evenly distributed on the

surface and no polish is fed into open cracks. (1 mk)

Shake the spray polish container hold it 6 inches away from the surface and spray sparingly. Leave it for ten minutes to enable the polish to set for easy shining buying immediately.

Use soft pad to buff in a circular motion. (4 mks)

(c)Personal appearance (4 mks)

Care of body.

Wearing clean and appropriate clothes.

Keep the hair neat and well groomed.

Use cosmetics, body creams and deodorants properly.

Use jewelry and accessories properly.

(d)Child play. (4 mks)

Provide plenty of room.

Allow for independence by encouraging a child to do things.

Encourages responsibility it is good for every child to have possessions.

Provide child with play things or tags.

Parents and older children take some time and play with small children.

Child should be dressed in clothing which does not restrict playing.

(a) Six points to consider when choosing and preparing weaning foods;-

– Balanced with first class protein, milk being the main food.

– Food should be easy to chew and digest i.e soft food.

– Foods should not be strongly seasoned hence avoid spices in foods.

– Fats and oils should be used minimally in their foods.

– Scare foods in small quantities.

– Foods should be cooked and served in a hygienic (clean) environment.

– Milk should be an important part of the diet.

(b) Three desirable qualities of deep frying fat.

– Should have a pleasant flavor.

– Should have a high smoking point.

– Should not solidify on cooling.

(c) Preserving food:

– Stop multiplication of micro-organisms which produce toxins harmful to human

health.

– Neutralize the action of enzymes which can cause food deterioration.

– Make food available for use when out of season.

– Stop wastage in bumper harvest when the yields are more than can be consumed.

– Maintain freshness and retain nutrients.

– Protect it from contamination by bacteria and other disease causing micro-organism.

– Retain as many qualities of fresh food as possible e.g. flavour, colour, texture and

nutritional value.

(d) Dietary needs of an elderly person.

– Balanced diet with normal amounts.

– Rich in body building foods like vitamins to boost the generating immunity as changes.

– Less energy giving foods.

– Non-fatty and non-greasy foods as they have weak digestive systems when may not be

able to digest fatty foods.

The food should be soft, palatable and easy to chew.
Provide foods rich in mineral salts like calcium, phosphorus, iron, iodine and vitamins A, B, C and D to strengthen their softening bones.
Serve in small amounts and at regular intervals.

*MAT*

List four fat soluble vitamins *MAT*

– Fat soluble vitamins

State two possible causes of anaemia *MAT*

Loss of blood (extreme)
Chronic malaria
Hook worm infestation
Lack of iron

Give two points to look for when buying spinach *MAT*

should be form a reputable grocer
should be leafy

State two effects of strong heat on proteins *MAT*

Denatures then
Hardness them making them indigestible

State two forms in which laundry soap is found in the market *MAT*

If food stored can cause food poisoning when contaminated
Flavour altered so needs strong flavouring
That can be a health hazard
Some foods becomes indigestible e.g protein
Colour may be lost ways of improving colour must be used.

Give the steps of removing chewing gum stain from a garment *MAT*

Use ice cubes / put in freezing coupantment
Scraple off the gum
Rib bitten/land
Use carbon tetrachloride/other grease solvents
Wash normally

Mention the three areas (centres of work that make up the work triangle in a kitchen

Cooking area
Storage area
Washing area

Suggest two measures to take immediately nose bleeding occurs

Melting person sit down – head slightly raised to prevent blood from flowing down throat.
Cooling person with cold wet towel

List two improvised abrasives in the home

Sieved sand
Ash
Crushed egg shells
Couched charcoal
Sisal fiber

Identify three tacks that are carried out only during special cleaning of a bedroom

Dinign bedding
Cleaning the bed; wardrobes chest of drawers and cupboards
Changing pillow and sheets

Mention two dangers of heavy smoking during pregnancy

Causes underweight babies
Causes long disease to mother

Give four methods of advertising

Brochures
Pamphlets
Decoration by promoters
Bill boards
Mass media
Through radio, t.v, newspapers, magazines, journals and books
Dealers /agents through displaying products and personnel available to explain to consumers about goods
Other consumers and consumer organizations ; one consumer to another/ two consumer organizations that each people on matters concerning goods and services.
B.S and government department – can be from different departments that deal some goods.

State two reasons why cotton fabrics are popular for the table linen

Its strong and stronger when wet
Its water proof
Can be mixed with other fibers to lower cost
Stands high temperature can be boiled of white to whiter

Give two reasons why silk is expensive

Its soft and draper well
It has lovely sheen and pleasant be handle
Its warm coz it’s a good inoculation in winter and cool in summer.
Its elastic so wears well
Shreds creates easily so good for travel

State three qualities of a good tape measure

Should be plastic coated to avoid fraying and stretch and firmly woven.
Should have metal ends to keep flat when measuring and prevent fraying.
Should clearly marked on both sides of 150cm.

Give three reasons for a needle freaking during machining

Beat needle
Machining close to zip teeth
Needle too fine for work
Press foot loose and needle hits its straight stitch foot is used for zigzag
Needle not firmly fixed in place
Fabric too thick for needle

Give two reasons why press studs are not suitable for use in children’s garments

are dangerous children may pluck off loose and swallow them
are difficult to fasten

(a) Ways of improving maize meal porridge
- enriching with milk
- sweetening with sugar
- adding a lemon
- adding an egg

(b) . Precautions to take when using an oven to bake

The oven must be preheated before putting in food to bake.
Oven and be cleaned and shelves arranged.
Over door should not be opened once it makes hot aim to escape and oven all take long to retreat
Temp should be lowered when the oven turns slightly brown to enable inside to cook
Baking time should be noted to avoid over baking/ under baking.

(c) Factors to look for when selecting a frying pan

Should balance well on the cooker and be thick for even distribution of heat
Should have a fitting lid
Should have a smooth finish

d) To be well moulded and no cracks

Uses of carrot in cookery
For garnishing
For flavouring
Enlarge foods e.g when added in meat
To improve flavour

(a) Mention four ways of improving maize meal porridge
- enriching with milk
- sweetening with sugar
- adding a lemon
- adding an egg

(b) . Explain three Precautions to take when using an oven to bake

The oven must be preheated before putting in food to bake.
Oven and be cleaned and shelves arranged.
Over door should not be opened once it makes hot aim to escape and oven all take long to retreat
Temp should be lowered when the oven turns slightly brown to enable inside to cook
Baking time should be noted to avoid over baking/ under baking.

(c) Explain six Factors to look for when selecting a frying pan

Should balance well on the cooker and be thick for even distribution of heat
Should have a fitting lid
Should have a smooth finish

(d) Explain four To be well moulded and no cracks

Uses of carrot in cookery
For garnishing
For flavouring
Enlarge foods e.g when added in meat
To improve flavour

(b) procedure of taking the following measurements

(i) Hips – Tape is place around fullest part between 18cm and 23cm waistline depending on

height of one.

(ii) Inside warm length

From armhole under arm to waist with arm outstretched at an angle of 45o

(iii)couch

(c)Using diagram to explain preparation of the collar without interfacing

Cut colour and under collar depending on pattern may be with stand or without

Transfer pattern markings

Place collar on under collar 2.s facing hatch raw edges, fl and notches
Pin tuck along fl leaving lower edge where its attached to neckline
Remove this machine sides and to edge leaving lower edge unsitched

Trim and layer seam allowance
Lay covered sections of collar and clip pointed edges
Neck collar
Top stitch round edge for a neat finish and flatness

R.s

W.s

Lower edge left free

(a) Discuss four Desirable qualities of a good clothes line:

Should be firmly held/strong
Should not be of a material that stretches
Should be strong not ward
Smooth not to damage clothes
Easy to excel clean and moist all weather conditions

(b) Explain five ways of disposing refuse in the home

Use of dust bins
Use of local authority
Compost pits
Feeding to animals (organic)
Using for mulching e.g. organic
Burying
Burning

(c) Explain five Factors to consider when selecting an electric iron

Should have a thermostat for controlling temperature
Should have a insulated long enough flex
Should have a plot indicator that shows when current temperature is riched
Parts must be firmly fixed with temperature control labeled according to fabric

(d) Giving a reason in each case, state three factors to consider when wearing a baby

Nutritive value of cereals
Carbohydrates in endosperm
Protein in germ bean and endosperm
Fat
Mineral salts calcium iron and phosphorous
Vitamins

(a) Explain three preparations to make on a sewing machine in readiness to stitching *MAT*

Threading correctly
Oiling he machine
Putting it at correct tension
Regulating the stitch correctly

*MUM*

Mention any three classes of stain removers used in laundry work

Bleaches
Grease solvements

State two uses of facings in garment construction

Decorating of edges of garments fabric sections.
Strengthening of portions of fabric enabling fiture of fastening e.t.c
Neatening raw edges of fabric.

State three uses of eggs in flour mixtures

Aeration: Expand with mixture on heating.
Liquidisation; Are partially liquid and add this to the mixtures
Improve the nutrive value of mixture as are of high biological value.
Imbue own unique inherent flavor to mixtures.

Give any two precautions measures to take when using dry cleaning fluid

Work in well ventilated rooms to avoid suffocation or poisoning.
Keep away from naked flames because it is usually inflammable.
Air all dry cleaned articles well to remove traces of fluid and or fumes.
Keep away from children as is hazardous in the most.

What is the cause of swelling of body tissues that is symptomatic of kwashiorkor*MUM*

– The Accumulation of interstitial fluid due to poor cellular metabolism and the lack of protein content.

Name any four common groups of people that are usually affected by anaemia *MUM*

Pregnant mothers
Women and girls who experience heavy menstrual flows.
Poorly nourished children or individuals who don’t get enough supplies of iron their diets.
People suffering from hookworm whipworm and other similar parasitic infection

List three functions of water in the bodies of human beings

forms the matrix in which almost all metabolic reactions take place.
Water is required for all bodily fluids e.g digestive juice, blood,lymph, sweat and urine.
Keeps the linings of all mucous membranes necessary for absorption and exchanges of elements moist
Dissolves nutrients and thus carries and transports them.

Define the term essential Amino acids correctly

Amino acids that cannot that be manufactured in the body from its pool of nutrient elements and must be obtained through consumption in food.

Why are there more than usual numbers of Tuberculosis victims in today’s

societies than in the past (i.e. after the 80’s than before)

– the incidence and prevalence of the HIV/AIDS pandemic in the contemporary diaspora and its singular effect of destroying or degrading the human immune system has rendered many a victim highly susceptible to infection and disease opportunistically, hence the aggravated onslaught of many of the said infections like Malaria, cancers and thus notably this particular one.

What is the work of a thermostat in an electric iron box

It is a bimetallic strip made up of two metals or conductive materials with different rates of expansively, such that when the strip is subjected to an increase in temperature, it bends due to the differential expansion of the parts fused together

What are the following parts of an enclosed drainage system ?

(a) WATER CLOSET: A toilet or ablution system that consists of manually automated flushing

process with water kept in a reservoir that employs potential energy to efficiently and effectively disposes sewage from the toilet pan or bowl below.

(b)MANHOLE: An externally placed lidded pit – junction between two or more drains or sewers that doubles up as an emergency access point through which examination, repair and regulation of the working of the enclosed drainage system is possible.

(c) SEPTIC TANKS: 1. A sewage disposal system usually made up two tanks; of which

The first is the Receptacle of all the wastes from the household, and in which it
separates out into the sludge; that sinks to its bottom compacting there and
the effluent; the liquid part that over flows into the second and is
Either passed off into the surrounding soils ( for soak-pits) or pumped out and

carried away for further disposal by tankers to the sewage works.

State three general causes of poor sanitation *MUM*

Carelessness and the lack of objective endevour in environmental hygiene and related practices in the wider community.
Poor planning of human settlements and other housing infrastructures in communities.
Overpopulation, overcrowding, poverty and general inefficacy and inebriation of personal, social, communal and other entities that exist in this scenario.

Give two advantages of frying as a method of cooking *MUM*

Produces usually very tasty food and foodstuffs.
Is usually quick and there saves time in execution.
Is consequentially cost effective on fuel.
Is relatively simple to execute in comparison with other methods of cooking e.g baking.

State any two common problems that may afflict a pregnancy before its full term *MUM*

Malnutrition and lack pf proper food for the pregnant mother due to unfavourable circumstances that may be prevalent as is.
Illness or disease that may be opportunistic, infective or even hereditary.
Psychological or emotional inebriation.
Physiological indisposition e.g in the case of underage pregnancies and underdeveloped bodily structures.
Trauma from environmental, climatic or sociological disasters.

It is decorative and attractive
It is strong

Breast feeding
Immunization at hospital

Give two advantages of using carpets in the home *MUM*

Decorative interiors
Protecting floors from damage
Keeping rooms cool
Keeping rooms clean

State two reasons why wooden surfaces in the home need finishing *MUM*

For decoration and enhancement of appearance
For protective covering from adverse effects of the weather

List four points to look for when buying cabbages *MUM*

Buy from a reliable seller
Buy in season
Avoid shriveled wrinkled ones
Prefer heavier samples
Avoid those whose leaves are faded

State two measures to take in order to control the incidence of bed sores in bed

ridden invalids *MUM*

Turn the patient over regularly in the bed
Turn over the mattress once in a while
Provide cushions and rests

*TNW*

Why figure type is an important factor in choice of clothes

So as to choose clothes that can enhance your personal appearance

Need to learn first aid

To save life
To prevent injury from becoming worse
To promote recovery
To present the injured to a medical practitioner 2×1 = 2 mks

Laundry processes carried out before washing a fast – colored cotton shirt

Mending
Removal of stains
Soaking/ steeping
Empting the pockets 2×1 = 2 marks

Difference between tear and wear

– Wear- thinning or weakening of a section of a garment

– Tear- A hole found on any part of a garment Each 1 mark = total 2 marks

Reasons why steel wool is not suitable for cleaning plastics

It removes color of the outside
It is difficult to rinse out steel wool particles
Steel wool will scratch and roughen the surface

Two main methods of purchasing goods and services in Kenya

Cash buying
Credit buying 1×2 = 2 marks

Advantages of dry cleaning

The solvent used are volatile, they therefore do not wet the garment and make it heavy as water does
It is a fast method of cleaning clothes, the solvents evaporate very fast leaving the garment dry
The method maintains the shape, size, color and luster of the garment and the fibres in it
The method does not demand a lot of energy since is little mechanical rubbing

Ways of minimizing wastage of detergents when washing

Using just enough
Avoid leaving bar soap in water
Do not use too much water
Wash many articles using the same water starting with less dirty ones
Use of soft water
Use of warm water 2×1= 2 marks

Uses of running stitches

It is used as a decorative stitch when a contrasting color is used
It is a joining stitch 1×2= 2 marks

How to identify warp threads in the absence of the selvedge

It is a thicker thread
Will not stretch when pulled
When the fabric is tagged or jerked, the warp threads produce sharper sound, higher pitch than the weft threads
It is a stronger thread 1×2= 2 marks

Factors that make dry meat dry and tough after roasting

Meat cut too thin for roasting
Heat too fierce or too hot
Meat exposed to heat for too long or too low heat
Wrong cut of meat used for roasting (tough cuts)
Meat not basted or turned during roasting 1×2 = 2 marks

Points to bear in mind when making seams on underwear

The seam should be flat and comfortable
Should be firmly stitched therefore durable
Seams should match where they cross
Have ever width
Accurately made, observing seam allowance and fitting line so that the drape and shape of the garment is maintained 1×3= 3 marks

Definition of the following terms
i) A course: Is a dish/ dishes eaten as part of a meal
ii) A dessert: A third course in a three course meal 2 marks

iii) A cover: A table mat with food items served for one person 2 marks

A flavoring that is suitable for salads

Garlic
Onions
Parsley
Lemon 1×1 = 1 mark

Two points to consider when selecting the baby’s layette

They should be loose and full so that the baby can be move its arms and legs freely
Of soft, light weight material that is easy to wash
Cool and warm to wear as needed
Easy to put on small babies e.g. skirts and gowns with openings 1×2 = 2 marks

Difference between complementary and supplementary feeding
Why management of fullness is important

It gives a good fit
It shapes the garment
It provides fashion features 1×3 = 3 marks

Uses of vinegar in cookery

As a preservation
As a flavoring ½ x2 = 1 mk

a) Dry cleaning a tie

Work in a well ventilated room away from the fire ( ½ )
Put sufficient dry cleaning solvent in a bowl ( ½ ) shake the tie to remove dust ( ½ )
Immerse ( ½ ) in the solvent and clean by kneading and squeezing ( ½) quickly to save the solvent from loss through evaporation ( ½ )
Squeeze out as much as possible ( ½ )
Hang out to dry in an open place ( ½ )
Leave the solvent in a covered bowl for dirt to settle then decant into a bottle for other use. Discard the dirt ( ½ )
Press ( ½ ) with a warm iron ( ½ ) 5 marks

b) Finish a cotton shirt

Sprinkle water and roll
Iron while damp
Iron double parts first on the w.s
Turn to the R.S and iron the skirt away from the worker
Air
Fold and store 5 marks

c) CLEAN THE LEATHER BAG

Cover the working surface
Dry dust to remove loose dirt
Clean using warm soapy water and a piece of cloth both inside and outside
Wipe with a damp cloth wrung out of clean water
Dry with a dry cloth both inside and outside
Air it under the shade 1×5= 5 marks

d) CLEAN A PAIR OF SLIPPERS

Remove any loose dirt
Use warm soapy water with a disinfectant
Scrub to remove fixed dirt using a soft brush
Rinse in warm water
Wipe dry using a clean cloth and put away
Clear up 1×5 = 5 marks

a) Changes that take place in a dough during frying mandazi

Color changes from original color to brown when exposed to hot oil
The mixture becomes porous due to expansion of air
The outside becomes porous due to expansion of air
The outside becomes crisp because of lack of starch granules (dextrin)
The size/ volume increases due to expansion of air
The mandazi becomes easily digestible because the starch granules are cooked 1×6 = 6 marks

b) Four faults in cooking of mandazi

Burning on the outside before the inside
Excessive hollowness
Heavy texture due to lack of enough raising agent
Sogginess due to low temperatures 1×4= 4 marks

c) Four nutritional needs of an adolescent

They need a balanced diet with plenty of proteins, minerals e.g. iron, calcium, phosphorous and vitamin C
Girls require additional supply of iron to compensate for the amount lost during menstruation
Include fatty foods to reduce the bulk of the food consumed e.g. bread and butter
Give adequate amount of food as teenagers have healthy appetite
Meals should be regular and be served attractively
Provide plenty of fresh vegetables and fresh fruits for roughage
Fluids should be included for compensation lost water during activities
Energy giving foods should be included because they are very active ½ x4 = 8 marks

d) Four qualities of a well made vegetable salad

The vegetables should be fresh
They should be attractive
They should have different nutrients
They should be greased to stop oxidation
It should be made of different types f vegetables
Vary in texture ½ x4 = 2 marks

a) Three points to consider when using a sewing machine

Ensure that there is good light to avoid straining the eyes and ensure adequate visibility
Ensure that machine is correctly threaded for efficiency in stitch formation’
Use appropriate needle for the fabric, the needle should be sharp to achieve good stitchery
Ensure that the correct stitches are set for the right stitch length and tension to work out good stitches
Test the machine before actual stitching to avoid handling the work
Ensure the work is guided through machine 1×6 = 6 marks

b) Six stitches used during the blouse/ skirt construction

Tailors tacking/ thread marking
Even tacking/ long tacking
Machine stitches
Hemming stitches
Running stitches
Basting stitches ½ x 6 = 3 marks

c) Five points to observe when laying pattern pieces onto the fabric and cutting out

Ensure the pattern pieces are smooth and flat for accuracy
Ensure all the pattern pieces required for the garment are available
Plan a rough layout using the provided layout for the width at the fabric before pinning to ensure that the fabric is enough
Pins should not be sticking out to avoid damaging the scissors
The fabric should be grained for straight edges 1×5= 5 marks

d) The procedure in preparation of around patch pocket ready for attaching

Neaten the top edge ( ½ ) of the pocket fold the hem ( ½ ) along the hemline ( ½ ) to the R.S ( ½ ) of the pocket
Stitch ( ½ ) the pocket along the stitching line ( ½ ) to fix hem in position
Trim the corners ( ½ ) of the hem to reduce bulkiness ( ½ )
Turn the hem to W.S ( ½ ) along stitching line
Snip/ notch ( ½ ) the turnings of the curves ( ½ )
Fold the edges ( ½ ) of the pocket along the stitching line

a) Two positive and two negative effects of advertisements
i) Positive effects

– Makes consumers aware of goods and services, which improve or add to their life style

by providing greater efficiency or pleasure

– Consumers are able to choose what they want 2 marks

ii) Negative effects

Consumers may be misled to prefer a product of low quality to one of high quality which is advertised less
Consumers bear the cost of advertising because the final price of the commodity is increased to cover the cost
Adverts sometimes appeals to the emotions and thus influences consumer psychologically

b) Precautions one would take when using kerosene

Reservoir should never be empty to prevent rusting
Do not overfill to avoid spills
Ensure lamps are replaced on flat and stable surfaces during use and storage to prevent spills
Do not light them near flammable substances e.g. textile materials, flammable liquids
Keep them out of reach of children to avoid accidents
Ensure flame is not too high to prevent production of smoke and soot
Handle them carefully to prevent falls- glass might break 1×4= 4 marks

c) Five advantages of breast feeding

Breast milk is at the right temperature
It contains all the nutrients needed in the right proportion
It is clean and free from contaminator
It does not need any preparation
It is available all the time
Improves the bond between mother and child
Assists the mothers uterus to turn to normal size and position 1×5 = 5 marks

d) Five problems related to weaning

The baby’s digestive system is not able to process the new foods leading to stomach upsets
Late weaning may lead to malnutrition due to shortages of nutrients with age
The weaning diet adopted may have too much fat and carbohydrate leading to obesity
Unhygienic handling of food and feeding equipment may lead to diseases such as diarrhea and cholera
The weaned baby is exposed to allergies from different foods 1×5=5 marks

e) Reasons for labeling products

Provide a products name
Provides the name of the manufacture
Gives information on the product e.g. ingredients, instructions for use, manufacturing and expiry dates
Enables the consumers to recognize the product 1×2=2 marks

*NDW*

State the importance of sebaceous glands in relation to a healthy skin (1mk)

Secrete an oily substance called sebum that keeps the skin oily preventing it from becoming dry,

Scaly and from cracking

Sebum makes the skin water proof and destroys micro-organism

State two qualities that make aluminium popular for household utensils (2mks)

Shinning in appearance
Light in weight
Does not rust
Good conductor of heat
Cheap
Does not react with food to form poisonous substances
Easy to clean
Easy to care for

Give a reason why nylon is unsuitable for sports wears (1mk)

Non-absorbent
Produce static electricity therefore it clings to the body
Does not conduct heat therefore it is not warm
Damaged by heat therefore cannot be foiled to remove stains and brighten colour

Mention two uses of dhania (coriander) leaves in cookery (2mks)

To improve flavour
As a garnish

Mention two advantages of blending cotton and nylon fibers (2mks)

When cotton is blended with nylon fibers it be comes more crease resistant
When nylon is blended with cotton fibers it increase resistance to abrasion

State any two reasons why a child’s growth monitoring is important (2mks)

Monitoring a child’s growth by weight for age is an immediate indicator of normal or abnormal growth
Monitoring a child’s growth by means of height for age helps to determine if the child is standard or is getting too tall
If the growth is too fast or too slow for the age the health clinic officers should suggest measures to correct it to avoid an obese or underdeveloped child

Four laundry processes that are harmful to woolen fibres and the harms they cause are; (2mks)

Soaking-causes wool to shrink and weaken
Rubbing/fiction washing stretching of wool
Starching-causes hardening and breaking of wool fibres
Ironing-causes stretching and produces shinning patches on the garment
Airing by hanging causes
Drying wool in the sun-causes hardening and breaking of wool
Washing in hot water-causes wool to shrink harden, and crease
Rinsing in cold water-causes wool to felt and matt

three ways of providing variety in meal planning and management (3mks)

Variety in colour-choose interesting colour combination
Texture-variety in texture e.g. crispy, crunching and tender
Flavours-variety of flavours e.g. salty, sweet, plain flat aromatic

two factors to consider when choosing where to buy vegetables (2mks)

Availability of vegetables
Variety of vegetables required
Availability of transport
Money available
Hygienic conditions of the place
Fresh vegetable
The price of vegetable should be affordable

Give two qualities of a good advertisement (2mks)

Message should be clear
It should attract consumers
It should be brief

three ways of economizing fuel when using electricity for cooking (3mks)

Soaking food that takes long to cook
Use energy devices e.g. pressure cooker
Use of energy only when required i.e. Electric power should be switched off when not in use
Use utensils that fit the entire cooking unit for electricity etc
Plan your activities such as cooking and ironing in such a way that conservation of energy is maximized
Covering cooking pots with well fitting lids
Electrical appliances should be well taken care of so that they work efficiently

two reasons for using interfacing during garment construction (2mks)

Give body or shape to the garment
Stiffening to add firmness
Prevent stretching or sagging
Obtain a good knife edge
Give a crisp tailored look to the area applied
Increase crease resistance

13 three methods of finishing the edges of sleeves other than using a cuff (3mks)

Facing
Binding
Lace
Frills
Piping
Hemming/shell hemming

State three reasons for labeling products in a factory (3mks)

Provide a product name
Provide the name of the manufacturer and contact
Provide information on the products; its ingredients, quality, instructions for use, manufacturing and expiry date.
For recognition by consumer.

Two precautions to be taken to prevent bed sores when taking care of a sick persons at home

-Turn the patient more often to change positions

Massage hip and back muscles
Ensure beddings are dry all the time
Check them for bed sores often

List two uses of lamp shades (2mks)

Add to interior decoration
Helps to avoid glare

State two factors to consider when planning lighting for various rooms in the home (2mks)

Purpose of the room
Size of the room
Existing colour scheme

Differentiate between advancing and receeding colours (2mks)

Advancing colours-colours that make a room or a figure appear larger
Receeding-colours that make a room or a figure appear smaller

Give two reasons why most women in the rural areas are less groomed (2mks)

They lack exposure
Environment in which they live in may not promote the art of good grooming
They have low income and lack of proper education to utilize the little resources they have
The kind of jobs they are involved in may not permit the exact art of grooming
Lack of clean water and cleaning materials

20 a) Describe the correct procedure of laundering a nylon dress (8mks)

Soak( ½ )in cold water( ½ )for a short time
Wash in warm soapy water( ½ )using kneading and squeezing methods(1mk)
Rinse severally in warm water( ½ )
Rinse in cold water( ½ )
Add fabric conditioner in the final cold rinse( ½ )
Drip dry( ½ )in the shade( ½ )
Iron( ½ )using warm iron( ½ )
Air to dry completely( ½ )
Fold( ½ )and store in a clean dry place( ½ )

b) Describe the correct procedure of cleaning white canvas shoes without shoe laces (7mks)

Dust them to remove loose dirt or remove mud if any(1mk)
Dash in warm soapy water( ½ )and scrub with a scrubbing brush( ½ )clean the inside( ½ )as well as the outside( ½ )
Rinse in warm water( ½ )
Final rinse in cold water( ½ )
Shake to remove excess water( ½ )
Dry( ½ ) by tilting them against the wall/ stone under the sun( ½ )
Apply white polish ( ½ ) while still damp ( ½ ) and leave to dry. use a clean dry duster to remove/wipe off excess polish( ½ )
Store in a cool dry place( ½ )

c) Give the correct procedure of cleaning two aluminium cups (5mks)

Rinse in clean water
Wash one at a time in warm soapy water using a mild abrasive
Rinse in warm water
Rinse in cold water
Wipe to dry or drip on a rack then dry later

21 a) Mention two uses of butter in the home (2mks)

Gives a delicious flavour in cakes and sauces
Soften cakes and baked items
Enriches food e.g. babies food
Greasing baking vessels

b) Identify four major nutrients found in butter

Energy
Vitamin A
Vitamin D
Fats

c) i)Describe four changes that take place when heating butter

Melts
Changes from solid to liquid
Burns and produces smoke
Turns brown
Finally turns black

ii) Name four main groups of fats giving an example for each

Animal fats e.g. cow fats, butter
Vegetable fats e.g. salad oil, margarine, palm
Solid fats-solid room temperature e.g. margarine
Oils liquid at room temperature e.g. Elianto

d) Explain three considerations to make when selecting a storage facility for butter (6mks)

a) Four tests undertaken at the clinic to an expectant mother in the first month of pregnancy Establish blood group

Weight
Pregnancy test
Establish level of iron in blood to determine whether there is need to administer pills or not.
Checking sugar and proteins in urine to ensure the uterus gets the normal flow of blood. b) Describe two supplementary foods for a baby (2mks)

Those which provide vitamin C e.g. Orange juice
Those which provide vitamin D e.g. Cod liver oil

c) Explain two benefits of supplementary food (4mks)

It helps meet the nutritional needs of the growing baby, because their nutritional requirement has increased
To substitute breast milk which may not meet all the nutritional needs of the baby.

d) i)Explain four reasons why a mother may be unable to breast feed

Being away from the baby because of work. This reduces feeding time.
Sickness, where the mother is too weak to breastfeed or is admitted to hospital or is taking medicine that can harm the baby.
Multiple births; a mother who gives birth to twins or triplets may not be able to adequately breastfeed all the babies
Successive births-A baby born before the older one has finished breastfeeding may cause the mother to stop breast feeding the older one in order to carter for the younger one.

ii) Explain four points on care of play items (2mks)

Keep clean according to type.
Store in clean places after play.
Wash the washable ones to ensure that the baby handles them when clean.
Assemble the dismantled ones and repair the broken ones in time.

23 a) Explain four properties of viscose rayon which are undesirable (8mks)

Creases badly, so needs a lot of ironing.
Flammable and can get burnt easily.
Develops mildew when left wet.
Yellows and rots when exposed to sunlight for long periods.
Its weaker when wet than dry so can get torn easily.

b) Suggest four features that can be used to finish a nigh dress decoratively (4mks)

Use of lace
Bias binding
Embroidery stitches
Frill

c) Give three reasons for ironing a night dress during construction (3mks)

Ensure seams are flat on attaching
Ensure parts are attached flat
Produce a neat article.

d) Explain five desirable qualities of an iron box (5mks)

Made of non rusting material
Medium weight.
Smooth soul.
Pointed toe to reach fullness.
If electric, should be thermostatic i.e. control heat automatically.

*RCH*

A,D,E and K (any 4x ½ =2mks)
List four causes of anaemia

Iron deficiency
Worm infestation
Chronic malaria
Excessive bleeding due to accidents etc
Hookworm infestation (any 4x ½ =2mks)

State two points to look for when buying spinach

Should be fresh
Examine well for grubs and insects (any 2×1=2mks)

Give two forms in which laundry soap is available in the market

Bar soap/had soap
Soap flakes
Soap power
Disinfectant or antiseptic soap
Liquid soap
Toilet soap
Toilet soap (any 2×1=2mks)

State two advantages of using firewood as a fuel for cooking

It is cheap
It is locally available
Can be used both for cooking, warming and lighting especially camp fires (any 2×1=2mks)

Identify two ways of storing dressmakers pins

Using a in cushion
Using a metal plastic set
Using pin wheel (any 2×1=2mks)

Give four special points to note when washing babies clothes

Use mild detergent
Use fabric conditioner in final rinsing water to soften garment
Rinse severally to ensure complete removal of detergents and laundry agents which may cause harm to the baby’s delicate skin
Disinfectant occasionally to kill germs
Dry whites in direct sunlight for further whitening (any 4×1=4mks)

State two measures taken immediately nose bleeding occurs

Let the persons sit down with he slightly raised to prevent the blood from floming down the throat
Plug nostril for about 15seconds,making the person to breath through the mouth
Cool the face with a cold wet towel
Repeat the treatment for another 15minutes if bleeching does not stop
Encourage the person to spit out any blood that flows into the month
If bleeding persist seek mechanical assistant (any2x1=2mks)

Name two improvised abrasives in the home

Charcoal
Ash
Sand
Rough leaves
Sisal
Egg shells
Maize cobs (2×1=2mks)

State two points to consider when choosing a refrigerator

Needs of the family
Ease of use
Type of fuel
Size
Cost or affordability
Efficiency
Space available for storage (any 2×1=2mks)

Name four methods of advertising

Mass media
Pamphlets/brochures/magazines/newspapers/promotions/sales
Packing
Posters
Billboards(any 4x ½ =2mks)

Give two reasons why cotton is popular for table linens

They are easy to launder
Are strong
Can withstand extremes of temperatures/can be boiled
Can withstand frequent washing (any 2×1=2mks)

Give two ways by which HIV/AIDS is transmitted

Through transfusion with HIV infected blood
Co-genital infection by an infected mother
Use of unsterilized infected equipment
Having intercourse with an infected person (any 2×1=2mks)

Mention four conditions necessary for growth of micro organism

Warmth
Moisture
Darkness
Dirt (any 4x ½ =2mks)

Give four factors to consider when renting a house

The family income
Size of the family
Composition of the family
Place of work and school
Social amenities (any 4x ½ =2mks)

Give four examples of air pollutants

Smoke from any burning
Dust blown by the wind
Bacteria released in to the air by infected people
Exhaust fumes from vehicles and aircrafts which produces CO₄
Cleansing agents
Natural pollutants such as pollen from flowering plants
Insecticides and pesticides used to control insects and pests
Hair and body sprays (any 4x ½ =2mks)

State two symptoms of food poisoning

Vomiting
Severe stomachache
Burning sensation in the stomach
Dizziness
Diarrhea
Fever
General body weakness (any 2×1=2mks)

Give two ways to ensure variety in meal presentation

Colour variation
Texture variation
Flavour variation (any 2×1=2mks)

Give two ways of avoiding impulse buying

Budgeting
Having a shopping list any time you go shopping and ensuring you stick to it
Carry just enough money to shop-avoid having a lot of extra-money (any 2×1=2mks)

Suggest two important ways of using mineral fibres in clothing

Used as overalls by fire fighters
For theatre curtains (any 2×1=2mks)

21.your mother is sick and has asked you to assist her with house work

a) Suggest how you would launder her loose coloured Khangal leso (10mks)

do not soak ½
wash very fast ½ in warm ½ soapy water ½ . wash using kneading ½ and squeezing method
do not ring ½
rinse in clean warm water ½
final rinse in cold ½ water to which salt (1)has been added to fix colour and some vinegar (1)to brighten
flat dry under the shade ½
iron while still slightly damp using a warm iron ½
air to remove excess moisture ½
store appropriately ½

b) Suggest how you would clean an aluminium sufuria used to prepare her breakfast

wash in hot ½ soapy ½ water
rub any strains with nylon scouring pad or steel wool ½
work thoroughly in clean hot water to remove all soap and dirt ½
dry well ½
store appropriately ½ (3×1=3mks)

c) Say how you would clean a cemented kitchen floor

remove light furniture ½
sweep floor and dispose of the dirt .dust the skirting board ½
use warm soapy water a hard scrubbing brush to scrub the floor starting from the furthest end in small sections including the skirting board. Ensure you are circular motions ½
wipe with a clean cloth or a mop wrung out of warm water ½
repeat until the room is complete ½
dry thoroughly with a floor cloth or a dry mop
rearrange furniture
clean equipment used and store appropriately ½ (7mks)

22.a)outline the points to consider when planning meals for a vegetarian

Should be balanced
Use vegetable fats and oil in the preparation
Vary foods cooked to avoid monotony
Season meats well to make it tasty
Include a good amount of vegetables to provide the would be omitted nutrients
Egg dishes milk and cheese in addition to pulses should be provided(for lacto- vegetarian) (any5x1=5mks)

b) Rough puff pastry has a well defined layers divided by air space ad should be very light. State

the four factors that its success depends on

sift flour and salt together

rub in fat very lightly into the flour and salt mixture
keep it as cool as possible during preparation so that on cooking, gases expand as much as possible giving light results
use a mixture of land and margarine for better results
roll lightly in a highly floured surface with light short and forward strokes
bake in a fairly hot over (any 4×1=4mks)

c) Outline the qualities of a good cloth storage facility

should be lockable
should have adequate deep drawers which should shide with ease
rod for hangers in the wardrobe should be strong enough be bear the weight of clothes
should be clean and dry and have smooth surface which are easy to clean
should be strong and durable with enough storage space
hangers should be smooth and durable (any 6×1=6mks)

d) Explain how kitchen waste contributes to environmental pollution (5mks)

bad smell
garbage especially is carelessly damped
can be health hazard if carelessly damped into water bodies

23.a)Explain five points to consider when weaning a baby (10mks)

Introduce new foods gradually .one food at a time to give the baby time to be come familiar with the food before giving another
Start by giving small portions and increase as you absence the baby’s reaction
Don’t force the baby’s to eat food they are not interested in stop and try again later.
Feed from a cup using a spoon
Sterilize all feeding equipment by boiling
First food should be very soft and become a less soft as the baby grows
Once the baby accepts a new food, give it fairly frequently so that it be comes familiar then gradually increase amount offered
Give food after breastfeeding
Ensure that milk continue to be a major part of the diet
Prepare foods hygienically
Allow the child to handle food and feeding equipment (any 5×1=5mks)

b) List five points to look for when choosing a toy for a child

should be attractive
must be durable to last long
must be appropriate for age and sex
shouldn’t be easy to dismantle because the child could put it in the mount
safe to use i.e. doesn’t contain poisonous substance
should be big enough so the child cannot swallow
shouldn’t be sharp which can injure the child
should be easy to clean (any 5×1=5mks)

c) Discuss five problems related to weaning a baby (5mks)

too early weaning
too late weaning
the diet may be too fatty and rich in carbohydrates leading to obesity poor muscle development and low resistance to infections
unhygienic handling of feeding equipment leads too disease e.g. diarrhea
bonding between mother and baby is interfered with since a baby who is weaned can be fed by any other person
the baby is expected to allergies from different foods
learning to use the feeding equipment may cause distress to the baby.

24.a)State two main nutrients found in each of the following foods

i) Beans-carbohydrates and protein
ii) Kales-minerals salt and vitamins

iii)Wheat-carbohydrate and proteins

b) Discuss the importance of repairing garments

to retain smartness/enhancing good grooming
to prevent further tear especially during laundry
in order not to expose the parts of the body they cover
to make clothes last long (any 5×1=5mks)

c) With the aid at east one well labelled diagram explain how to work a single pointed dart (6mks)

fold the dart along the fold line so that the fitting lines are matching
pin and tack from the wider and tapering to the point to hold the two layers of fabric firmly
remove pins and machines along the tacking line from the wider end to the tapering end at a point
secure stitching at the point by

-stitching backwards-0.5cm

-threading both stitching thread in a needle and concealing them in the fold or wearing

a few stitches

Press waist and shoulder darts to either (CF) or (CB) and underarm darts downwards.

d) State three importance of meal planning (3mks)

it ensures that meals are

i)adequate for the family members and meet their individual preferences

ii)balanced to meet dietary requirements of all the family members such as children,

the elders, adolescents and the sick

presented and served attractively to stimulate appetite and enjoyment (any 3×1=3mks)

*KKE*

It will prevent an individual from getting irritation and damage of the skin
To prevent an artificial look

To ensure good health by keeping away harmful; micro- organisms
To ensure original appearance of surface is retained/ surface free from stains remain attractive and in good condition
To ensure maintenance cost is retained

Drainage – System of getting id of waste water, run off and sewage from house or building

Refuse disposal – It is getting rid of rubbish or waste matter from a house

Give 1 mk for each well defined

To help retain colour
Reduce bulk
Retain nutrients
Retain flavour

Maintain high standards of cleanliness to contain infection by insects and other pests
Ensure the house is well lit
Beddings should be changed regularly and be properly aired
Use of insecticides
Sleeping under nets
Draining stagnant water
Clear the bushes around the home

To neaten raw edges
To decorate the garment
To shape and give body where applied
To provide enough thickness for attaching fasteners
To give strength to withstand strain

Drought
Scarcity
Transportation cost
Tastes/ fashion
A lot of money in circulation

Store in cool dry conditions
Away from chemicals
Cover it properly during storage
Store in clean conditions

10.

Knife
Potatoe peelers
Spalular
Forks
Spoons
Graters 1×2=2mks

11.

Excretion of wastes materials from the kidney and in sweat
Maintaining body temperature by perspiration
Aiding the digestion and absorption of food
The formation of all body fluids

12.

Use the correct method of cooking as per cut of beef to preserve nutrients
Take correct precautions to ensure food hygiene
Use correct temperature during its cooking to prevent denaturing of proteins and loss of other nutrients
Use correct time for cooking as required for the method chosen

13.

Balanced food provided plenty of proteins, minerals, salts such as iron, calcium, phosphorous and vitamin C
Include plenty of energy rich foods to reduce the bulk of food consumed e.g. bread with butter, rice starch and vegetables
Serve adequate amount of food as teenagers have healthy appetite
Serve regularly and attractively

14.

The strong flavour is disguising
Its yellowing effect is undesirable

15.

Making into jam
Canning/ bottling
Store in a cool and well ventilated area
Drying
Salting/ sugar
Smoking

16.

Ready to serve e.g. bread, cakes, ice cream
Partially prepared – require minimal preparation and coking e.g. dehydrated soups
Foods that are prepared and ready to cook e.g. cake mix

17.

Skipping stitches
Uneven stitch length
No movement of fabric

18.

It can withstand high temperatures
Can be boiled to disinfect and remove stain
It is absorbent and less fluffy thus suitable for drying glass utensils
It is strong thus withstands frequent washing

19.

Should have mitred corners
Have mouth reinforced
Fix hem using appropriate stitches

20.

21.

Soak ( ½ ) in cold ( ½ ) water for at least 30 mins
Wring out of soaking (1) water
Wash in hot (1) soapy water ( ½ ) using friction method (v)
Rinse in warm water ( ½ )
Final rinse in cold ( ½ ) water in which a disinfectant(1) is added
Drip dry (1) in the sun ( ½ ) secure with pegs

FINISHING

Dampen ( ½ ) by sprinkling warm water (1) roll ( ½ ) and leave for a while
Iron ( ½ ) double part ( ½ ) on WS ( ½ )
The whole surface ( ½ ) on the WS away from the worker (1)
Air ( ½ ) and fold
Clear up

Clean in warm (1) soapy (1) water (1) with sisal fibre/ sponge/ clothe(1)
Disinfect with a suitable disinfectant e.g. vim (1)
Rinse (1) severally in cold ( ½ ) clean water
Dry ( ½ ) thoroughly using a dry cloth

Some foods are cooked with seasoned flour or milk, eggs, wheat flour

Bread crumbs and eggs or melted margarine, butter

Garnishing/ decorating food property
Serving food on clean plates/ bowls
Use various/ varied cooking bowls
Use clean or well ironed table linen
Good flower arrangement/ centerpiece
Use of menu cards

Cut into thin strips
Dry on a tray covered with a thin cloth netting nustiline/ wire mesh
Place it away from reach of animals and children
Can be dried in a cage

Provide a well balanced diet with normal amount of Vitamin and mineral to improve the immune system
Provide food rich in calcium, phosphorous, iron, iodine and vitamin A, B, C and D, protein for repair of body tissues and less carbohydrates and fats because they are not very active
Avoid fatty and greasy foods for easy digestion
Ensure the foods are soft and easy to chew
Consider likes and dislikes to ensure they eat what is presented to them’
Ensure good seasoning and attractive serving to attract and stimulate appetite

23.

Tailors tucks
Use of tracing wheel and carbon paper
Use of tailors chalk
Long and short tacking
Thread marking

Caters for those who lack funds for hospitalization
Elderly people prefer to be nursed at home in a familiar environment not surrounded by strangers
It is cheap especially for illness that is not life threatening like minor wounds/ terminal cases
It is suitable for lactating mothers so as not to expose their babies to a hospital environment
Patients receive emotional support from family members

Stain should be removed when they are still fresh
Reason: They get fixed when old and become difficult and expensive to remove
Identify the kind of stain and type of fabric affect: in order to use a suitable stain remover
If the composition of the stain is unknown start with a milder removal method followed by mildies reagents to avoid damaging the fabric
After stain is removed rinse the article well Reason: To remove traces of reagents
Work from outside towards when removing stain Reason: To avoid spreading the stain

a) Physical development – A child’s muscles develop through running
b) social development – A child learns to co-operate with play mates and observe the rules of

the game and make friends

c) Mental development- A child learns how to put similar things together, model colour or

paint and construct patterns

Both cuff and under cuff should be of the same size
The width should be even on both the cuff and the under cuff
The cuff should be flat
The cuff should be of right proportion to the rest of the garment
The cuff should fit the weave well

Place raw edges together ( ½ ) wrong sides facing
Pin tack and machine ½ stitch 1.5cm from edge or along the fitting line ( ½ )
Trim ( ½ ) both seam allowance to allow 1.2cm( ½ )from front 6mm ( ½ ) on the back
Fold ( ½ ) front turning over back turning from a fell
Press/ crease the turning in position ( ½ )
Pin/ tack and machine stitch ( ½ ) close to the fold ( ½ )
Remove tackings and press (½ )

Dust (½ ) with a dry duster ( ½ ) to remove loose dirt
Clean (½ ) using warm soapy water ( ½ ) and scrubbing brush ( ½ )
Scrub in direction of the grain ( ½ ) ensure overlapping ( ½ ) the surface previously cleaned
Wipe ( ½ ) with a duster wrung out of soapy water ( ½ )
Clean ( ½ ) under pants ( ½ ) and legs ( ½ )
Rinse ( ½ 0 with a cloth wrung out of clean water
Dry ( ½ ) with a cloth well rinsed and wrung out

*STK*

The term hue refers to name of colour e.g. red, blue, yellow e.t.c. (1mk)
Benefits of studying home science to an individual are:-

Equips an individual with knowledge, skills and attitudes one requires for quality life
Helps an individual to adopt to the changing living conditions in the home, community and nation
Prepares an individual to take care of their personal hygiene, feeding, clothing, resources and health
Lays foundation for career development in industries such as catering, accommodation, hotel management and interior decorations e.t.c. (Any pts 2mks)

Two uses of a collander are:-

(i) Used as a separating tool-for separating liquids from other foodstuffs – e.g. for cleaning rice over

a tap of running water

(ii) Used for steaming foods (2mks)

Basic instructions on the use of medicine

(i) Dosage

Instruction
Frequency
Storage
Caution
Duration (1ny 4pts – ½mk each Total (2mks)

Accidents that may cause fractures
- Road accidents
- Heavy blow
- Falls caused by slippery floor, pot holes and cracks on the floor, split water or fruit peelings, loose tiles, littered clothes e.t.c. (any 2pts – 2mks)

Points to consider when choosing a toilet brush are:-

The bristles should be firmly fixed
The handle should be smooth
The handle should be of reasonable length (Any 2pts – 2mks)

Reasons for dampening clothes before ironing are;- (1mk)

For easy removal of creases
Smoothening of fibres (Any 1pt 1mk)

Precautions to take while cleaning wooden surfaces

Scrub along the grains to avoid damaging the grains
Avoid rough abrasives as they roughen the surface
Avoid use of hot water – it discolours the wood
Do not expose to direct sunlight as it will warp
Avoid sharp objects as it scratches the wood hence making it rough (Any 3pts 3mks)

Points to look for when buying a saucepan are:-

The base should be flat to help the pan balance and for even distribution of heat
The lid should be well fitting
Fairly thick- walled for even thermal distribution and for durability purposes
The handle should be strong and firmly fixed to support the weight of the pan
The handle should be heat resisting
It should be smooth and well rounded for easy cleaning (Any 3pts 3mks)

Uses of eggs in flour mixtures are:-

For aeration – e.g. in cake mixtures
For enriching the mixtures
To improve on colour of mixtures – e.g. cakes (Any 3pts 3mks)

Linen fibres are identified as follows:-

Burns rapidly in and out of flame
Smells like burning papers when burnt
Resembles glass rod when viewed under the microscope (Any 2 different pts (2mks)

Decorative methods of disposing off fullness are:-

Use of pleats
Use of wills
Use of smoking
Shirring (Any 4pts – 4mks)

Causes of needle breaking when machine stitching are:-

Machining over pins/zip teeth
Pulling the fabric from the front when machining or while removing it from the machine
Needle crossly fixed
Bent needle (Any 2pts- 2mks)

Suitability of French seams on fraying fabrics are:-

It’s exceptionally strong
It’s self-neatening

Importance of consumer education

Helps people to understand their roles as consumers and their importance to manufacturers and service providers
Informs people on their rights as consumers so as not to be exploited
Enables one to interpret and use advertisements wisely and to their own advantage
Informs one on the importance of family finance and the need to budget and spend family resources wisely and economically (2mks)

Factors that will affect the efficiency of a laundry soap are;-

Temperature of water used – whether warm or cold
State of water – whether hard or soft
Degree of soiling
Washing time
Mechanical agitation applied
Quality of soap being used (Any 3pts – 3mks)

(a) Reasons for using tucks on children’s clothing are:-

For decoration
For letting out-to increase size
For management of fullness
To provide fashion features (Any 2pts – 2mks)

(b) Factors that may affect normal foetal development are:-

Nutrients
Drugs
Sexually transmitted infections
HIV/AIDS
Alcohol
Smoking
German measles, malaria, e.t.c. (Any 4pts – 2mks)

Advantages of home-based care of the sick are:-

Caters for those who lack funds for hospitalization
Elderly people prefer to be nursed at home in a familiar environment not surrounded by strangers
Its cheap especially for illness that are not life threatening e.g. minor wounds, colds and flu, e.t.c
Its suitable for nursing/lactating mothers so as not to expose their babies to a hospital environment
Patients receive emotional care from relatives and friends (Any 2pts 2mks)

(a) Steps in laundering wool

Take measurements and record to later confirm whether there was any change in size
Prepare warm water –wool is laundered in warm water throughout
Immerse a basin of heavily built warm soapy water and wash under water by kneading and squeezing keeping under water throughout the washing time
Warm water since wool shrinks when cold water is used
Water heavily built to ensure article is well immersed in water/soapy solution
Kneeling and squeezing used since wool felts and stretches if exposed to friction method of washing
Wash quickly and do not soak – soaking leads to shrinkage
Rinse severally in warm water
Final rinse in warm water to which a disinfectant has been added, Wool should never come in contact with cold water, Disinfect to kill germs
Dry under shade on well protected ground/surface wool is affected by sunlight – it makes the fibres harsh and felt protected surface because wool is eaten by moths
Take measurements and compare with previous to confirm whether there was any change in size –incase of any pat and pull gently where applicable.
Finish with a cool iron whilest damp – high temperature affects wool/wool air stretches and felts if ironed
Air and store appropriately (well explained pts (10mks)

(b) Steps in cleaning white canvas shoes with laces

Protect the work surface
Remove shoe laces
Dust or remove mud as is appropriate
Clean in warm soapy water with a laundry brush’ – scrub to remove all dirt
Rinse severally in warm water
Final rinse in cold water to freshen
Flick to remove excess water
Apply white polish sparingly using an old piece of cloth or polish brush
Dry in the hot sun tilted on it’s heels
Remove when dry and rub with a dry cloth to remove excess polish. Clean shoe laces appropriately
Dry n the sun
Lace up the shoes and leave ready for use (Well explained points 6mks)

(c) A stained cup is cleaned by the following process:-

Soak in a hot solution of household bleach. Pour the solution when cold
Clean in warm soapy water and sponge
Rinse in warm water severally
Drip dry or dry with a soft cloth
Store appropriately (4mks)

(a) Danger signs of pregnancy are;-

Vaginal bleeding – may lead to miscarriage
Oedema – signs of poor blood circulating or poisoning the foetus
Varicose veins – swollen and twisted painful veins on the legs may burst and cause anaemia
Excessive vomiting – prevents proper nourishment to both mother and foetus
Dizziness-may be caused by inadequate iron in the blood (Toxaemia)
Haemorrhoids/piles – varicose veins in the anus. These are painful and may encourage constipation and loss of blood
Severe abdominal pain/backache signs of threatened miscarriage (Any5pts well explained 10mks

(b) Factors to consider when buying hand sewing needles are;-

Weight and thickness of fabric – the needles should be fine for the fabric
Eye should be big enough to take in thread
Rust proof for easy slipping
Farm,, straight and sharp- i.e. should not be deformed
Buy a variety of needles to carter for the sewing needs (5pts stated & explained 5mks)

(c) Causes of each of the following common faults.

(i) A course texture in rubbed in cakes

Too high temperature
Too much raising agent
Insufficient mixing (Any 2pts – 2mks)

(ii) Heavy and close texture in creamed cakes:-

Too slow an oven
Too much liquid
Insufficient creaming
Inadequate raising agent
Insufficient cooking
Too hot an oven, resulting in mixture forming in hard crust before air expands (Any2pt–2mks)

(a) Three labelled diagrams to explain the working of a lapped seam

Fold the overlay along the seam or fitting line to the W.s and press. The under lay remains unfolded
Place the overlay on the R.S of the underlay, matching the F.L pin and tack
Working on the R.S machine stitch close to the fold through all the three layers of fabric
Remove tackings and press
On the W.S trim the raw edges to about 1cm
Neaten the two raw edges together by overcastting, or machine zigzag
Press the seam on the R.S and W.S

(b) Functions of the following machine parts

(i) Balance wheel

– Controls the movement of the machine/needle-it’s used for starting and stopping stitching

(ii) Bobbin case – Secures the bobbin in place and for effective stitching (1mk)

(iii) Pressure foot lifter – Holds the fabric in place onto the feed dog during sewing (1mk)

(c) Qualities of a good cutting out shears

Must be rustproof
Sharp and firmly hinged
Long blades of at least 15cm for effective cutting
One blade should be narrower to slip under the fabric and another heavier to weigh down the fabric
Handles should have a smaller round hole for the thump and a larger heavy hole for the first three fingers

(d)(i) Importance of care labels

Gives the correct laundry treatment so that the article is not damaged
Assist in the selection of the garment so that one does not buy a garment which he/she is unable to care for appropriately
Assists professional dry cleaners to know which dry cleaning solvents to use for a particular garment

(d) (ii) Undesirable properties of nylon are;-

Its absorbent
Generates static electricity
Destroyed by long exposure to sunlight
Poor conductor of heat
Forms piles
Yellows with age
Slippery and frays easily (Any 2pts – 2mks)

(a) Changes that occur when cooking ugali are;-

Boiling water softens the starch in the maize
Starch grains swell and burst releasing starch granules. This is termed as gelatinization
Stirring vigorously causes even distribution of water and starch granules and prevents formation of lumps
Further heating causes water that’s not combined with starch grains to evaporate thus setting the ugali
Continuous stirring of the ugali as it sets ensures even distribution of heat for thorough cooking
Covering the heat for a while ensures thorough cooking (Any 5pts well explained – 10mks)

(b) (i) Food fortification refers to the addition of a food nutrient into a given food e.g.

addition of vitamins ABDE into blue band, iodine in salt, e.t.c

(ii) Food vehicle- Food to which fortification is carried out –e.g. when iodine is added to salt, salt becomes the food vehicle

(iii) Food supplements – These refer to alternative sources of food nutrients. Usually in form of

pills, tablets or capsules. They are taken in addition to the normal meals. E.g. iron

tablets, vitamin A or C tablets e.t.c

(c) Factors influencing consumer buying are;-

Price fluctuation
Complementary products
Substitute products
Income available
Time and energy
Family set-up
Inflation
Customs and traditions
Need to keep a certain self image/class
Rural/urban set-up (Any 4pts well explained 4mks)

*STK²*

Economical ways of disposing refuse

Recycling
Making a compost pit
Mulching
Feeding animals Any 2 pts = 2 mks

To descale/ defur

Means removing deposits caused by hard water on the walls of bodies 1 mk

Types of drainage

Free drainage – This is where waste water is poured anywhere around the house. Mainly common in the rural 2 mks
Open drainage system – This consists of open drains which directs waste water away from the house and compound 2 mks
Conceded drainage system – In this drainage system waste water from the kitchen bathrooms and water closet is directed away from the house through waste pipes which lead it to the sewage works

Uses of mangles

It rinses out water from wet clothes
It presses flat articles

Categories under which clothes are sorted out

Amount of dirt
Use of the garment
Fibre content
Colour
Nature of garment/ article i.e. whether loose or fast coloured 3 mks

Two common sponging solution

Warm water
Warm water and soap

Natural immunizations def:

This refers to the immunization a child receives from the mother while in the womb and while

breast feeding

Functions of Vitamin K

Essential for blood clotting
Necessary for normal functioning of the liver 2 mks

Effects of heat on Vitamin C

Vitamin C is water soluble and is destroyed (lost) during preparation and cooking
Foods rich in vitamin C should be cooked quickly and served immediately to avoid reheating
The vitamin is also readily oxidized hence vegetables should be cooked with the lid on to minimize oxidation
Vegetables and fruits should be preferably served raw 2 mks

Differences between weaning and supplementary feeding

A baby is introduced to supplementary feeds at early stages in life – e.g. may begin at one month – weaning is introduced at 3 months and above- though there is no specified set age
In weaning, the child us introduced to solid foods, supplementary feeds are mainly in liquid form
Supplementary feeding comes before weaning – it is the introduction to weaning
Supplementary feeds are given in very small quantities – in weaning the proportion are larger

11 Medicine are chemical preparation that are used to prevent/ cure various diseases as prescribed

by a qualified medical personnel 2 mks

Precaution to take when using grease solvents

Work in an open airy place as they are highly toxic
Work away from flame as they are highly inflammable
Wash hand thoroughly immediately after use as they are poisonous

What is valeting in home science? Explain its importance

Valeting involves simple tasks that are carried out to clothes and accessories to maintain or

enhance their appearance

Major processes through which sodium is lost in the body

Perspiration
Urination
Tears

Methods of neatening an overlaid seam

Loop stitching
Blanket stitch
Machine zigzag
Overcastting
Bin ding 3 mks

Give two reasons why consumer education is taught in schools

Makes people to plan for the family resources and budget so as to spend family resources wisely
Informs people about their rights to avoid being exploited by manufacturers and sellers
Helps to interpret and use advertisements wisely
Helps people understand their role as consumers and their importance to manufactures and service providers 3 mks

The most important meal for the day is – Breakfast

Why

Because it is taken after most of the food eaten the previous day have been absorbed leaving

the stomach empty

It is the meal that starts the day 1 mk

a) Methods of sponging woolen coat

Shake and brush the garment thoroughly to remove surface dirt
Spread the garment on clean surface
Remove any stains using appropriate stain removers
Prepare two basins of warm water, add detergent to one and the other free of detergent
Dip a folded cloth in the warm soapy water and squeeze out excess solution
Sponge a small section at a time, overlapping parts
Rinse in clean warm water using a clean folded cloth
Final rinse in warm clean water
Clean systematically, starting from the W.S and move inwardly to the R.S. pay attention to double parts on W.S
Rinse each portion appropriately
Dry in an airy place
Press with a warm iron
Air fold and store appropriately 10 mks

b) Laundering a white cotton blouse with chewing gum stain

Remove the stain appropriately by pouring very cold water or rub an ice cube over the stain. This hardens the chewing gum and then you can scrap it off using a blunt object e.g. knife
Treat the stained area with a solvent e.g. benzene or petrol then wash normally
Wash in hot soapy water using friction method
Rinse severally in hot water and finally in cold water to freshen
You can boil to further bleach or use laundry blue
Rinse in cold water
Dry on the clothes line in the hot sun
Iron with a hot iron
Air fold and store appropriately 6 mks

c) Points to consider when buying a washing machine

Consider the price and cost of maintenance should be reasonable
Select a well designed machine that is pleasant to work with
Bug from a reliable dealer who can service and repair when need arises
Check to ensure that all electrical are in good working order are of appropriate length and that the plug is of the proper cottage
Buy a machine made from rust proof material
The size and cleansing action must be suitable for the work it is expected to perform
Consider the control of the machine
It should be supplied with an instruction manual and a guarantee it is sighed and date
Consider the amount of space available. There should be adequate space for storage and operation of the machine 4 mks

a) Principles of nutrient conservation in preparing vegetables

Foods e.g. legumes and pulses should be cleaned before soaking
Foods should be thinly placed before couching. Using a sharp knife. Cutting and exposing them for long periods causes oxidation of vitamin such as A, C and E leading to their wastage
Wash vegetables and fruits before cutting them. Washing after cutting dissolves away vitamins and minerals that are lost since the washing water disorded
Clean vegetables and fruits using cold water. Hot water destroys heat sensitive vitamins e.g. vitamin C and B
Do not soak vegetables in the washing water because this dissolves vitamins nd minerals

b) Functions of advertisements

Informs the consumer on the availability of certain goods or services and goods to access them
It is a quick and effective way of passing information about a new product
Advertising gives information on the varieties available of a specific product
Good advertising gives additional information about the product e.g. the nutritive value of foods or characteristics of textile fibre
Advertisements also entertain 5 mks

c) Explain five factors to consider when renting a family house

Family size
Location
Tenancy conditions
Transport
Security
Amount of rent
Location 5 mks

d) Uses of salt in the house

For flavouring foods
For removal of blood stains
To fix colour in loose coloured garments and articles
For dissolving mucus in handkerchiefs 2 mks

a) Procedure of working machine fell seam, at shoulder

Place two pieces of fabric together W.S facing – working on the right side
Pin tack and machine stitch along the tacked line
Remove tackings and press the seam flat
Trim the back turning to within 3-4 mm. (The front turning remains uncut)
Fold the front turning over the cut back turning
Pin and tack close to the fold. (The seam should be flat)
Machine stitch close to the fold
Remove tackings and press the seam flat

b) Ways of neatening an open seam

Loop stitching
Over casting
Binding
Machine zigzag
Edge stitching
Pinking

c) Types of beriberi

Wet beriberi
Dry
Infertile beriberi
Infertile beriberi

Wet beriberi

Dry beriberi

Fluids are retained in the body
Pronounced and rapid heart beat
Chest pains
Reduction in the amount of urine passed due to water retention in the body

Fluids not retained

Numbness and feeling of pin pricks

Weakness and wasting of muscles

Difficulty in walking or rising from a squarting position

d) Points to consider when packing foods

Pack hot foods and drinks in flasks to be served hot
Pack each type of food separately
Remember to pack seasonings
Consider the number of people – pack adequate food according to number of people
Include cutlery in the packing
The meal should be easy to pack and eat
Include a refreshing drink 4 mks

a) Five social needs of an expectant mother

Friends and family members should be considerate and to ensure that they do not sideline her in their activities and decisions
It is important that the expected mother is assured that while she will be away someone will take care of her children while away
She should not be exposed to pressure or frustration both at home and at place of work
Nasty remarks about the pregnant mother should be avoided
Young children in the family should be informed about the coming baby and encouraged to welcome and accept the situation 10 mks

b) Points to consider when choosing personal clothes

Weather
Occasion
Fashion
Personal tastes and preferences
Figure type
Colour 10 mks

PAPER TWO

Answers 441/2

*NYR*

	PRESENTATION
1.	PRESENTATION – Label on single fabric – Well pressed work – neat and no pins – Firm attachment of the label – Left half of the dress
2	CUTTING OUT – Smooth cutting (1) Dress front (2) Dress back (3) Sleeve -Cutting on straight grain for the 1. Front 2. Back 3. Sleeve 4. Back neck facing 5. Front neck facing Cutting diagonally for the sleeve binding and tiles
3.	OPEN SEAM – At the shoulder line award zero if or open seam used – Straight stitchery line – Well neatened seam allowance – Even width of the neatened seam allowance – Seam pressed to lie flat – Matching well with the seam of the facings
4	FACINGS – Joining of the front and back neck facings – With an open seam – well neatened and neat work – Straight stitchery
5	FRENCH SEAM – Worked at the sides – Award zero if not French seam – Worked from R.s to W.s – Finishing on the W.s – Straight stitchery – Good tension of stitches – Knife edging – Neat – Within 0.4-0.8 final full – Fell facing the back
6	SLEEVE FACED SLIT OPENING – Preparation of the facing – Attaching on the R.S – Slashing the opening – Turning to the wrong side evenly – Pressed to lie flat – Finishing on the W.s
7	UNDERARM SEAM – French seam – Fell 0.4-0.8mm – From R.S – W.s – Even in width
8	THE BINDIGNS – Attached onto the sleeve – Neat stitchery – Evenness of the binding
9	ATTACHMENT OF SLEEVE – Straight stitchery along the armhole – Good hang of sleeve – Gathers at the crown – Well distributed gathers – Armhole not neatened – Notches matching i.e. single to single and double to double – Underarm seam matching the side seam

*MGN*

	PRESENTATION MGN
1.	PRESENTATION – Work well pressed ( ½ ) and folded( ½ ) – Label firmly (1) fixed on a single (1) layer of fabric. – Pins and unnecessary tackings removed. (1) – Made up LEFT HALF (1)
2	CUTTING OUT MGN – CB/CF smoothly cut. (1) – Fabric cut on straight grain. (2) – BF (½) BB ((½)) Bindering (½) Facing (½) – Lower edge of blouse well cut. (1)
3	WORKING ON DOUBLE POINTED DART MGN – Correctly positioned dart (1) – Straight stitching (1) – Tapering to nothing on both ends (1) – Correct length of dart ( ½ ) (with 2 mm) – Firmly secured points ( ½ ) – Darts pressed towards C.F. (1) – Middle of double dart snipped (1) to lie flat on both sides. (1)
4	SHOULDER SEAM (FRENCH SEAM) (AWARD ZERO IF NOT FRENCH SEAM) MGN – Good straight stitching. (1) – Correct width of seam (1) (0.5 – 06 cm) – Evenness in width (1) – Self neatened raw edges all enclosed.. (1) – Good knife edge produced.. (1) – Seam pressed flat. (1)
5	SIDE SEAM (NEATENED OPEN SEAM) MGN (AWARD ZERO IF OT OPEN SEAM) – Good straight stitchery.(1) – Evenness of both sides. (1) – Flatness at the armhole joint. (1) – Correct size of seam (1) (0.8 – 1.2 cm each side) correctly neatened with edge stitching. (1) – Presses open. (1)
6	NECKLINE FACING MGN – Facing correctly joined (1) to back facing using plain seam. (1) – Free edge of facing correctly. (1) – And neatly neatened (1)
	ATTACHMENT TO FACING (Front Facing and Back Facing) MGN – Correct (½) placing of facing to neckline. – Good stitchery (1) (Back Front flatness of facing. (½) – Smoothness of neckline. (½) – Facing firmly fixed. (1) – Facing under stitched (½) from Top of neckline correctly produced.
7	CUTTING AND REPAIR OF HEDGE TEAR USING DARNING MGN – Correctly (1) cut triangular hedge tear repair using hand darning. (½) – Marked the vent of the tear. (½) – Used fish boned (1) – stitches to bring edges together. – Darn extending beyond vent. (½) – Threads firmly secured. (½) – Raw edges completely enclosed. (1)
8	BINDING ARMHOLE – Joining the binding piece. (1) – Correctly joined to armhole. (1) – Evenness of binding on both sides.(1) – Correct final stitching. (1)

*KSM*

	Maximum score	Actual score	remarks
1 PRESENTATION -clean -Well pressed -Neatly pressed -Tacks and pins removed -Label firmly fixed and on singles fabric	½ ½ ½ 1 1
	3 ½
2.CUTTING OUT -Straight grain to within 2mm -C.F straight to within 2mm -C.B straight to within 2mm	½ ½ ½
	1 ½
PREPARATION
A)WAIST DART -correct length -straight width -straight stitchery -dart tapering to nothing -dart fastened on and off -pressed flat -dart facing C.F	½ ½ ½ ½ ½ ½ ½
	3 ½
B)CALICO PATCH -patch correctly aligned -straight grain running continuously -good stitchery -straight stitchery -stitching close to fold -regular shape of patch -regular shape of patch -pressed flat	½ ½ ½ ½ ½ ½ ½ 1/2
	4
C)FRENCH SEAM -Straight stitchery -Good knife edging -Raw edges enclosed -Seam allowance trimmed -Seam ¼ wide -pressed	½ 1 ½ ½ 1 ½
	4
D)OPEN SEAM -straight stitching -open seam 1 wide when finished -pressed open -neatened by edge stitching	½ ½ ½ ½
E) CONTINUOUS WRAP OPENING -Straight stitchery -Raw edges enclosed -seam allowance trimmed ½ wide -turning hemmed on W.S -turning even throughout	½ 1 ½ 1 1
	6
F) CUFF PREPARATION AND ATTACHMENT -Straight stitchery -Raw edges trimmed -Good knife edging -Cuff interfaced -Under cuff interfaced -Correct alignment of cuff on sleeve -Straight stitchery	½ ½ ½ ½ ½ ½ ½
	3 ½
g)-seam allowance trimmed pressed -cuff hemmed down to position -cuff even	½ 1 1/2
	2
H)PREPARATION AND FIXING OF NECKLINE FACING -front and back facing joined -pressed -edge stitching on free edge of facing -correct alignment at neckline -under stitching done -seam allowance trimmed -facing pressed and catch Stitched in position	½ ½ ½ 1 1 ½ 1
	5
I) ATTACHING OF SLEEVE -Sleeve correctly aligned -Smoothly attached -Gathers evenly distributed at crown -Good hang -Good stitchery -Armhole seam neatened with loop stitches -Armhole seam and side seam crossing to within 2mm	½ ½ ½ ½ ½ ½ 1
	4
J)SLIP HEMMING BACK BODICE LOWER HEM -correct section hemmed -hem edge stitched -slip hemmed -hem even pressed flat	½ ½ ½ ½ ½
	2 ½
K)WORKING OF BUTTONHOLE AND ATTACHING SHIRT BUTTON -Button hole cut along the thread -Correct Button hole stitch used -Button hole stitch even -Round end over sewn -Bar end with a bar of stitches -button correctly positioned -Shank created -Button hole stitch worked to fasten WS -Button firmly fixed	½ ½ ½ ½ ½ ½ ½ ½ ½
	4 ½
total	45

*KKC*

	AREAS MARKED	MAXIMUM SCORE	ACTUAL SCORE	REMARKS
1.	PRESENTATION (a) Pins and threads removed. (b) Work well pressed. (c) Work well folded. (d) Labeled. (e) Label firmly fixed. (f) Label fixed on single layer of fabric.	½ ½ ½ ½ ½ ½
		3 ½
2.	CUTTING OUT (a) Pieces cut out on straight grain of fabric as shown in the pattern pieces. (b) C.F. and C.B. well cut on grain line.	5 2
		07
3.	DART (a) Straight stitchery. (b) Tapering to the point. (c) Thread well fastened at the point. (d) Flatness of the dart on W.S. and R.S. (e) Pressed to C.B. (f) Correct length of dart. (g) Correct width.	1 1 1 1 1 1 1
		07
4.	FRENCH SEAM (a) French seam made (if not French seam give 0). (b) Straight stitchery. (c) Even in size. (d) Well knife edged. (e) Raw edges not showing through the seam. (f) Pressed flat to face the back. (g) Appearing on the W.S. of dress.	1 1 1 1 1 1 ½
		6 ½
5.	PLAIN SEAM (a) Plain seam made (If not give 0). (b) Made on W.S. of dress. (c) Straight stitchery. (d) Both seam allowance held together and neated. (e) Evenness in width. (f) Pressed flat to face the C.B.	1 1 1 1 1 1
		06
6.	PATCH POCKET (a) Appearing on the R.S of dress. (b) Evenly made hem at the pocket mouth. (c) Edge of pocket well tacked under. (d) Bulky seam allowances cut off rendering pocket flat. (e) Well stitched all round. AREAS MARKED (f) Pocket mouth reinforced appropriately. (g) Bace well curved (not gathered).	½ 1 1 1 1 1 1 ½
		06
7.	FACINGS (a) Both back and front facings used. (b) Back and front facing appearing on W.S. Front on Front. Back on Back dress. (c) Both joined well on stitching line. (d) Seam trimmed and pressed open. (e) Both well neatened at the edge. (f) Well attached at the neckline with the neat stitches. (g) Stitching line followed, rendering the neckline smooth and well curved. Seams matching. (h) Pressed flat W.S. to face W.S. (i) Seams well trimmed to avoid bulk. (j) Well under stitched.	½ ½ 1 1 1 1 2 1 1 1
		10
8.	HEM SLIP HEM (a) Straight stitchery. (b) Evenness in width. (c) No bulk.	1 1 1 1
		4

*RCH*

	*PROCESSES*
1.	*PRESENTATION* · *well pressed work(1) and well folded(1)* · *label (1)well fixed on single(1) fabric* · *unnecessary temporary stitches* · *tacking, threads and pins removed(1)* · *made up of the left half(1)*

2.	*CUTTING OUT AND GRAINING* · *All eight pattern pieces cut on* · *straight grain( ½ x8)max 4* · *Smooth cutting out of edges at CB* · *of yoke(1) and skirt(1)* · *Smooth cutting out of edges of CF* · *of yoke (1) and skirt(1)*

3.	*OVERLAID SEAM AT YOKE* *If not overlaid seam give zero* · *quality of stitchery (1)* · *stitched close to the edge of front( ½ ) of back (1/2 ) yoke* · *evenness of seam allowance on W.S of* · *front( ½ ) on back (1/2 )yoke*

4.	*OPEN SEAM AT SHOULDER* *If not open seam give zero* · *Straight stitchery(1)* · *Right size(1cm when finished)(1)* · *Seam pressed flat/open(1)* *(if seam is neatened deduct 1)*

5.	*INTERFACED COLLAR* · *Interfaced(1)firmly fixed(1)* · *Well knife edged(1)* · *Correctly positioned(1)* · *Flatness of the attached collar(1)* · *Correct shape (1) and size(1)of the attached collar* · *Neckline seam evenly trimmed( ½ )and snipped(1)* · *Collar well trimmed(1) and snipped(1) evenly*

6.	*FREE EDGE OF FACING* *If not neatened give zero* · *Edge neatened by machine(1)* · *Straight stitchery( ½ )* · *Trimmed to less than 3mm (1)*

7.	*FRENCH SEAM AT SIDE OF DRESS* *If not French seam give zero* · *Correct width of seam* · *Evenness(1)* · *All raw edge enclosed(1)* · *Straight stitchery(1)* · *Pressed flat to wards CB(1)* · *Underarm seam and side seam meeting the point to within 2mm(1)* · *Knife edged(1)*

8.	*PREPARATION AND ATTACHMENT OF FRILL* · *Inverted pleats well positioned(1)* · *Straight stitchery of open seam(1)* · *Frill attached to front skirt only(1)* · *Neatened by use of loop stitches(1)* · *Loop* *stitches 0.2cm from the edges (1)*

*MUM*

1. PRESENTATION *MUM*

– Clean work and neatly folded, well pressed

– Tackings and pins removed

– label firming sewn and on single fabric

– RIGHT hay made

2. CUTTING

– If smoothly cut and straight to within 2mm

– CB smoothly cut and straight to within 2 mm

– Pocket facing cut on cross grain

– Both waist bands cut on fold

3. WAIST

– Correct length

– Correct width

– Straight stitchery

– Tapering to notching

– correctly reinforced

– Well pressed on RS

– Fold facing CB

4. PATCH POCKET

– Pocket and facing correctly matched and stitched RS together

– Facing under stitched

– A good knife edge between pocket and facing

– Facing edge stitched

– Facing neatly hemmed onto the pocket

– Pocket seam allowance trimmed

– Pocket lower corners mitred

– Pocket stitched close to the edge

– Straight stitchery

– Pocket mouth correctly reign forced

– Pockets flat and on straight grain

– Correct position onskirt

5. GATHERS

– Gathers made not pleats

– Evenly distributed on front skirt

– Gathering stitches removed

– Well pressed

6. OPEN SEAM

– Straight stitchery

– Straight wide when finished

– Neatened by edge stitching

– Pressed open

– Even

– Correct tension of stitches

7. ZIP– Correct position

– Back turning stitched with the fold close to the zip teeth

– Front turning machined 1cm from the fold

– Machined on RS and across to the seam

– Upper zip end enclosed in waist band

– Lower zip and enclosed in the seam

– Zip completely hidden

8. UN-INTERFACED WAIST BAND

– Correct size of waist band

– Waist attached on RS

– Correctly folded along fold line

– Hemmed on W.S by picking on the stitches

– Waist band flat

– Sharp corners at tie ends

– A good knife edge at the ends

– Tie ends stitched RS together and turned over

– Tie ends even in size and length

9. HEM

– Edge stitched and folded on hem hire

– Open seam flat

– Hem even and flat

– Running stitches even and small in size, and rein forced

KKE*

1. PRESENTATION	Marks
(a) Well pressed (a) well folded (1)	1
(b) Clearly written and firmly sewn label (1) on single fabric (1)	2
(c) Removal of unnecessary stitches (½) threads (½) pins (½)	1 ½
(d) Made up of right half (1)	1
(e) Clean work, not dust, not stained (1)	1
	9mks
2. CUTTING OUT AND GRAINING
(a) CB of dress smoothing cut (1) and on grain to within 2mm (1)	2
(b) CF of dress smoothly cut (1) and on grain to within 2mm (1)	2
(c) Front and back neck facings smoothly cut (1) and on grain to within 2mm (1)	2
(d) Collar smoothly cut (1) and on grain to within 2mm (1)	2
(e) Sleeve smoothly cut (1) and on grain to within 2mm (1)	2
(f) Ties smoothly cut (1) to within 2mm (1)	2
	12mks
3. French seam at the shoulder (if not French seam give 0)
(a Joined with straight stitchery (1)	1
(b) Evenness of seam (1) width about 6mm (1)	1
(c) Flatness of seam (1)	2
(d) Facing right direction back (1)	1
	5mks
4. SLEEVE
(a) Good hang (1)	1
(b) Well distributed gathers at the crown (on R.S) (2) but the notches (2).	4
(c) Under arm seam joining with straight stitching line (1)	1
(d) Under arm seam meeting side seam to within 2mm (1)	1
(e) Arm hole seam joined within straight stitchery line (1)	1
(f) Under arm seam flat at arm hole (1)	1
(g) Facing used on sleeve opening (1)	1
(h) Lower edge of sleeve bound (1)	1
(i) Ties well finished by top stitching(1)	1
(j) Notches correctly matched (1)	1
	13mks
5. COLLAR
(a) Inter faced (1) well done (1)	1
(b) Straight stichery (1)	1
(c)Seam allowance trimmed (1) simp (1)	2
(d) Flatness of coillar (2)	2
(e) Collar well positioned and fitting (2)	2
	11mks
6. FACINGS
(a) Straight stitchery when joining F and B facings (1)	1
(b) Facings well fixed (1) to finish collar raw edges (1) lying flat (1), trimmed ( ½ )	3 ½
	5mks
7. SIDE SEAM(if not open seam do not crowd)
(a) Good stitchery (2) straight
(b) Correct width (1m) (2)	2
(c) Appropriately edge stitched (2)	2
(d) Flatness (2) pressed open (2)	4
(e) Seam allowance even in width (2)	4
	12mks
8. SLEEVE OPENING (a) Slit opening (1) (b) Correct length (5cm) to within 2mm (2) (c) correctly faced (1) flat (1) and lying on the wrong side of garment (2) (d) Straight stichery (1)	1 2 2 2 1
	8mks

*NDW*

PRESENTATION

1.PRESENTATION

Work labelled firmly on single fabric
When pressed and carefully folded
Pin unnecessary tacking remove
Made up for the left leg

2.CUTTING OUT STRAIGHT GRAINING

Short front cut on straight grain ( ½ )
Short bank smoothly cut( ½ ) on

straight grain( ½ )

Waist and cut on straight grain ( ½ )
Fig( ½ )opening facing cut on straight grain( ½ )
Fly binding cut on bias(1)

3.WORKING OF BACK DART

Straight stitchery ( ½ )tapering

to nothing( ½ )

Thread well reinforced(1)
Correct length ( ½ )and width( ½ )
Dart pressed towards C.B( ½ ) and lie flat( ½ )

4.FACING OF THE SHORT OPENING

Correct position( ½ )
Avoid stitching-size( ½ )tension( ½ )

and straight( ½ )

Well pressed( ½ )and flat( ½ )

5.PREPARATION AND ATTACHMENT OF FLY

Fly appropriately prepared( ½ )
Fly lined( ½ )with the attached facing ( ½ )
Raw edge neated together( ½ )using the bias binding(1)
Quality of stitching-tension( ½ )size( ½ )and straight(1)
Fly fixed in position by top stitching(1)

6.WORKING OF PLAIN SEAM AT THE SIDE

Correct seam plain(1)(if open award zero)
Straight stitchery(1)
Correct tension( ½ )and size of stitches( ½ )
Seam appropriately neatened(1)
Only half of seam neatened(1)

7.NEATENED OPEN SEAM(INNER LEG)

Correct seam(1)if not open award zero
Quality of stitchery-tension( ½ )
Size(1/2)and straight( ½ )
Evenness of seam( ½ )
Seam appropriately finished(1)
Pressed hem( ½ )lie flat( ½ )

8.PREPARATION AND ATTACHMENT OF

WAIST BAND

Waist band interfaced( ½ )
Interfacing correctly held(1)
Turning trimmed on both sides(1)
Correct width( ½ )size( ½ )and even
( ½ )according to the pattern
Correct stitchery-tension( ½ )size( ½ ) and straight( ½ )
Waist band knife edged(1)
Waist b and appropriately finished( ½ )

9.PREPARATION OF HEM

Correct width of hem( ½ )
Evenness of width(1)
Correct edge stitched before turning under(1)
Slip hemming used(1)firmly done(1)
Not showing on R.S( ½ )
Only half neatened ( ½ )(from side seam to inner leg) (1)
Hem pressed flat(1)

*STK*

(1) PRESENTATION	MAX SCORE	REMARKS
Work well pressed ( ½ ) and folded( ½ ) Label firmly (1) fixed on a single (1) layer of fabric. Pins and unnecessary tackings removed. (1) Made up LEFT HALF (1)	5
(2) CUTTING OUT CB/CF smoothly cut. (1) Fabric cut on straight grain. (2) BF (½) BB ((½)) Bindering (½) Facing (½) Lower edge of blouse well cut. (1)	4
WORKING ON DOUBLE POINTED DART Correctly positioned dart (1) Straight stitching (1) Tapering to nothing on both ends (1) Correct length of dart ( ½ ) (with 2 mm) Firmly secured points ( ½ ) Darts pressed towards C.F. (1) Middle of double dart snipped (1) to lie flat on both sides. (1)	7
SHOULDER SEAM (FRENCH SEAM) (AWARD ZERO IF NOT FRENCH SEAM) Good straight stitching. (1) Correct width of seam (1) (0.5 – 06 cm) Evenness in width (1) Self neatened raw edges all enclosed.. (1) Good knife edge produced.. (1) Seam pressed flat. (1)	6
SIDE SEAM (NEATENED OPEN SEAM) (AWARD ZERO IF TO OPEN SEAM) Good straight stitchery.(1) Evenness of both sides. (1) Flatness at the armhole joint. (1) Correct size of seam (1) (0.8 – 1.2 cm each side) correctly neatened with edge stitching. (1) Presses open. (1)	6
NECKLINE FACING Facing correctly joined (1) to back facing using plain seam. (1) Free edge of facing correctly. (1) And neatly neatened (1)	4
ATTACHMENT TO FACING (Front Facing and Back Facing) Correct (½) placing of facing to neckline. Good stitchery (1) (Back Front flatness of facing. (½) Smoothness of neckline. (½) Facing firmly fixed. (1) Facing under stitched (½) from Top of neckline correctly produced.	4
CUTTING AND REPAIR OF HEDGE TEAR USING DARNING Correctly (1) cut triangular hedge tear repair using hand darning. (½) Marked the vent of the tear. (½) Used fish boned (1) stitches to bring edges together. Darn extending beyond vent. (½) Threads firmly secured. (½) Raw edges completely enclosed. (1)	5
BINDING ARMHOLE Joining the binding piece. (1) Correctly joined to armhole. (1) Evenness of binding on both sides.(1) Correct final stitching. (1)	4
GRAND TOTAL 50 MKS
GRAND TOTAL 50 MKS

*TNW*

	MAX. SCORE	SCORE	REMARKS
A. PRESENTATION a) Well pressed¹, well folded¹. b) Firmly labelled¹, on single fabric¹. c) Pins^1/2 and unnecessary ^½threads removed. d) Made up of the left half¹.	2 2 1 1
Sub -Total	06
B. CUTTING a) All nine pieces cut 9 x ½ . b) Back bodice well cut², on straight grain to within 3 mm (0.3 cm) smooth¹ on C/F. c) Front bodice well², cut on straight grain to within 3 mm (0.3 cm)¹ smooth on C/F¹. d) Collar smoothly on C/B¹, cut on straight of grain to within 2 mm (0.2 cm)¹. e) Front and back facing well and smoothly cut (1 x 2) on straight of grain to within 2 mm (0.2 cm) (½ x 2). f) Sleeve well cut¹ straight of grain¹. g) Cuff well cut on¹ straight of grain¹. h) Skirt well (2 x 2) cut smooth at the lower edge. (1 x 2)	4 ½ 3 4 2 3 2 2 6
Sub – Total	26 ½
C. MARKING UP 1. Working of shoulder and neck line darts. a) Machine from wider part tapering to nothing¹. b) Straight stitchery made¹. c) Firmly secured (either by knot, weaving or by slipping into the fold. d) Correct length made 7 cm within 2 mm (0.2 cm) (1 x 2). e) Correct width 1cm made to within 1 mm (0.1 cm) (1 x 2). f) Pressed to the right direction neck dart to C/F and shoulder dart to C/B (1 x 2)	1 1 2 2 2 2
Sub – Total	10
2. Working of shoulder seam. French Seam 2or zero (0) a) Straight stitchery of the first row. b) Seam trimmed evenly to 6 cm to within 4 mm (0.4 cm). c) Free edge well enclosed. (No threads scan or R.S) d) Straight stitchery of the 2^nd along the seam allowance². – Seam knife edged¹ and pressed towards the back¹. e) Correct width made of 0.6 cm (6 mm) to within 1 mm. f) Seam flat on both R.S. & W.S. free from pucker.	1 1 1 4 1 1
Sub- Total	09
3. BACK AND FRONT FACING JOINING a) Using open seam to join. b) Made with straight stitchery. c) Trimmed to 1 cm to within 1 mm. d) Pressed open. e) Neatened the free edge close to the edge. f) Neatened with even straight stitchery.	1 1 1 1 1 1
Sub- Total	06
4. PREPARATION OF INTERFACED COLLAR a) Collar well interfaced. b) Good smooth stitchery² along the seam allawance¹. c)Trimmed to 4 cm to with in 2 mm (0.2 cm). d) Collar knife edged² sharp pointed tip infront¹ and back left open¹.	1 3 1 4
Sub- Total	09
5. ATTACHING OF COLLAR USING INTERFACING a) Front interfacing attached to the front bodice (Do not trim the turnings). b) Collar correct positioned at the centre front^{1 ½} and free edge at the centre back^{1 ½}. c) Neatening the neckline with the front & back facing¹ with smooth stitchery¹, trimmed to 1 cm¹, snipped¹, stay stitched the facing at the shoulder line¹. d) Collar lay flat on both sides. (R.S. & W.S). e) Correct length 29 cm to within 2 mm (0.2 cm). Measure from the ship T.P. at the front to free edge at the back. f) Correct width (depth) of collar of 8 cm to within 2 mm (0.2 cm). – Finish the base of the wrap by machine stitch.	1 3 5 2 2 2
Sub- Total	18
6. WORKING OF SIDE SEAM Using Open Seam or zero (0) a) Machine stitch straight stitchery along seam line. b) Neatened the turning close to the edge with straight stitchery. c) Seam pressed open, correct seam width of 2 cm to within 2 mm (0.2 cm). d) Seam flat both R.S. & W.S.	1 2 2 1
Sub- Total	06
7. WORKING OF SKIRT Joining the skirt with double stitchery. a) 1^st row made with straight stitchery. b) Back turning evenly trimmed to 1 cm. c) Front turning well enclosed² the fell laying towards the back^1/2(no thread seen on R.S.) d) 2^ndrow stitched close to the edge. e) Correct width of 1 cm to within 2 mm (0.8 – 1.2 cm) f) Seam flat on both R.S. and W.S. g) Inverted plea created at the side seam ½ cm each side of seam. h) Knife pleats made facing the C/F and C/B respectively.	1 2 2 ½ 1 1 1 1 2
Sub- Total	11 ½
8. BODICE ATTACHMENT ON SKIRT Use Overlaid or zero (0) a) Smooth stitchery of both the front and the back dress. b) Seam laid over the fitting line (seam allowance) seam not neatened or trimmed. c) Front skirt aligned with front blouse and back with back skirt.	2 2 1 ½
Sub- Total	6 ½
9. WORKING OF SLEEVE Use Open Seam or zero (0) a) Underarm seam made with straight stitchery. b) Seam turning well neatened with even stitchery and close to the edge. c) Seam press open. d) Gathers made at the sleeve head and lower edge along fitting line. – Gathers well distributed to 18 cm at the head to within 2 mm. – The lower edge of the sleeve with gathers well distributed evenly all round.	1 4 1 2 1 2
Sub- Total	11
10. ATTACHMENT OF THE CUFF – Joining the two ends with an open seam. – Seam trimmed to 1 cm. – Attaching the seam to the low edge of the sleeve with a smooth stitchery using plain seam. – Seam trimmed to 6 mm (0.6 cm) to within 2 mm (0.2 cm). – Neatening with slip hemming stitches evenly spaced.	1 1 4 1 4
Sub- Total	11
11. SETTING IN SLEEVE – Good hang of sleeve. – Gathers well distributed around the crown between the notches. – Notches matching¹ seam of both the underarm hole and side seam matching (2 x 2) & meeting at the point to within 2 mm². – Good smooth stitchery² around the armhole maintaining seam allowance². – Left untrimmed and unneatened.	1 1 ½ 7 4 1
Sub- Total	14 ½
HORIZONTAL BUTTON HOLE – Cut on straight of grain – Using button hole stitch. – Work of one side & overcastting the round edge (thread not cut) N/B: Thread should be single.
TOTAL	150/2 75 MKS

PAPER THREE

*KKC*

1.	CHOICE OF ITEMS – Recipe availability. – Correct quantities. – Suitability of meals.

2.	ORDER OF WORK – Availability – Correct sequence LIST OF EQUIPMENT AND MATERIALS – Availability. – Adequacy. – Appropriateness.

3.	PREPARATION – Correct procedure. – Appetizer. – Protein. – Carbohydrate. – Cereal – Beverage. Methods of cooking. – Appetizer (juice) – Protein – CHO. – Cereal – Beverage

4.	Hygiene & Presentation. – Personal – Handling food. – Centre piece. – Table well set. – Clean utensils.

5.	ECONOMY: § On fuel § On water § On resources

6.	CLEANING UP: § During work 1 § After work 1

*NYR*

DETAILS *NYR*

ACTUAL PLAN OF WORK

-Choice of dishes suitable choice

– List of equipment

– List of food stuffs

– Availability of recipe

– Proper sequencing of activities

– Quantities of food stuffs and equipment

PREPARATION, COOKING AND SERVING

– choice meal

– varied the methods of cookings (at least two)

– Correct preparation and cooking methods

(i) Protein dish

(ii) Carbohydrates dish

(iii) Vegetable dish

(iv) Baked item

QUALITY OF DISHES

Protein dish
Carbohydrates
Vegetable dish
Baked dish

GENERAL EFFICIENCY

– Personal hygiene

– Food hygiene

– Kitchen hygiene Economy of food, water and other resources

SERVING AND PRESENTATION

– Use of clean and suitable tea towel and clothes

– Clean and well pused

– Appropriate serving dishes

– Attractive centpiese

– Food not pieled

– Appropriate gravity

– General appearance

CLEANING UP

– During work

– After work

*KSM*

Area of assessment	Max score	Actual score	remarks
1. PLAN a)Recipe Availability Correct qualities Suitability of menu b)order of work availability correct sequencing c)list of food stuff and equipment availability adequacy(quantities) appropriateness	1 1 1 1 1 1 1 ½
	Total 7 ½
2. PREPARATION a)correct procedure item 1 item 2 drink variety of cooking methods at least 2 b)quality of results item 1 item2 drink	2 2 2 1 1 1 1
	Total 10
3. SERVING/PRESENTATION cleaning and well pressed table cloth centre piece appropriate and clean serving equipment logical arrangement of items on the table correct amount of food prepared and served	½ ½ 1 ½ ½
	Total 3
4. HYGIENE AND ORGANIZATION a)During work personal(½) food(½)working area(½) b)Economy of resources water(½) food( ½)fuel(½) cleaning materials(½) c)cleaning and tidying up during work after work	1 ½ 2 1
	Total 4 ½
Grand total	25

*MGN*

	PLAN AREAS OF ASSESSMENT
1.	Recipes *MGN* – Availability. – Correct quantities. – Correct choice. Order of work – Availability – Proper sequencing. List of food studs & Equip. – Availability. – Adequacy. – Appropriateness.
2.	PREPARATION *MGN* Correct Procedure – 1^st course. – 2^nd course. Methods of cooking (2) Quality of results. – 1^st course. – 2^nd course.
3.	PRESENTATION *MGN* Utensils – Appropriate – Cleanliness – Centre piece – General impression – Personal (½ ) food hygiene (½ )
4.	Economy of resources *MGN* – Water – Food – Fuel – Material

5.	Clearing Up *MGN* – During work – After work.

*NDW*

AREAS OF ASSESSMENT	MAXIMUM SCORE	ACTUAL SCORE	REMARKS
1.PLAN Recipes Availability Correct quantities Correct choice Order of work Availability Proper sequencing List of food stuffs and Equipment Availability Adequacy Appropriateness	½ 1 1 ½ ½ 1 ½ 1
	6
2.PREPARATION Correct procedure Carbohydrates Proteins Vitamin Drink -cereal -tea Methods of cooking (at least two) Quality of results Carbohydrates Protein Vitamin Cereal Tea	1 1 1 ½ ½ 2 1 1 1 1 ½ ½
	10
3.PRESENTATION Food presented on a tray(1)use clean( ½ ) well ironed( ½ )tray cloth correct placement of all items(1) Utensils Appropriate Cleanliness Centre piece General impression Personal( ½ )and Food hygiene( ½ )	2 1 ½ ½ ½ ½ ½ ½

4.ECONOMY OF RESOURCES Water Food Fuel Cleaning materials	½ ½ ½ ½
5.CLEARING UP During work After work	½ ½
TOTAL	25

*MAT*

	PLAN AREA OF ASSESSMENT MAT
1	Availability · Correct quantities · Correct choice
2	Order of work · Availability · Proper sequencing
3	List of food stuffs · Equipment · Availability · Adequacy · Appropriateness
4	Preparation · Correct procedure · Course I – protein · Course II – Vegetale · Carbohydrates · Salad
5	Methods of cooking · Protein · Vegetable · Carbohydrate · Salad preparation
6	Presentation · Utensils · Appropriate · Cleanliness · Centre piece · General impression
7	Economy of resources · Water · Food · Fuel · material
8	Clearing up · During work · After work

*UGU*

AREAS OF ASSESSMENT PLAN *UG*

1. Plan

– Recipe

– Availability

– Correct quantities

– sustainability

Order of work

– Availability

– Proper sequencing

List of Foodstuff, Materials and Equipment

– Availability

– Adequacy

– Appropriateness

2. PREPARATION

– Correct Procedure

– Proteins

– Carbohydrates

– Vitamins/mineral |Salts

– Drink

Quality of results

– Proteins

– Carbohydrates

– Vitamins/Mineral Salts

– Drink

3. Presentation

Utensils

-appropriate

– cleanliness

Garnishing

General impression

Personal(1) and Food(1) Hygiene

4. Economy of Resources

– Water (½ )

– Food (½ )

– Fuel(½ )

– Materials(½ )

5. Clearing up

– During work (1)

– After work (1)

*RACH*

	*PLAN AREAS OF ASSESSMENT*
1.	*PLAN* *RECIPES* *Availability* *Correct quantities* *Correct choice of menu* *ORDER OF WORK* *Availability* *Proper sequencing* *Correct time budgeting* *LIST OF FOODSTUFF & EQUIPMENT* *Availability* *Adequacy* *appropriateness*
2.	*PREPARATION* *CORRECT PROCEDURE* *Protein dish* *Carbohydrate dish* *vitamin dish* *Nutritious drink* *METHOD OF COOKING(at least two)* *QUALITY OF RESULTS* *Protein dish* *Carbohydrates dish* *Vitamin dish* *Nutritious drink*
3.	*PRESENTATION* *UTENSILS* *Appropriate* *Cleanliness* *CENTRE PIECE* *GENERAL IMPRESSION* *HYGIENE-personal hygiene* *– food hygiene*
4.	*ECONOMY OF RESOURCES* *water* *food* *fuel* *materials*
5.	*CLEARING UP* *during work* *after work*

*KKE*

	AREAS OF ASSESSMENT	Max score	Actual score	Remarks
1	RECIPE (a) Availability (b) Correct qualities (c) Suitability of menu Order of work (a) Availability (b) Correct sequences List of food stuffs and equipment (a) Availability (b) Adequacy (c) Appropriateness	1 2 1 1 1 1 1 1
		9
2.	PREPARATION Correct procedure Main meal Drink Method of cooking (at least 2) Quality of results (a)Main meal (b) Drink	2 2 1 1 1
		7
3.	PRESENTATION Utensils (a) Appropriate (b) Clean (c) Centre piece	1 ½ ½
		2
	Grand total	18

*MUM*

AREAS OF ASSESSMENT	MAX SCORE	ACTUAL SCORE	REMARKS
1. PLAN – Recipe – Correct quantities – Suitability of items Order of work – Availability – Proper sequence List of food stuffs materials and equipments – Availability – Adequacy – Appropriateness	1 1 1 1 ½ 1 ½ 1 7
2. PREPARATION Correct procedure – Protein – Carbohydrates – Vitamin – Drink Methods of cooking (atleast 2) Quality of results – Protein – carbohydrate – Vitamin – Drink	1 2 1 1 1 1 1 1 1 10
3. PRESENTATION Utensils – Appropriate – Clean – All placed in one container Hygiene – Personal ( ½ ) Food ( ½ ) Economy of resources – Water ( ½ ) – Fuel ( ½ ) – Materials ( ½ ) – Food ( ½ ) Cleaning up During work (1) After work (1) TOTAL	1 1 1 3 1 2 2 5 25

*STK*

	AREAS OF ASSESSMENT	MAXIMUM SCORE	ACTUAL SCORE	REMARKS
1.	PLAN
	(a) RECIPES – availability – correct quantities (for two people) – correct choice (meals for adolescents) i.e well balanced meal	½ ½ 1
	(b) – order of work – availability – proper sequencing	½ 1
	(c) List of foodstuffs, equipment and other materials – Availability – Adequacy – Appropriateness	½ ½ ½ 5
2	PREPARATION
	a) Correct procedure of – protein dish – Carbohydrate dish – Vegetable – Fruit juice	2 2 2 2 8
	b) Methods of cooking (at least two) Quality of results – protein dish – Carbohydrates dish – Vegetable – Fruit juice	1 1 1 1 1 5
3.	PRESENTATION
	a) Utensils – appropriateness – cleanliness – presence of a centre piece – general impression – personal hygiene – food hygiene	½ ½ ½ ½ ½ ½ 3
4.	ECONOMY OF RESOURCES – Water – food – fuel – materials	½ ½ ½ ½ 2
5.	Clearing up – During work – After work	1 1 2
	GRAND TOTAL	25MARKS

*TNW*

PLAN AND AREAS OF ASSESSMENT		Remarks
A. Plan i) Recipes – Availability. – Correct quantities for two. – Correct choice for a visitor. ii) Order of work availability. – Proper sequencing. – Dovetailing / overlapping of activities. iii) List of food stuff & equipment. – Availability. – Adequacy. – Appropriate	1 1 1 2 2 1 1 1
Sub total	10
B. The Test i) Preparation – Correct procedure – Protein – Starch – Vegetables – Nutrients N/B: ½ Mark for fruit juice. ii) Methods of cooking (at least 2) iii) Quantity of the items enough for two.- Protein – Starch – Vegetables – Nutritious drink iv) Quality of items (results). – Proteins – Starch – Vegetables – Nutritious drink	2 2 2 2 2 2 2 2 2 2 2 2
Sub total	26
C. Presentation i) Utensils – Appropriate. – Cleanliness. ii) Table setting – cleanliness. – Centre piece. – Correct cover for the course. N/B: Check the laying of cartulary. iii) Personal & food hygiene – Personal appearance. – Cleanliness during food preparation.	1 1 1 1 1 1 1
Sub total	8
D. Economy of resources. – Water – Food – Fuel – Material	1 1 1 1
Sub total	4
E. General Cleanliness (i) During work. (ii) After work.	1 1
Sub total	2

*STK 2*

AREAS OF ASSESSMENT PLAN	MAX SCORE	SCORE	REMARKS
Recipe – Availability – Correct quantities – Suitability of menu Order of work – Availability – Correct sequencing – List of foodstuff and equipment – Availability – Adequacy – Appropriateness	1 1 ½ 1 ½ 1 1
	7
PREPARATION – Correct procedure /manipulative skills – Proteins – Carbohydrates – Vitamins – Beverage – Methods of cooking-at least two Quality of results – Proteins – Carbohydrates – Vitamins – Beverage	1 1 1 1 1 1 1 1 1

Presentation Utensils -clean – appropriate Use of garnishes/decorations – Availability of a centre piece – – General impression	1 1 1 ½ 1

General Hygiene – Personal – Food – Economy of resources – Water ( ½ ) food ( ½ ) – Fuel ( ½ ) materials ½ Clearing up – – during work – – after work	½ ½ 2 ½ 1
Sub total	9
Total	25

*STK 3*

PLAN

RECIPES

– Availability

– Adequacy

– Correct choice

Order of work

– availability

– Logical sequencing

– Appropriate timing of tasks

– Divertaiting

List of food stuff and equipment

-Availability

– Adequacy

– Appropriateness

PREPARATION OF COOKING MEAL

Correct choice of one course meal

Correct procedure

– Carbohydrate

– Protein

– Vegetable

– Drink

Variety of cooking methods at least two

QUALITY OF RESULTS

– Proteins

– Carbohydrate

– Vegetable

– Drink

PRESENTATION

Utensils

Appropriateness

Free from smudges

Garnishes

Presence of a centre piece

General impression

GENERAL IMPRESSION

Hygiene

– Personal and food

– Economy of resources

– Water

– Food

– Fuel

– materials

CLEANING UP

Daring work

After work

TOTAL

Teachers' Resources

LIVESTOCK HEALTH III (LIVESTOCK DISEASES)- AGRICULTURE NOTES

October 5, 2025 Hillary Kangwana Leave a comment

LIVESTOCK HEALTH III (LIVESTOCK DISEASES)

This topic entails:

Description of causes and vectors of the main livestock diseases.
Protozoan diseases
Bacterial diseases
Viral diseases
Nutritional diseases
Signs of each stated livestock disease
Stating predisposing factors where applicable
Control measures of livestock disease

Name two diseases that affect female animals only

Mastitis
Milk fever

What is a vaccine?

An active disease pathogen reduced in strength /virulence or killed and is introduced into an animals body to induce immunity

a) Define the term notifiable disease in cattle

A disease that once noticed prompts an urgent need for informing the relevant authority.

b) Name four notifiable diseases of livestock

Rinderpest
Anthrax
Rift valley fever
New castle disease
mad cow disease
Black quarter
Foot and mouth diseases
Lumpy skin disease
Rabies

State three signs of anthrax disease observed in the carcass of cattle

Blood does not clot
No rigor mortis after death
Stomach swells/ bloat
Darkened blood oozes out through the natural opening

Differentiate between active immunity and acquired passive immunity

Active immunity – animal producing antibodies
Acquired/ passive immunity – external source of immunity

List three causes of ruminal tympany (Bloat) in ruminant animals

Lack of fibre in the diet
Feeding on succulent feeds e.g. lush grass
Rapid production of gas ( methane) in the rumen
Fermentation of feeds in the rumen
Obstruction of the oesophagus by food e.g. potatoes

List two symptoms of bloat attack in cattle

Constipation
Immobility
Digestive complications
Distension of the left side of the abdomen due to gas accumulation
Difficulty in breathing
Profuse salivation
Animal lies down and is unable to rise up
Grunting and kicking at the belly
Death within hours due to pressure on blood vessels, heart and lungs

State one chemical used in relieving a ruminant animal of bloat

Epson Salt
Methyl silicon
Mixture of turpentine and vegetable oil

Name two diseases of poultry that are controlled by vaccination

New castle
Fowl pox
Fowl typhoid
Gumboro
Marek disease

Name the casual organism for foot rot disease

Fusiformis spp/ Fusiformis necrophorous/ Fusiformis nodosus

Give four pre disposing factors of foot rot disease in sheep

Overgrown / untrimmed hooves
Tick infestation between hooves
Muddy / filthy living / grazing areas
Presence of sharp objects e.g. stones

Give two symptoms of foot rot in sheep

Swollen foot
Lameness
Pus and a rotten smell from the hoof
A sheep kneels while grazing if the front feet are affected
Sheep spends most of the time lying down if the hind feet are affected
Emaciation due to lack of feeding

State two control measures of foot rot in sheep

Trimming overgrown hooves regularly ( reject cutting hooves)
Treating affected sheep to avoid spread
Isolating sick animals from healthy animals
Keep grazing land free from sharp objects
Use disinfectant in footbath e.g. copper sulphate solution / formalin
Keep animal house dry
Avoid grazing sheep on swampy areas

Discuss Foot Rot disease under the following sub headings
a) Causal Organism

A bacterium/Fusiformis species

b) Predisposing factors

Dirty and overgrown hooves/ untrimmed hooves
Presence of injurious objects e.g. stones, nails
Injuries /wounds on hooves
Muddy / filthy living / grazing areas
Invasion of hoof by other organisms e.g. tick bites and nematodes which cause injuries.

c) Symptoms of attack

Animal limps as it walks
Foot infected is swollen
Infected hoof produce pus
Foul smell is produced from the infected hooves
Animal may become lame in severe cases / inability to walk.
Infected foot feels hot upon touch
Lack of appetite / anorexia
Animal become emaciated/ weak/ loss of condition
Animal graze when kneeling in case forelegs are infected
When all legs are infected, the animal graze when lying down

d) Control Measures

Treat wounds on hooves using appropriate antibiotics
Let the animals walk on appropriate foot bath
Isolate infected animals from healthy ones
Ensure the environment of the animal is not damp and muddy
Practice hoof trimming regularly
Treat sick animals with appropriate antibiotics.
Graze animals in areas free from sharp objects.
Move healthy sheep to dry clean areas.
Walk sheep on footbath with appropriate chemicals solution e.g. formalin and blue vitriol
(copper sulphate)

State six symptoms shown by poultry when suffering from Newcastle disease

Birds have difficulty in breathing
Loss of appetite / Anorexia
Paralysis / Staggering motion
Yellowish , watery greenish diarrhoea
Drop in production
Production of soft shelled eggs
Often birds have their beaks and wings down/Drooping wings
Birds produce a harsh granting raspy sound when breathing
Beaks remain wide open and neck are stained
Birds become dull
Birds stand with eyes closed all the time
Nasal discharge which forces birds to shake head to clear it

Discuss Newcastle disease under the following sub headings
a) Casual organisms

Virus

b) Signs of attack:

Difficulty in breathing.
Beaks remain wide open and necks are strained
Birds stand with eyes closed all the time.
Loss of appetite.
Nasal discharge which force the birds to shake their heads to clear it.
Birds walk in a staggering motion since the nervous system is affected.
Often the bird have their heads and wings drooping,
Birds produce watery greenish diarrhoea.
Eggs laid have soft shells

c) Control Measures:

Vaccination during the first six weeks and then two to three months later.
Kill the infected birds and burn them.
Obtain stock from reputable source

Give four predisposing factors of mastitis disease in cows.

Mechanical injury to the udder.
Old age of animals
Unhygienic conditions
Incomplete milking of cows
High level of milk production
Genetic factors
Pendulous udder /teat hang too low
Stage of lactation/ late stage of lactation.

State four symptoms of mastitis in a dairy cow

Death of the infected quarter may result.
Milk has a salty taste and there are flakes particularly the fore milk.
Blood or pus in milk
Pain in the udder or teats/ Animal rejects suckling or milking and kicks due to pain
Swollen or inflamed under
Rise in body temperature
Clots in milk or turns watery
Drop in milk yield.

Discuss mastitis disease under the following sub-headings:
a) Causal organism

Streptococcus agalactiae
Staphylococcus urens

b) Predisposing factors.

Age- Older animals that are lactating are affected
Stage of lactation period- Affects during early or late lactation
Udder attachment- Large and pendulous udders are at risk
Incomplete milking.
Mechanical injury.
Poor sanitation- Poor hygiene leads to infection
Poor milking technique- Pulling teats makes the sphincter muscles of the udder weak and loose
Sex
Hereditary factors
Level of production/high producers are more prone to mastitis than low producers
Genetic factors – some breeds are more susceptible to mastitis than others

c) Symptoms.

Milk contains pus, blood, thick clots and turns watery
Swollen udder and teats/ cow kicks when udder is touched/ Pain on udders
Death of infected quarter
Milk has a salty taste
Small clots/ flakes in milk

d) Control and treatment

Empty affected quarter of udder and treat with antibiotics.
After milking, use teat dip on every quarter.
Use right milking technique
Observe strict cleanliness.
Dry cow therapy/ infusing a long acting antibiotics into the teat canal when drying off the cow
Use strip cup to detect infection.
Use separate udder cloths for each animal.
Treat open wounds immediately
Remove sharp objects from grazing land to avoid udder infection

State two practices which are carried out to control mastitis in lactating cows

Proper milking technique
Administering dry cow therapy
Complete milking
Infected cows should be milked last
Open wounds on the teats should be treated immediately

a) Name the causative organism of contagious abortion

Brucellus abort – Cattle
Brucellus suis – Pigs
Brucellus malitensis – sheep and goats

b) Give four symptoms of contagious abortion in cattle

Retained after birth
Sterility in cows
Spontaneous abortion
Yellowish – brown, slimy discharge, odourless discharge from the vulva after abortion

c) State three methods of controlling contagious abortion in cattle

Use of artificial insemination (A.I).
Vaccination against the disease in young animals
Avoid contact with the aborted foetus
Blood tests of all breeding animals before mating
Cull, slaughter infected animals

Name the causal agent of black quarter disease in livestock

Clostridium chauvei

Discuss black quarter under the following sub-headings:-
a) Animal affected

cattle, sheep, goats

b) Casual organism

Clostridium chauvei

c) Symptoms of disease

Rise in body temperature
Lameness and swelling of upper part of limbs, making animals lie on side
Swollen shoulders on either side of body, chest or back, formation of gas under skin
Difficulties in breathing
Muscle appear black and spongy
Grunting and grinding of teeth
Failure to chew cud
On exposure to air, muscle of body rapidly darken

d) Control measures

Annual vaccination using black quarter vaccine
Burning of carcass
Carcass should not be skinned or opened
Cleaning and treating of all wounds with antiseptics

State two symptoms of Coccidiosis infection in poultry.

Diarrhoea with varying nature watery whitish – brown or blood stained
Dysentery /blood in faeces
Emaciation
Ruffled feathers
Dullness with drooping wings
Sudden death

Name four ways of controlling Coccidiosis in the farm

Isolation of infected animals
Avoid filthy, unhygienic animal surroundings
Avoid common dunking points for livestock from different farms
Avoid overcrowding in poultry houses
Provision of coccidiostat in feeds and water
Use of portable calf pen

Discuss Coccidiosis disease under the following headings:-
a) Causal organism

Protozoan/coccidian elmeria/coccidia spp)

b) Livestock species attacked

Poultry
Calves
Young rabbits
Kids
Lambs

c) Symptoms of attack

Diarrhoea
Dysentery /blood in faeces
Emaciation
Ruffled feathers
Dullness with drooping wings
sudden death in birds, rabbits and kids

d) Control measures

Isolation of infected animals
Avoid filthy, unhygienic animal surroundings
Avoid common dunking points for livestock from different farms
Avoid overcrowding in poultry houses
Provision of coccidiostat in feeds and water
Use of portable calf pen

State four predisposing factors of scour in calves

Unhygienic condition in the house of the young ones/ Poor sanitation
Feeding the calves on cold milk
Lack of colostrums
Feeding at irregular intervals
Over feeding.

a) Give four symptoms of milk fever

Dullness
Body functions i.e. urination, defecation of milk and milk secretion stops
Stomach contents are drawn into mouth, causing lung fever
Complete loss of appetite
Muscular twitching
Walking in staggering manner
Animal lies down on its side most of the time
Animals lies on sternum with head twisted on one side
General paralysis/ inability to more or arise
Breathing becomes slow and weak
Stiffening of the whole body
Head turned back
Animal fall down and becomes unconscious
Sudden death.

(b) State two methods of controlling milk fever

Feed animal on diet/ mineral salts rich in calcium
Give intramuscular injection of calcium and phosphorus 2-3 days before calving down
Partial milking on known cases
Cull susceptible animal

a) What causes milk fever in dairy cows?

Low calcium level in the blood/ high milk yield without calcium replenishment

b) Name two animals that may suffer from milk fever

Goats
Pigs
Sheep

Discuss milk fever (parturient paresis) under the following sub-headings
a) Cause

Low calcium level in the blood / high milk yield without calcium replenishment

b) Predisposing factors.

Low calcium level in the blood
High producing cows in first few months of lactation
Increase in the magnesium and sugar level in the blood

c) Symptoms

Dullness
Body functions i.e. urination, defecation of milk and milk secretion stops
Stomach contents are drawn into mouth, causing lung fever
Complete loss of appetite
Muscular twitching
Walking in staggering manner
Animal lies down on its side most of the time
Animals lies on sternum with head twisted on one side
General paralysis/ inability to more or arise
Breathing becomes slow and weak
Stiffening of the whole body
Head turned back
Animal fall down and becomes unconscious
Sudden death.

d) Control and treatment
Intravenous injection of calcium borogluconate
Feeding animals with calcium salt two months before calving down
Partial milking on known cases

Discuss East Coast Fever (E.C.F) under the following sub-topics:
a) Animal attacked

cattle

b) Causal organisms

Protozoa/Theileria parva

c) Vector

Brown ear tick / Rhipicephalous appendiculatus

d) Incubation period

15 days.

e) Symptoms of attack

Fever/ high temperature
Animal salivates profusely/ Excessive salivation
Lachrimation/ tears from eyes
Difficulty in breathing
Haemorrhages in vulva/ mouth
Coughing
Sight impairment/ Poor vision/Corneal opacity
Swollen lymph nodes especially around the base of the ears shoulder
Reduction in production.
Loss of appetite
Dullness

f) Control and treatment

Regular spraying/ dipping/ hand dressing with acaricide to kill the vector organism/ticks
Fencing/ rotational grazing
Treatment using appropriate drugs/antibiotics

List three control measures of East coast fever (E. C.F)

Control ticks by dipping / spraying/Rotational grazing /Hand picking / deticking and killing/Hand dressing/Burning pastures
Double perimeter fencing.
Slaughtering all affected cattle
Provide chlorotetracycline and oxytetracycline drugs as feed supplement

Explain ten measures used to control livestock diseases

Proper feeding
Animals fed on balanced ration adequate in quantity and quality are strong and able to resist diseases
Proper breeding and selection
Animals selected that are free from diseases or resistant to diseases will prevent transmission of diseases
Proper housing and hygiene
Animals houses should be built to meet construction requirement e.g. ventilation, space, drainage, leak proof, lighting and will prevent and protect animals from contracting diseases
Isolation of sick animals
Is separation and confinement of animals from health ones while undergoing treatment, this prevents spread of the diseases
Imposition of quarantine
Is restriction of movement of animals and their products from and into affected areas, thus prevents spreads of diseases
Prophylactic measure and treatment
Involves use of drugs before disease attack to prevent occurrence e.g. use of coccidiostat to control Coccidiosis, drenching to prevent helminthes
Also involve vaccination, spraying with appropriate acaricide and treatment to restore good health
Slaughtering affected animal
Highly infection and contagious diseases e.g. Rinderpest, new cattle foot and mouth animals should be slaughtered and carcasses will dispose to prevent spread
Use of antiseptics and disinfectants
Applied on skin to kill pathogens or clean livestock to maintain hygiene
Drenching / deworming to control internal parasites
Practice proper milking techniques to avoid mastitis.
Avoid physical injuries to animals caused by sharp objects
Prevention of stress factors.
Carrying out fencing of the farm to keep away strange animals from the farm which may spread diseases
Culling – to prevent spread of contagious) disease

Explain the general methods of Disease control in livestock

Proper hygiene- animals house must be hygienic
Proper housing – to provide suitable conditions for animal
Proper spacing in houses – to avoid risks of overcrowding
Well ventilated house- for free circulation of air
Leak proof house- to avoid dampness
Well sheltered house- to avoid cold draughts
Proper disposal of carcasses by burning or burying to avoid spread of diseases
Proper nutrition- to avoid nutritional diseases
Proper breeding – to select and breed healthy animals
Use of quarantine- to avoid spread of diseases
Isolation- to facilitate treatment and avoid spread of disease by a sick animal
Culling- removing sickly animal from the herd after they recover
Vaccination- to prevent attack by a disease
Use of prophylactic drugs- used in feeds and water to prevent infection
Slaughtering of diseased animals and disposed off to prevent spread to healthy ones.
Treatment of sick animals- to return to good health
Keeping proper farm records on animal health – to predict attack
Control of vectors- to prevent protozoan diseases
Use of antibiotics – against bacterial diseases
Use of antiseptics – to dress wounds
Deworming – to eliminate endo – parasites
Hoof trimming – Prevent dirt accumulation / filth in the hoof hence control foot rot disease

Describe the control measures of disease in livestock, for each control measure give an example of a disease controlled

Use prophylactic drugs-animals are given drugs routinely to control certain diseases
Use of antiseptics and disinfectants for cleaning poultry houses or calf pens to
control disease e.g. scours
Quarantine during an outbreak of certain diseases e.g. foot and mouth
Isolation animals suffering horn infectious diseases e.g. scours are not allowed to mix with others
Mass & slaughter / cull animals suffering from certain dangerous diseases e.g. anthrax
Vaccination -animals usually vaccinated against certain diseases e.g. black quarter
Control of vectors-diseases carrying parasites e.g. tsetse flies are controlled by spraying the bush to control diseases like Nagana
Use healthy breeding stock/ AI prevent the spread of diseases like brucellosis
Proper nutrition well balanced diet to be provided to animals to prevent nutritional diseases e.g. anaemia in piglets
Drenching/ control of internal parasites e.g. roundworms
Keep resistant type of livestock e.g. zebu to prevent occurrence of E.C.F
Proper housing to prevent diseases like pneumonia
Foot trimming to prevent foot rot/removal of sharp objects
Feed animals with dry roughages before feeding them succulent roughages to minimize occurrence of bloat /other nutritional disorders

a) Give the method used in introducing a vaccine to poultry against fowl typhoid

Injection/ Intramuscular injection

b) State two other methods introducing vaccines to livestock

Orally
Inhalation
Through cloaca in poultry
Inhalation through the nose

State four major routes of administering vaccines in day old chicks

Nostrils
Mouth
Eyes
Under the skin (sub cutaneous)

Explain four major causes of lamb mortality from birth to weaning

chilling
scours
internal parasitic infestation
loss of mother/lack of foster parents
inadequate mother’s milk/malnutrition
crushing by t he mother

What organism causes Brucellosis in dairy cattle?

Brucella abortus

Describe brucellosis under the following sub headings
Causal organism

Bacterium/Brucellus abortus

ii) Transmission

sexually transmitted/it is a breeding diseases

iii) Symptoms

Premature birth/spontaneous abortion
yellowish slimy and odourless discharge through the vulva
retained afterbirth/placenta
the cow may become barren
Bulls have low libido and orchitis/ inflamed testes

iv) Control measures

use of healthy semen/bull/Al
proper disposal of foetus and carcass
Use of artificial insemination
Cull and slaughter the infected animals
Vaccination of all young animals against the disease
Avoid contact with aborted foetus
Cleanliness in animal house must be maintained
Carry blood test for breeding animals in order to detect the infected ones

Name the causative organism of the Gumboro disease.

Birna virus

State one way by which each of the following practices help in disease control
Proper feeding

Prevents deficiency diseases
Imparts resistance to diseases

Proper housing

Prevents draughts/ colds wind
Prevents dampness due to proper drainage and ease of cleaning

a) Name two diseases in cattle that may be spread through breeding/mating

Brucellosis /contagious abortion/ bang’s diseases
Leptospirosis
Scrotal hernia

b) State two practices that may be carried out to control breeding diseases among cattle.

Artificial insemination
Treatments
Proper selection

a) Name the cause of fowl typhoid.

Bacterium / Salmonella gallinarum

b) list common symptoms of fowl typhoid

Dark green diarrhoea

Describe the symptoms of diseases that can be observed from the faecal matter. Give an example in each case

Hard dung in cattle – constipation /anaplasmosis
Yellow green diarrhoea in poultry- new castle disease
Diarrhoea with blood stains – Coccidiosis in poultry
Dark green diarrhoea – fowl typhoid
Presence of eggs or cysts in the dung in cattle – worm infestation

a) Name the causative organism of Pneumonia in calves

Bacterium/mycoplasma mycoides

b) Give two predisposing factors to Pneumonia in calves
Poor ventilation
Over crowding
Age of the animal
Dampness/chilliness in the animal house/Wet conditions
Dirty conditions
Poor nutrition

c) State two symptoms of Pneumonia in calves
Severe respiratory problems
Abundant mucous nasal discharge
Difficulty in breathing
Dullness
Loss of appetite/anorexia
Abnormal lung sound/bubbling sound/hissing sound/ gurgling sound.
Coughing due to congestion of bronchioles
Where land is not accessible by a tractor
Irregular shaped pieces of land
Where the cost of hiring a tractor is high
Where tractor for hiring one not available/very steep slopes

Give two signs that would indicate a cow has died of anthrax

Absence of rigor mortis/no stiffness.
Dark watery blood oozing from natural openings.
Excessively blown stomach.
Blood does not clot.

Discuss anthrax disease in cattle under the following subheadings

a) Causal organism
Bacillus anthracis/ bacteria

b) Symptoms

Absence of rigor mortis/no stiffness.
Tar like blood /Dark watery blood oozing from natural openings.
Difficulty in breathing
Extensive bloat after death
Presence of blood in faeces and milk
Shivering
Sudden death and fast decomposition
Blood does not clot.
High temperature

c) Control measures and treatment

Animals should be vaccinated using blanthax
Impose quarantine in infected areas
Proper disposal of carcass
Disinfect animal house e.g. with formalin
Do not open carcass if suspected of the disease
Proper inspection of meat.
Large doses anti anthrax serum
Treatment of wounds

Discuss bloat disease under the following sub-headings.
a) Species of the animals affected by the disease

Cattle
Sheep
Goats

b) Causes of the disease
Obstruction of the oesophagus due to bulky food particles such as potatoes, carrot, mangoes
Abnormal pressure exerted on the oesophagus by swelling in the wall of the chest
Indigestion – caused by an accumulation of gases due to paralysis of the rumen and the value at the entrance
Feeding animals on feeds containing a lot of pasture legumes cabbage leaves and lush pasture
Abrupt change in feeds given to animals/ from very dry feeds to very succulent feeds.

c) Symptoms of the disease

Distension of the left side of the abdomen due to gas accumulation
Difficulty in breathing
Profuse salivation
Animal lies down and is unable to rise up
Grunting and kicking at the belly
Death within hours due to pressure on blood vessels, heart and lungs

d) Control measures of the disease

Provide dry roughages just before feeding the animals on green and succulent or wet pasture
Feed animals on wilted grasses and pasture legumes

e) Treatment of the disease

Treatment measures
Exercise the sick animal by walking it around & up-hill
Use medicinal oils as defrothing agents such as liquid paraffin
Epsom salt can be used to empty the stomach
A stomach pump can be inserted into the rumen through the oesophagus
In extreme cases Trocar and canula or sterilized sharp knife is used to pierce through the skin of the rumen
Methyl silicone injection

a) What is the causal organism of Anaplasmosis in cattle?

A protozoa / Anaplasma marginale

b) State two symptoms of Anaplasmosis

Fever/high temperature
Sudden drop in milk production
Anaemia/paleness in the gums eyes (lips) jaundice/ Pale mucous membrane
Constipation/Hard dung
Anorexia/loss of appetite
Reluctant/inability to move
Animal becomes aggressive.

Outline ways in which diseases can spread from one animal to another

By ingestion of contaminated feed and water.
By carrying agents e.g. vectors, utensils, sacks and grass animal attendant.
By abrasion on body of affected animals/contact
Through wounds
Through inhalation of pathogens

Give two reasons for laying soft membranes shelled eggs by layers

Lack of phosphorus/calcium in feeds.
Sickness

State five importance of keeping livestock healthy

Give high quality production with high market value
Fast growth rate/early maturity to ensure long productive life
Economical to keep-saves expenditure on veterinary services and drugs
Produces healthy products-no risk of transmitting Zoonotic diseases to human beings
High yields-hence high profits/returns
Fetch good market prices hence high returns
Have longer lifespan i.e. economic life
Have high fertility rate and reproduce more and faster
Give more draft farm power e.g. during ploughing.
Do not become a source of infection to other animals
Enable the fulfilment of farm operations , budgets and plans

Give two ways by which proper nutrition helps to control livestock diseases

Helps to prevent nutrient deficiency diseases
Gives the livestock ability to resist diseases

Name four livestock nutritional diseases

Milk fever
Oesteomalacia / rickets
Pica
Grass tetany / staggers / hypomagnesaemia
Enzootic neonatal ataxia / sway back disease
Parakeratosis

a) Define the term Zoonotic diseases

Are diseases that are transmitted from animal to man or from man to animal

(b) Name two Zoonotic diseases.

Anthrax
Brucellosis
Rabies
Tuberculosis
Rift valley fever
Bird flu (avian flu)
Trichomoniasis
Mad cow disease

Discuss the disease trypanosomiasis under the following sub titles.
a) Causal organism.

Protozoa/Trypanosoma species (trypanosome)

b) Animal attacked

Cattle, man, sheep, goats, donkeys, pigs, horses and wild animals.

c) Mode of transmission

Vector borne by tsetse fly

d) Symptoms

Anaemia
Loss of appetite
Intermittent fever
Abortion in females
Oedema
Enlarged lymph nodes
Loss of hairs at the tail end
General weakness / emaciation
Dullness
Decline in milk production / yield
Coat cracked/coat is rough
Lachrimation causing blindness.

e) Control.

Keep resistance
Confine game animals in parks
Control tsetse flies by regular spraying with acaricide
Restrict animals movements from mixing with wild game
Effective control of tsetse flies
Treat the animal with trypanocidal drugs to curb spread of the protozoa through the vectors.

Name two cattle diseases caused by virus

Foot and mouth
Rinderpest
Yellow fever
Rift Valley fever
Rabies
Blue tongue
Lumpy skin
Ephemeral fever

The illustration below shows a dairy cow suffering from a disease three days after calving down. The cow went down with its head turned back and was unable to stand.

Which disease did the cow suffer from?

Milk fever/paulurient peresis/hypocalcaemia

State two ways of preventing the disease you have identified in (i) above.

Give feeds rich in minerals (Ca²⁺_, P₂O^–₅) starting from the last 2 months of gestation/steam up.
Give vitamin D injection a week before parturition.
Dry off the cow sufficiently.

Discuss Foot and Mouth disease under the following headings:
a) Casual organisms

Virus/ virus types O, A, C/ south African types– SAT1, SAT2, SAT3, / Asian type 1

b) Livestock species attacked
Cattle
Pigs
Goats
Sheep

b) Mode of transmission and incubation period

Through contaminated litter, machinery feet, infected saliva& feeds, vaccines, garbage

c) Symptoms of attack

Profuse salivation
Blisters which are painful around the mouth and hooves of the feet leading to lameness
Drop in milk production in lactating cows
Sharp rise in temperature/ high fever
Emaciation
Complete loss of appetite
Diarrhoea
Kicking of feet

Control measures
Vaccination every six months
Quarantine where there is an outbreak/Regulations of livestock movement by issue of movement permits
Slaughter and destruction of carcass
Isolation of farm animals from wildlife
Strict hygiene to avoid contamination.
Burn/ bury dead animals

Name two non-infectious causes of livestock diseases.

Poor nutrition.
Physical injuries.

Name two livestock diseases controlled through quarantine.
Black quarter.
Foot and mouth.

List two routes through which pathogens can enter the body of an animal.
Skin pores.
Nose
Mammary glands.
Navel/umbilical cord.
Genital/reproductive organs.

a) Describe African swine fever disease under the following;
- Animals affected
Pigs (1mark)
- Causal organisms
Virus (Irido virus) (1mark)
- Symptoms of attack
Rise in temperature upto 40⁰C – 41⁰C
Lack of appetite
Animals become depressed
Animals become weak
Animals start coughing
Nosal discharge
Diarrhea
- Control measures
Vaccine animals in case of an outbreak
Imposition of quarantine
Kill and dispose affected animals
Double fencing to keep wild animals

23(a) Describe the procedure followed when using the hypodermic syringe and needle to administer liquid drugs to cattle.
Fix the needle to the syringe
Withdraw the right amount from the bottle
Remove air/bleed needle
Disinfect site
Insert needle and push butt to release drug
Remove the needle
Release the animal.

(b) Outline six reasons for maintaining livestock in good health.
Increase quality of livestock products/work outputs/regular breeding
Increase quantity of livestock products/yields
Reduce spread of diseases
Increase profits/reduce costs of production
Increase productive life of livestock.

Name the two diseases which are controlled by one vaccine in livestock.
Anthrax and blackquater.

Describe foot rot disease in sheep management under

Cause
Bacterium fusiformis species / fusiformis nodusus / F. necraforus/F. spirochitis

-Lameness / inability to walk
Swelling of affected feet
Wounds and ulcers / pus / foul smell in affected areas
-Anorexial of appetite
Loss of weight / emaciation.

Control
- Trim hooves regularly
- Keep grazing land free from sharp objects
- Avoid swampy / dump conditions
- Apply footbath using disinfectant e.g copper Sulphate solution

How does each of the following practices help in controlling diseases among livestock.
- Fencing
Prevents intrusion of other animals that may spread diseases

Hoof trimming

Prevent dirt accumulation / fith in the hoof

Vaccination

Imparts resistance to disease s

List four predisposing factors of livestock diseases
Species
Breed
Age
Sex
Skin colour

The diagram below illustrate a dairy suffering from a disease condition
- Identify the disease
Mastitis

Name the tool used to detect the disease in (i) above

Strip cup

State any two control measures for the disease

-Use of antibiotic
-Complete milking
-Correct technique of milking
-Clean milk man

State two ways by which proper feeding contributes to disease control in poultry. (1mk)
Improves production
Helps prevent deficiency diseases
– Enhances resistance to diseases ( ½ x 2 = 1 mk)

Give four qualities of a good vaccine. (2mks)
Imperting long life immunity on a single dose
Easy to administer
Has no side effects
Compactible with other vaccines
Has long keeping life
Immunity imperted is as good as natural immunity

( ½ x 2)

(a) Outline the ways in which diseases can spread from one animal to another.(4 marks)
contact
ingestion of contaminated food
air
During mating.
Through contaminated equipment

(a) Discuss the factors that may predispose livestock to certain diseases.
Skin colour
Age of the animal
Sex of the animal
Species of the animal
Breed of the animal
Environmental factors
Housing conditions
(c) Describe the general methods of controlling livestock diseases.
Vaccination
Hygiene
Isolation
Quarantine
Use prophylactic drugs
Proper carcass disposal
Culling
Proper feeding
Proper housing
Dipping / spraying
Drenching / dosing / deworming

Use the diagram given below to answer the questions that follows:

Name the routine practice carried out on the part labeled R.

20 (a) (i) Debeaking

Give two reasons for carrying out the practice named in a (i) above
To control egg eating
To control cannibalism

(i) Name one disease that affect the part labeled S

(b) (i) Fowl pox

State two control measures of the disease named in b (i) above
– Vaccination
Use vitamin supplements to promote fast manufacturing of blood.
Control any opportunity infections that may occur due to immunosuppression.
(b) Describe the symptoms of diseases that can be observed from the faecal matter
Give an example in each case (8mks)
- Hard dung in cattle – constipation anaplasma
Yellow green diarrhea in poultry- new castle disease
Diarrhea with blood stains – conccidiosis in poultry
Dark green diarrhea – fowl typhoid
Presence of eggs or cysts in the dung in cattle – worm infestation. 8mks

Differentiate between antibiotics and antibodies. (1mk)
Antibiotics are chemical substances (drugs) that kill biotic agents e.g. bacteria, protozoa while antibodies are proteineus chemical substances produced within the body that fight against the entry and multiplication of biotic factors.
(a) List six routes through which pathogens can enter the body of an animal. (6 marks)
Oral ( mouth), broken skin ( wounds), nasal, ocular ( eyes), anal, ears, reproductive organs, umbilical cord (6×1=6mks)

18 Below is an illustration of an activity carried out to detect an infection of the udder before milking. Study it carefully and answer the questions that follow

Identify the equipment labeled U in the illustration above

Strip cup
- State Two changes in milk that would be observed if the udder illustrated above is infected by a disease detected by equipment identified in (a) above

Pus in milk/ blood in milk
Tiny clots

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Updated Jesma Exams, Marking Schemes, Notes and Revision Books

October 5, 2025 Hillary Kangwana Leave a comment

Download all the Latest Jesma Exams, Marking Schemes, Notes and Revision Books (Primary and Secondary) here at no cost:

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PHYSICS ELECTRONICS REVISION QUESTIONS

October 5, 2025 Hillary Kangwana Leave a comment

ELECTRONICS

Sketch curves to show the variation of current and time as displayed on the CRO in each of the
State the majority carriers for a p-type semi conductor.
a) Using examples explain the difference between a semiconductor and a good conductor.
b) A radio repairer wishes to use an ammeter to detect a faulty diode. With the aid of a circuit diagram describe how he will go about this task.
Using examples, explain the difference between a semi conductor and a good conductor.
p- type and n-type semiconductors are made from a pure semiconductor by a process known as “doping”.
i) What is doping?
ii) Explain how the doping produces an n-type semiconductor.
Sketch a current-voltage characteristic of a junction diode with a forward bias.
Using the components symbols shown in the fig, sketch a series circuit diagram for a forward biased diode.

(a)
i) Distinguish between semiconductors and conductors
ii) Give an example of a semiconductor and one for a conductor.
In the circuit below, when the switch s is closed, the voltmeter shows a

When the cell terminals are reversed and the switch is closed, the voltmeter reading is zero.

Explain these observations.

What is meant by Donor Impurity in semiconductors?
You are provided with a diode, a resistor R, an a.c source of low voltage and connecting wires. In the space provided, sketch the circuit diagram for a half-wave rectifier and indicate the terminals where the output voltage v₀ may be connected.
Explain how doping produces an n-type semiconductor for a pure semiconductor material.
Distinguish between intrinsic and extrinsic semi-conductors.
The diagram below shows a rectifier circuit for an alternating current (a.c) input.

i) Describe the rectification process.
ii) Draw the traces of the signal obtained on CRO connected across QS and PR.
The figure 8 below shows a bridge rectifier.

Figure 8

i) Define the term rectification.
ii) Describe how the illustrated rectifier works.

iii) State the modification that can be made on the arrangement to improve the quality of the output.

iv) Sketch on the grid below how the improved output is displayed on a C.R.O screen.

a) Distinguish between intrinsic and extrinsic conductors
b) You are provided with 4 diodes, A resistor, an a.c of low voltage and enough connecting wires.
i) In the spaces provided below, sketch the circuit diagram for a full wave rectifier and indicate the terminals where the output voltage v may be connected.
ii) On the axes provided below, sketch the graph of output voltage against time for the rectifier
c) A capacitor is now connected across the output. Explain its effect on the output.
(a) Define doping

(b) Distinguish between a p-type and n-type semi conductors

A capacitor has been connected across the resistor as shown

(i) Sketch the wave form when a C.R.O is connected across the resistor, R

(ii) On the same axes, sketch a wave form when a C.R.O is connected across R and when the capacitor has been removed.

The figure below shows a bridge rectifier.

A.C.

input

i) Define the term rectification.
ii) Describe how the illustrated rectifier works.

iii) State the modification that can be made on the arrangement to improve the quality of the output.

iv) Sketch on the areas below how the improved output is displayed on a C.R.O screen.

The figure 5 below shows a block diagram of a p-n junction diode.

On the same diagram, show how a cell may be connected so that it is reverse biased.

Fig 5

Figure 4 below shows the supply of d.c. to a resistor, R through a diode, D.

1. Give the bias of the diode.
2. An a.c supply is now supplied to the resistor R. On the axes provided below, sketch the output observed in the C.R.O connected across R.

a) A student connected a circuit as shown in figure 13 below hoping to produce a rectified output.

i) Sketch the graph of the output on the CRO
ii) Explain how the output above is produced.

iii) Name other two uses of a junction diode.

In the figure below, the voltmeter shows a reading when the switch S is closed.

When the cell terminals are reversed and the switch closed, the voltmeter reading is zero. Explain this observation.

(a) Define the term doping.

The diagram below shows a bridge rectifier for alternating current. Complete the diagram by placing the diodes in the correct order.

(d) What happens to depletion layer when diode is reverse biased.

(a) You are provided with a 12V a.c. source, four diodes and a resistor.
i) Draw a circuit diagram for full wave rectifier and show the points at which the output is taken
ii) Sketch a graph of voltage against time before rectification.

iii) Sketch a voltage – time graph after rectification.

iv) Sketch a voltage –time graph after rectification with a capacitor connected across the resistor in (i)
b) A radioactive sample of half life 130 days initially has 1.0x 10²⁰ radioactive atoms. Determine the number of radioactive atoms that would have decayed after 390 days.
In the figure shows a rectifier circuit for an alternating current input.

(a) On the circuit, indicate the flow of current to illustrate rectification.

(b) Sketch a graph to show how the voltage across R varies with time.

(a) (i) State the meaning of the statement diode characteristic.

(ii) Sketch a circuit diagram that can be used to investigate p-n junction diode characteristics.

Define the term acceptor atom as applied in semiconductor.
Study figure 7 below and use it to answer questions that follow.
- Briefly explain how the circuit works to produce a rectified alternating current.
- Draw on the diagram to show the position of the capacitor.
- State the functions of the capacitor in the circuit.
- Sketch the graph of the output as seen on a CRO screen.

The figure below shows a bridge rectifier.

A.C.

input

i) Define the term rectification.
ii) Describe how the illustrated rectifier works.

iii) State the modification that can be made on the arrangement to improve the quality of the output.

iv) Sketch on the areas below how the improved output is displayed on a C.R.O screen.

(b) Figure 10 shows a circuit whose output voltage with time as displayed on the CRO screen.

(i) Sketch a graph to show the variation of output voltage with time as displayed on the CRO screen

(ii) Show on the diagram (Figure 10) how a capacitor should be connected to smooth the output voltage

(iii) Sketch a curve of smoothed output voltage against time.

(i) Using a diagram explain how doping produces a p-type semi-conductor.

(ii) What is biasing?

(iii) The diagram below shows a circuit with a p-n junction and a very low power bulb.

State with reason the observations made on the bulb when the switch is closed.

(a) (i) Distinguish between intrinsic and extrinsic conductors

(ii) The figure bellows shows a p-n junction diode.

Complete the diagram to show the forward bias state

(b) Extrinsic semiconductors are made through a process called doping. Explain how doping produces an n-type semi conductor

(d)The figure below shows a rectifier circuit for an alternating current input using four diodes

To CRO

Explain how rectification is done
State the function of the capacitor
Sketch a graph to show how the p.d. across the resistor R varies with time.

Figure below shows two ways of biasing a P.N junction.

(i) In which circuit will current flow?

(ii) Explain your answer in (i) above.

Figure below shows a circuit consisting of ideal diodes.

Determine the current flowing through the resistors

The diagram below shows a junction diode.

P n

Complete the diagram to show how the diode can be connected in a reverse bias mode.

a) Explain how doping produces a p-type semi conductor for pure semi conductor material.
b) You are provide with 4 diodes, A resistor, an a.c of low voltage and enough connecting wires

In the spaces provided below, sketch the circuit diagram for a full wave rectifier and indicate the terminals where the output voltage v may be connected.
On the axes provided below, sketch the graph of output voltage against time for the rectifier

Output voltage

time

A capacitor is now connected across the output. Explain its effect on the output.

(a) Explain why the conductivity of a metallic conductor decreases with increase in temperature while that of an intrinsic semiconductor increases with increase in temperature.

(b) Explain what happens to the depletion layer when diode is reverse biased.

(d) The figure shows a circuit used for a full wave bridge rectification.

(i) Insert diodes D1, D2, D3 and D4 to complete the circuit.

(ii) What is the use of capacitor C?

(iii) On the axes below draw a voltage – time display of the

rectification observed on the C.R.O.

a) Explain the following terms:
Extrinsic semiconductor:
Dopping:
b) i. Explain briefly the dopping process involved in making n-type semiconductor.
Draw a circuit diagram to illustrate a forward biased p-n Junction
c) In an experiment to investigate the variation of voltage with current for certain p-n Junction diode.

p.d(voltage)	0	1.0	1.2	1.4	1.6	1.8
Current (mA)	0	3.0	9.0	19.0	32.0	60.0

Draw a circuit diagram that can be used to obtain results in the table above.
Plot a graph of current against p.d on the grid provided.

iii. Find the resistance when the voltage is 1.3V

a) Figure below shows a circuit of a rectifier using two diodes D₁ and D₂
Explain how rectification output is produced from the set up when an a.c input in connected across AB.
On the axes provided, sketch the graph of output voltage against time for the rectifier.

iii) A capacitor is now connected across XY. Explain the effect of the capacitor on the output.

b) Explain how doping produces an n- type semi conductors from a pure semi conductor material.
c) Briefly explain what happens to the depletion layer when a diode is forward biased.
d) What is a zener diode?
(a) Explain how you can obtain an n-type extrinsic semiconductor.

(b) What do you understand by term full wave rectification of A.C ?

(c ) The figure below shows a bridge rectifier

(i) Describe how the illustrated rectifier works.

(ii) State the modification that can be made on the arrangement to improve the quality

of the output.

(iii) Sketch on the axes below how the improved output is displayed on a C.R.O screen. ( 1 mark )

Figure 10(a) and 10(b) shows a p – n junction connected to a battery. It is observed that the current in figure 10(a) is greater than the one in figure 10(b)

State the reason for this observation

a) Distinguish between a conductor and a semi conductor
b) What is meant by doping?
c) Give the difference between intrinsic and extrinsic semiconductor.
d) Using examples explain the difference between n-type and p-type semiconductor.
e) The diagram below shows a circuit for full wave rectification.

i) Insert diodes in the gaps left
ii) Explain how the rectifier works

iii) A CRO is connected across R, draw the wave output display.

a) Give two differences between P – type and n – type semiconductor
b) Explain using a diagram how a diode can be used as a half-wave rectifier
c) Figure below shows the output of a wave from an a.c source

Using a circuit show how the above output is produced

d) Name two ways of enhancing the conductivity of a semiconductor
Figure below shows two identical diodes connected in a circuit.

State and explain what happens to each lamp when the switch is closed.

Below is part of a circuit that was set up by form four students of Okok Secondary school during a physics practical lesson to demonstrate full wave rectification using two diodes.

Complete the circuit by correctly placing the load R and the two diodes

a) Figure below shows a circuit of a rectifier using two diodes D₁ and D₂
Explain how rectification output is produced from the set up when an a.c input in connected across AB.
On the axes provided, sketch the graph of output voltage against time for the rectifier.

iii) A capacitor is now connected across XY. Explain the effect of the capacitor on the output.

b) Explain how doping produces an n- type semi conductors from a pure semi conductor material.
c) Briefly explain what happens to the depletion layer when a diode is forward biased.
d) What is a zener diode? (1mk)
When a radiation was released into a diffusion cloud chamber, short thick tracks were
State with a reason, the type of radiation that was detected.

(b) The half-life of an element X is 3.83 days. A sample of this element is found to have an activity rate of 1.6 x 101 disintegrations per second at a particular time.

Determine its activity rate after 19.15 days.

(d) Figure 12, shows n depletion layer in an unbiased p-n junction.

State how a battery can be used to make the depletion layer narrower.

(e) Figure 13, shows an incomplete circuit of a full wave rectifier.

(i) Draw in the figure two more diodes to complete the circuit.

(ii) Show on the figure the points across which the output of the rectifier should he obtained.

a) The figure below shows a bridge rectifier.

i) Define the term rectification.
ii) Describe how the illustrated rectifier works.

iii)What modifications can we make on the arrangement to improve the quality of the output.

iv) Sketch on the areas below how the improved output is displayed on a C.R.O screen.

(b) The figure below shows an expansion cloud chamber.

(i) What is the purpose of the Vapour?

(ii) Explain how the radiations emitted by the radioactive source in the chamber are detected.

(a) Distinguish between intrinsic and extrinsic semiconductors. (b) (i) A junction diode is used as a rectifier. Draw a simple circuit to show how two junction diodes and a centre tapped transformer can be used to produce a full wave rectified a.c.

(ii) Name two other uses of a junction-diode.

p.d (v)

The depletion layer decreases from O to A. Explain what is meant by depletion layer.

(d) What is the advantage of rectifying using four diodes instead of two?

c) A student connected a circuit as shown below, hoping to produce a rectified output.

i) Sketch the graph of the output as seen on the C.R.O screen.
ii) Explain how this output is produced.
Figure below is a circuit with 2 bulbs and components D.

Fig. 3

(i) State the observation made when switch K is closed.

(ii) Account for the observation made above.

The figure 6 shows a p.n junction connected to a cell.

Fig 6

(i) Identify the biasing.

(ii) Represent the circuit in the correct circuit symbols.

a) Define the following terms:
i) Doping
ii) Diode
b) With the aid of a circuit diagram, differentiate between forward biased and reverse diode.
c) Sketch a graph to show how the current through p-n junction varies with p.d across it.
d) The figure shows an incomplete circuit for full wave rectification:-

i) Complete the diagram to show how the diodes should be arranged for the current to flow through R in the direction shown.
ii) Sketch the output voltage as observed in the C.R.O.

Teachers' Resources

Latest CRE Form 3 Exams and Marking Schemes Free Downloads

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Latest CRE Form 3 Exams and Marking Schemes Free

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Teachers' Resources

PHYSICS FORM 1 NOTES (EDITABLE)

October 5, 2025 Hillary Kangwana Leave a comment

INTRODUCTION TO PHYSICS

The primary school science syllabus covers topics such as matter and its properties, energy in its various forms for example heat, light, sound and their corresponding sources, machines and the way they make work easier, balancing and weighing of various shapes of objects, electricity and magnetism.

These topics and more are covered in physics.

MEANING OF PHYSICS

Physics is the study of matter and its relation to energy. Matter is anything that occupies space and has weight.

The study of physics allows one to understand and enjoy other subjects

As a subject, the study of physics involves measurement of quantities and collection of data. Through experimentation and observation, hypotheses are drawn, test and laws and principles established.

Physics explain the how and why behind the following phenomena;

Formation of rainbow.
Occurrence eclipse.
The falling of the objects towards the earth’s surface.
The seasonal occurrence of ocean and sea tides
The crackling sound heard when nylon cloth is removed from the body.
Formation of shadow and many more.

Physics gives scientific, systematic and consistent explanation based on the concepts of physics.

BRANCHES OF PHYSICS

Physics may be split into the following key areas;

Mechanics- is a branch of physics that deals with the study of the motion of the bodies under the influence of forces. It is divided into two key areas namely; kinematics and dynamics. Kinematics is the study of the motion of the bodies disregarding the forces acting on it while dynamics is the study of the motion of bodies with regard to forces acting on the body. Under this branch, we look into details the aspects of linear, circular and oscillatory motions as well as motion of fluids.
Electricity and magnetism- this branch looks at the interaction between electric fields and magnetic fields and the applications of such interactions g. electric motors, microphones, electric speakers etc.
Thermodynamics- This branch looks at how heat as a form of energy is transformed to/from other forms of energy.
Geometrical optics- This branch takes a keen look at the behavior of light in various media g. optic fibre, microscopes, and lenses e.t.c.
Waves- It deals with the study of the propagation of energy through space. It involves properties of waves such as refraction, reflection, diffraction and polarization
Atomic physics– This area of study is targeted at the behavior of particles of the nucleus and the accompanying energy changes. It involves radioactivity, nuclear fission and fusion. It is the basis of the production of nuclear energy.

RELATIONSHIP BETWEEN PHYSICS AND OTHER SUBJECTS

Physics does not only relate the remaining two science subjects but also enjoys a relationship with other subjects as well. For instance, it is the foundation of technological development in any country.

Physics and history- Carbon dating is an application of radioactivity which serves as a crucial tool to history in establishing fossil age and hence past pattern of life.
Physics and Geography- Establishment of weather patterns rely on accurate use of instruments like thermometer, wind vane and hygrometer .Heat transfer by convection explains the formation of conventional rainfall and pressure variation that determine wind patterns. All these are physics concepts.
Physics and Home Science
Physics and religion- Systems in the universe reveal great orderliness which can be traced back to the creator. Study of physics has come up with findings which are in total agreement with orderliness. Matter can be reduced to nothing scientifically the reverse is true which confirms that matter was created from nothing by God.
Physics and Biology- Knowledge of lenses in physics are used in making microscope used in study of cells in biology. Physics formulae are used in calculation of magnification by microscopes.
Physics and Chemistry- Physics has helped in explaining forces within atoms and therefore atomic structure. It is this structure of the atom that then determines the reactivity of the atom as explained in chemistry
Physics and Mathematics- Many physics concepts are expressed mathematically. Many physics formulae are expressed mathematically.
Physics and Technology- some areas of technology that requires knowledge of physics are:

a) Medicine; in medicine, x-rays, lasers, scanners which are applications of physics are used in diagnosis and treatment of diseases.
b) Communication; satellite communication, internet, fibre optics are applications of internet which requires strong foundation in physics.
c) Industrial application; in the area of defense, physics has many applications e.g. war planes, LGB (laser-guided bombs) which has high level accuracy.

In entrainment industry, knowledge of physics has use in mixing various colours to bring out the desirable stage effects. Is application of science to solve problems in everyday situation most forms of technology are due to Physics e.g. Information and Technology, Computer Science, Mobile Phones, building technology, automotive technology.

CAREER OPPORTUNITIES IN PHYSICS

The study of Physics can open up many avenues of professions including engineering, degree, diploma or certificate courses.

A physics student will have the following opportunities in the following areas;

Bachelor of Architecture.
Bachelor of pharmacy.
Bachelor of medicine.
Bachelor of dental surgery.
Bachelor of science(nursing)
Bachelor of education science(physics)
Bachelor of science(Electrical and electronic Engineering)
Bachelor of Veterinary Medicine.

At college level, some of the courses are offered.

Diploma in building and construction.
Diploma in mechanical Engineering.
Diploma in physiotherapy.
Diploma in electrical Engineering.
Diploma in computer science.

BASIC LABORATORY RULES

LABORATORY– This is a room containing facilities, apparatus and equipment that aid the investigative study of physics

BASIC LABORATORY RULES

Proper dressing
Note the location of electricity switches, fire-fighting equipments, First aid kit, gas supply and water supply taps.
When in the laboratory open doors and windows to let in fresh air.
Follow instructions given carefully.
No eating or drinking in the laboratory.
Turn off electrical switches, gas and water taps when not in use.
When handling electrical apparatus hands must be dry.
Do not plug foreign objects into electrical sockets.
Keep floors and working surfaces dry.
Clean and return all apparatus used in their correct location.
All equipments should not be taken out of the laboratory.
Wash your hands before leaving the laboratory.
All instructions given must be followed strictly. Never attempt anything while in doubt.
Windows and doors should be kept open while working in the laboratory
Any wastes after experiments must be disposed appropriately after use

FIRST AID MEASURES

CUTS -These may result from poor handling of glass apparatus or cutting tools like razors and scalpels. In case of cuts, assistance should be sought to stop bleeding and for immediate depressing up of the wound.
BURNS – Burns may result from naked flames or even splashes of concentrated acids and bases. In case of burns caused by acids or bases, quickly run cold water over the affected part as you seek help for further treatment.
POISONING – This may result from inhaling poisonous fumes or actual swallowing of poisonous chemicals. Assistance should be sought immediately.
EYE DAMAGE -Eyes must be safeguarded from dangerous chemicals and bits of solids. In case an irritating chemical lands in the eye, it should be washed off immediately with a lot of cold water
ELECTRIC SHOCK -This may result from touching exposed wires or using faulty electrical appliances. When such an accident occurs, first put off the main switch before treating for the shock.

TOPIC 2: MEASUREMENT

Scientists from various parts of the world were giving measurements in different units and languages. Some used pounds, inches and seconds while others were using grams, centimetres and seconds. This was undesirable, especially when a comparison of results was necessary.

This made it impossible for them to compare discoveries. Consequently, scientists agreed on one international system of units to be used, the Systeme International d’Unites (International System of Units), shortened to SI units, in all languages. This system has seven basic physical quantities and units on one Universal System of units called system international d’ unites (International system of units) SI units which assigned seven basic quantities as shown below.

UNIT	Symbol of quantity	S.I UNIT	SYMBOL OF UNIT
1. Length	L	metres	m
2. Mass	m	kilogram	kg
3. Time	t	seconds	s
4. Electric Current	I	ampere	A
5. Thermodynamic temperature	T	kelvin	K
6. Luminous Intensity		Candela	Cd
7. Amount of Substance		mole	mol

These quantities above cannot be obtained from any other physical quantities. Measurements are made by comparing the magnitude of a quantity with that of a given unit of that quantity. A physical quantity is a measurable aspect of matter.

Basic Physical Quantity -These are quantities that cannot be obtained by any other quantity e.g. mass, time, length.

Derived Quantity-These are quantities obtained by multiplication or division of basic physical quantities e.g. Area, Volume, Density.

LENGTH

This is the distance between two fixed points. It is the measure of distance between two points in space. The SI unit for length is the metre (m).

Other units of length include;

unit	symbol	Equivalence in metres
Kilometre	Km	1000
Hectometre	Hm	100
Decametre	Dm	10
Decimetre	dm	0.1
Centimetre	Cm	0.01
Millimetre	mm	0.001
Micrometre	μm	0.000001

MEASUREMENT OF LENGTH

Length can be estimated or measured accurately using appropriate measuring instrument. The type of instrument to be used at any time depends on two factors:

The size of the object to be measured
The desired accuracy

The methods used include;

Approximation/ Estimation
Accurate measuring using standard instruments
Estimation

This method involves comparing the object to be measured with another of standard measure. For example, the height of a tall flag post can be compared with that of a wooden rod whose length is known. Thus at any given time;

Height of flag post = Length of shadow of post

Height of rod Length of shadow of rod

From this expression, the height of the flag post can be estimated.

Example;

Suppose the height of the rod= 1m, length of shadow of rod= 120cm and length of shadow of post= 480cm, then the height of the flag post is given by;

Height of post, H_p = 480cm

100cm 120cm

Height of post, H_p= 100 x 4

= 400cm

Also, the thickness of a sheet of paper may be estimated by taking several sheets of the paper and measuring their thickness then dividing by the number of sheets of paper;

Thickness of a sheet of paper = Thickness of n papers

Number of papers, n

Using a standard measure(instruments)

This involves the use of standard measure or instruments. To measure length accurately, the instruments used are metre rules, half metre rules, tape measure, vernier calipers and micrometer screw gauges

Metre rule

A metre rule is marked in centimetres. It is marked 0 and 100cm at its extreme ends.

0 100cm

a metre rule

The smallest scale division of a metre rule is 0.1cm (1mm). The smallest scale division of any instrument is known as its accuracy. Thus the accuracy of a metre rule is 0.1cm.

When using a metre, one must ensure the following:

That the object to be measured is in contact with the metre rule.
That one end of the object is at 0cm mark i.e. zero (0) mark to coincide with the start of the object to be measured.
That the eye is perpendicular to the scale so as to avoid parallax error. This ensures that accurate reading is obtained.

Metre rules and half metre rules used are graduated in centimetres and millimetre.

They are made of wood, plastic or steel.

When using a ruler the following precautions should be taken;

Never drop a metre rule
Never use it as a walking stick
Never use it as a cane
Keep it in a dry place away from corrosive substances

EXAMPLE 1

The reading should be taken in terms of the least count of the metre rule. For a metre rule the least count is 0.001m=0.1cm=1mm.

The reading shown above is 0.0165m=1.65cm=16.5mm.The metre rule cannot read 4th, 2nd or 1st decimal places of metre, centimeters or millimeters respectively. This is only approximated.

EXAMPLE 2

Figure below shows a fencing post whose length is being measured using a strip of a measuring tape.

(a) State the accuracy of the tape:

(b)What is the length of the post?

SOLN

(a)Accuracy of measuring tape is 10mm or o.1 cm + 5cm or o.o5m.

(b)Length of post is 1.5 m

Tape measure

It is graduated in millimetre (mm) or centimetre (cm)

They are three types;

Tailor’s tape measure
Carpenter’s tape measure

Surveyor’s tape measure

NOTE: The choice of a tape measure depends on accuracy required and the size of object to measure. A tape measure can be made up of cloth, steel or flexible plastic. Always ensure that the tape measure is taut when measuring.

MEASUREMENT OF CURVED LENGTH

Curved length can be measured using a thread. The thread is placed along the required length and the length is found by placing the thread on a scale.

EXPERIMENT: Measuring the circumference of a cylinder using a thread.

APPARATUS: A cylinder, a thread and a metre rule

PROCEDURE

Wrap a thin thread say 10 times around the cylinder
Mark with ink the beginning and end of turns as shown

The circumference of the cylinder will be given by;

Circumference = [length of thread]

But; Circumference =π d or 2πr (where r is the radius of the cylinder)

ESTIMATION OF LENGTH

EXPERIMENT: To estimate the height of a tree

APPARATUS: A metre rule, tape measure

PROCEDURE

Measure the length of the metre rule when upright using a tape measure followed by measuring its shadow.
Measure the shadow of the tree in the school compound.

RESULTS

Height of metre rule = …………Cm

Height of shadow of metre rule=…………Cm

Height of shadow of the tree =……………Cm

Estimation of the height of the tree is given by the formula provided above.

AREA

Area is defined as the measure of surface enclosed by the boundaries of the body. Its SI Unit is the square metre (m²). Since it is measured in metre-square (m²), this means it’s a derived quantity.

Other multiples and sub-multiples of area are; cm², mm², km², hectares etc.

Area can also be estimated or calculated accurately.

CONVERTING

mm²to m2

1m²= 1000 X 1000

= 1000000 mm²

1mm² = {1÷1000000} m2 (Divide by 1million)

= 0.000001 m²

m²to mm²

1m²= 1000000 mm² {multiply by 1 million}

cm²to m²

1cm = 0.01m

1cm² = 0.01m X 0.01m

= 0.0001m²{multiply by 0.0001}

m2 to cm²

1m = 100cm

1m2 = 100cm X 100cm

= 10000cm² {multiply by 10000}

EXERCISE

Convert 7.5m² to cm²
Convert 940mm² to cm²
Convert 12000mm² to m²

Measurement of area (Accurate Measurement)

The area of regularly shaped objects can be found by applying an appropriate formula shown below;

APPROXIMATION OF AREA OF IRREGULAR BODIES

We trace their outline on the square paper of 1cm² e.g.

Full squares = …………cm²

½ full squares = ………..cm²

AREA = full square+½full squares

Consider the figure below of an irregularly- shaped object.

The number of complete squares covered by the shape= 14

The number of incomplete squares covered by the shape=19

Therefore, the number of complete squares covered by the shape is approximately (14+ 19/2) = 23.5 squares.

Suppose the area of one square is 1cm², and then the area of the shape is approximately;

Area = 23.5 x 1

= 23.5 cm²

EXAMPLE 3

Estimate the area of the irregular surface shown below by counting the small squares.

SOLN

The number of complete squares = 39

Number of incomplete squares = 34

These are equal to 34 = 17 complete squares

Therefore, the number of complete squares = 39 + 17 = 56

Hence, the estimated of the area of the surface = 56 x 1 cm²= 56cm²

VOLUME

Volume is the amount of space occupied by space. The SI unit of volume is cubic metres [m³].

It is a derived quantity of length

Multiples and submultiples are; mm³, cm³ and km³

CONVERTING

a) From m³ to mm³

1m = 1000mm

1m³ = 1000mm X 1000mm X 1000mm

= 1000000000mm³

To change m3 to mm3 you multiply by 1 billion

b) From mm³ to m³

To change m³ to mm³ you divide by 1 billion i.e. 1/10000000000

EXAMPLE 4

Express 9cm³ in m³
Express 9000000000mm³ in m³
Express 0.0546m³ to cm³

MEASUREMENT OF VOLUME

The volume of regularly shaped solids can be obtained by applying the appropriate formula i.e

EXAMPLE 5

A block of glass is 5.0 cm long, 4.0 cm thick and 2.5 cm high. Calculate its volume.

SOLN

Volume of the glass block = area of cross section x height

= 5.0 x 4.0 x 2.5

= 50.0 cm³

EXAMPLE 6

Find the volume of cylindrical tin of radius 7.0 cm and height 3.0 cm.

SOLN

Volume of the tin = area of cross section x height

= 22 x 7 x 7 x 3

= 462.0 cm³

EXAMPLE 7

Find the volume of the triangular prism shown below given that base length is 12.0 cm, h= 5.0 cm and the width 6.0 cm:

SOLN

Volume of the prism = area of cross section x height

= ½ x 6.0 x 5.0 x 12.0

= 180.0 cm³

EXAMPLE 8

Find the volume of a sphere whose radius is 3.0 cm

SOLN

Volume of a sphere = 4/3 πr³

= 4 x 22 x 3.0 x 3.0 x 3.0

3 7

= 113.14 cm³

EXAMPLE 9

A sphere of diameter 6.0 cm is moulded into a thin uniform wire of diameter 0.2 mm. Calculate the length of the wire in metres. (Take π = 22/7)

SOLN

Volume of the sphere and the wire are equal

Volume of the sphere = volume of the wire

4 x 22 x 3.0 x 3.0 x 3.0 = 22 x 0.01 x0.01 x L

3 7 7

4 x 3.0 x 3.0 x 3.0 = L

3 x 0.01 x 0.01

Therefore, length L = 360000cm

= 3600 m

MEASUREMENT OF VOLUME OF LIQUIDS

Liquids have no definite shape but they assume the shapes of the container in which they are put.

One of the methods which can be used to measure the volume of liquids is to pour the liquids into a container with a uniform cross-section as shown,

Volume = Area of cross-section x height

= A h; where A=LX b

= l b h

Instruments can also be used to measure the volume of liquids. They include; Burette, Pipette, Measuring cylinder, graduated beaker and Volumetric flask.

NOTE: The scale of the Burette begins from zero at the top and increases downwards to the maximum value e.g. a reading of 31.0ml on the burette means that volume of the liquid is [50-31] ml = 19ml.

MEASUREMENT OF VOLUME OF IRREGULAR OBJECTS

Using a measuring cylinder

PROCEDURE

Fill the measuring cylinder with water.
Record the volume of water as V₁
Submerge gently a stone [irregular object] tied around a thread.
Record the volume of water and the stone as V₂.
Volume of the stone = V₂– V₁

Using a Eureka can

A Eureka or displacement can is a container with a spout from the side.

Apparatus; Eureka can, measuring cylinder, irregular object e.g. a stone, water

Procedure

Fill the Eureka can with water until it flows out of the spout.
Place a measuring cylinder under the spout of the can.
Tie the solid [irregular object] with a thread and submerge it gently inside the can.
The result [water] collected to the measuring cylinder is the volume of the irregular object.

EXERCISE 2.5 KLB

MASS

Mass is a quantity of matter in a body. Its S.I unit is kilogrammes (Kg)

It is measured using a beam balance or top pan balance.

The multiples and submultiples include;

Unit symbol Equivalence in Kg

Tonne t 1000

Gram g 0.001

Milligram mg 0.000001

The mass of an object is the same everywhere because the number of particles in an object remains constant.

MEASUREMENT OF MASS

There are two common types of balances for measuring mass; Electrical and mechanical types.

Electrical types are very accurate and the mass of the object is read on display

(Top Pan Balance).

A Mechanical type (Beam Balance), the object whose mass to be measured is balanced against a known standard mass on an equal level.

The three balances used in measuring are;

1) Top Pan Balance

2) Beam balance

3) Level balance

In a level balance combination of levers moves the pointer along a scale when the mass is placed on it.

EXERCISE 2.6 KLB

DENSITY

The density of a substance is defined as its mass per unit volume. Its symbol is rho (ρ).

The SI unit is kilogram per cubic metre (Kg/m³)

Conversion from kg/m³ to g/cm³

1g/cm³ = 1000kg/m³

EXAMPLE 10

A Block of glass of mass 187.5g is 5cm long, 2.0cm and 7.5cm high. Calculate the density of the glass block.

Solution

Density = mass

Volume

= 187.5g

2.0cm X 5cm X 7.5cm

= 2.5g/cm3 or 2500kg/m³

EXAMPLE 11

A block of glass of mass 187.5 g is 5.0 cm long, 2.0 cm thick and 7.5 cm high. Calculate the density of the glass in kgm-3.

SOLN

Density = mass / volume

= (187.5 /1000) / (2.0 × 7.5 × 5.0 /1,000,000)

= 2500 kgm^-3.

EXAMPLE 12

The density of concentrated sulphuric acid is 1.8 g/cm3. Calculate the volume of 3.1 kg of the acid.

SOLN

Volume = mass / density

= 3,100 / 1.8

= 1722 cm³or 0.001722 m³.

MEASUREMENT OF DENSITY

The density of an object is calculated from the formula;

Density = mass

Volume

Density of common substances

DENSITY BOTTLE

A Density bottle is a small glass bottle fitted with a glass stopper which has a hole through which excess liquid flows out.

Normally, the density bottle has its capacity indicated on the side.

To find the density of the liquid using a density, measure the mass m₁ of a dry clean density bottle with its stopper.

Fill the bottle with liquid and replace the stopper. Dry the bottle on outside (excess liquid overflows through the hole in the stopper).

Measure the mass m₂ of the bottle plus the liquid.

If the volume of the liquid is V then;

Density = (m₂-m₁)

PRECAUTIONS

The bottle is held by the neck when wiping it dry. This is because when held in hands, it may expand due to warmth from the hand.
The outside of the bottle must be wiped carefully.
Ensure that there is no air bubbles when the bottle is filled with liquid

TO MEASURE THE DENSITY OF A SOLID USING A DENSITY BOTTLE

This method is used for solids in form of grains, beads or turnings

Apparatus: density bottle, lead shots and beam balance.

PROCEDURE

Measure the mass m₁ of a clean dry empty density bottle
Fill the bottle partly with the solid (lead shots) and measure mass m₂
Fill up the bottle with water up to the neck and measure its mass as m₃.
Empty the bottle and rinse it
Fill it with water and replace it with the stopper, wipe outside dry and measure the mass m₄ of the bottle filled with water.

RESULTS

Mass of water = (m₄– m₁) g

Volume of water = (m₄– m₁) cm3 (since density of water is 1g/cm3)

Mass of lead shots (solid) = (m₂– m₁) g

Mass of water present when the bottle is filled with lead and water = (m₃– m₂) g

Volume of water = (m₃– m₂) cm³

Volume of lead shots = (m₄-m₁)-(m₃-m₂) cm³ (since density of water is 1g/cm³)

Therefore density of lead shot = (m₂-m₁)-{(m₄-m₁)-(m₃-m₂)}

NOTE: This method is unsuitable for solids which are either soluble or react with it.

EXAMPLE 13

The mass of a density bottle is 20g when empty and 45g when full of water. When full of mercury, its mass is 360g. Calculate the density of mercury.

SOLUTION

Mass of water = 45-20 =25g

Volume of water = 25g/1g/cm³

= 25cm³

Volume of bottle = 25cm³

Mass of mercury = 360-20 =340g

Volume of mercury= 25cm³

Density of mercury= 340 ÷25

=13.6g/cm³ or 13600kg/m³

EXAMPLE 14

In an experiment to determine the density of sand using a density bottle, the following measurements were recorded:

Mass of empty density bottle =43.2g

Mass of density bottle full of water =66.4g

Mass of density bottle with some sand =67.5g

Mass of density bottle with some sand filled up with water=82.3g

Use above data to determine the;

(a) Mass of water that completely filled the bottle.

(b) Volume of water that completely filled the bottle.

(d) Mass of sand.

(e) Mass of water that filled the space above the sand.

(f) Volume of the sand.

(g) Density of the sand.

SOLN

a) 66.4 – 43.2 = 23.2g
b) 23.2cm³
c) 23.2cm³
d) (67.5 – 43.2) g = 24.3g
e) 82.3 – 67.5 = 14.8g
f) Volume of the sand = volume of bottle – volume of added water

= 23.2 – 14.8= 8.4cm³

g) P = M/V = 24.3g / 2.893cm³

= 8.4cm³

EXAMPLE 15

The mass of an empty density bottle is 20 g. Its mass when filled with water is 40.0 g and 50.0 g when filled with liquid X. Calculate the density of liquid X if the density of water is 1000 kgm^-3.

SOLN

Mass of water = 40 – 20 = 20 g = 0.02 kg.

Volume of water = 0.02 / 1,000

= 0.00002 m³.

Volume of liquid = volume of bottle

Mass of liquid = 50 – 20

= 30 g = 0.03 kg

Therefore density of liquid = 0.03 / 0.00002

= 1500 kgm^-3

DENSITY OF MIXTURES

A Mixture is obtained by putting together two or more substances such that they do not react with one another. The density of the mixture lies between the densities of its constituent substances and depends on their proportions.

Density of the mixture = mass of the mixture

Volume of the mixture

EXAMPLE 16

100cm3 of fresh water of density 1000kg/m3 is mixed with 100cm3 of sea water of density 1030kg/m3. Calculate the density of the mixture.

Solution

Mass of fresh water = density x volume

= 1g/cm³ x100cm³

= 100g

Mass of sea water = 1.03 x 100

= 103g

Mass of the mixture = 100+103

= 203g

Volume of the mixture= 100+100

= 200cm³

Density of the mixture = 203÷200

= 1.015g/cm³

Exercise 2.7 no. 2 &3 KLB

TIME

It is a measure of duration of an event. Some ancient measuring instruments were the sundial and the hour glass

The SI unit of time is seconds (s)

MULTIPLES AND SUBMULTIPLES OF TIME

Time	symbol	Equivalent in seconds
Microsecond	µ s	0.000001
millisecond	ms	0.001
Minute	min	60
Hour	hr	3600
Day	day	86400
Week	wk	604800

Measurement of time

Time is measured using either a stopwatch (digital) or stop clock

They are used depending on the accuracy required.

QUESTIONS ON THE TOPIC

State two factors that should be controlled in manufacturing a cylindrical container of uniform thickness, which should normally be in a standing position.
The figure shows a measuring cylinder which contains water initially at level A. A solid mass 11g is immersed in the water, the level rises to B.

Determine the density of the solid. (Give your answer to 1 decimal point)

A butcher has a beam balance and masses 0.5 kg and 2 kg. How would he measure 1.5 kg of meat on the balance at once?

Determine the density in kg/m³ of a solid whose mass is 40g and whose dimensions in cm are 30 x 4 x 3
Record as accurately as possible the masses indicated by the pointer in figures A.

Figure 1 shows the reading on a burette after 55 drops of a liquid have been used.

If the initial reading was at 0cm mark, determine the volume of one drop

1 shows the change in volume of water in a measuring cylinder when an irregular solid is immersed in it.

Given that the mass of the solid is 567g, determine the density of the solid in gcm^-3. (Give your answer correct to 2 decimal places.

A thin wire was wound 30 times closely over a boiling tube. The total length of the windings was found to be 9.3 mm. Calculate the radius of the wire.
(a) Given that a kilogram of copper contains about 10²⁵ atoms and that density of copper is about 9000kg/m³_,estimate the diameter of the copper atom?

(b) State the assumption made in (9a) above.

The density of concentrated Sulphuric acid is 1.8gcm^-3. Calculate the volume of 3.6kg of the acid.
1600 cm³ of fresh water of density l g/cm³ are mixed with 1400cm³ of seawater of density 1.25g/cm³. Determine the density of the mixture.
With the aid of a diagram, illustrate the meaning of the parallax error
Describe how you can measure the density of a rock which has no definite shape.
A shopkeeper has a scale balance and masses of 250g and 2kg. How would he measure 1.75kg of flour on this scale at once
A pebble of mass 50g is placed in a measuring cylinder containing some water. The reading of the water level increased from 75cm³ to 95cm³. Calculate the density of the pebble
The container shown below is filled to a depth of 5cm with a liquid.

3.5cm

9cm

Liquid 5cm

Using pie as 22/7, determine the volume of the liquid.
If the mass of the liquid in the container is 2.554kg, estimate the density of mercury in g/cm³.
Calculate the mass of water that would be needed to completely fill the remaining space in the container above the liquid. (Density of water is 1g/cm³)
A pebble of density 9g/cm³ is gently dropped into the container full of water and the liquid. Describe and explain what is observed.

SOLUTIONS

height, base area
Volume of one molecule = 18/ (6×10²³) = 3x 10^-23cm

X³ = 3x 10^-23 cm³

X = 3.11 x 10 ^-8 cm³

d= m/v=40g/ 30 x 4 x 3cm^{3 =}1111 g/cm³
5 kg
D= m/r =⁵⁶⁷/_(150-80) = ^576-80 /_70g/cm3
2000 cm³
12g/cm³

TOPIC 3: FORCE

Force is a pull or a push or that which changes a body way of motion and distort it

Its SI unit is newtons (N)

EFFECTS OF FORCE

It can increase the speed of a moving object or make a stationary object start moving.
Slow down or stop a moving object.
Change the direction of a moving object.
Distort (change) the shape of an object.

Force is that which changes a body’s state of motion or shape. Some forces are small and others are large.

Force is represented by a line with an arrow showing the direction it acts. i.e.

Force can be categorized in two ways. These are:

As either a push or a pull
As either contact or non-contact force

Contact forces are those forces between bodies which are in contact e.g. action and reaction, viscous drag, friction etc. Non-contact forces act between bodies at a distance e.g. gravitational force, magnetic force, electrostatic force etc.

TYPES OF FORCES

Gravitational force
Tensional force

Upthrust

Frictional force
Magnetic force
Centripetal force

Cohesive and adhesive force
Molecular force

Electric force
Nuclear force
Electrostatic force

GRAVITATIONAL FORCE

This is a force of attraction between two bodies of given mass. Objects thrown from the earth’s surface always falls back to the surface of the earth. This force which pulls the body towards the centre of the earth is called Gravitational force.

Moon and other planets also have their gravitational force to objects.

The pull of gravity on the body towards the centre is called weight. The weight of an object varies on different planets because of different gravitational pull.

TENSION FORCE

Tension force is as a result of two opposing forces applied. The pull or compression of a string or spring at both of its ends is called Tension.

Compressed or stretched object will tend to regain its original shape, when the stretching or compressing force is removed .Materials that can be extended without breaking are called elastic materials. Such materials can be used to make a spring balance an instrument used to measure force. Other examples include; bows and catapults.

UPTHRUST FORCE

The upward force acting on an object immersed in a fluid (liquid or gas) is called upthrust force.

An object in a vacuum will not experience upthrust.

EXAMPLE 1

An object weighs 80N in air and 60N when immersed in water. Calculate force acting on the object.

Solution

Upthrust force = weight of object in air –weight of object in the liquid

= 80 – 60

= 20N

Exercise

An object weighs 100N in air and 26N when immersed in water. Calculate the apparent loss weight of the object. Calculate also the mass of object in water. (1Kg=10N).
2kg blue band weighs 20N when placed in air .The apparent loss in water is 2N .Calculate the mass of blue band in water.

FRICTIONAL FORCE

Frictional force is a force that opposes relative motion between two surfaces in contact.

The opposing force involving a fluid is called viscous drag (viscosity).This viscous drag limits the speed with which a body can move in a liquid.

Friction can be applied during walking.

EXPERIMENT: To investigate frictional force.

Apparatus: wooden block, rollers.

Procedure:

Put a block of wood on a horizontal surface such as a bench as shown.
Pull the block gradually, increasing the force.
Repeat the experiment, this time resting on rollers as shown above

Conclusion

The wooden block starts to move when the applied force is just greater than frictional force between the block and the surface of the bench.

Frictional force can be reduced by using rollers, oiling and smoothening.

MAGNETIC FORCE

Magnetic force is the force of attraction or repulsion between a magnetic material and a magnet.

A magnet has two types of poles, a north pole and a south pole. Like poles repel while unlike poles attract. Some materials are attracted by a magnet while others are not .Those that are attracted are called magnetic materials e.g. iron ,steel ,nickel and cobalt while those that are not attracted are called non-magnetic materials e.g. wood and aluminium.

COHESIVE AND ADHESIVE FORCES

The force of attraction between molecules of the same kind is known as cohesive force e.g. A water molecule and another water molecule. The attraction between molecules of different kinds is known as adhesive force e.g. between water molecules and molecules of the container in which the liquid is put.

EXPERIMENT: To see the behaviour of water on different surfaces.

Water wets glass

Observation

Water on the glass slide spreads

Water forms spherical water drops on waxed surface

OBSERVATION

Small spherical balls was observed on a waxed glass

EXPLANATION

Water wets the glass surface because the adhesive forces between the water molecules and the glass molecules are greater than the cohesive forces between water molecules.

Water does not wet the waxed glass surface because the cohesive force is greater than the adhesive.

If mercury was used in the experiment it could be observed that small drops on a clean glass dish collect into spherical ball as shown below

This is due stronger cohesive forces between mercury molecules which forms small spherical drops. The adhesive force between mercury and glass makes mercury not wet glass.

N/B: Mercury is poisonous and should not be handled in ordinary laboratory.

EXPERIMENT: To demonstrate cohesive and adhesive forces of liquids on narrow tubes

APPARATUS: narrow tubes of different size of bore, beaker and water

a) Glass tubes dipped in water b) Glass tubes dipped in mercury

OBSERVATION

The level of the water inside the tubes is higher than outside the tubes. A meniscus is formed at the top of the water level and it curves upwards (concave).

The rise in the tube with a smaller bore is higher than in the tube with a larger bore.

Different liquids rise by different heights depending on the diameter of the glass tube.

When mercury is used, the level of mercury inside the tubes goes lower than that outside the tubes. The surface of the mercury will curve downwards (convex).

EXPLANATION

Adhesive forces between the water and glass is greater than cohesive forces between the water molecules, the water rises up the tube so that more water molecules can be in contact with the glass. This wets the glass. Liquids such as glycerol, kerosene and methylated spirit rise in tubes.

On the other hand, the force of cohesion with the mercury is greater than the force of adhesion between glass and mercury. The mercury sinks to enable mercury molecules to keep together.

SURFACE TENSION

This is a force that causes the surface of a liquid to behave like a stretched plastic skin.

The force is due to the force of attraction between individual molecules in a liquid. Its due to this force that liquids form drops, water wets the surface but runs off others, some insects like pond skaters manage to rest on the surface of water without sinking, water rises up in narrow glass tubes but mercury is pushed down to a lower level in the same tube and steel needle or razor blade floats on water even though steel is denser than water

EXPERIMENT: To investigate the behaviour of a liquid surface

APPARATUS: Beaker, water, soup solution, razor blade or steel needle.

PROCEDURE:

Fill the beaker with clean water to the brim as shown

Place a dry steel needle or razor blade at the edge of the beaker and carefully introduce it on the surface of water. Take care not to break the surface of water. Observe what happens.
Put a few drops of soap solution and observe what happens.
Depress the tip of the needle into the water and observe what happens.

OBSERVATIONS

The razor blade/needle floats on the surface of water and remains resting so long as the water surface is not broken.
When drops of soap solution are put on the surface of the water around the razor blade/steel needle, the razor blade/steel needle sinks after a few minutes.
Depressing the razor blade highly allows it to sink very quickly

EXPLANATION

The razor blade/needle floats because the surface of water behaves like a fully stretched, thin, elastic skin. The force which causes the surface of a liquid to behave like a stretched skin is called surface tension. This force is due to the force of attraction individual molecules of the liquid (cohesive force)

The needle or blade sinks when drops of soap solution are put near the razor/needle because the soap solution reduces surface tension of the water.

When the tip of the needle or razor is depressed into the liquid, it pierces the surface skin and sinks.

MOLECULAR EXPLANATION OF SURFACE TENSION

A Molecule say C deep in the liquid is surrounded by molecules on all sides so that the net force in it is zero. However, molecules of the surface, say A and B will have fewer molecules on the vapour side and hence it will experience a resultant inward force causing the surface of the liquid to be in tension.

FACTORS AFFECTING SURFACE TENSION

Impurities – impurities reduces surface tension of a liquid. Detergents weaken the cohesive forces between the liquid molecules.
Temperature – Increasing the temperature of a liquid increases kinetic theory of molecules. The inter-molecular distance increases and the force of cohesion is decreased hence surface tension is lowered.

CONSEQUENCES/EFFECTS OF SURFACE TENSION

Water insects can rest on the surface of water without breaking the surface. The insects skate across the surface at high speed.
Mosquito larvae float on water surface. Oiling the surface using kerosene lower surface tension making larvae to sink

NOTE:

Behaviour of soap bubbles- the soap bubbles flatten into thin films and try to rise up the funnel. This is because the surface tension makes it to behave as if it is a stretched elastic skin. As it tries to make its surface as small as possible, the bubble rises up the funnel.
Behaviour of soap film-the soap films in the wire loop with thread loosely tied across are used in this case. It is observed that when the film is broken on one side, the thread assume a perfect curve. This is because the surface tension will act on one side of the thread. Water tries to make its surface as small as possible, thus pulling the thread in such a way that it forms a perfect curve.
The appearance of water drops coming out of a tube- it is observed that the water drop grows to a large spherical drop before falling down. The water behaves as if there is an elastic membrane which stretches as more water gets into it. When it can not hold any more water, it falls.
Surface tension of soap is less than that of water- A matchstick or a small toy boat is rubbed with soap at one end and placed on the water surface, it start moving immediately. It moves in one direction only and in such a way that the end that is not rubbed with soap is always in front. The soap lowers/weaken/reduce the surface tension at the end of the stick. The surface tension at the other end which is now greater pulls the stick and makes it move in that direction. The movement gradually weakens and ultimately ceases when the whole surface of water is covered with soap solution. Camphor has the same effect as that of soap.
A glass tumbler can be filled with water above the brim. This is because the surface of the water behaves as if it is a thin elastic membrane as it stretches to hold more water.
When a brush is in water, the bristles spread but when it is taken out of water, they cling together. When in water, there in no surface tension since the tension is only on the exposed surface. When the brush is taken out of the water, the surface tension acting on the surface of water tends to be as small as possible thus pulling the bristles together.
When it is raining, it is advisable not to touch a canvas tent from inside. Touching the canvas tent or umbrella with lower/reduce/weaken the surface tension thus making water to leak into the tent.

ELECTROSTATIC FORCE

This is a type of force which causes attraction or repulsion between charges.

Charges can be positive or negative.

Like charges repel and unlike charges attract

EXAMPLES

A plastic pen or ruler rubbed on a dry hair or fur picks up small pieces of paper lying on a table when it’s brought near them. (Charges are created on the pen and attract the pieces of paper). The same pen or ruler attracts a stream of water from a tap. The rubbing creates static charges
When a glass window is wiped with a dry cloth on a dry day, dust particles are attracted on it.
When shoes are brushed, they tend to attract dust particles
When you remove cloth at night you observe sparks. The sparks are due to neutralization of the static charges formed when a nylon cloth is being pulled off.

ELECTRIC FORCE

It’s a force which acts on two conductors carrying electricity.

ACTION AND REACTION

They are two equal forces but acting in opposite to each other. When a block of wood is placed on a table, its weight acts on a table (action). It is pressed on the surface downwards. The reaction (opposite force) of the table acts on the block.

When one force acts on a body, an equal and opposite force acts on one another.

MASS AND WEIGHT

Mass is the quantity of matter in an object while weight is a measure of the pull of gravity on an object. The S.I unit of mass is kg (kilogram) and of weight is Newton (N).

Mass of an object is a scalar quantity while weight is a vector quantity (since weight is a pull of gravity directed to the centre of the earth).

Due to the shape and rotation of the earth, the weight of an object varies from place to place while mass is constant (does not change).

A body weighs more at the poles than at the equator.

DIFFERENCES BETWEEN MASS AND WEIGHT

Mass	Weight
1. Its a quantity of matter on a body.	1. It is a pull of gravity on a body.
2. It’s measured in kg.	2. It is measured in (N)
3. Same everywhere.	3. Varies from one place to another.
4. Measured using a beam balance.	4.Measured using a spring balance
5.Has magnitude only (scalar quantity)	5.Has both magnitude and direction.(vector quantity)

RELATIONSHIP BETWEEN MASS AND WEIGHT

Weight = Mass x gravitational

W = mg

EXAMPLE 2

Find the weight of an object whose mass is 50 kg.

W = mg

= 50 x10

= 500 N

Find the mass of an object whose weight is 900N

W = mg

900/10 = 10/10m

Mass, m = 90kg

An astronaut weighs 900N on earth .On the moon; he weighs 150 N.

Calculate the moon’s gravitational strength. (g=10N/Kg)

Mass, m = w/g

= 900/10

= 90kg

On moon, w = mg

g = w/m

= 150/90

= 1.67N/Kg

3.2(NOs. 1, 2, 4) KLB

MEASURING FORCE

Force is measured using an instrument called a spring balance.

The extension of a spring can be used to measure an applied force. The larger the force, the more the spring extends.

A spring balance measures forces and should therefore calibrated in newtons.

Some spring balances are calibrated in kilograms. In such cases, one is advised to convert from kilograms to newtons. (1Kg=10N)

EXAMPLE 3

The length of a spring is 16.0cm. Its length becomes 20.0cm when supporting a weight of 5.0N. Calculate the length the length of the spring when supporting a weight of; a)2.5N b)6.0N c)200N

Solution

a) 5N – 4cm b) 5N – 4cm c) 5N = 4cm

2.5 N- ? 6 N- ? 200N =?

(2.5 x 4)/5=2cm (6 x 4)/5 =4.8cm (200 x 4)/5= 160

2+16=18cm 4.8+16 = 20.8cm 160+16 =176cm

Note; In c) extension is too large and spring may straighten out.

EXAMPLE 4

A spring stretches by 8.0mm when supporting a load of 2.0N. (i) By how much will it stretch when supporting a load of 6.0N? (ii) What load would make the spring extend by 2.5cm?

Solution

i) 0mm -2.0N ii) 8.0mm -2.0N

?-5.0N 25mm=?

x 8)/2 =20mm (25 x2)/8 = 6.25N

EXAMPLE 5

8kg

The figure below shows two identical spring balances supported as shown:

A B

State the reading on each spring balance.

Each spring will read =80/2=40N

EXAMPLE 6

Three identical arranged as shown below were used to support a load of weight 20N. If the beam has a weight of 1N and each spring would extend by 1cm if a load of weight 4N is suspended from it, determine the extension of each spring.

20N

A B

Extension in spring A = Extension in spring B

= {(21/2) x1cm}/4N

= 2.265cm

Extension in spring C = (20Nx1cm)/4N

= 5cm

Exercise 3.3 no.2 KLB

SCALAR AND VECTOR QUANTITIES

A SCALAR QUANTITY – is a quantity which has magnitude (size) only. It can be specified by a number and unit. Examples include; mass, area, density, volume, energy, time, pressure, temperature, and length.

Scalar quantities are added by the normal rules of arithmetic e.g.3cm2+4cm2=7cm2

A VECTOR QUANTITY – is a quantity which has direction and magnitude (size). It can be specified by a number, unit and direction. Examples include; weight, force, velocity, displacement, acceleration, momentum and magnetic field strength.

A vector quantity is represented on a diagram by a straight line with an arrow i.e.

10N or 2N

The sum of two or more vectors is the resultant vector. Parallel forces which act on an object can be added arithmetically.

Examples of addition of parallel forces on a body

NOTE; Forces acting in opposite directions, the resultant is their difference.

To specify resultant force, both magnitude and direction are given

QUESTIONS ON THE TOPIC

A student was heard saying “the mass of a ball on the moon is one sixth its mass on earth”. Give a reason why this statement is wrong.
In the study of a free fall, it is assumed that the force f acting on a given body of mass m is gravitational, given by F= mg. State two other forces that act on the same body.
State how a lubricant reduces friction in the bearings of moving part of a machine.
Distinguish between mass and weight of a body stating the units for each.
State with reason the purpose of the oil that circulates in a motorcar engine.
Name two types of forces which can act between objects without contact.
A house in which a cylinder containing cooking gas is kept unfortunately catches fire. The cylinder explodes. Give a reason for the explosion.
Give a reason why the weight of a body varies from place to place
State why a pin floating on water sinks when a detergent is added.

Fig 8 shows water drops on two surfaces. In 8 (a), the glass surface is smeared with wax while in 8 (b) the glass surface is clean.

Explain the difference in the shapes of the drops.

An astronaut is on the moon. He drops a hammer from a height of 3.2m and it takes 2.0s to hit the lunar landscape. What is the acceleration due to gravity of the moon?
An unloaded spring has a length of 15cm and when under a load of 24N it has a length of 12cm. What will be the load on the spring when length is 10cm?
Give a reason why the weight of the body varies from place to place
A metal pin was observed to float on the surface of pure water. However the pin sank when a few drops of soap solution were carefully added to the water. Explain his observation.
A bag of sugar is found to have the same weight on planet earth as an identical bag of dry sawdust on planet Jupiter. Explain why the masses of the two bags must be different.
Fig 4 shows water drops on two surfaces. In (a) the glass surface is smeared with wax while in (b) the glass surface is clean.

Explain the difference in the shapes of the drops.

The diagram in figure 5 shows two glass tubes of different diameters dipped in water. Explain why h2 is greater than h1
Name two forces that determine the shape of liquid drop on the solid surface.

SOLUTIONS

The mass of the body is constant as the number of particles in a body remains constant. Mass is constant everywhere
Up thrust and frictional force
By going between two moving parts so that the parts slid on oil instead of each other.
– Weight is a vector quantity while mass is a scalar quantity.

– Weight varies from place to place while mass is constant.

– Weight is measured using a spring balance while mass is measured using beam balance.

To lubricate the engine/ reduce frictional force
Magnetic, electrostatic and gravitational.
Kinetic energies of molecules increase hence the pressure increases.
Because gravitational force varies with distance from the centre of the earth. Since weight depends on the gravitational pull, then it also varies.
The soap reduces the surface tension and hence the weight of pin becomes greater the surface tension.
In (a) adhesive forces between glass and wax are weaker than cohesive forces between water & water. The opposite is true (b)
6m /s²
40N
Either altitude or latitude/ radius of earth changes/ acceleration due to gravity from place to place away from the earth
Addition of soap solution to pure water reduces the strength of the skin total was holding pin from sinking and so it sinks. Surface tension supports the pin. Addition of soap reduces tension/weakens/broken.
Acceleration of gravity on Jupiter is higher than that of earth, so a bag of saw dust must be less massive if the greater acceleration on earth is to produce the same pull as sugar bag on earth.
In (a) cohesive forces between water molecules are greater than adhesive forces between water and wax while in (b) adhesive forces between water and glass molecules are greater than cohesive forces between water molecules.
Surface tension / adhesive forces supports water column or more capillarity in tube 2 than tube 1Surface tension is the same in both tubes and equal to the weight of water column supported Narrow tube has longer column to equate weight to wider tube. Volume of water in the tubes is same hence narrower tube higher column

MORE QUESTIONS

Figure 2 shows a funnel dipped into a liquid soap solution.

Explain what happens to the soap bubble when the funnel is removed.

An alloy contains 40% by mass of lead and 60% by mass of tin. Determine the density of the alloy in kgm³. (Density of lead = 1 l.4g/cm³ and density of tin = 7.3g/cm³

The water level in a burette is 35cm³. If 20 drops of water are added, what is the new level if each drop has a volume of 0.15cm³? A cylinder of height 25cm is completely melted and a sphere of the same radius made. Determine the radius of the sphere in metres and express your answer in standard form.
The figure below shows the change in volume of a liquid in a measuring cylinder when an irregular solid is immersed in it.

Given that the mass of the solid is 540g, determine the density of the solid in g/cm³.

Figure 2 below shows a measuring cylinder containing some water.

New reading …………………
New reading

Another 10 cm³ of water was added to the cylinder from a burette delivering volume from 0cm³ to 50cm³. Record in the spaces provided the new reading indicated on each vessel.

Figure 1 shows a millimeter scale placed in a position to measure the length of a block. An observer takes readings from position A and then from position B

3cm

2cm

1cm

•

Fig 1

State the difference in readings.

Two burettes A and B were arranged as shown below.

Burette A leaked into burette B at a rate of 10 drops per minute. If the initial reading on both burettes was 25ml, what would be their readings at the end of one hour if B does not leak and the average volume of one drop of water is 2.0 x 10^-8m³?

State any two factors that determine the choice of instrument for measuring length
The figure 1 below shows the level of mercury and water in a beaker.

Water

Mercury

Explain the difference in the shape of the meniscus.

The figure below shows part of a measuring cylinder containing a certain liquid

Use this information to answer questions below

State the accuracy of the measuring cylinder
What is the volume of the liquid in the measuring cylinder?

TOPIC 4: PRESSURE

Pressure is the force acting normally (perpendicularly) per unit area. The SI unit of pressure is N/m² or Nm^-2, which is also called Pascal (Pa).

Pressure in solids depends on two main factors i.e. force and area

EXAMPLE 1

A force of 100N is applied to an area 100mm2. What is the pressure exerted on the area in Nm^-2.

Solution

Area; 100mm² = .0000001m² and Force = 100N

Pressure = F/A

= 100 ÷ 0.0000001

= 1.0 x 10⁹Nm^-2

A man whose mass is 90kg stands on a floor.

If the area of contact between his feet and the floor is 0.0368m², determine how much pressure he able to exert on the floor.

Pressure, P = F/A

= 900N/0.0368m²

= 24,456.5217N/m².

What pressure will he exert on the floor if now he stands on one foot?

Pressure, P = 900N/ (0.0368/2)

= 48,913.0435N/m²

MAXIMUM AND MINIMUM PRESSURE

Maximum pressure = Force

Minimum area

Maximum Pressure P_max = F

A_min

Minimum pressure = Force

Maximum area

Minimum pressure P_min = F/A_max.

EXAMPLE 2

A block of wood measures 2cm by 3cm by 4cm and has a mass of 6 kg.

Calculate its pressure when; a) Area is minimum (maximum pressure) b) Area is maximum (minimum pressure).

Area -2 x 3 =6cm2

-2 x 4 =8cm2

-3 x 4 =12cm2

A min =6cm2 =0.006m2 and F =60N

P max =60/0.006 =100,000Nm^-2

A max =12cm2=0.0012m2 and f = 60 N

P_min = 60/0.0012 =50,000Nm^-2

EXERCISE

A block of wood measures 3m by 6m by 2m and mass 3kg. Calculate;
Maximum pressure
Minimum pressure
A brick 20cm by 10cm by 5cm has a mass of 500g. Find maximum and minimum pressure. (take g = 10N/kg)
How much force must be applied on a blade of length 4cm and thickness 0.1mm to exert pressure of 5,000,000 Pa.?

Exercise 4.1 (no 1, 2, 3, 4, 5) KLB

PRESSURE IN LIQUIDS

Pressure in liquids depends on the following;

Ø Depth of the liquid

Ø Density of the liquid

Pressure in liquids increases with depth and density.

EXPERIMENT: To show variation of pressure in liquids

APPARATUS: A tall tin, nail and water

PROCEDURE

Using the nail, make 3 holes A, B, C of the same diameter on a vertical line of one side of the tin
Fill the tin with water as shown below.
Observe water jets from the holes A, B, C.

OBSERVATION

The lower hole, A, throws water farthest, followed by B and lastly by c

EXPLANATION

The pressure of water at A is greatest than pressure at B and pressure at B is greater than pressure at C. Hence, pressure increases with depth.

QUESTION

Explain why a diver at the bottom of the dam experiences greatest pressure

At the bottom of the dam depth is greatest and therefore the diver experiences greatest pressure due to the weight above him.

LIQUID LEVELS

When a liquid is poured into a set of connected tubes with different shapes, it flows until the level are the same in all tubes as shown

This shows that the liquid flows to find its own level.

LIQUID LEVELS IN A U-TUBE

When water is poured into a u-tube, it will flow into other arm. Water will settle in the tube with the levels on both arms being the same.

When one arm is blown into with the mouth, the level moves downwards, while on the other arm it rises. This is caused by pressure difference between the two arms as shown,

Pressure in liquids increases with depth below its surface

Pressure in a liquid at a particular depth is same in all directions.

Pressure in a liquid increases with density of the liquid.

FLUID PRESSURE FORMULA

Consider a container containing a liquid as shown below;

If A is the cross-section area of the column, h the height of the column and ρ the density of the liquid then;

Volume of the liquid = cross-section area x density

= Ah

Mass of the liquid = volume of the liquid x density

= A h ρ

Therefore, Weight of the liquid = mass x gravitational force

= A h ρ g

From definition of pressure P = force/area

Pressure = A h ρ g

= h ρ g

From the formula (p = h ρ g) pressure is directly proportional to;

Height of the column
The density of the liquid

NOTE: Pressure in liquids does not depend on the cross-section area of the container.

The formula is also used to determine pressure due to a gas column.

EXAMPLE 3

A diver is 10m below the surface of water in a dam. If the density of water is 1000kg/m3, determine the pressure due to the water on the diver. (Take g=10N/Kg)

Solution

Pressure = h ρ g

= (10 x 1000 x 10)

= 100,000 N/m2

EXAMPLE 4

The density of mercury is 13600Kg/m3. Determine the liquid pressure at a point 76cm below mercury level.

Solution

Pressure = hρg

= 0.76 x 13600 x 10

= 103,360 N/m²

EXAMPLE 5

Calculate the pressure due to water experienced by a diver working 15m below the surface. (Take g = 10N/kg and density of sea water = 1.03g/cm³)

TRANSMISSION OF PRESSURE IN LIQUIDS

Pressure applied at one part in a liquid is transmitted equally to all other parts of the enclosed liquid. (Plunger)

This is the principle of transmission of pressure in liquids called Pascal’s principle which states that pressure applied at a given point of the liquid is transmitted uniformly or equally to all other parts of the enclosed liquid or gas.

Gases may transmit pressure in a similar way when they are confined and incompressible.

HYDRAULIC MACHINES

The principle of transmission of pressure in liquids is made use in hydraulic machines where a small force applied at one point of a liquid produces a much larger force at some other point of the liquid.

HYDRAULIC LIFT

The hydraulic lift consists of a small piston S of cross-section A1 and a large piston L of cross-section area A₂. When a force is applied on piston S, the pressure exerted by the force is transmitted throughout the liquid to piston L.

At the smaller piston S the force applied F₁ cause a pressure P₁ at the cross section area A₁.

Therefore, Pressure P₁= F₁

A₁

The pressure is equally transmitted throughout the liquid to the larger piston.

Thus at small piston pressure is equal to the pressure at the large piston

F₂= P₁ x A₂

But, P₁ = F₁

A₁

F₂= F₁ x A₂

A₁

F₂ = A₂

F₁ A₁

NOTE; Equation applies if pistons are at the same level

EXAMPLE 6

Find F₂ if A₁ = 0.52m², A₂ = 10m²and F₁= 100N

F₂ = 10

100 0.25

F₂= (100 x 10)

0.25

= 4000N

EXAMPLE 7

Determine f2 in the figure below. Density of the liquid =800kg/m3 and

g=10N/kg

Pressure at A, P_A= Pressure at B, P_B

(60 x 10) = (F₂) + (0.15 x 800 x 10)

0.008 0.00025

0.00025(7500 -1200) = F₂

F₂= 18.45N

Exercise 4.2 no.7

HYDRAULIC BRAKE SYSTEM

The force applied on the foot pedal exerts pressure on the master cylinder. The pressure is transmitted by the brake fluid to the slave cylinder. This causes the pistons of the slave cylinder to open the brake shoe and hence the brake lining presses the drum. The rotation of the wheel is thus resisted. When the force on the foot pedal is withdrawn the return spring pulls back the brake shoe which then pushes the slave cylinder piston back.

Advantage of this system is that the pressure exerted in master cylinder is transmitted equally to all four wheel cylinders.

The liquid to be used as a brake fluid should have the following properties;

Be compressible, to ensure that pressure exerted at one point is transmitted equally to all other parts in the liquid
Have low freezing point and high boiling point.
Should not corrode the parts of the brake system.

ASSIGNMENT (exercise 4.2 no 1, 2, 3,4,5,6 & 8) KLB

ATMOSPHERIC PRESSURE

Atmosphere means the air surrounding the earth. The air is bound round the earth by the earth’s gravity. The atmosphere thins outwards indicating the density of air decreases with the distance from the surface of the earth

The pressure exerted on the surface of the earth by the weight of the air column is called air pressure

Atmospheric pressure can be demonstrated by crushing can experiment.

EXPERIMENT: To demonstrate the existence of the atmospheric pressure

APPARATUS: Tin container with a tight-fitting cork, water, tripod stand, Bunsen burner.

PROCEDURE

Remove the cork from the container and pour in some little water.
Boil the water for several minutes.
Replace the cork and allow the container to cool or pour cold water to cool it faster.

OBSERVATION

During cooling, the container crushes in.

EXPLANATION

Steam from boiling water drives out most of the air inside the container. When heating, the steam pressure inside the container balances with atmospheric pressure outside.

On cooling the steam condenses. A partial vacuum is therefore created inside the container. Since pressure inside the container is less than the atmospheric pressure outside, the container crushes in.

NOTE: Steam inside the container condenses lowering the pressure. The outside atmospheric pressure exceeds the pressure inside the container thereby crushing it.

MAXIMUM COLUMN OF LIQUID THAT CAN BE SUPPORTED BY

ATMOSPHERIC PRESSURE

When water is sucked up a straw, the air inside the straw reduces. The atmospheric pressure acting on the surface is now greater than the pressure inside the straw. Water is thus pushed up the straw by atmospheric pressure.

If the straw was long enough and sealed at the top, it would be possible to estimate the height of water that would be supported by atmospheric pressure

In case of water the column is too large.

At sea level the atmospheric pressure supports approximately 76cm of mercury column or approximately 10m of water column.

EXAMPLE 8

A girl in a school situated in the coast (sea level) plans to make a barometer using sea-water of density 1030 kg/m³. If atmospheric pressure is 103,000 N/m², what is the minimum length of the tube that she will require?

Solution

P = h e g but p is atmospheric pressure

103,000 = h x 1030 x 10

H = 10m

EXAMPLE 9

A sea diver is 35m below the surface of sea water. If the density of the sea water is 1.03g/cm³ and g=10N/kg. Determine the total pressure on him.

Solution

Total pressure, P_T = Pa + h e g

= 103,000 + (35 x 1030 x 10)

= 463,500N/m²

EXAMPLE 10

The air pressure at the base of a mountain is 75cm of mercury while at the top is 60cm of mercury. Given that the average density is 1.25kg/m³ and density of mercury is 13,600kg/m³. Calculate the height of the mountain.

Solution

Pressure difference due to column of air = pressure difference due to mercury column

h_aρ_ag = h_m ρ_m g

h_a= h_mρ_m g

ρ_a g

h_a = (0.15 x 13600 x 10)

(1.25 x 10)

= 1632m

EXERCISE

The barometric height at sea level is 76cm of mercury while that at a point on a highland is 74cm of mercury. What is the altitude (height) of the point? Take g =10N/kg, density of mercury =13600kg/m³ and density of air =1.25kg/m³.
A student in a place where the mercury barometer reads 75cm wanted to make an alcohol barometer, if alcohol has a density of 800kg/m³, what is the minimum length of the tube that could be used?

MEASUREMENT OF PRESSURE

THE U-TUBE MANOMETER

Is an instrument used to measure fluid pressure.

It consists of a u-tube filled with water or any other suitable liquid or gas as shown

Pressure at Z = Atmospheric pressure due to column of water.

Pressure at X = pressure at Z

Pressure at X = P_g

Pressure at Z = atmospheric pressure + pressure due to column of water

P_g = P_a + h ρ g.

Since the density of water and gravitational force is known we can determine pressure of a gas if the atmospheric pressure is known.

EXAMPLE 11

Suppose h=20cm, Pa = 103,000N/m² and density=1000kg/m³, determine the total pressure (P_g)

Solution

P_g = 103,000 + (0.2 x 1000 x 10)

= 105,000N/m²

SIMPLE MERCURY BAROMETER

At sea level atmospheric pressure supports approximately 76cm of mercury column or 10m of water column. This difference in height column between mercury and water is that mercury is much denser than water.

Mercury column forms a simple barometer, its height changing inside on the glass tube as air pressure outside changes.

The space above mercury in the barometer tube must contain air or water vapour since the barometer reading will be as shown above.

The space above in mercury in the tube when upright is called toricellian vacuum

The height h of the column is a measure of the atmospheric pressure.

At sea level, h=76cm since density of mercury = 13600kg/m³.

Atmospheric pressure, Pa = h ρ g

= 0.76 x 13600 x 10

= 103,360N/m² (it is also referred as one atmosphere 1 atm)

FORTIN BAROMETER.

This is an improved version of a simple mercury barometer. Was designed by

FORTIN

The ivory pointer acts as the zero mark of the main scale. The leather bag acts as reservoir of mercury height.

Before taking the reading, the level of mercury surface in the reservoir is adjusted by turning the adjusting screw until the surface of mercury just touches the tip of the ivory index.

The height is the read from the main scale and vernier scale. The readings obtained from the barometer are in terms of the height of mercury column and written as mmHg or cmHg.

For example at sea level h=760mmHg and density of mercury=13600kg/m3

Pa = h ρ g

= 0.76 x 13600 x 10

= 103,360Nm^-2

ANEROID BAROMETER

Is a portable type of barometer consisting of a sealed, corrugated metal box as shown below

The pointer would indicate a particular value of atmospheric pressure of the surrounding so that any changes in pressure would be noticeable by movement of the pointer to either side of this atmospheric value on the scale.

The aneroid barometer movement makes it adaptable to measure heights.

Aneroid barometers (Altimeters) are used in aircrafts to measure heights. Its normally calibrated in millibars. 1 bar=100,000Nm^-2

1millibar (mbar) = 100Nm^-2

PRESSURE GAUGES

They are portable and are used mostly for measuring gas pressure, tyre pressure, pressure of compressed air compressors and steam pressure

It is made of coiled flexible metal tubes which uncoil when the pressure inside increases. The movement of the tube is made to drive a pointer across a scale, through a combined system of levers and gears.

EXAMPLE 12

The pressure of a car tyre, measured with a pressure gauge is 40Ncm-2. What is the total pressure of the tyre in Nm^-2?

P_Total= P_a +gauge pressure

= 103,360 + (40 x 10,000)

= 503,360Nm-2

APPLICATION OF PRESSURE IN LIQUIDS AND GASES

THE BICYCLE PUMP

A bicycle pump is a simple form of compression pump.

The pump is connected to a tyre which has a rubber valve in it. When the pump handle is drawn out air below the washer expands and its pressure is reduced below the atmospheric pressure.

Air from outside the pump the flows past the leather washer into the barrel. The higher air pressure in the tyre closes the tyre valve.

When the pump handle is pushed in, the air in the pump barrel is compressed.

The high pressure in the barrel presses the leather washer against the sides of the barrel. When the pressure of the compressed air becomes greater than that of air in the tyre, air is forced into the tyre through the tyre valve which now opens.

NOTE: There is an increase in temperature of the pump barrel during pumping because work is done during compressing the air.

THE LIFT PUMP

It is used to raise water from wells. It consists of a cylindrical metal barrel with a side tube. It has two valves P & Q.

UPSTROKE

When the plunger moves during upstroke, valve P closes due to weight and pressure of water above it. At the same time, air above valve Q expands and the pressure reduces below atmospheric pressure.

The atmospheric pressure on the water surface in the well below this pushes water up past valve Q into the barrel. The plunger is moved up and down until the space between P and Q is filled with water.

DOWNSTROKE

During down stroke valve Q closes due to its weight and pressure of water above its piston.

Limitations of Lift Pump

The atmospheric pressure support only 10m column of water, which is actually a theoretical value but practically this pump raises the water less than 10m because of;

Low atmospheric pressure in places high above sea level.
Leakages at the valves and pistons

FORCE PUMP

This pump can be used to raise water to heights more than 10m.

UPSTROKE

During upstroke, air above the valve S expands and its pressure reduces below atmospheric pressure. The atmospheric pressure on the water in the well below pushes water up past valve S into the barrel.

NOTE: Pressure above valve T is atmospheric hence the valve does not open.

DOWNSTROKE

During down stroke, the valve S closes. Increase in pressure in the water in the barrel opens valve T and forces water into chamber C so that as water fill the chamber air is trapped and compressed at the upper part.

During the next stroke, valve T closes and the compressed air expands ensuring continuous flow.

Advantages of a Force Pump over a Lift pump

Force pump enables continuous flow of water.
Height to which water can be raised does not depend on the atmospheric pressure. It depends on;
Amount of forces applied during down stroke.
Ability of the pump and its working parts to withstand pressure.

THE SIPHON

A tube can be used to empty tanks or draw petrol from petrol tanks in cars.

When used in this way it is referred as a siphon

Pressure on the surface of the liquid is atmospheric pressure. Since end C of the tube is below the surface A by height h, pressure at C is greater than that at the surface.

The tube is first filled with the liquid after which it will continue to run so long as end C is below the liquid surface.

Pressure at C = pa + h e g. The excess pressure (h e g) cause the liquid to flow out of end C

The siphon will work only if;

End of the tube C is below the surface of A of the liquid to be emptied.
The tube is first filled with the liquid, without any bubbles in it.
The tube does not rise above the barometric height of the liquid from the surface A of the liquid to be emptied.
One end of the tube is inside the liquid to be emptied.

NOTE: A siphon can operate in a vacuum.

REVISION QUESTIONS

The atmospheric pressure on a particular day was measured as 750mmHg. Express this in Nm-2. (Density of mercury = 13600kg/m³ and g=10N/kg)

Solution

P = h e g

= 0.75 x 13600 x 10

A roof has a surface area of 20,000cm². If atmospheric pressure exerted on the roof is 100,000Nm^-2, determine the force on it. (Take g = 10N/kg)

The diagram below shows a simple barometer

(i)Name the part labeled A

(ii)Explain what would happen to the level of mercury in the tube if the barometer was taken high up the mountain

Force applied to brake pads

Figure 2 below represents a car hydraulic braking system.

Fluid

Slave piston

Master piston

Foot pedal

Use the information given in the diagram above to answer questions

a) State one property the fluid should have.
b) Explain briefly how the system operates.
The diagram below shows a water tank of height h?

What is the relationship between the velocity V of the water jet and the height h

State the possible reason why, if water is used as a barometer liquid, the glass tube required to hold the column of the liquid is longer
State the definition of atmospheric pressure
What is the density of alcohol?
A person’s lung pressure as recorded by a mercury manometer is 90 mm Hg. Express this pressure in SI units.
The barometric height at sea level is 76cm of mercury while at a point on a highland it is 74cm of mercury. What is the altitude of the point? (Take g = 10m/s^2, density of mercury = 13600kg/m³and density of air as 1.25kg/m³)
Figure 4 below shows a measuring cylinder of height 30cm filled to a height of 20cm with water and the rest occupied by kerosene

Fig. 4

Given that density of water = 1000Kgm^-3, density of kerosene = 800Kgm^-3 and atmospheric pressure = 1.03×10⁵ Pa, determine the pressure acting on the base of the container

State Pascal’s principle of transmission of pressure
A helical spring extends by 1 cm when a force of 1.5N is applied to it. Find the elastic potential energy stored in it.
Two immiscible liquids are poured in a container to the levels shown in the diagram below.

If the densities of the liquids A and B are 1g/cm³ and 0.8g/cm³ respectively, find the pressure acting upon solid C at the bottom of the container due to the liquids

Mark the position of the water levels in the manometer when the gas supply is fully turned on
Calculate the pressure of the gas supply (Atmospheric pressure = 1.0×10⁵Pa)

A small nail may pierce an inflated car tyre and remain there without pressure reduction in the tyre. Explain the observation
(a) State two ways of increasing pressure in solids

(b) The figure 1 shows a liquid in a pail

Suggest a reason why pail manufacturers prefer the shape shown to other shapes

A block measuring 20cm x 10cm by 5cm rests on a flat surface. The block has a weight of 3N. Determine the maximum pressure it exerts on the surface.

(Effort)

10KN

LOAD

Liquid X

60cm

The figure below shows a hydraulic press P which is used to raise a load of 10KN. A force F of 25N is applied at the end of a lever pivoted at O to raise the load

(a) State one property of liquid X

(b) Determine the distance x indicated on the press if force on piston B is 100N

Mercury –in-glass barometer shows a height of 70cm. What height would be shown in the barometer at the same place if water density 1.0 x 10³kg/m³ is used. (Density of mercury = 13600kgm^-3)
The total weight of a car with passengers is 25,000N. The area of contact of each of the four tyres with the ground is 0.025m². Determine the minimum car tyre pressure
(a) The diagram below represents a u-shaped glass tube sealed at one end and containing mercury

(i) What is the pressure of the gas as shown in the diagram above?

(ii) Explain why the gas should be dry if it is to be used to verify a gas law

(iii) Describe how the arrangement can be used to verify Boyle’s law.

(b) Use the kinetic theory of gases to explain why;

(i) The pressure of a gas increases with temperature increase

(ii) The pressure of a gas decreases as volume increases

The reading on a mercury barometer at Mombasa is 760mm. Calculate the pressure at Mombasa (density mercury is 1.36xl0⁴Kgm^-3 )
The figure below is a manometer containing water. Air is blown across the month of one tube and the levels of the water changes as the figure below.

Blow air

Explain why the level of water in the right limb of manometer is higher.

In the diagram below, the U-tube contains two liquids; X and Y which do not mix. If the density of liquid Y is 900Kgm^-3 and that of X is 1200Kgm^-3, calculate the height of liquid Y

SOLUTIONS

Because of its low density
Atmospheric pressure is the pressure exerted on the surface of the surface of the earth by the weight of the air column
h_wƍ_wg = h_wƍ_wg

∴ h_wƍ_w =h_aƍ_a

Density of alcohol = 16 cm x 1g/cm³ x 1000

20 cm

= 800 kgm^-3

P = h ƍ g

= 90 m x 13600kgm^-3 x 10Nkg^-1

1000

= 12 240 Nm^-2

(76 – 74) X 13600 X 10 = h X 1.25 X 10

100

H = 2 X 13600

100 1.25

= 217. 6 m

Pressure due to kerosene = h kg

= 800 x 0.1 x 10 = 800p.aÖ1

Pressure due to water = w h w g

= 1000 x 0.2 x 10 = 2000p.aÖ1

Atmospheric pressure = 103,000p.a

Total pressure = 800 + 2000 + 103000

= 105800 Pa

Pressure applied at one pat in a liquid is transmitted equally to all other parts of the enclosed
Pressure on = L f g

Solid at c = (0.02 x 1000 x 10) + (0.04 x 800 x 10);

= 200 + 320

= 520 N/m²

Difference in the level of water should be 20cm
Pressure of the gas = Atmospheric pressure + ehg;

= 1.0 x 10⁵ + 20 x 1000 x 10

100

= 1.0 x 105 + 2.0 x 103Nm^-2

= 1.02 x 105Pa;

– Rubber is elastic; and when a nail is pushed through it stretches and grips firmly the nail without allowing air leakage; or – Valve effect pressure from inside causes tyre rubber to press firmly on the nail;
(a) – Increasing the force (weight)

(b) Slanting sides increase the area supporting the weight of the liquid, hence its effect

on the bottom of the container

Max pressure = ^Force/_{Min Area} Ö 1

= ^3N/ 0.1 X _0.05Ö1

= 600N/m² Ö 1

(a) – Incompressible

– Not corrosive

– Has low freezing point and high boiling point (any one)

h₁p₁g = h₂p₂g

h₂ = h₁p₁

p₂

= 0.7 x 13600Kg/m³

1000kgm^-3

= 9.52m

Pressure = Force

Area

= 2500

4 x 0.025

= 250,000Pa

a) i) Atmospheric pressure 1.05 x 10⁵N/M²
ii) Any water vapour available is near its condensing point. Intermolecular forces

are therefore appreciable Ö, so it does not behave like an ideal gas

iii) – Fix a millimeter scale to read the length ( L) of air column B Ö and the difference in height (h) between the levels A and CÖ

– Adjust the level of C by adding more mercury a little at a time and record the

corresponding values of L and h each time Ö

A graph of L against h represents Boyle’s law Ö
i) Increase in temperature causes gas molecules to move faster(increases in kinetic energy), Ö hence they generate greater/ higher impulsive force on impact Ö
With increase in volume gas molecules are sparsely spaced Ö so the rate of collision is reduced/ lowered

MORE QUESTIONS

The total weight of a car with passengers is 25000N. The area of contact of each of the FOUR tyres with the ground is 0.025m².

Determine the minimum car tyre pressure.

I Write an expression for pressure on a liquid in hydraulic jack
II While using a jack, a mechanic applied a force of 100N on the effort piston while raising the rear part of a car.

Determine the maximum load that can be raised
Give a reason why gas is not suitable for use in place of the liquid in a jack.

The lift pump is effective for pumping water as long as the well is less than 10m deep. Explain.
The reading on a mercury barometer at Mombasa is 760mm. Calculate the pressure at Mombasa (density of mercury = 1.36 x 10⁴ Kgm^-3)
State one property of a barometer liquid and explain its effects.

Figure 1 below shows a liquid being siphoned from one beaker to another. Refer to this diagram where answering questions 5, 6 and 7

Indicate on the diagram the direction of flow of the liquid
Show that the force driving the liquid through the U – tube is proportional to the height, h
State what would happen to the flow if the system in figure 2 were put in vacuum.
Figure above shows a U tube containing two liquids L1 and L2 of densities 0.8 g cm^-3 and 1.8 cm^-3 respectively in equilibrium. Given that h2 = 8 cm determine the value of h1
A small nail may pierce an inflated car tyre and remain there without pressure reduction in the tyre. Explain this observation
The height of the mercury column in a barometer at a place is 64cm. What would be the height of a column of paraffin in barometer at the same place? (Density of paraffin = 8.0 x 102 kgm^-3)
A vacuum pump was used to pump out air from the glass tube immersed in liquids as shown in figure 3.

After sometime the level of paraffin rose to position X. Mark the corresponding position for the water level. Give a reason for your answer.

A hole of area 2.0 cm²at the bottom of a tank 2.0m deep is closed with a cork. Determine the force on the cork when the tank is filled with water. (Density of water is 1000kg/m³ and acceleration due to gravity is 10m/s²).
The reading on a mercury barometer at a place in 700mm. What is the pressure at the place Nm^-2 (Density of mercury is 1.36 x 104 kgm^-3)
In an experiment to demonstrate atmospheric pressure, a plastic bottle is partially filled with hot water and the bottle is then tightly corked. After some time the bottle starts to get deformed

(a) State the purpose of the hot water.

(b) State the reason why the bottle gets deformed. Explain your answer.

Figure 4 shows a lift pump.

(a)Explain why, when the piston is;

i) Pulled upwards, valve A opens while valve B closes.
ii) Pushed downwards, valve A closes while valve B opens.
After several strokes, water rises above the piston as shown in Figure 5.
State how water is removed from the cylinder through the spout.
c) A lift pump can lift water to a maximum height of 10m.

Determine the maximum height to which the pump can raise paraffin. (Take density of paraffin as 800kgm^-3 and density of water as 1000kgm^-3).

State one factor that determines the height to which a force pump can lift water.
Explain why a dam is thicker at its base than at the top.
The pressure exerted by the atmosphere on a table is 100,000Pa. What does this mean?
On a dining table of area 1m², air pushes down with force of 101,000N (atmospheric pressure = 101,000Pa). Explain why the table does not collapse or break.
Explain why the level of mercury in a mercury barometer varies from day to day.
If atmospheric pressure is 101,000 N/m², what force is exerted on a wall of area 12m²?
Explain why you can fill a bucket from a downstairs tap quicker than from an upstairs tap
Explain why a giraffe must have a stronger large heart compared to a human being.
State why a barometer will show a greater reading when taken down a 200m pit.
A hydraulic press has the small piston of area 5cm² and a force of 40N is applied to it.
(i) Calculate the pressure transmitted throughout the liquid.

(ii) If the larger piston has an area of 20cm², what is the force exerted on it?

Explain why a sharp knife cuts well than a blunt one.
State Pascal’s principle of pressure.
Explain why the atmospheric pressure decreases with increasing the height or altitude.
Explain why we do not feel the great air pressure around us.
Why do deep sea divers wear diving suits?
Why are planes pressurized?
Explain how a drinking straw operates when in use.
Explain how a syringe operates when being used.
Describe the working of a hydraulic press
Study the diagram below:

ρ₁ρ₂20cm

h₁

If ρ₁= 2000kg/m³ and ρ₂ = 1500kg/m³, calculate h₁.

Explain why walking on a murrum road in bare feet is more painful than walking on sand.
A pressure of 2000Pa acts on an area of 0.05m². What force is produced?
At sea level, what is the approximate value of atmospheric pressure in

(a) Pa

(b) MmHg

Why is mercury used in a barometer rather than water?
Study the diagram below:

65 Mercury

Gas supply

40cm meter rule

(a) Record the excess pressure shown by the meter in mmHg

(b) If the atmospheric pressure is 760mmHg, what is the pressure of the gas supply?

State one advantage of fitting wide tyres on a vehicle that moves on earth roads.
A small nail may piece an inflated car tyre and remain there without pressure reduction in the tyre. Explain this observation.
The height of the mercury column in a barometer at a place is 74cm. What would be the height of a column of a water barometer at the same place? (Density of mercury is 13.2g/cm³ and water 1g/cm³.)
Explain why it may not be possible to suck a liquid into your mouth using a drinking straw on the moon surface
Derive the formula P=h ρ g where P = pressure, h = height or depth, ρ = density of liquid and g = gravity.
The figure below shows a manometer connected to a small funnel whose mouth is covered by a rubber membrane. The funnel is dipped into water in a container.

h₁

Water

Mercury

3.0m

Rubber and funnel

(a) Given that the density of mercury is 13.6g/cm³ and that of water is 1g/cm³, determine the pressure indicated by the manometer.

(b) Determine the height h₁.

The diagram below shows a liquid being siphoned from one beaker to another. Use this information to answer the questions that follow:

(a) Indicate on the diagram the direction of flow of the liquid

(b) Show that the force driving the liquid through the pipe is proportional to the height h.

State and explain what would happen to the flow in question 2 above if the system in the diagram were put in a vacuum.
Give a reason why water is not a suitable liquid for a barometer.
A rectangular block measures 10cn x 5cm x 4cm and has a mass of 2.2kg.
a) (i) If the gravitational field intensity is 10N/kg, what is the weight of the block?

(ii) What is the area of the smallest face of the block?

(iii) What pressure will the block exert when it is resting on a table on its smallest face?

(iv) What is the least pressure the block exerts on the table?

(b) Calculate the volume of the block.

A diving bell is pressurized inside to a pressure of 1,000,000Pa above atmospheric pressure. This diving bell is made for use at 100m below the sea surface for oil exploration. The pressure outside the diving bell must be equal to the pressure inside for its door to open. (Opens from inside.)
1. Calculate the pressure at 100m depth in water.
2. Explain what would happen to the diving bell when the door opens at :
  1. 10m below the surface.
  2. 200m below the surface.

When the diving bell is under the sea, how is the pressure on top of it different from that underneath it?

Explain why the pressure difference in (c) produces buoyancy (upthrust).

Study the figure below:

The piston can be pushed in and out but no water can escape. If the larger piston is pushed into the pipe by a force of 200N,

Calculate the pressure applied to the water.
Determine the force exerted on the smaller piston.

pipe

Piston area 500cm²waterpiston area120cm²

(a) The figure below shows two cylinders connected by a pipe. in each cylinder there is a piston and the space below each piston is full of water.

10kg mass

P Q

Water

The area of piston P is 40cm² and the area of piston Q is 2500cm². A 10kg mass is placed on piston P.

Calculate the weight of the 10kg mass.
What is the downward force on piston P.

Determine the pressure on the water

State the pressure on the water at Q.
Calculate the upward force on Q.

(b) Kamau suggested that the above device could be used as a car jack.

Which piston (A, or B) would you use to support the car? Explain your answer.
Name the above device.
(a) If a lorry weighs 100,000N and has 4 tyres.
- Calculate the force exerted on the road by each tyre
- What assumption have you made in the calculation above
- If each tyre has an area of 0.2m² in contact with the road, calculate the pressure exerted.

(b) Using a diagram, explain how a bicycle pump operates when filling a tyre with air.

clip

30cm 50cm

Density density (ρ)

1000kg/m³

Calculate the density ρ of the other liquid.

(a) A car containing six adults and their luggage weighs 20500N. The area of contact of each tyre with the ground is 0.025m².
- Calculate the pressure exerted by each tyre on the ground.
- State any two assumptions made.
- The car has to be driven off the road and cross a patch of soft damp sand. The driver thinks that the tyres will sink into the sand and stop the car moving. One of the passengers suggests that the sinking can be prevented by letting some air out of the tyres.
  - I What effect would this have on the shape of the tyres?
  - II How would letting air out of the tyres stop the wheels from sinking.
  - III What other change could be made to stop the tyres sinking into the sand.
- The air pressure near the ground is about 101KPa. Some aircrafts fly at height of about 20km where the air pressure is only 27KPa.
  1. State two reasons why the outside air pressure is less at 20km than at the ground.
  2. If the air inside the aircraft is 101KPa, what is the difference in air pressure between the inside of the aircraft when fling at a height of 20km?

How does this difference in air pressure influence the choice of material used in the construction of the aircraft.

The door of the aircraft is designed to fit into the door frame from inside the aircraft. Explain why the door is designed to fit in this way.
If the fuselage of the aircraft has an area of 4000m², determine the force acting on the fuselage due to the difference in air pressure between the inside and outside of the aircraft at a height of 20km.

(a) The diagram below shows a manometer connected to a gas supply.

Gas in

U – Tube

The pressure of the gas supply above atmospheric pressure is equivalent to 20cm column of water.

Complete the diagram by marking the position of the levels of the water in the manometer when the gas supply is connected.
If the gas supply had only been partly turned on, what effect, if any, would this have had on the levels of the water in the manometer? Explain your answer.

Calculate the pressure of the gas supply above atmospheric pressure in Pascal’s. (ρ_w=1000kg/m³ )

(b) The diagram shows water standing to a depth of 20cm in a measuring cylinder. There are 500cm³ of water in the measuring cylinder.

Water 20cm

I If the density of water is 1g/cm³, calculate the mass and weight of the water in the measuring cylinder
II Using the weight in part (i), calculate the pressure exerted by the water on the bottom of the measuring cylinder.
III Mark with a letter P on the diagram above a position where the pressure exerted by the water is a quarter of the pressure calculated in part (ii)

a) A newspaper article claimed that a woman wearing shoes with heels which had a small area exerted more pressure on the ground than a n elephant.
- Explain in terms of the area how this is possible.
- The article claims that the pressure exerted on the ground by a woman weighing 600N wearing shoes with heels each having an area of 0.9cm² was 666.7N/m². What assumption was made about the way the woman was standing? Explain your answer.
- A typical elephant weighs 30,000N. If each of the elephant feet has an area of 600cm², calculate the pressure exerted by the elephant on the ground.

(b) A water storage tank is 20m above a tap. Given the density of water as 1g/cm³,

Calculate the pressure of the water at the tap in N/m².
The area at the end of the tap is 2.0x m²; calculate the force needed to stop the water leaving the tap.

When a shower is directly connected to another water storage tank, it is found that water will only flow when the shower head is lowered and not when it is raised. Why is this so? In which way can this problem be overcome?

(a) Describe a laboratory experiment to show that the pressure in a liquid increases with depth.

(b) The experiment in (a) is repeated with a liquid of lower density. What effect, if any, does this have on the pressure at different depths? Explain your answer.

Taken into account when constructing the wall of a dam.
Used in the measurement with a manometer of the excess pressure of the gas supply.

(b) The diagram below shows the inner details of a device called bourdon gauge which can be used to measure air pressure.

B C Pivots

Scale Flexible tube

Air pressure

As the air pressure increases the flexible tube straightens out. Explain why the pointer moves towards B when the air pressure increases.

The graph below shows how the pressure in water changes with depth below the water surface of a creek.

Pressure (kPa)

(880, 960)

(0, 100) Depth (m)

Use the graph to find the pressure at a depth of 800m.
Calculate the force exerted by the water on 2.0m² of the outside surface of a submarine at a depth of 800m.

State why the pressure is not zero at the surface of the water.

The part of the submarine containing the crew contains air at normal atmospheric pressure. Explain why the outside walls of this part of the submarine are usually made from very thick steel.
Explain why at a depth of 100m the pressure in sea water is different from lake water.
The diagram below shows a water storage tank supplying water to a tap at A.

Water storage tank

B A

If the water level in the tank is 4m above tap at A, calculate the pressure at A due to this water. (density of water = 1000kg/m³)
The tap is moved from A to B. Explain why the water pressure at the tap is unchanged.

The diagram is drawn to scale. An object becomes stuck in the pipe at C and the water is unable to flow to the tap. Calculate the pressure at C due to the water and explain your calculation.

If the cross section area of the pipe is 1.2x m², what force is acting on the object at C due to the water above it?
A pressure sensor attached to an airbag can be used to determine the weight of passengers in a train carriage. See diagram below.

Movable floor

Pressure sensor

Trail

In a trial using different number of passengers in a carriage the following results were obtained.

Numbers of passengers in a carriage	20	40	60	80	100	120
Pressure in MPa	8.8	11.2	12.2	14.0	15.0	16.8

Plot a graph of pressure (y-axis) against the number of passengers in the carriage.
What is the pressure when we have 55 passengers in the carriage?

Explain why
1. The graph does not pass through the point (0,0)
2. The points do not lie on a straight line
3. Similar readings would have been obtained if the pressure sensor had been placed at the other end of the airbag.

Rubber sucker– this is a shallow rubber cap. Before use it is moistened to get a good seal then pressed firmly on a smooth surface so that the air inside is pushed out. The atmospheric pressure will then hold it firmly against the surface as shown below. They are used by printing machines to lift papers, lifting glass panes, heavy metal sheets

-Drinking straw– when a liquid is drawn using a straw air is sucked through the straw to the lungs. This leaves the space in the straw partially evacuated. The atmospheric pressure pushing down the liquid in the container becomes greater than the pressure inside the straw and this forces the liquid into your mouth.

-The syringe– they work in the principle as the straw. They are used by the doctors in hospitals for giving injections.

State two reasons why mercury is preferred as a barometric liquid and not water
The diagram in figure 5 below shows hydraulic brake system.

Oil

Master cylinder

Slave piston

5000N

Foot pedal

Fig 5

A force of 20N is applied on the foot pedal to a piston of area 50cm² and this causes a stopping force of 5000N.

Determine;

Pressure in the master cylinder.
Area of the slave piston.

The height of mercury column in a barometer density 13600kg/ m^-3, at a place is 64cm. What would be the height of a column of paraffin in barometer at the same place?

(Density of paraffin = 8.0 x 10² kg /m³).

The figure 3 shows hydraulic press system using a lever of negligible mass, on the ride of the small piston pivoted at a point P. A force of 50N is applied at R.

Oil

Weight

Area 100cm²

Area 5cm²

50N

Calculate

Force exerted by small piston on the liquid.
Pressure of liquid below the small piston.
The weight of object supported on the larger piston

Water tanks in houses are erected as high as possible. Explain.

– Water will flow at high pressure√¹

Or- for water to have high potential energy √

The figure below is a gas jar completely filled with water and covered with a wire gauze.

Water

State the observation when the set-up is suddenly inverted.
Explain the observation made in (a) above.

TOPIC 5: PARTICULATE NATURE OF MATTER

Matter is anything that occupies space and has mass. Matter commonly exists in three states i.e. solid, liquid and Gas

The process of sub-dividing matter into smaller units and smaller units continues indefinitely, suggesting that matter is not continuous, but is made up of even smaller parts e.g. A piece of paper can be cut endlessly until a stage when the small pieces cannot be cut into pieces. This suggests that the sheet of paper is made up of tiny particles

DEMONSTRATION OF DILUTION

APPARATUS: Beaker and potassium permanganate crystals

PROCEDURE

Pour water into the beaker to half full.
Dissolve the potassium permanganate crystals until the solution is purple.
Transfer half of the solution to another beaker and add water
Continue the process with other beakers, comparing the colour to each other.

OBSERVATION

The process of dilution can continue until the solution appears colourless. This suggests that the particles of potassium permanganate are spread evenly on water.

As water particles increase, the particles of potassium permanganate are spread further, making the purple colourless and less until it appears colourless.

CONCLUSION

Potassium permanganate is made up of tiny particles.

DISSOLVING A SOLID IN A SOLVENT

100g of salt is put into the flask and water added carefully using a pipette without shaking the salt until it is full.
The stopper is then inserted to the mouth of the flask and shaken to dissolve the salt.

OBSERVATION

The volume of the solution of salt is less.

CONCLUSION

Particles of salt are able to occupy some spaces between the water particles.

This suggests that the particles of salt differ in size.

The particles of the solution pack more closely in the available space, thus reducing the volume. This further suggests that particles of salt are broken down to fit into spaces between water particles.

BROWNIAN MOTION

This is the random movement of particles of a substance in fluids. A fluid is anything that is capable of flowing, e.g. a gas or a liquid.

The particles in a fluid are in a constant random motion.

BROWNIAN MOTION IN LIQUIDS

DEMONSTRATION OF THE BROWNIAN MOTION

Apparatus: Beaker, hand lens, chalk dust, transparent lid.

PROCEDURE

Pour water into the beaker about full as shown

Sprinkle pollen grains or chalk dust on the surface of water (particles should be small in size, light and sprinkled evenly).
Cover the beaker with a transparent lid and with the help of a hand lens observes what happens to pollen grains or chalk dust.

OBSERVATION

The pollen grains or chalk dust is in constant random motion.

CONCLUSION

The particles are hit continually by the movement of small invisible particles of water. The movement is random, suggesting that the particles of water are in constant random movement. This kind of movement is called Brownian motion a tribute to a scientist Robert Brown who first observed the effect.

BROWNIAN MOTION IN GASES

THE SMOKE CELL EXPERIMENT

DEMONSTRATION OF THE BROWNIAN MOTION IN AIR

Apparatus: Drinking straw, smoke cell, microscope and a bright light source

In this case, one end of the straw is burnt and let the smoke from the other end of the straw into the smoke cell as shown above. The smoke is then covered using a transparent glass lid. The smoke cell is covered to seal the content of the smoke cell. This ensures that the smoke molecules do not escape from the smoke cell. The lid is transparent to allow for easy visible of the smoke cell. The cell is illuminate with bright light. Therefore, the work of lamp in this case is to provide light which illuminates the content of the smoke cell. A hand lens is used to focus the light on the smoke particles in the smoke cell. The microscope is adjusted until bright specks are seen against the grey background. The work of the microscope is therefore to enlarge/magnify the smoke particles in the smoke cell for easy visibility.

OBSERVATION

In this experiment, the smoke particles (which are seen as bright specks) are seen moving in continuous random motion.

EXPLANATION

The smoke particles appear as bright specks since they scatter the light shining on them and appear as bright points. They move about in a continuous random movement because of uneven bombardment by the invisible particles or molecules in air. This suggests that air is made up of small particles which are in constant motion.

When this experiment is repeated at a higher temperature, the smoke particles move faster in a continuous random manner. This is due to increased kinetic energies of the molecules. The opposite is true when the temperature of the content is reduced.

CONCLUSION

From the experiments above, matter is made up of very small particles which are in constant random motion. This is called kinetic theory of matter.

ARRANGEMENT OF PARTICLES IN THE STATES OF MATTER

SOLID

The particles of solids are closely packed together in an organised way.
The closely knit structure is due strong attractive forces (cohesive forces) between the particles.
In their fixed positions, they vibrate to and from so that increasing the temperature of the solid increases this vibratory motion.
At a certain temperature the solid breaks away from this knit structure and the solid is said to have melted.

LIQUIDS

The particles are further apart. They are not fixed as in solids but move about in Brownian motion.
Liquids can break a solute put in it. It’s easier to dissolve a solute in hot water because the particles have increased energy.
The cohesive forces between the particles in liquids are weaker compared to those in solids. Due to this liquids can flow and take up the shape of the container in which they are put.
When a liquid is heated molecules gain kinetic energy, they vibrate about and expand. The space between them widens further apart and the liquid changes into gaseous state by a process called

GASES

The particles are further apart and have increased random motion compared to those in the liquid state.
The cohesive force between the particles is extremely small and as the particles move they collide with each other and with the walls of the container in which they are trapped. This produces gas pressure.
Gases are easier to compress indicates that there exists a large intermolecular distance in gas than in liquids. Gas molecules or particles can lose some of their energy and fall back into the liquid state by a process known as

NOTE: Solids which when heated change directly into gas undergo the process called sublimation.

DIFFUSION

This is the process by which particles spread from regions of high concentration to those of low concentration. Diffusion takes place in solids, liquids and gases.
In solids, diffusion is exceedingly slow but occurs when two metals are placed in contact with each other e.g. lead and gold, metal block vibrating atoms breaks away from the substances to which they belong and enter the other substance to be trapped by its attractive forces. This process is speeded up by high temperature.
Diffusion in liquids occurs at a faster rate than in solids.
Diffusion in gases is faster due to their low density, high kinetic energy and weak cohesive forces.

DIFFUSION IN LIQUIDS

To investigate diffusion in liquids

Apparatus: Funnel, beaker, copper (II) sulphate solution.

PROCEDURE

Pour water into the beaker until it is half full.
Pour saturated copper (II) sulphate solution down the funnel slowly and notice how the two liquids settle.
Remove the funnel carefully so that the liquids are not disturbed.
Repeat the same steps for another set of apparatus but using warm liquids. Make observation.

OBSERVATION AND EXPLANATION

Initially, the water layer floats on top of the saturated copper (II) sulphate because it is less dense. After sometime, the boundary disappears and the liquids form a homogeneous pale blue mixture.
Formation of the mixture is faster with hot liquids than because the movement of particles is faster due to increased energy. There is greater movement of water particles (molecules) from the water layer into copper (II) sulphate layer because it has greater concentration of water molecules than copper (II) sulphate particles.
Similarly, there is a greater movement of particles from copper (II) sulphate layer into the water layer because of greater concentration of copper (II) sulphate particles than water molecules.

DIFFUSION IN GASES

OBSERVATION AND EXPLANATION

The bromine gas spreads into the gas jar B at a greater speed than it returns to gas jar A because of high concentration of bromine particles.
Likewise, air spreads in gas jar A at a greater rate than it returns to gas jar B because of high concentration of air particles in B.
A homogenous pale brown mixture forms in the two jars and because this happens in a very short time, it suggests that the random movement of particles is rapid (faster) than diffusion in liquids.

NOTE: Performing the same experiment with the jars held vertically instead of horizontally slows down the rate of diffusion because of the densities of the gases. The less dense gas diffuses much faster into the more dense gas.

RATES OF DIFFUSION

To investigate the rates of diffusion of ammonium gas and hydrochloric gas

OBSERVATION AND EXPLANATION

A white deposit of ammonium chloride forms on the walls of the glass tube in the region nearer end B. This suggests that ammonia gas diffused at a higher rate than hydraulic acid gas.
Different gases have different rates of diffusion. A gas of high density has heavier particles hence moves more slowly than lighter one.

DIFFUSION THROUGH POROUS MATERIALS

The porous pot has very fine holes through which the hydrogen gas diffuses into the pot and air diffuses out.
Hydrogen gas bubbles out of the glass tube as shown in the set up above.
When the gas supply is stopped hydrogen gas diffuses out of the pot through the fine holes at a faster rate than air gets back to the pot. This decreases the gas pressure acting on the water surface in the beaker to push water up the tube.

NOTE: The beaker is used to confine the hydrogen gas around the porous pot.

QUESTIONS

Explain why rotten eggs broken at one end soon spreads the room.
Explain the cause of random motion of smoke particles as observed in Brownian motion experiment using a smoke cell.
Two identical tubes A and B held horizontally contain air and water respectively. A small quantity of coloured gas is introduced at one end of A while a small quantity of coloured water is introduced at one end of B. State with reason the tube in which the colour will reach the other end faster.
Distinguish between solid and liquid states of matter in terms of intermolecular forces
A bottle containing a smelling gas is opened at the front bench of a classroom. State the reason why the gas is detected throughout the room.
Motion of smoke particles can be studied by using the apparatus shown in figure 9 to observe the motion; some smoke is enclosed in the smoke cell and then observed through the microscope.

Explain the role of the smoke particle, lens and microscope in the experiment
State and explain the nature of the observed motion of the smoke particles
State what will be observed about the motion of the smoke particles if the temperature surrounding the smoke cell is raised slightly.

SOLUTIONS

The spreading is due to diffusion. The odour moves from a region of higher concentration to a region of lower concentration through diffusion.
Air molecules are in constant random motion; smoke particles collide with these air molecules hence their random motion.
A or tube with air; Gas molecules move faster/quicker than water molecules OR Diffusion of gases is Faster/more than in water/Grahams law the density of air is less than that of water
In solids the molecules are held in position by intermolecular forces that are very large. In liquids the molecules are able to roll over one another since the forces are smaller
The gas diffuse/ from the region of higher concentration to a region of low concentration.
(a) Smoke particles show the behavior or movement of air molecule

Smoke particles are larger than air molecules/ visible and light enough to move when bombarded by air molecules; Lens Focuses the light from the lamp on the smoke particle; causing them to be observable; Microscope enlarge the smoke particles that they are visible/ magnifies smoke particles.

(b) Smoke particle move randomly / zigzag / haphazardly Air molecules bombard the smoke particles/ knock/ hit Air molecules are in random motion

(c)The speed of motion of smoke particles will be observed to be higher smocking particles move faster, speed increases, increased random motion

MORE QUESTIONS

Describe the motion solid molecules experience.
What type of motion do molecules in the liquid and gaseous state experience
Describe Brownian motion.
When food is being cooked in the kitchen, why is it possible to smell this food in other rooms in the house?
State the forms of energy possessed by particles in (a) solids (b) liquids (c) gases.
State the type of motions described by a molecule in (a) solid (b) liquid (c) gas.
What do you see when you use a microscope to study illuminated smoke floating in air?
Describe the main difference between molecules in the gaseous state and those in the liquid or solid state.
Describe and explain Brownian motion.
Explain why perfume can be smelt some distance away from the person wearing it.
A house in which a cylinder containing cooking gas is kept unfortunately catches fire. The cylinder explodes. Explain why.
Two identical containers A and B are placed on a bench. Container A is filled with oxygen gas and container B with hydrogen gas. The two gases have equal masses. The containers are maintained at the same temperature. State with reason the container in which the pressure is higher.
(a) A substance has molecules which are moving completely free and random manner.
1. Is the substance a solid, liquid or gas?
2. Draw below a diagram to show the path followed by one of these molecules when it is moving randomly.

How can the speed of such a molecule be reduced?

What name is given to the temperature at which all molecular motion ceases?

(b) The behavior of substances as they change from solid state to the liquid state can be described using kinetic theory of matter. This assumes that matter is made of small moving particles or molecules.

What is the typical diameter of one of these molecules?
In the spaces in the table below describe the difference in solids and liquids.

	Solids	Liquids
Type of motion of molecules
Position of molecules
Spacing of molecules

(a) A substance has molecules which are in a close packed regular arrangement undergoing vibrations about fixed positions.
1. Is the substance a solid, liquid or a gas?
2. What is meant by `undergoing vibrations about fixed positions’?

How can the size of these vibrations be increased?

State the name given to the temperature at which the arrangement ceases to be close packed and regular.

(b) Describe a laboratory experiment using a syringe which shows that molecules of water are closely packed. How can this closely packed arrangement are completely destroyed.

(c) Matter exists in three states, solid, liquid, and gas. Complete the following table by writing in the state best described by each molecular property.

Molecular Property	State
1. Close packed
2.Spacing very large
3. Moving independently
4. Very strong forces of attraction
5. Vibrating about a fixed point

A small amount of air is trapped in an open glass capillary tube by a pellet of mercury as shown below.

Glass capillary tube

Mercury pellet

Trapped air

Describe the spacing and motion of the molecules in the liquid mercury and then the trapped air.
How does the pressure of the trapped air compare with that of the air outside the tube?

What difference, if any, are there in the speed and spacing of the trapped air molecules compared with those of the outside air (Temperature of both samples of air is the same.)

(a) The diagram below shows an apparatus which may be used for observing Brownian motion
When the apparatus was being used, points of light were observed moving about in a random manner.
1. What are these points of light?
2. Why are they moving randomly?
3. Name two ways by which this random motion could be made less vigorous.

(b) A sealed packet of crisps bought in a shop at sea level was found to appear like a balloon when taken to the top of a mountain.

Why did the packet appear to be inflated in this way?
Assuming there was no difference in temperature between sea level and the top of the mountain, what were the similarities and differences in motion of the air molecules inside the packet at sea level and on the top of the mountain.

(a) Some smoke is trapped in a small glass cell containing air and is brightly lit. When the mixture is viewed through a microscope, small bright specks which dance about in a random fashion can be seen.
1. What are small bright specks?
2. Explain what makes them dance in a random fashion.

Complete the diagram below by adding lines to show the movement of the small speck shown.

Bright speck

State three assumptions of the kinetic theory of gases.
Figure below shows apparatus used to observe the behaviour of smoke particles in a smoke cell.

Explain what was observed
Explain what happens if the temperature was raised.
State why diffusion is faster in gases than in liquids.

TOPIC 6: THERMAL EXPANSION

TEMPERATURE

This is the degree of hotness or coldness of a body. Temperature of a body is measured by an instrument called a thermometer.

Temperature is a basic physical quantity and is measured in degrees celcious (⁰C) or Kelvin (K).

The S.I unit of temperature is Kelvin (K) which is a scalar quantity.

MEASURING TEMPERATURE

A thermometer is an instrument used for measuring temperature. There are various types of thermometers in use. A thermometer is designed according to the purpose for which it is required. The following are some of the commonly used thermometers:

Liquid-in-glass thermometer.
Clinical thermometer
Six’s maximum and minimum thermometer

LIQUID-IN-GLASS THERMOMETER

A liquid-in-glass thermometer commonly in use is mercury or coloured alcohol as the thermometric substance.

The volume of the liquid changes uniformly with the change in temperature

The characteristics of the liquid in the bulb include;

Be easily seen (visible).
Expand or contract uniformly and by a large amount over a small range of temperature.

Not stick to the inside of the tube. (Should not wet the inside of the tube)

Have a wide range of temperature.

THERMOMETRIC LIQUIDS

The most common in use is mercury and alcohol.

Mercury freezes at -39^oC and boils at 357^oC while alcohol freezes at -115^oC and boils at 78^oC. Alcohol is therefore suitable for measuring temperatures below – 39^oC.

PROPERTIES OF THE TWO THERMOMETRIC LIQUIDS

ALCOHOL MERCURY

Low boiling point, 78oC – High boiling point, 357oC
Low melting point, -115oC – Relatively higher melting point, -39oC
Poor thermal conductor – Good thermal conductor
Expansion slightly irregular – Expands regularly
Wets glass – Does not wet glass
Coloured to make it visible – Opaque and silvery

Water is not used as a thermometric liquid because it undergoes anomalous expansion.

TEMPERATURE SCALE

The scale of a thermometer is obtained by selecting two temperatures called fixed points; the lower fixed point and the upper fixed point. The lower fixed point is the temperature of pure melting ice. It is taken to be 0⁰C. The upper fixed point is the temperature of steam above pure boiling water at normal atmospheric pressure. It is taken to be 100⁰C. The temperature of steam is used since impurities do not affect its temperature but will raise the boiling point of water. The temperature of boiling water itself is not used because any impurities in water would raise its boiling point. The temperature of steam is not affected by impurities in water.

The range between these two points is then divided into equal divisions. Each division is called degree.

FEATURES OF A COMMON THERMOMETER

The basic features of a common laboratory are as shown below.

Bulb- Carries the liquid in the thermometer. It has a thin glass wall for effective heat transmission between the liquid and body whose temperature is taken.
Capillary bore – Liquid expands and contracts along the capillary tube. It is narrow for high degree of accuracy.
Glass stem – this is a thick wall surrounding the capillary bore. It also serves as a magnifying glass for easy reading of scale.

CELCIOUS AND KELVIN SCALE

They are the commonly used temperature scale. The celcious scale has the fixed points at 0^oC and 100^oC. In Kelvin scale, the temperature of pure melting ice is 273K while that of pure boiling water at normal atmospheric pressure is 373K.

The lowest temperature in the Kelvin scale (0K) is referred as absolute zero.

This is the temperature at which the energy of the particles in material is zero.

To change ^oC to Kelvin

T = (ѳ – 273) K where ѳ is the temperature in ^oC

EXAMPLE 1

Convert 25^oC in Kelvin

SOLN

T = (25 + 273)

= 298 K

To change Kelvin to ^oC

Ѳ = (T- 273) ⁰C where T is the temperature in Kelvin

EXAMPLE 2

Convert 1 K

SOLN

Ѳ = 1-273

= -272^oC

ASSIGNMENT

Convert the following into Kelvin:

35⁰C b) -111⁰C c) -273 ⁰C

Convert the following into ⁰C:

123 K b) 323 K

NOTE: Temperature in Kelvin scale cannot have a negative value because the absolute zero, (0K), is the lowest temperature attainable.

CLINICAL THERMOMETER

A clinical thermometer is an instrument used to measure the temperature of a human body.

It uses mercury as its thermometric substance and has a narrow constriction in the tube just above the bulb.

The diagram below shows the main features of a clinical thermometer.

The constriction prevents the mercury level from falling down when it contacts with the human body.

The clinical thermometer has a short scale of temperature from 35^oC to 43^oC spread over its entire level. This is because the human body temperature falls slightly above or below 37^oC which is the temperature of a normal and healthy person. Methylated spirit is used to sterilize the clinical thermometer. Boiling water is not used because its temperature is quite far away from the maximum temperature of the clinical thermometer. This can destroy the thermometer. The thermometer can be reset by a simple flick.

SIX’S MAXIMUM AND MINIMUM THERMOMETER

This thermometer is used to record the maximum and minimum temperature of a place during a day. The thermometer consists of a U-tube connected to two bulbs. The U-tube contains mercury. The two bulbs contain alcohol.

The figure below shows the main features of a six’s maximum and minimum thermometer.

Working of the Thermometer

When temperature raises alcohol occupying volume of bulb A expand and forces mercury in the U-tube to rise on the right hand side.

The mercury in turn pushes the steel index A upwards. The maximum temperature can be noted from the lower end of the steel index A.

On the other hand when the temperature falls, alcohol in the bulb A contracts and the mercury is pulled back rising u the left hand side of the U-tube. The index B is then pushed up. During contraction of the alcohol, index A is left behind (in the alcohol) by the falling mercury.

The minimum temperature is then read from the lower end of index B.

NOTE: To reset the thermometer, a magnet is used to return the steel indices to the mercury surfaces.

THE BIMETALLIC THERMOMETER

It is made up of a coiled bimetallic strip whose one end is fixed and the other end connected to a pointer. Commonly used metals are brass and invar. When the temperature rises brass expands more than invar. The strip thus curls forcing the pointer to move over a calibrated scale.

THERMAL EXPANSION AND CONTRACTION OF SOLIDS, LIQUIDS

AND GASES

All substances increase in size when heated. This increase in size of a substance is called expansion. On the other hand when a substance is cooled it decreases in size. This decrease in size is called contraction.

EXPANSION IN SOLIDS

Thermal expansion and contraction in solids can be demonstrated using a ball and ring experiment. Set the apparatus as shown below.

NOTE: The ball should pass through the ring when both are at room temperature

Heat the ball and try to pass it through the ring. Observe what happens.
Leave it for sometime

OBSERVATION

When both the ball and the ring are at the same room temperature, the ball just passes through the ring.
When the ball is heated; it does not go through the ring but when left there for sometime, it goes through.

EXPLANATION

When heated, the ball expands so that it cannot go through the ring.

When left on the ring for some time, the temperature of the ball decreases and it contracts.

At the same time, the temperature of the ring increases and it expands so that the ball goes through.

WHY SOLIDS EXPANDS ON HEATING

The molecules of a solid are closely packed together and are continuously vibrating in their fixed positions When a solid is heated the molecules gain more kinetic energy and therefore make larger vibrations about their fixed positions. This increase in vibration means that the molecules collide with each other with larger forces and the molecules increases and so the solid expand.

LINEAR EXPANSIVITY

The measure of the tendency of a particular material to expand is called its expansivity e.g. aluminium expands more than iron thus aluminium has higher expansivity than iron.

The knowledge of linear expansivity values is applied in the designing of materials to ensure that they are able to operate well under varying thermal conditions.

Ordinary glass expands at a higher rate than Pyrex glass. When hot water is poured into a tumbler made of glass it breaks but does break in Pyrex glass.

Concrete and steel are reinforced together because they are of the same linear expansivity. Hence cannot crack under varying thermal conditions.

THE BIMETALLIC STRIP

When two metals of different linear expansivity are riveted together they form a bimetallic strip.

Brass and iron are used to make the bimetallic strip.

On heating the bimetallic strip, brass expands more than iron. The brass thus becomes longer than the iron for the same temperature range. Hence, the bimetallic strip bends with brass on the outside of the curve as shown in (b) below

On cooling, the brass contracts more than iron. It therefore becomes shorter than the iron and thus ends up being on the inner side of the curve as shown in (c) above

APPLICATIONS OF EXPANSION AND CONTRACTION IN SOLIDS

RAILWAY LINES

Gaps are left between the rails. Expansion for the rail is provided by overlapping the plane ends using overlapping joints as shown in the figure below

If these gaps for the expansion are not provided then during hot weather, they rails may buckle out, bend and cause derailment of the train leading to destruction and accidents.

STEAM PIPES

Pipes carrying steam from boilers are fitted with loops or expansion joints to allow pipes to expand and contract easily when steam passes through and when it cools down.

TELEPHONE WIRES

They are loosely fixed to allow for contraction and expansion. During cold weather, they contract and when it is warm they expand.

Telephone or electricity wires appear to be shorter and taut in the morning.

However in hot afternoons, the wires appear longer and slackened.

STEEL BRIDGES

In bridges made of steel girders, one end is fixed and the other end placed on rollers to allow for expansion as shown

RIVETS

Thick metal plates, sheets and girders in ships are joined together by means of rivets.

The rivet is fitted when hot and then hammered flat. On cooling, it contracts, pulling the two firmly together as shown

ELECTRIC THERMOSTAT

A thermostat is used to maintain a steady temperature in some devices such as electric iron box, refrigerators, fire alarm and flashing unit for indicator lamp in motor cars.

EXPANSION AND CONTRACTION IN LIQUIDS

The experimental set up below can be used to demonstrate expansion of a liquid.

A glass flask is filled with coloured water and heated as shown above

OBSERVATION

Immediately the level of coloured water on the tube drops slightly at first and then starts rising.

EXPLANATION

The initial fall of the level of the water is due to the expansion of the glass flask which gets heated first. The water starts expanding when heat finally reaches it and it rises up the tube.

NOTE: The water expands faster than the glass.

QUESTION

Explain why there is a drop in the level of the water initially followed by a steady rise in the level of water.

Different liquids expand more than others for a given temperature as shown in the diagram

In this case, methylated spirit expands most, followed by alcohol and finally water.

EXPANSION IN GASES

The experiment below can be used to demonstrate expansion of air.

Invert the flask with glass tube dipped into the water as shown.

Warm the flask with your hands for some time and note what happens.

Remove your hand and let the flask cool while the tube is still inserted in water.

OBSERVATION AND EXPLANATION

When the flask is warmed the level of water column inside the glass tube drops indicating air expands. When the flask is warmed further, some bubbles are seen at the end of the glass tube.

On cooling the air inside the flask contracts and water rises up the glass tube.

THE ANOMALOUS (UNUSUAL) EXPANSION OF WATER

Solids, liquids and gases expands when heated and contracts when cooled.

Water however shows an anomalous (unusual) behaviour in that it contracts when it is temperature is raised from 0^oC to about 4^oc.

When ice is heated from say -20^oC, it expands until its temperature reaches 0^oC and it melts with no change in temperature. The melting is accompanied by contraction. The water formed will still contract as its temperature rises from

0^oC as shown

Above 4⁰C, the water expands with increase in temperature. Since volume of a given mass of water is minimum at 4^oC, water at this temperature has a maximum density, slightly higher than 1g/cm³.

A sketch of the variation of density with temperature

At the melting point of water (^o0C) there is a drastic increase in the volume, resulting in a large decrease in density as the ice forms.

EFFECTS OF ANAMALOUS EXPANSION OF WATER

Freezing of lakes and ponds

Water in lakes and ponds usually freezes in winter. Ice is less dense than water and floats on water. Since ice a bad conductor of heat it insulates the water below against heat losses to the cold air above.

Water remains at 40C being the most dense, remains at the bottom of a lake while ice being less dense floats on layers of water at different temperatures as shown.

Fish and other aquatic animals and plants can therefore survive by living in the liquid layers below the ice.

Icebergs

Since the density of ice (0.92g/cm³) is slightly less than that of water it floats with only a small portion above the water surface. The rest and bigger portion rests under water. A big mass of such submerged ice is known as an iceberg.

It poses a great danger to ships as navigators cannot see the submerged part.

Weathering of Rocks

When water in a crack in a rock freezes, it expands. This expansion breaks the rock into small pieces.

Water pipes

Water pipes bursts when the water flowing through the pipes freezes

QUESTIONS

One property of a liquid that is considered while construction a liquid – in – glass thermometer is that the liquid expands more than the glass for the same temperature change. State any other two properties of the liquids that are considered
Explain why a glass container with thick walls is more likely to crack than one with a thin wall when a very hot liquid is poured into them.
Figure 1 shows a circuit diagram for controlling the temperature of a room.

Describe how the circuit controls the temperature when the switch is closed

Fig 2 shows a fire alarm circuit. Explain how the alarm functions.
Figure 3 shows a bimetallic strip at room temperature. Brass expands more than invar when heated equally.

Sketch the bimetallic strip after being cooled several degrees below room temperature.

In the set up shown in Figure 5, it is observed that the level of the water initially drops before starting to rise.

Explain this observation.

Figure 6 shows a bimetallic strip with a wooden handle, suspended horizontally using a thin thread.

The strip is heated at the point shown. Explain why the system tips to the right

A clinical thermometer has a constriction in the bore just above the bulb. State the use of this constriction.
7 shows a flask fitted with a glass tube dipped into a beaker containing water at room temperature. The cork fixing the glass tube to the flask is airtight.

Explain what is observed when ice- cold water is poured on the flask.

The melting point of oxygen is given as -281.3⁰ Covert this temperature to Kelvin

SOLUTIONS

The liquid expand uniformly, expansion is measurable (large enough), thermal conductivity
Glass is a bad conductor of heart, the difference in temperature between the inside and the outside cause unequal expansion.
Bimetallic strip bends and straightens or the metals expand differently. Current flows, heating takes place, temperature rises, strip is heated and bends way from contact; disconnects heater; temperature; drops reconnected heater or completes circuit.
When mercury is heated (during a fire); it expands and makes contact, completing the circuit to ring the bell. Since the strip is bimetallic when temperature rises the outer metal expands more than the inner metal; causing the strip to try and fold more; this causes the pointer to move as shown
Glass flask initially expands / Heating increases the volume of the flask; hence the level drops. Eventually water expands more than glass, leading to the level rising.; Cold water causes air in the flask to contract // reduces pressure inside flask or when cold water is poured it causes a decrease in volume of air the flask or pressure increases in the flask // volume of the flask decreases.
On heating, the bimetallic strip bends; this causes the position of the centre of gravity of the section to the left to shift to the right causing imbalance and so tips to the right.
Prevents/ holds, traps breaks mercury thread/ stops return of mercury to bulb When thermometer is removed from a particular body of the surrounding
Water rises up the tube into the flask or water is sucked into the tube or bubbles are seen momentarily.
273+ -281.3 = 8.3K

MORE QUESTIONS

Figure 5 shows a clinical thermometer which is not graduated.

Name the parts indicated with letters: A and
Mark the appropriate scale range in degrees Celsius

A bimetallic strip is made from aluminium and copper. When heated, it bends as shown below.

Aluminium

Copper

Sketch a diagram showing the strip when cooled below room temperature.

Explain why fish can survive under water when the surface is already frozen.
Explain the purpose of the constriction in a clinical thermometer.
It is not advisable to fix electrical cables tightly during the day. Give a reason for this.

Cell

The diagram below shows circuit of a fire alarm. When fire breaks it rings the bell to alert people that there is fire. Name two properties of mercury that makes it suitable to be used.

Mercury

Bell

In an attempt to prepare a cup of tea, a student placed boiling water into a glass tumbler. The glass tumbler broke into pieces. Explain this observation.
Figure 5 shows a flask fitted with a tube dipped into a beaker containing water at room temperature. The cork fixing the glass tube is tight.

State with reason what would be observed if cold water is poured on to the flask

Explain why steel is selected for use to reinforce a concreter beam
State two properties of mercury that make it a suitable thermometric liquid.
The diagram below shows a six’s maximum and minimum thermometer.

Saturated vapour

Mercury

What is the thermometric liquid in the thermometer?
Why is it necessary for the vapour in bulb B to be saturated?

Explain how the thermometer indicates maximum and minimum temperature.

Indicate on the figure the two points where the reading of the temperature shown by the thermometer can be made.
Explain why a lemon juice bottle always has space between the top of the liquid and the cap.
Explain the difference between heat and temperature.
Convert 450⁰C to Kelvin.
The figure below shows a bimetallic strip.

Invar

Brass

This strip is at room temperature. Sketch the bimetallic strip after being cooled several degrees below room temperature. Explain your answer.

A metallic disc is thin and has a hole passing through its centre. Describe what happens to the size of the hole when the disc is heated uniformly.
Give a reason why a concrete beam reinforced with steel does not crack when subjected to changes in temperature.
Describe the thermal expansion of a solid using kinetic theory of matter.
Explain the application of expansion in telephone and electric overhead cables.
Describe how a bimetallic thermometer works.
Explain why aquatic animals are able to survive under water when the surface is already frozen.
When a mercury thermometer is used to measure the temperature of hot water, it is observed that the mercury level first drops before beginning to rise. Explain this observation.
The coefficient of linear expansion of lead is 2.7 x per ⁰ Explain this statement.
Compare the expansion of brass and iron.
Air in a bulb may be used as a thermometric substance. State:
- One property of air that would enable the temperature to be measured.
- One limitation of such a thermometer.
What is meant by absolute zero temperature?
Explain why a thick glass container is more likely to crack than a thin one when boiling water is suddenly poured in.
One property of a liquid that is considered while constructing a liquid in glass thermometer is that the liquid must expand more than the glass for the same temperature range. State any other two properties of the liquid that are considered.
Describe and explain the features of a thermometer which will make it: (a) sensitive (b) Quick acting.
Why would you crawl close to the flow in a smoke filled room when trying to move out?
State three properties of a liquid for it to be considered in constructing a glass thermometer.
Sketch a volume against temperature graph for water that cools from 10⁰C to – 4⁰C
The figure below shows a flask fitted with a glass tube dipped into a beaker containing water at room temperature. The cork fixing the glass tube to the flask is air tight. The flask is warmed with the hands.

Warm hands

Air

Flask

Water

State and explain the observations made.

(a) Explain why in warm coastal regions, a cool breeze often blows from the sea to the land during the day time.

(b) Describe and explain what happens at night in question (a).

State	Temperature ⁰C	Density (kg/m³)
Liquid	8.0	999.85
Liquid	6.0	999.94
Liquid	4.0	999.97
Liquid	2.0	999.94
Liquid	0.0	999.84
Solid	0.0	916.59

Use the density data above to describe how the volume of the liquid changes as it cools from 8⁰C to 0⁰C^.
Describe the change in volume of water as it changes from liquid to solid.
Describe what happens to a sealed glass bottle full of water if it were placed in the freezing compartment of a refrigerator.

(a) Two glass spheres contain equal volumes of air at the same temperature and pressure. The spheres are connected by a narrow glass tube containing a mercury pellet as shown below.

Glass sphere P air glass sphere Q

Narrow glass tube

Mercury pellet

Describe how the air molecules exert a pressure on the walls of the glass spheres.
Describe and explain using the ideas of molecules what happens to the mercury pellet when sphere Q is gently heated while sphere P is kept at its original temperature.

(b) The diagram below shows an experiment which can be used to demonstrate the thermal expansion of a solid metal bar. Pointer

Heavy weight solid metal bar

Heat roller

Table

Describe what happens when the bar is heated.
Explain what happens in (i) using kinetic theory of matter.

Give an example of an everyday situation where allowance must be made for the expansion of a solid. Explain how this allowance is made for the expansion.

(a) When liquids are stored in a sealed bottle, they are not completely filled out, but a space is left between the cap and the surface of the liquid as shown below.

Cap

Space

Bottle liquid

Describe what happens to the contents of the bottle when the temperature is increased slowly and uniformly.
Explain what happens in (i) in terms of the expansion of liquids and solids.
Give a use of the above effect.
Describe and explain what happens to the gas in the space above the liquid using kinetic theory.
A cylindrical copper rod is heated. State and explain what happens to the density of copper as the rod is being heated.

a) The diagram below shows a long silver rod, a light pointer and a pivot.

Fixed support

Long silver rod

Light pointer

Pivot

Describe how this apparatus can be used to measure the expansion of the silver rod as its temperature increases.
State a problem of repeating the above experiment using a polythene rod of the same shape and size as the silver rod.
State two extra pieces of apparatus that would be needed

(a) Place in ticks in the table below to show which liquid is better in each case.

Characteristic	Mercury	Alcohol
Expands more evenly
Expands more
A better conductor of heat
Useful at higher temperatures
Useful at lower temperatures

(b) In terms of the forces of attraction between the particles, the particle spacing and their motion describe and explain the change in volume that occurs on boiling.

TOPIC 7: HEAT TRANSFER

HEAT AND TEMPERATURE

Heat is a form of energy which passes from a body at high temperature to a body at a lower temperature. When a body receives heat energy its temperature increases whereas the temperature of a body that gives away energy decreases.

Thermal equilibrium- Condition when if two bodies at the same temperature are in contact, there is no net flow from one body to the other.

The SI unit of heat is joules.

Heat cannot be measured directly by an instrument as temperature is measured by a thermometer.

MODES OF HEAT TRANSFER

Heat can travel through a medium as well as in a vacuum. There are three (3) modes of heat transfer namely;

Conduction – takes place in solids.
Convection – takes place in fluids (liquids and gases).

Radiation – takes place in gases (vacuum)

CONDUCTION

In stirring a hot tea the handle of a spoon becomes warm. The mechanism to this is explained below,

Heat energy entering the spoon from the hot end increases vibrations of the atoms at this ends. These atoms in turn collide with neighbouring atoms, increasing their vibrations and hence passing the heat energy along.
Metals have free electrons which travel throughout the body of the metal. Heat energy injected at the hot end of the metal spoon increases the vibration of the particles at the end. The free electrons in that region gain more kinetic energy and because they are free to move, they spread heat energy to the other parts of the spoon.

THERMAL CONDUCTIVITIES OF VARIOUS CONDUCTORS

Different materials have different thermal conductivities. Metals are generally good conductors of heat. Non-metals are poor conductors of heat (insulator).

Solids that are good conductors of heat use both atom vibration and free electrons to conduct heat.

Solids that are poor conductors of heat like glass, wood, rubber make use of atom vibration as a mechanism to conduct heat because they have no free or mobile electrons.

The table below shows some of the good and poor conductors in decreasing order of thermal conductivity.

Good conductors	Poor conductors
Silver	Concrete
Copper	Glass
Aluminium	Brick
Brass	Asbestos paper
Zinc	Rubber

NOTE: During thermal condition, heat flows through the materials without the material shifting or flowing. Conduction is therefore transfer of heat as a result of vibration of particles.

CONDUCTIVITY OF WOOD AND IRON RODS

The following set up is used;

Observation and explanation

The paper gets charred (blackened) on the region covering the wooden rod. This is because the wood does not conduct heat from the paper. Wood is said to be a bad conductor of heat while iron is a good conductor.

FACTORS AFFECTING THERMAL CONDUCTIVITY

Thermal conductivity in materials depends on the following factors;

Temperature difference ( Ѳ) between the ends of the conductor.
The length of the conductor.
The cross-sectional area (A) of the conductor.
The nature of the material (K)

Temperature difference

To demonstrate how temperature difference ( Ѳ) affects thermal conductivity, the following set up is used.

Observation

It will be observed that the rod placed in the flame becomes too hot faster than the one placed in the boiling water.

Explanation

The rate of heat flow (thermal conduction) increases with increase in temperature.

Thermal conduction in metals is by two mechanisms i.e. vibration of atoms and by free electrons.

A high temperature difference between the ends of the conductors sets the atoms into vibrations more vigorously and the vibrations are passed more quickly to the cooler end. The electrons on the other hand gain a lot of kinetic energy causing them to spread the heat energy to cooler parts of the metal within a short time.

Length of the conductor

Consider the set up below

Observation

It will be observed that the end of metal B held in hand becomes too hot earlier than metal A. Thermal conductivity increases with decrease in length.

Explanation

Heat travels within a conductor along imaginary lines called lines of heat flow.

These lines diverge from the hot end as shown

The graph of temperature (Ѳ) against length (l) is as shown.

When the heat energy gets to the surface of the metal it is easily lost to the surroundings.

The lines of heat are more divergent near the hot end than they are far away (position A and B).

The slope of the graph in the above figure is steeper at A (near the hot end) than at B further away. This indicates that the shorter the length of the material, the higher the rate of heat flow.

The cross-sectional area of the conductor

Consider the set up below,

Observation

The end of metal A held in the hand becomes too hot earlier than metal B.

Thermal conductivity increases with increase in area of cross-section of the conducting material.

Explanation

The number of free electrons per unit length of the thicker length A is more than those in the thin metal rod B.

The nature of the material K

To demonstrate how the type of the material K affects thermal conductivity, consider the diagram below,

Observation

In this case, it is observed that end of copper rod held in the hand becomes too hot earlier than iron rod.

This shows that thermal conductivity depends on the nature of the material.

Explanation

Different materials have different strength of force bonding the atoms within the material. The number of free electrons also differs from one material to another material.

Materials with many free electrons are better conductors of heat e.g. copper has more free electrons than iron.

Rate of heat flow = thermal conductivity x cross-sectional area x temperature difference

Length L

LAGGING

This is the covering of good conductors of heat with insulators to reduce heat loss through surface effects. For example, iron pipes carrying hot water from boilers are covered with thick asbestos material.

The figure below shows lines of heat flow in a lagged metal bar.

A graph of temperature (ѳ) against the position along the lagged conductor is as shown below.

THERMAL CONDUCTIVITY IN LIQUIDS

To demonstrate that water is a poor conductor, the following set up considered,

Observation and explanation

It will be noted that water at the top of the boiling tube boils while ice remains unmelted. This shows that water is a poor conductor.

NOTE: The boiling tube is made of glass (poor conductor of heat) which limits possible conduction of heat down the tube.

The ice is wrapped in wire gauze to ensure it does not float. The fact that the wire gauze is a good conductor of heat and yet ice remained unmelted shows that there is very little heat conduction in water, unable to melt the ice.

Water is heated at the top to eliminate possibility of heat transfer to the ice by convection.

Although liquids are in generally poor conductors of heat, some liquids are better heat conductors than others e.g. mercury is a better conductor of heat than water.

Why Liquids Are Poor Conductors of Heat

Pure liquids have molecules further apart from each other. Although molecules move about within the liquid, they are slow to pass heat to other regions compared to the free electrons in metals. This is because there are large intermolecular distances between liquid molecules. There are also fewer and rare collisions between the molecules.

Electrolytes e.g. salt solution, are better conductors of heat than pure liquids because of increased compactness of the particles.

Mercury is a metal existing as a liquid at room temperature. Bromine, the only non-metal existing as a liquid at room temperature, is a poor conductor.

THERMAL CONDUCTIVITY IN GASES

Since thermal conductivity is by means of vibration of atoms and presence of free electrons, gases are worse conductors of heat because of large intermolecular distance.

A match stick held within the unburnt gas region of a flame cannot be ignited by the heat from the hot part of the flame. This is because gas is a poor conductor of heat.

APPLICATIONS OF GOOD AND POOR CONDUCTORS

Cooking utensils, soldering irons and boilers are made of metals which conduct heat rapidly. For cooking utensils, the handles are made of insulators such as wood or plastic. Metal pipes carrying hot water from boilers are lagged with cloth soaked in a plaster of Paris to prevent heat losses.
Overheating of integrated circuits (ICs) and transistors in electronic devices can drastically affect their performance such components are fixed to a heat sink (a metal plate with fins) to conduct away undesired heat. The fins increase the surface area of heat sink and conduct more heat away to the surrounding.
Fire fighters put on suits made of asbestos material to keep them safe while putting out fire.
Birds flap their wings after getting wet as a means of introducing air pockets in their feathers. Air being a poor conductor reduces heat loss from their bodies.
In modern buildings where desired inside temperatures is to be stabilised, double walls are constructed. Materials that are good insulators of heat and can trap air put between the walls. Examples of such materials that are glass, wool (fibre glass) and foam plastic Air on its own may not effectively give the desired insulation because it undergoes convection. Double glazed windows used for the same purpose have air trapped between two glass sheets.
In experiment involving heating water or liquid, the beaker is placed on the wire gauze. The gauze is heated and spreads the heat to a large area of the beaker. If the gauze is not used, heat from the Bunsen burner may concentrate on a small area and may make the beaker crack.

CONVECTION

Convection is the process by which heat is transferred through fluids (liquids and gases). The heat transfer is by actual movement of the fluid called convection currents, which arise out of the following;

Natural convection – It involves change in density of the fluid with temperature.

Forced convection – Mixing of hot and cold parts of the fluid through some external stirring like a fan or pump.

CONVECTION IN LIQUIDS

To demonstrate convection in liquids the set up below is used

Observation

A purple colourisation rises up from the potassium permanganate, forming a loop.

Observation

The colourisation arising from the potassium permanganate flow in clockwise direction

From the experiments, it is clear that when a liquid is heated, it rises while cold liquid replaces it.

Explanation

When a liquid is heated, it expands and this lowers its density. The less dense liquid rises and its place is taken by more dense colder liquid. This movement of liquid forms convection currents

CONVECTION IN GASES

To demonstrate convection currents in gases, consider the set up below

Observation

Smoke is sucked into the box through chimney A and exists through chimney B.

When the candle is put off, the smoke is not drawn into the box.

This shows convection currents are set up when air or gas is heated.

Explanation

The candle heats up the air above it, which expands and rises up because of lower density. Cold heavier air particles is drawn into chimney A, carrying along the smoke which replaces the air that is escaping through chimney B.

MOLECULAR EXPLANATION OF CONVECTION IN FLUIDS

Molecules in fluids are further apart and have negligible cohesive force. Heating a fluid increases the kinetic energy of the vibrating molecules and their random movement.

As the fluid rises, these molecules pass energy to the molecules in the colder regions which have less energy. Because the molecules are further away from the heating source, their temperature is reduced.

Pressure near the heating source decreases because of the depletion of molecules as they rise. Colder molecules move into the low pressure zone to fill up the void being created.

This movement of molecules constitutes convection currents. Convection currents are set up much faster in gases than in liquids because of relatively low cohesive force in gases.

APPLICATION OF CONVECTION IN FLUIDS

Domestic hot water system

Initially, the two beakers A and B have cold water. Water in beaker A is coloured to distinguish it from that in beaker B. When the water in beaker A is heated, it is observed to rise up through tube X and emerges on top of cold water in beaker B. The cold water flows down from beaker B to beaker A.

As long as heating continues, there will be movement of hot water into beaker B and cold water will flow down into beaker A. Thermometer will show increase in temperature for water in beaker B.

The commercial domestic hot water system utilizes the same principle of operation. The hot water rises up because of the effective lowering of density.

The force of gravity helps the cold water to flow down from the cold tank.

The hot water tap and expansion pipe are connected to the upper region of the cylinder. The expansion pipe is an outlet for excess water that could have resulted from overheating.

Once the cold water flows down the cylinder, the main pipe allows more cold water to flow into the tank. When filled to capacity, the ball cork floating on water closes a valve i the main pipe, stopping further in flow of cold water.

An overflow pipe lets out water from the cold tank when the valve is not sufficiently functional.

Lagging is done on the pipe that conveys hot water to minimise heat losses.

Ventilation

This is the supply of fresh air into the room. Air expelled by the room occupants is warm and less dense. It rises up and escapes through the ventilation holes.

Cold fresh air flows into the room to replace the rising warm air. The room gets continuous flow of fresh air.

NOTE: Some devices are fitted with air conditioning devices which cause forced convection of air, giving out cold dry air and absorbing warm moist air.

Car Engine Cooling System

Heat conduction and convection play a very crucial role of taking away heat from a car engine that would reduce its efficiency.

The engine is surrounded by a metal water jacket that is connected to the radiator. The metal surface conducts heat away from the engine. This heats up the water, setting up convection currents. The hot water is pumped into the radiator which has thin copper fins that conduct away heat from water.

Fast flowing air past the fins speeds up the cooling process.

Land And Sea Breezes

This is a natural convection of air, and occurs at sea shores because of temperature difference between the mass of water and the land.

The mass of water takes longer time than land nearby land by the same temperature from the sun. Water also takes a longer time to cool than the land after being raised at the same temperature.

During the day, the land heats up much faster than the sea. The air just above the land gets heated up and rises because of reduced density. Cold air above the sea blows towards the land to replace the void created by warm air rising. This is called sea breeze.

In the evening, temperature of the sea water is higher than that of the land. The air above the sea gets heated up and rises. Cold air from the land blows to the sea. This is called land breeze.

RADIATION

Heat from the sun to the earth reaches us by radiation. Thermal radiation is heat transfer through a vacuum.

All bodies absorb and emit radiation. The higher the temperature of the object, the greater the amount of radiation A body emitting thermal radiation can also emit visible light when it is hot enough.

An electric bulb in a room produces both light and radiant heat. The radiant heat is absorbed by the materials in the room, which in turn give out radiant heat of lower energy.

NATURE OF RADIANT HEAT

To demonstrate the radiant heat;

Consider light rays travelling from sun light to hand lens as shown,

OBSERVATION

When light rays are focused onto the paper, it burns out.

EXPLANATION

Radiant heat, like light can be concentrated to a point using a lens. Thermal radiation is a wave like light and can be reflected. Because of the nature of production, radiant heat is an electromagnet wave which causes heating effect in objects that absorb it.

Radiation can also be described as the flow of heat from one place to another by means of electromagnetic waves.

EMISSION AND ABSORPTION OF RADIATION

To compare radiation from different surfaces (shiny and black surfaces),

Consider the set up below,

The two surfaces are heated to a certain temperature say 80⁰C. The temperatures of the two tins taken after sometime

Observation

After sometime, it is noted that the temperature recorded by T_Bis lower than that recorded by T_S.

Explanation

The experiment shows that black surfaces are better emitters than shiny surfaces.

A graph of temperature against time for temperatures recorded by each thermometer

The graph shows water in a shiny tin lost heat less rapidly than the blackened tin (good emitter).

To Compare Absorption of Radiant Heat by Different Surfaces

Set up the apparatus as shown

Observation

The cork fixed on the dull/black surface falls off after the wax, melts, while the cork polished/shiny plate remains fixed for a longer time.

Consider also the set up below,

Observation

The thermometer T_B immersed in water in the blackened tin records higher reading than that of thermometer T_S, when the heater is placed mid-way between tin A and tin B.

A graph of temperature (^oC) against time (minutes) is as shown,

The graph shows that temperature of water in the polished tin does not increase as fast as temperature of water in blackened tin.

EXPLANATION

Black surfaces are good absorbers of radiant heat than polished surfaces.

NOTE: Good absorbers of radiant heat also good emitters while poor absorbers of heat are also poor emitters.

Poor emitters of heat are also good reflectors.

APPLICATIONS OF THERMAL RADIATION

Kettles, cooking pan and iron boxes have polished surfaces to reduce heat lose through radiation.
Petrol tanks are painted silvery bright to reflect away as much heat as possible.
Houses in hot areas have their walls and roofs painted with bright colours to reflect away heat, while those in cold areas have walls and roofs painted with dull colours.
In solar concentrators, the electromagnetic waves in form of radiant heat are reflected to a common point (focus) by a concave reflector. The temperature at this point can be sufficiently high to boil water.
The green house effect- A green house has a glass roof through which radiant heat energy from the sun passes. This heat is absorbed by objects in the house, which then emit radiation of lower energy that cannot penetrate through glass. The cumulative effect is that temperature of the houses increases substantially. Greenhouses are used in providing appropriate conditions for plants in cold regions.

NOTE: Carbon dioxide (CO2) and other air pollutants in the lower layers of the atmosphere show the same properties of glass, raising the temperature on earth to dangerous levels.

Solar heater

The solar heater uses solar energy to heat water. The figure below shows the solar heater,

The solar heater consists of a coiled blackened copper pipe on an insulating surface. Radiant heat from the sun passes through glass and is absorbed by black copper pipes that contain water, which is heated up. Copper pipes are used because they are good conductors and they are painted black to increase their absorbing power.

Lower energy emitted after absorption of radiant energy does not escape because it cannot penetrate the glass. The temperature of the air above the pipe thus increases boosting the heating of water. A good insulating material is used at the base.

THERMOS FLASK (VACUUM FLASK)

A thermos flask is designed such that heat transfer by conduction, convection and radiation between the contents of the flask and its surrounding is reduced to a minimum.

The vacuum is a double walled glass vessel with a vacuum in the space between the walls. This minimises the transfer of heat by conduction and convection.

The inside of glass walls, in the vacuum side, is silvered to reduce heat losses by radiation (Poor emitter and absorber). The felt pads on the sides and at the bottom support the vessel vertically.

The heat loss by evaporation from the liquid surface is prevented by a well fitting cork.

QUESTIONS

In the set up shown in figure 1, water near the top of the boiling tube boils while at the bottom it remains cold.

Give a reason for the observation

When a Bunsen burner is lit below wire gauze, it is noted that the flame initially burns below the gauze as shown in Figure 2 (i).After sometime, the flame burns below as well as above the gauze as shown in Figure 3(ii).

Explain this observation

Two identical aluminum rods as shown in figure 3. One rests on metal block the other on the wooden block. The protruding ends are heated on Bunsen burners shown.

State with reason on which bar the wax is likely to melt

4 shows a hot water bath with metal rods inserted through one of its sides. Some wax is fixed at the end of each rod. Use this information to answer questions below

What property of metals could be tested using this set-up?

Two identical empty metal containers P and Q are placed over identical Bunsen burners and the burners lit. P is dull black while Q is shiny bright. After each container attains a temperature of 100⁰C the burners are turned off. Identical test tubes containing water are suspended in each container without touching the sides as shown

Explain why the container Q may become hot faster than P.
Explain why the water in test- tube in P becomes hot faster than in Q

In a vacuum flask the walls enclosing the vacuum are silvered on the inside. State the reason for this.
Give a reason why heat transfer by radiation is faster than heat transfer by conduction.
A wooden bench and a metal bench are both left in the sun for along time. Explain why the metal bench feels hotter to touch.
An electric heater is placed at equal distances from two similar cans A and B filled with water at room temperature. The outer surface of can A is shiny while that of can B is dull black. State with reasons, which of the cans will be at higher temperature after the heater is switched on for some time.
In the set up shown in figure 4, it is observed that the level of the water initially drops before starting to rise.

Explain this observation.

In a vacuum flask the walls enclosing the vacuum are silvered on the inside. State the reason for this

Figure 4 shows two identical balloons A and B. The balloons were filled with equal amounts of the same type of gas. The balloons are suspended at distances X₁ and X₂ from a metal cube filled with boiling water and placed on an insulating material. Use this information to answers questions 12 and 13 below:

State the mode by which heat travels from the cube to the balloons
The face of the cube towards A is bright and shiny and the face towards B is dull black. State with reason the adjustments that should be made on the distances X₁ and X₂ so that the rate of change of temperature in both balloons is the same.
Temperature scale in clinical thermometer ranges from 35⁰c to 43⁰ Explain.
State one application of expansion in gases
Why is it that boiling is not used for sterilization of clinical thermometer?
Describe ONE advantage and ONE Disadvantage of anomalous behavior of water.
(a) Draw a well labeled diagram of a vacuum flask

(b) Stating the specific parts in the flask explain how heat loss is reduced through:

(i) Conduction

(ii) Convection

(iii) Radiation

SOLUTIONS

Water/ or glass are poor conductor of heat
Initially the wire gauze conducts heat away so that the gas above does not reach the ignition temp/point. Finally the wire gauze becomes hot raising the temp of the gas above ignition point.
Wooden Block; Wooden block is a poor conductor of heat all the heat goes in melting the wax.
Heat conductivity/ rates of conduction/ thermal conductivity
Dull surface radiate faster than bright surface P- Looses more of the heat supplied by burner than Q or Q shinny surface is a poorer radiator/ emitter of heat thus retains more heat absorbed Or P- Dull surface is a better radiator/ emitter i.e. retains less of the heat absorbed. Heat travels from container to test tube by radiation so the dull surface P, gives more heat to the test tube.
Reduce/ minimize the transfer of heat by radiation OR Reduce the loss of heat OR gain of heat by radiation.
Radiation is at the electromagnetic waves Φ infrared while conduction involves particles, which move at lower speed
This is because metal is a good conductor, so that heat is conducted from outer parts to the point touched; while wood is a poor conductor
Can B is a good absorber of radiation/better absorber of radiation or heat.
Glass flask expands first (creating more volume for water) Water then expands using the tube.
To reflect heat outwards or inwards hence reduce heat loss by radiation.
– x² is made larger than X₁
– Since B receives radiation at a higher rate, it must be moved further from source for rates to be equal.
Since the quantity of water in A is smaller, heat produces greater change of temperature in A; a decrease in density causing the cork to sink further.

MORE QUESTIONS

Figure below shows two corks X and Y fixed on a polished plate and a dark plate with candle wax

Explain the observation, when the heater is switched on for a short time.

What feature of a vacuum flask minimizes heat loss by radiation? Explain how this is achieved.
Explain why fuel carrying tankers are painted white or silvery.
When a thermometer is immersed in ice cold water, the mercury thread is observed to rise before dropping steadily in the capillary tube. Explain.
Figure below shows two glass bulbs C and D of the same size. Bulb C is painted dull black while D is polished. A hot metal ball is placed equidistant from the two bulbs.

State and explain what will happen to the levels of the liquid in the manometer.

When a Bunsen burner is lit below wire gauze, it is noted that the flame initially burns below the gauze as shown in figure 4 below. After sometime the flame burns below as well as above the gauze.

Explain this observation

State the reason why it is colder during the night when the sky is clear than when it is cloudy.

Wax

The figure below shows an experiment carried out by form one students.

Thin iron rod

Thick iron rod

Hot water

The students dipped two iron rods of the same length but different thickness into a beaker of hot water at the same time. What was the experiment about?
State and explain the observations made after about 10 minutes.
If the two rods were much longer, state and explain any difference from C (ii) above that would be made in the observation.

TOPIC 8: RECTILINEAR PROPAGATION AND REFLECTION AT PLANE SURFACES

Light is a form of energy. It enables us to see the surrounding objects. Light itself is not visible but its effect is felt by the eye.

Light is also very essential as a source of energy for the process by which plants their own food (photosynthesis).

SOURCES OF LIGHT

Luminous (incandescent) source – these are objects that produce their own light e.g. sun, stars, burning candles, wood or charcoal, electric bulbs, television screens, glow worms e.t.c.

Non-luminous source – these are objects which do not produce light of their own. They are seen when light falling on them from luminous sources is reflected (bounces off their surfaces) e.g. the moon, planets, plants, people, books, walls, clothes e.t.c.

RAYS AND BEAMS OF LIGHT

A source of light produces pulses of energy which spread out in all directions.

The path along which light energy travels is referred to as a ray of light. Rays are represented by lines with arrows on them to show the direction of travel.

A stream of light energy is called a beam. It is also considered to be a bundle of rays of light. Beams of light can be seen;

In the morning as the sunlight breaks through the clouds or leaves.
When a spotlight is shown in a smoky room or a car driven along a dusty road at night with its headlamps on.
When sunlight streams into a smoky dark room through a small opening

TYPES OF BEAMS OF LIGHT

Diverging beam
Converging beam
Parallel beam

Diverging beam – These are beams of light that appear to spread out (diverging) e.g. light from a spotlight.

Converging beams – these are beams which appear to collect (converge) to a point.

Parallel beam – are those beams which appear to be perfectly parallel to each other e.g. a beam of light from the sun reaching the earth’s surface.

OPAQUE, TRANSLUCENT AND TRANSPARENT OBJECTS

OPAQUE – these are objects that do not allow light to pass through them at all e.g. brick walls, metals, wood, stones e.t.c.

TRANSLUCENT – these are objects that allow light to pass through but we cannot see through e.g. glass panes used in toilets and bathroom window and greased paper.

TRANSPARENT – these are objects which allow light to pass through and we see clearly through them e.g. car wind screen and ordinary window panes.

RECTILINEAR PROPAGATION OF LIGHT

Light does not need a material medium to carry it. In a vacuum, the speed of light is 3.0 x 10⁸m/s. Light from the sun reaches the earth having travelled mostly through a vacuum.

When light falls on an opaque object, it casts a shadow of the object with sharp edges on a screen behind it. This suggests that light travels in a straight line.

TO INVESTIGATE HOW LIGHT TRAVELS

Apparatus: three cardboards, source of light.

Arrange the apparatus as shown

The cardboards are arranged such that holes are exactly in line.

OBSERVATION

When the holes in the three cardboards are in line, the eye can see the lamp.

However when the middle cardboard is displaced, the eye can no longer see the lamp.

EXPLANATION

When the holes in the cardboards are in a straight line, light travels through the holes and the lamp is seen from the other side. When one of the cardboards is displaced, the beam of light is cut off and since light cannot bend to follow the displaced hole, the lamp cannot be seen.

CONCLUSION

Light travels in a straight line. This property is known as rectilinear propagation of light.

SHADOWS

Shadows are formed when an opaque object is on the path of light. The type of shadow formed depends on;

The size of source of light.
The size of opaque object.

The distance between the object and the source of light.

To study the formation of shadows by a point source of light

Consider the set up below,

Observation and Explanation

A uniformly and totally dark shadow is seen on the screen. This shadow is called umbra (Latin for shade)

The shadow has a sharp edge, supporting that light travels in straight lines.

To study the formation of shadows by extended (larger) source of light

Consider the set up below (source of light made larger)

Observation

The centre of the shadow remains uniformly dark as before, but smaller in size.

The shadow is edged with a border of partial shadow called penumbra.

Explanation

The centre of the shadow still receives no light at all from the source. Light from some parts of the extended source of light reaches the centre parts of the shadow on the screen, but light from other parts is cut off by the opaque object, resulting in a partial shadow at the edges.

NOTE: Extended light source produce light that is much softer and without sharp edges.

Application

It is used in frosted light bulbs and lamp shades to provide a more a more pleasant lighting with less sharp edges.

To study the formation of shadows by extended (larger) source of light when object distance is changed

Consider the set ups below,

Object moved closer to source

Object moved away from the source

Observations

When the ball is moved closer to the source, a ring of penumbra is formed. No umbra is seen.

When the ball is far away from the source, there is umbra surrounded by penumbra.

Explanation

The centre of the shadow receives light from the extended source. Since the object (ball) is smaller than the source of light, its umbra does not reach the screen because of the distance.

When the object is moved away from the source, the tip of the umbra reaches the screen.

ECLIPSE

An eclipse is a phenomenon of shadow formation which occurs once in a while.

It’s the total or partial disappearance of the sun or moon as seen from the earth.

Eclipses are explained in terms of relative positions of the earth, the moon and the sun.

THE PHASES OF THE MOON

At any given moment, about half the surface of the moon is lit by the sun while another half is in darkness.

The lighted part is bright enough to be seen easily at night from the earth and can be seen at day time. The darkened part is usually invisible.

When we look at the moon, we normally notice only the shape of the lighted part.

SOLAR ECLIPSE (ECLIPSE OF THE SUN)

When the moon, revolving around the earth, comes in between the sun and the earth, the shadow of the moon is formed on the earth. This is called eclipse of the sun.

Depending on the position of the moon, some parts of the earth lie in the region of umbra and some in the region of penumbra. Total eclipse occurs in the regions of umbra and partial eclipse in the regions of penumbra.

ANNULAR ECLIPSE

Sometimes the umbra of the moon is not long enough to reach the earth because sometimes the distance between the moon and earth varies (the moon’s orbit is elliptical). When the moon is further away from the earth, its disc is slightly smaller than the sun’s disc. So when a solar eclipse occurs, the moon is not large enough to cover the sun totally. A bright ring of sunlight can be seen round the edge of the dark disc of the moon. This is called Annular or ring eclipse.

LUNAR ECLIPSE (ECLIPSE OF THE MOON)

The moon is a non luminous object. It can only be seen when light from the sun is incident on it. When we look at the moon, we see only the shape of the lighted portion. When the earth comes in between the sun and the moon, lunar eclipse occurs. Depending on the position of the moon, a total or partial eclipse of the moon will occur. Total lunar eclipse will occur if the moon is in the region of umbra and partial eclipse will occur if any part of the moon is in the region of penumbra as shown,

A lunar eclipse occurs when the moon passes through the earth’s umbra.

PINHOLE CAMERA

A pinhole camera consists of a box with pinhole on one side and a translucent screen on the opposite side. Light rays from an object pass through the pinhole and form an image on the screen as shown

The image formed is real and is inverted. A pinhole camera has a large depth of focus i.e. objects that are far and near form focused images on the screen.

CHARACTERISTICS OF IMAGES FORMED ON THE PINHOLE

Consider the sets below;

When the object is near the pinhole, the image is larger.

When the object distance is increased from the pinhole the image is smaller.

When more holes are added close to the first pinhole, images of each point are seen overlapping on the screen.

If the camera was made in such a way that it could be elongated by moving the screen farther away from pinhole but keeping the distance between the object and pinhole fixed, it could be seen that the image enlarges when length of the camera is increased and diminishes when the length of the camera is reduced.

Length of camera decreased, image smaller
Length of camera increased, image bigger (larger)

MAGNIFICATION

Magnification is the change in size of an image to that of the object or it’s the ratio of the height of the image and that of the object.

Magnification, m= Image distance, v

Object distance, u

Also,

Magnification, m= Height of the image, h_i

Height of the object, h_o

Hence, magnification, m = Image distance, v = Height of the image, h_i

Object distance, u Height of the object, h_o

= h_i = v

h_ou

EXAMPLE 1

The distance between the pinhole and screen of a pinhole camera is10cm. The height of the screen is 20cm.At what distance from the pinhole must a man 1.6m tall stand if a full length is required

SOLN

h_i = v

h_ou

But, hi=20cm, ho=1.6m and v=10cm

Magnification, m = 20 = 10

160u

Hence, u = (160 x 10) / 20

= 80 cm or 0.8 m

EXAMPLE 2

An object of height 5m is placed 10m away from a pinhole camera. Calculate

The size of the image if it’s magnification is 0.01
The length of the pinhole camera.

SOLN

a) Magnification, m = h_i = v

h_ou

0.01 = h_i

Thus, hi =0.05m (image is 0.05m high)

b) h_i = v

h_ou

0.05 = v

510

Hence, v =0.1m (length of pinhole camera is 0.1m)

EXERCISE

The length of pinhole camera is 25cm. An object 2m high is placed 10cm from the pinhole. Calculate the height of the image produced and its magnification.
a) A pinhole camera of length 20cm is used to view the image of a tree of height 12m which is 40m from the pinhole. Calculate the height of the image of the tree obtained on the screen.
b) If the pinhole is moved by 10m towards the tree, what will be the height of the tree on the screen?

TAKING PHOTOGRAPHS WITH A PINHOLE CAMERA

The pinhole camera can be used to take still photographs if it is modified as follows,

The box should be painted black to eliminate reflection of light.
The translucent screen should be replaced by a light-tight lid with a photographic film fitted on the inside. The film should be fitted in a dark room.

The pinhole should be covered with a thin black card which acts as a shutter as shown,

REFLECTION OF LIGHT (PLANE SURFACES)

All objects, except self luminous objects, become visible because they bounce light back to our eyes. This bouncing off light is called reflection.

There are two types of reflection namely regular and diffused reflections.

When light is reflected by a plane smooth surface, the reflection is regular (specular) and when reflection occurs at a rough surface it is called a diffused reflection. Plane mirrors forms images while shiny sheet of papers cannot. This is because with papers, there is irregular/diffused reflection while image formation requires regular/specular reflections only.

REFLECTION BY PLANE MIRRORS

A plane mirror is a flat smooth reflecting surface which forms images by regular reflection. It is often made by bounding a thin polished metal surface to the back of a flat sheet of glass or silvering the back side of the flat sheet of glass.

The silvered side is normally coated with some paint to protect the silver coating. If the clear and the silvered surfaces are in parallel plane, the mirror is called a plane mirror.

If the surfaces are curved, the mirror is called curved mirrors.

The silvered side of the mirror is shown by shading behind the reflecting surface.

DEFINITION OF TERMS USED IN REFLECTION

Consider the set up below,

Incident ray – is the ray that travels from the source to the reflecting surface.

Angle of incident (i) – is the angle between the incident ray and the normal.

Normal – is the line drawn perpendicularly at the point where the incident ray strikes the reflecting surface.

Reflected ray – is the ray that bounces from the reflecting surface.

Angle of reflection (r) – is the angle between the reflected ray and the normal.

LAWS OF REFLECTION

The incident ray, the reflected ray and the normal at the point of incidence all lie on the same plane.
The angle of incidence, i, equals the angle of reflection, r.

Experiments to show the laws of reflection (exp. 8.6) KLB

ROTATION OF A MIRROR THROUGH AN ANGLE

Consider the mirrors below,

In figure (a), the angle of incidence is 30⁰. The angle of reflection is also 30^o.

Therefore the angle between the incident ray and the reflected ray is 60^o i.e., (30^o + 30^o).

In figure (b), mirror m₁ is rotated by an angle 10^o to the new position m₂. The normal BN moves through an angle 10^o. Angle between the two normals is 10^o.

In figure (c), for the same incident ray AB, the new angle of incident = 30^o+

10^o =40^o. The new angle of reflection = 40^o. Hence the new angle between the angle of incidence and the angle of reflection = 40^o+ 40⁰=80⁰.

In figure (d), the angle between the two reflected rays BC and BD =20^o.

For the same incident ray, the angle of rotation of the reflected ray is twice the angle of rotation of the mirror.

EXAMPLE 3

A ray of light is incident along the normal in a plane mirror. The mirror is then rotated through an angle of 200. Calculate the angle between the first reflected ray and the second reflected ray.

SOLN

Angle of rotation of reflected rays = 2 x angle of rotation of the mirror

=2 x 20⁰

=40^o

EXAMPLE 4

The figure below shows a ray incident at an angle of 25o at position 1.

The mirror is turned through 6⁰ to position 2. Through what angle is the reflected ray rotated.

SOLN

Rotation change the angle of incidence from 25^o to (25+6) =31⁰.

Hence the angle of reflection is 31o from the new normal. The total change in the angle of reflected ray is 12^o

EXAMPLE 5

A suspended plane mirror makes an angle of 20^o with a wall. Light from a window strikes the mirror horizontally. Find;

Angle of incidence.
The angle between the horizontal and the reflected ray

FORMATION OF IMAGES BY PLANE MIRRORS

Images formed are far behind the mirror as the object is in front of the mirror i.e. image distance is equal to object distance from the mirror

Characteristics of images formed by plane mirrors

Image formed is the same size as the object.
The image is formed far behind the mirror as the object is in front of the mirror.
Images formed are laterally inverted g. when you raise your right hand, the image raises its left hand.

Virtual images – are formed by rays that appear to come from the image. Such images are not formed on the screen as they are only imaginary.

EXAMPLE 6

A girl stands 2m in front of a plane mirror.

Calculate the distance between the girl and her image
If the mirror is moved 0.6m to the girl, what will be the distance between her and image.

SOLN

2+2 = 4m
Object distance =2-0.6 =1.4m

Total distance = 1.4 + 1.4 = 2.8m

IMAGES FORMED BY MIRRORS AT AN ANGLE

When an angle Ѳ is 90^o, the number of images formed, n, is 3, i.e.

n = 360− 1 =3 images

When the angle Ѳ is 60^o, the number of images formed, n, is 5, i.e.

n = 360− 1 = 5 images

In general if the angle between two placed mirrors is Ѳ, then the number of images formed, n, is given by,

n = 360^o − 1

EXAMPLE 7

Two plane mirrors are kept inclined to each other at 120^o. Calculate the number of images formed by the mirrors.

SOLN

n = 360− 1 =2 images

120

EXAMPLE 8

At what angle would the two mirrors inclined to form 17 images.

SOLN

17 = 360 – 1

18Ѳ = 360⁰

Ѳ = 20^o

Mirror Parallel To Each Other

When the mirrors are parallel i.e. Ѳ= 0^o, the number of images is given by,

n = 360^o− 1 =∞ (infinite number of images)

0^o

In this case, each image acts as an object in the second and first mirror as illustrated below;

EXAMPLE 9

Two parallel plane mirrors are placed 30cm apart. An object placed between them 10cm from one mirror. Determine the image distance of two nearest images formed by each mirror.

SOLN

Image distance = object distance

Image distance on mirror 1= 10cm

Image distance on mirror 2 = 20cm

EXAMPLE 10

Two plane mirrors inclined at an angle 60^o to each other. A ray of light makes an angle of 40^owith mirror M₁ and goes on to strike mirror M₂.

Find the angle of reflection on the second mirror M₂.

The angle of reflection = 10^o

APPLICATIONS OF PLANE MIRRORS

The kaleidoscope

A kaleidoscope or mirror scope is a device used to produce a series of beautiful symmetrical images. Two plane mirrors are placed at an angle of 60^o inside a long tube.

The bottom of the tube is a ground glass plate for admitting light. On this plate is small scattered small pieces of brightly coloured glass, which act as objects.

When one looks down the tube, five images of the object are seen which together with the object form a symmetrical pattern in six sectors as shown below

The instrument is used by designers to obtain ideas on systematic patterns.

The periscope

This is an instrument used to view objects over obstacles. It is used in submarines and also to watch over crowds. The images seen with the aid of the instrument are erect and virtual.

A periscope uses two plane mirrors kept parallel to each other and the polished surfaces facing each other. Each plane mirror makes an angle of 45^owith the horizontal. Light from the object is turned through 90⁰at each mirror and reaches the eye as shown

The rays from the object are reflected by the top and then reflected again by the bottom into the observer. The image formed is virtual, upright and same size as the object.

Barber shops and saloon

QUESTIONS

What is meant by a virtual image?
The figure below shows an object O being viewed using two inclined mirrors M₁ and M₂.

Complete the diagram by sketching rays to show the position of the image as seen by the eye E

The figure below shows an object O placed in front of a plane mirror

On the same diagram, draw rays to locate the position of the image 1 as seen from the eye E.

The diagram shows a ray of light incident on a plane mirror at point O.

The mirror is rotated clockwise through an angle of 30⁰ about an axis perpendicular to the paper. Determine the angle through which the reflected ray rotated.

A luminous point object took 3 s to move from P to Q in front of a pinhole camera as shown below.

What is speed in cm/s of the image on the screen?

The diagram shows the image of a watch face in a plane mirror

What is the time shown on the watch face?

(a) Give two main reasons why concave mirrors are unsuitable as driving mirrors

(b) State one disadvantage of a convex mirror as a driving mirror

Explain why a concave mirror is suitable for use as a make up mirror.
In the space provided below, sketch a labeled diagram to show how a pinhole camera forms an image of a vertical object placed in front of the pinhole
A building standing 100m from a pinhole camera produces on the screen of the camera an image 5 cm high 10 cm behind the pinhole. Determine the actual height of the building.
What property of light is suggested by the formation of shadows?
State the reason why when a ray of light strikes a mirror at 90o, the reflected ray travels along the same path as the incident ray.
Figure 1 shows two point objects A, and B, placed in front of a mirror M

Sketch a ray diagram to show the positions of their images as seen by the eye.

What is meant by virtual image?
Figure 2 shows a ray of light incident on plane mirror at point O.

The mirror is rotated clockwise through an angle 300 about an axis perpendicular to the paper. Determine the angle through which the reflected ray rotated.

3 shows an object O being viewed using tow inclined mirrors M1 and M2.

Complete the diagram by sketching rays to show the position of the image as seen by the eye.

Sketch the same diagram, the path of the ray until it leaves the two mirrors. Indicate the angles at each reflection

In a certain pinhole camera, the screen is 10cm from the pinhole. When the camera is placed 6m away from a tree, a sharp image of the tree 16cm high is formed on the screen. Determine the height of the tree
Figure 4 shows three point sources of light with an opaque object placed between them and the screen.

Explain the nature of the shadow formed along B and C.

State the number of images formed when an object is between two plane mirrors placed in parallel.
Figure 5 shows a ray of light incident on a mirror at an angle of 450. Another mirror is placed at an angle of 450 to the first one as shown .Sketch the path of the ray until it emerges

SOLUTION

– Image that cannot be formed on screen.

– Always on the opposite side of the object

Angle of rotation of reflected ray = 2(angle of rotation of mirrors)

= 2x 30⁰

=60⁰

Measure P₁Q₁in cm (i.e. length of image on the screen as shown below)

Divide this value by 3 seconds i.e. velocity = distance / time

4:05 p.m
a) -Key form real inverted images

-Highly magnified images which give a wrong perception of object distance.

-Small field of view.

b) Very small images, giving the illusion that the objects are far away.

Can from magnified, erected images.

Where O = object; h = pin-hole; u- Object distance; v- Image distance

u =100m

h_i = 0.5cm

TOPIC 9: ELECTROSTATICS 1

This is the study of static charges. There are two types of charges i.e. negative charge and positive charge.

When a plastic ruler is brought near to small pieces of paper, it will be noted that it cannot be able to attract the small pieces of paper. This is because the ruler is electrically neutral.

When the ruler is rubbed against fur or hair the static charges becomes active. In this case, between the ruler and fur or hair they interchange charges whereby one becomes positively charged and the other negatively charged. Because of this the ruler is able to attract the small pieces of paper.

The SI unit of charge is coulomb (C). Millicoulombs and micro-coulombs are also used.

1000 millicoulombs = 1 coulomb

1000000 micro-coulomb = 1 coulomb

Origin of Charge

Matter is made up of atoms. An atom has particles known as protons, electrons and neutrons. Protons are positively charged, electrons are negatively charged and neutrons are neutral.

Protons and neutrons are found at the centre and nucleus of the atom while electrons are found moving around the energy levels.

The nucleus has positive charge due to the charges on the protons. Electrons in the outermost orbit are weakly held by the nucleus and can be transfer easily from one material to another by rubbing.

The material that gains electrons becomes negatively charged and that which loses electrons becomes positively charged. A negatively or positively charged atom is called an ion.

Materials like polythene and plastic they acquire electrons when they are rubbed hence they become negatively charged while materials like acetate, Perspex and glass have their electrons removed from their surface when rubbed and they become positively charged.

In general origin of charge is based on the atom of any given substance; each atom contains protons, electrons and neutrons.

Basic Law of Charges

This law is based on the relationship between charges when they are brought near to each other. It states that unlike charges attract while like charges repel.

CHARGING MATERIALS

Materials can be charged by the following methods;

Induction
Contact
Separation

INDUCTION

This is the ability in which a body which is charged finds to influence another adjacent to acquire an opposite.

A positively charged material, when it is brought near to another uncharged material, it will influence another body to acquire some charge.

The positive charges in B which has been repelled are removed by the process of earthing.

Earthing is the process through which electrons are made to the ground or from the ground through a conductor.

In the above case when a conductor is connected to B, electrons will flow from the ground to neutralise the positive charges.

After the positive charges have been neutralised, the conductor in B is removed fast while the two bodies are maintained adjacent to one another. This is to enable the electrons in B to remain within that body but if you remove body A while the conductor is connected with B, those electrons in B will escape to the ground.

When body A and B are separated as far as possible the negative charges will distribute uniformly.

CHARGING BY CONTACT

In this method two bodies are brought directly into contact, because of this some charges are able to cross over between their surfaces.

In this method, one of the bodies must be charged. That charge will influence the other body to acquire some charge.

NOTE: When a body is charged by contact method, it acquires charges that are similar to the ones on the charging rod.

In the diagram above body A was charged positively and because of this charge when it is in contact to body B it attracts negative charges and repel with positive charge.

When the two are made to be in contact the negative charge in body B crosses to body A to neutralise part of its positive charge.

If this process continues with time the number of positive charges in A will reduce and the number of the positive charges in B will increase.

Finally when the two bodies are separated the positive charges in B will distribute uniformly.

CHARGING BY SEPARATION

In this case two uncharged bodies are brought near to charged material. By the process of induction the two bodies will acquire an opposite charge because of attraction and repulsion.

The positive charge in A influence negative charges in X because of attraction while it influences positive charges in Y because of repulsion.

NOTE: In order to sustain the two opposite charge in X and Y in the two bodies, they are first separated while the position in body A is maintained. Finally when they are separated the two bodies will distribute uniformly as shown.

THE ELECTROSCOPE

This is an instrument which works on the principle of electrostatic charges. It is also used for investigating the effects of electric charges.

The gold-leaf electroscope consists of a thin gold or aluminium leaf of plate connected to a metal rod that has a brass cap at the top as shown,

The cap acquires the charges through induction or contact and spreads it through the rod to the plate and leaf.

The cap is circular to ensure uniform distribution of charges.

Both the leaf and the plate show the presence of charges by repelling each other, making the leaf to diverge. The absence of charges is also shown when leaf divergence decreases.

Metal casing is for protecting the leaf from the effects of draught. The casing has a glass window through which observations are made.

The rod is supported by passing it through a plug of good insulating material such as rubber. The insulator stops charge given to the cap from spreading onto the case and leaking away. The casing may be a terminal connected to the earth.

When the electroscope is touched by a finger or connected to the earth by a wire, electrons either flow to the earth, depending on the charge on the electroscope.

The process of losing to or gaining charges from the earth through a conductor is called earthing.

Charging an Electroscope by Contact Method

In this method, a charged body is brought into contact with the cap of the electroscope as shown in the figure below,

Because the positive charge on the rod are in contact with the negative charge at the cap, the two charges neutralise i.e. negative charges move to the rod and positive charge move to the cap.

It will be observed that at the leaf, the leaf diverges because of like charges at the point (positive charges).

The more positive charges at the leaf will make the leaf to diverge at a greater angle. If the process is continued, the electroscope will charge to a maximum point in which the leaf cannot diverge any further.

NOTE: The charged material coming into contact with the cap of the electroscope is an insulator. Only charges on the rod’s surface coming into contact with the cap are used in neutralizing the charges induced on the cap.

Charging Through Induction

In this method a charged body is brought near to the cap of the electroscope and because of attraction the cap is going to have opposite charge while at the leaf is going to have same charge because of repulsion as shown,

The positive charges at rod attract the negative charge at the cap and repel positive charge at the leaf. The positive charges at the leaf repel one another thus making the leaf to diverge through an angle.

In order to eliminate the charges at the leaf, one is required to earth the cap by the use of a finger or a wire while maintaining the position of the charging rod as shown;

Through earthing electrons are going to flow from the ground through the cap down the leaf to neutralise the positive charge hence making the leaf to fall.

These electrons when they are passing through the cap, they are not affected by the negative charge at the cap. This is because the negative charge at the cap and the positive charge on the rod are strongly attached because of attraction.

While maintaining the position of the rod removes the finger or the earth wire first in order to avoid the negative charge at the cap not to escape down to the ground.

Finally remove the positive charged rod away from the cap. Because of like charges at the cap they will repel one another in order to distribute uniformly on the cap and the leaf.

The negative charges which move to the leaf diverge once more indicating electroscope has been charged.

ASSIGNMENT

Use a negatively charged rod to explain how to charge an electroscope using induction method.

USES OF THE ELECTROSCOPE

To detect the presence of charge on a body

–The material to be tested is placed on or close to the cap of the electroscope. If it is not charged, the leaf does not diverge.

To test the sign of charge on a charged body

–Charge an electroscope negatively by contact method. Slowly bring a negative rod to be tested close to the cap of the electroscope. The leaf diverges more. It does so because the negative charges on the rod repel more charges from the cap to the plate and the leaf. Similar charges in the plate and the leaf are repelled more.

–When a strong positively charged rod is brought from high position towards a negatively charged electroscope, the leaf divergence first decreases then increases as the rod approaches the cap. The leaf divergence reduces slightly first because the positive on the rod attract negative charges on the leaf and plate, making the electroscope neutral. On moving the rod, much lower, the leaf divergence increases again to higher position. This is because the strong positively charged rod attracts more electrons from the plate and leaf, making them more positive. Hence, they repel further.

NOTE:

The same observations are made when a negatively charged rod is brought towards a positively charged electroscope. On moving a neutral conductor close to a charged electroscope, leaf divergence decreases. Charges on the electroscope induce opposite charges on the conductor.

Charge on the electroscope	Charge brought near the cap	Effect on the leaf divergence
+	+	Increase
–	–	Increase
+	–	Decrease
–	+	Decrease
+ or –	Uncharged	Decrease

An increase in divergence of the leaf is therefore the only sure way of confirming the kind of charge on a body.

To test the quantity of charge on a charged body

–Small bodies have few charges compared to big ones of the same kind.

To test for insulation properties of a material

–Materials like copper, iron, aluminium, zinc and graphite make the leaf divergence decrease. Materials like plastic, glass, charcoal and wood do not affect the divergence of the leaf. For metals and graphite, the leaf decreases in divergence because they allow electrons to flow between the electroscope and the earth. Such materials are called conductors. In conductors, electrons freely move from one atom to another. Such electrons are called free electrons.

For materials like plastic, glass, wood there is no change in leaf divergence because they do not allow electrons to flow between the electroscope and the earth. In these materials, electrons are not free to move and are strongly bound to their nuclei. These materials are called insulators. There are other materials like silicon and germanium which conduct under special conditions. This conductivity is between conductivity of insulators and conductors. Such materials are called semi-conductors.

CHARGES IN AIR

Air can also be charged. It is shown by heating air above a charged electroscope. It is observed that the leaf divergence decreases.

When fuel burns, chemical reactions yield ionised products. The ions move and collide with air molecules making air to be ionised. Ionisation produces both negative and positive charges.

The ions carrying opposite charge to the electroscope are attracted to the cap of the electroscope, resulting in the discharge of the electroscope.

APPLICATION OF ELECTROSTATIC CHARGES

Electrostatic precipitator

It is used in industries to reduce pollutants. The figure below shows a common precipitator used in chimneys.

It consists of a cylindrical metal plate fixed along the walls of the chimney and a wire mesh suspended through the middle. The plate is charged positively at a potential of about 5000V while the wire mesh is negatively charged.

A strong electric field is set up between the plates, which ionises the particles of the pollutants. These are attracted to the plate.

Spray painting

The can is filled with paint and nozzle charged. During spraying, the paint droplets acquire similar charges and therefore spread out finely due to repulsion.

As they approach the metallic body they induce opposite charges which in turn attract them to the surface. Therefore little paint is used.

Finger printing and photocopying

DANGERS OF ELECTROSTATICS

When a liquid flows through a pipe its molecules become charged due to rubbing on the inner surface of the pipe. If the liquid is inflammable it can cause sparks and explode.

Similarly, explosive fuel carried in plastic cans can get charged due to rubbing which may result in sparks and even explosion.

It is therefore advisable to store fuels in metal cans so that any charges generated continually leak.

QUESTIONS

Explain why fuel tankers have a loose chain hanging under them to touch the ground as they move?
Why do some motor tyres contain graphite?
Two isolated and insulated spheres A and B carry the same positive charge. Sketch the electric lines of force of their field when placed close to each other but not touching some.
State the observation on the leaves of a positively charged electroscope when a negative charge is brought near it.
The fig shows sketches of two types of houses built in a lighting prone area. State with reasons, which house is safer to stay in during lighting and thunderstorms?

The diagram below shows a circuit with a capacitor C and a lamp L. When the sketch is closed at Y, the lamp L lights. When the switch is closed at X, L does not light. Explain the observation.

In the clothing and textile industries the machines experiences electrostatics forces at certain points. Suggest one method of reducing these forces.
State two other factors to be considered in constructing a capacitor other than the surface area of the plates.
State the precaution that is taken when charging a metal object.
(a) (i) State coulombs law of electrostatic force

(ii) Define capacitance

(b) Describe how the type of charge on a charged metal rod can be determined

(c) The fig. Shows hollow negatively charged sphere with a metal disk attached to an insulator placed inside. State what would happen to the leaf of an uncharged electroscope if the metal disk were brought near the cap of the electroscope. Give a reason for your answer.

(d) State two ways of charging the magnitude of the deflection of the leaf of an electroscope.

Explain why the leaf of an uncharged object is brought near the cap.
A glass rod can be charged positively by rubbing it with silk. Explain what happens when the glass rod is being charged.
State the law of electrostatic charges.
A positively charged rod is brought near the cap of a leaf electroscope. The cap is the earthed momentarily by touching with the finger. Finally the rod is withdrawn. The electroscope is found to be negatively charged. Explain how this charge is acquired.

SOLUTIONS

To induce/effect earthing process thus allows unnecessary charges to leak to the ground, causing neutralization of the charges. This prevents the formation of sparks which can cause explosion

Graphite has free and mobile electrons. This causes neutralizations of the electrostatic charges.

The leaf in the electroscope falls
Metal roofed house. Because there is less resistance of the flow of charges to the ground so if struck by lighting it would conduct it to the ground. The other one would burn or have the people inside struck by the lightening.
At x the capacitor is charged only once and the keeps charging and discharging in opposite directions hence current keeps alternating at the a.c frequency. This lights the bulb continuously.
Earthing the machines/using spikes.
Material used between the two plates of the capacitor.
Well insulated / avoid touching
a)Ability to store charge given by the quantity of charge it can store per unit p.d
b) Bring it near a charged electroscope (say +vely). If not, charge the electroscope – vely and bring the rod near. If divergence is observed then they have the same charge. Note that if decrease in divergence is observed in both cases then the rod is simply a conductor and it’s not charged.
c) Nothing would happen to the leaf of the electroscope. This is because in a hollow charged conductor, the charged conductor and not inside
d) – Earthing or using another

– Charged body

Like charges repel unlike charges attract.
On earthing negative charges flow to the leaves from earth to neutralize positive charges when the rod is withdrawn the leaves are left with net negative

Maths Form 4 notes free

October 5, 2025 Hillary Kangwana Leave a comment

FREE FORM FOUR MATHEMATICS NOTES

Read all the form 4 notes here. You can also download a copy of the pdf notes on this link; MATH FORM FOUR NOTES

Specific Objectives

By the end of the topic the learner should be able to:

(a) Relate image and object under a given transformation on the Cartesian

Plane;

(b) Determine the matrix of a transformation;

(d) Determine and identify a single matrix for successive transformation;

(e) Relate identity matrix and transformation;

(f) Determine the inverse of a transformation;

(g) Establish and use the relationship between area scale factor and determinant of a matrix;

(h) Determine shear and stretch transformations;

(i) Define and distinguish isometric and non-isometric transformation;

(j) Apply transformation to real life situations.

Content

(a) Transformation on the Cartesian plane

(b) Identification of transformation matrix

(d) Single matrix of transformation for successive transformations

(e) Identity matrix and transformation

(f) Inverse of a transformations

(g) Area scale factor and determinant of a matrix

(h) Shear and stretch (include their matrices)

(i) Isometric and non-isometric transformations

(j) Application of transformation to real life situations.

Matrices of transformation

A transformation change the shape, position or size of an object as discussed in book two.

Pre –multiplication of any 2 x 1 column vector by a 2 x 2 matrix results in a 2 x 1 column vector

Example

If the vector is thought of as apposition vector that is to mean that it is representing the points with coordinates (7, -1) to the point (17, -9).

Note;

The transformation matrix has an effect on each point of the plan. Let’s make T a transformation matrix T Then T maps points (x, y) onto image points

Finding the Matrix of transformation

The objective is to find the matrix of given transformation.

Examples

Find the matrix of transformation of triangle PQR with vertices P (1, 3) Q (3, 3) and R (2, 5).The vertices of the image of the triangle sis.

Solution

Let the matrix of the transformation be

Equating the corresponding elements and solving simultaneously

2a= 2

2c= 0

Therefore the transformation matrix is

Example

A trapezium with vertices A (1 ,4) B(3,1) C (5,1) and D(7,4) is mapped onto a trapezium whose vertices are .Describe the transformation and find its matrix

Solution

Let the matrix of the transformation be

Equating the corresponding elements we get;

Solve the equations simulteneously

11b = -11 hence b =-1 or a = 0

3c + d =3

The matrix of the transformation is therefore

The transformation is positive quarter turn about the origin

Note;

Under any transformation represented by a 2 x 2 matrix, the origin is invariant, meaning it does not change its position.Therefore if the transformtion is a rotation it must be about the origin or if the transformation is reflection it must be on a mirror line which passses through the origin.

The unit square

The unit square ABCD with vertices A helps us to get the transformation of a given matrix and also to identify what trasformation a given matrix represent.

Example

Find the images of I and J under the trasformation whose matrix is;

Solution

NOTE;

The images of I and J under transformation represented by any 2 x 2 matrix i.e., are

Example

Find the matrix of reflection in the line y = 0 or x axis.

Solution

Using a unit square the image of B is ( 1, 0) and D is (0 , -1 ) .Therefore , the matrix of the transformation is

Example

Show on a diagram the unit square and it image under the transformation represented by the matrix

Solution

Using a unit square, the image of I is ( 1 ,0 ), the image of J is ( 4 , 1),the image of O is ( 0,0) and that of K is

Successive transformations

The process of performing two or more transformations in order is called successive transformation eg performing transformation H followed by transformation Y is written as follows YH or if A , b and C are transformations ; then ABC means perform C first ,then B and finally A , in that order.

The matrices listed below all perform different rotations/reflections:

This transformation matrix is the identity matrix. When multiplying by this matrix, the point matrix is unaffected and the new matrix is exactly the same as the point matrix.

This transformation matrix creates a reflection in the x-axis. When multiplying by this matrix, the x co-ordinate remains unchanged, but the y co-ordinate changes sign.

This transformation matrix creates a reflection in the y-axis. When multiplying by this matrix, the y co-ordinate remains unchanged, but the x co-ordinate changes sign.

This transformation matrix creates a rotation of 180 degrees. When multiplying by this matrix, the point matrix is rotated 180 degrees around (0, 0). This changes the sign of both the x and y co-ordinates.

This transformation matrix creates a reflection in the line y=x. When multiplying by this matrix, the x co-ordinate becomes the y co-ordinate and the y-ordinate becomes the x co-ordinate.

This transformation matrix rotates the point matrix 90 degrees clockwise. When multiplying by this matrix, the point matrix is rotated 90 degrees clockwise around (0, 0).

This transformation matrix rotates the point matrix 90 degrees anti-clockwise. When multiplying by this matrix, the point matrix is rotated 90 degrees anti-clockwise around (0, 0).

This transformation matrix creates a reflection in the line y=-x. When multiplying by this matrix, the point matrix is reflected in the line y=-x changing the signs of both co-ordinates and swapping their values.

Inverse matrix transformation

A transformation matrix that maps an image back to the object is called an inverse of matrix.

Note;

If A is a transformation which maps an object T onto an image ,then a transformation that can map back to T is called the inverse of the transformation A , written as image .

If R is a positive quarter turn about the origin the matrix for R is and the matrix for is hence

Example

T is a triangle with vertices A (2, 4), B (1, 2) and C (4, 2).S is a transformation represented by the matrix

Draw T and its image under the transformation S
Find the matrix of the inverse of the transformation S

Solution

Using transformation matrix S =

Let the inverse of the transformation matrix be. This can be done in the following ways

Therefore

Equating corresponding elements and solving simultaneously;

Therefore

Area Scale Factor and Determinant of Matrix

The ratio of area of image to area object is the area scale factor (A.S.F)

Are scale factor =

Area scale factor is numerically equal to the determinant. If the determinant is negative you simply ignore the negative sign.

Example

Area of the object is 4 cm and that of image is 36 cm find the area scale factor.

Solution

If it has a matrix of

Shear and stretch

Shear

The transformation that maps an object (in orange) to its image (in blue) is called a shear

The object has same base and equal heights. Therefore, their areas are equal. Under any shear, area is always invariant ( fixed)

A shear is fully described by giving;

The invariant line
A point not on the invariant line, and its image.

Example

A shear X axis invariant

Example

A shear Y axis invariant

Note;

Shear with x axis invariant is represented by a matrix of the form under this trasnsformation,J (0, 1) is mapped onto .

Likewise a shear with y – axis invariant is represented by a matrix of the form ( ). Under this transformation, I (0,1) is mapped onto .

Stretch

A stretch is a transformation which enlarges all distance in a particular direction by a constant factor. A stretch is described fully by giving;

The scale factor
The invariant line

Note;

i.)If K is greater than 1, then this really is a stretch.

ii.) If k is less than one 1, it is a squish but we still call it a stretch

iii.)If k = 1, then this transformation is really the identity i.e. it has no effect.

Example

Using a unit square, find the matrix of the stretch with y axis invariant ad scale factor 3

Solution

The image of I is therefore the matrix of the stretch is

Note;

The matrix of the stretch with the y-axis invariant and scale factor k is and the matrix of a stretch with x – axis invariant and scale factor k is

Isometric and Non- Isometric Transformation

Isometric transformations are those in which the object and the image have the same shape and size (congruent) e.g. rotation, reflection and translation

Non- isometric transformations are those in which the object and the image are not congruent e.g., shear stretch and enlargement

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

Matrix p is given by 1 2

4 3

(a) Find P^-1

(b) Two institutions, Elimu and Somo, purchase beans at Kshs. B per bag and

maize at Kshs m per bag. Elimu purchased 8 bags of beans and 14 bags of maize for Kshs 47,600. Somo purchased 10 bags of beans and 16 of maize for Kshs. 57,400

(c) The price of beans later went up by 5% and that of maize remained constant. Elimu bought the same quantity of beans but spent the same total amount of money as before on the two items. State the new ratio of beans to maize.

A triangle is formed by the coordinates A (2, 1) B (4, 1) and C (1, 6). It is rotated

clockwise through 90⁰ about the origin. Find the coordinates of this image.

On the grid provided on the opposite page A (1, 2) B (7, 2) C (4, 4) D (3, 4) is a trapezium

(a) ABCD is mapped onto A’B’C’D’ by a positive quarter turn. Draw the image A’B’C’D on the grid

(b) A transformation -2 -1 maps A’B’C’D onto A”B” C”D” Find the coordinates

0 1 of A”B”C”D”

A triangle T whose vertices are A (2, 3) B (5, 3) and C (4, 1) is mapped onto triangle T¹ whose vertices are A¹ (-4, 3) B¹ (-1, 3) and C¹ (x, y) by a

Transformation M = a b

c d

a) Find the: (i) Matrix M of the transformation

(ii) Coordinates of C₁

b) Triangle T²is the image of triangle T¹ under a reflection in the line y = x.

Find a single matrix that maps T and T₂

Triangles ABC is such that A is (2, 0), B (2, 4), C (4, 4) and A”B”C” is such that A” is (0, 2), B” (-4 – 10) and C “is (-4, -12) are drawn on the Cartesian plane

Triangle ABC is mapped onto A”B”C” by two successive transformations

R = a b

c d Followed by P = 0 -1

-1 0

(a) Find R

(b) Using the same scale and axes, draw triangles A’B’C’, the image of triangle ABC under transformation R

Describe fully, the transformation represented by matrix R

Triangle ABC is shown on the coordinate’s plane below

(a) Given that A (-6, 5) is mapped onto A (6,-4) by a shear with y- axis invariant

Draw triangle A’B’C’, the image of triangle ABC under the shear
Determine the matrix representing this shear

(b) Triangle A B C is mapped on to A” B” C” by a transformation defined by the matrix -1 0

1½ -1

(i) Draw triangle A” B” C”

(ii) Describe fully a single transformation that maps ABC onto A”B” C”

Determine the inverse T^‑1 of the matrix 1 2

1 -1

Hence find the coordinates to the point at which the two lines

x + 2y = 7 and x – y =1

Given that A = 0 -1 and B = -1 0

3 2 2 -4

Find the value of x if

(i) A- 2x = 2B

(ii) 3x – 2A = 3B

(iii) 2A – 3B = 2x

The transformation R given by the matrix

A = a b maps 17 to 15 and 0 to -8

c d 0 8 17 15

(a) Determine the matrix A giving a, b, c and d as fractions

(b) Given that A represents a rotation through the origin determine the angle of rotation.

CHAPTER FIFTY SEVEN

Specific Objectives

By the end of the topic the learner should be able to:

(a) State the measures of central t e n d e n c y;

(b) Calculate the mean using the assumed mean method;

(d) Estimate the median and the quartiles b y

– Calculation and

– Using ogive;

(e) Define and calculate the measures of dispersion: range, quartiles,interquartile range, quartile deviation, variance and standard deviation

(f) Interpret measures of dispersion

Content

(a) Mean from assumed mean:

(b) Cumulative frequency table

(d) Meadian

(e) Quartiles

(f) Range

(g) Interquartile range

(h) Quartile deviation

(i) Variance

(j) Standard deviation

These statistical measures are called measures of central tendency and they are mean, mode and median.

Mean using working (Assumed) Mean

Assumed mean is a method of calculating the arithmetic men and standard deviation of a data set. It simplifies calculation.

Example

The masses to the nearest kilogram of 40 students in the form 3 class were measured and recorded in the table below. Calculate the mean mass

Mass kg	47	48	49	50	51	52	53
Number of employees	2	0	1	2	3	2	5

54	55	56	57	58	59	60
6	7	5	3	2	1	1

Solution

We are using assumed mean of 53

Mass x kg	t= x – 53	f	ft

47 48 49 50 51 52 53 54	-6 -5 -4 -3 -2 -1 0 1	2 0 1 2 3 2 5 6	-12 0 -4 -6 -6 -2 0 6
55	2	7	14

56	3	5	15
57	4	3	12
58	5	2	10
60	7	1 1	6 7
		Σf = 40	Σft = 40

Mean of t

Mean of x = 53 + mean of t

= 53 + 1

= 54

Mean of grouped data

The masses to the nearest gram of 100 eggs were as follows

Marks	100- 103	104- 107	108- 111	112-115	116-119	120-123
Frequency	1	15	42	31	8	3

Find the mean mass

Solution

Let use a working mean of 109.5.

class	Mid-point x	t= x – 109.5	f	f t

100-103	101.5	-8	1	– 8
104-107	105.5	-4	15	– 60
108-111	109.5	0	42	0
112-115	113.5	4	31	124
116- 119 120 -123	117.5 121.5	8 12	8 3	64 36
			Σf= 100	Σft = 156

Mean of t =

Therefore,mean of x = 109.5 + mean of t

= 109.5 + 1.56

= 111.06 g

To get the mean of a grouped data easily,we divide each figure by the class width after substracting the assumed mean.Inorder to obtain the mean of the original data from the mean of the new set of data, we will have to reverse the steps in the following order;

Multiply the mean by the class width and then add the working mean.

Example

The example above to be used to demonstrate the steps

class	Mid-point x	t=	f	f t

100-103	101.5	-2	1	– 2
104-107	105.5	-1	15	– 15
108-111	109.5	0	42	0
112-115	113.5	1	31	31
116- 119 120 -123	117.5 121.5	2 3	8 3	16 9
			Σf= 100	Σft = 39

= 0.39

Therefore = 0.39 x 4 + 109.5

= 1.56 + 109.5

= 111.06 g

Quartiles, Deciles and Percentiles

A median divides a set of data into two equal part with equal number of items.

Quartiles divides a set of data into four equal parts.The lower quartile is the median of the bottom half.The upper quartile is the median of the top half and the middle coincides with the median of the whole set od data

Deciles divides a set of data into ten equal parts.Percentiles divides a set of data into hundred equal parts.

Note;

For percentiles deciles and quartiles the data is arranged in order of size.

Example

*Height in cm*	145- 149	150-154	155-159	160- 164	165-169	170-174	175-179
*frquency*	2	5	16	9	5	2	1

Calculate the ;

Median height
)Lower quartile

ii) Upper quartile

80^th percentile

Solution

There are 40 students. Therefore, the median height is the average of the heights of the 20^th and 21^st

class	frequency	Cumulative frequency
145-149	2	2
150 – 154	5	7
155 – 159	16	23
160 – 164 165 – 169	9 5	32 37
170 – 174 175 – 179	2 1	39 40

Both the 20^thand 21^ststudents falls in the 155 -159 class. This class is called the median class. Using the formula m = L +

Where L is the lower class limit of the median class

N is the total frequency

C is the cumulative frequency above the median class

I is the class interval

F is the frequency of the median class

Therefor;

Height of the 20^th student = 154.5 +

= 154.5 + 4.0625

=158.5625

Height of the 21^st = 154.5 +

= 154.5 + 4.375

=158.875

Therefore median height =

= 158.7 cm

(I ) lower quartile = L +

The 10^th student fall in the in 155 – 159 class

= 154.5 +

5 + 0.9375

4375

(ii) Upper quartile= L +

The 10^th student fall in the in 155 – 159 class

= 159.5 +

5 + 3.888

3889

Note;

The median corresponds to the middle quartile or the 50^th percentile

the 32^nd student falls in the 160 -164 class

= L +

= 159.5 +

5 + 5

Example

Determine the upper quartile and the lower quartile for the following set of numbers

5, 10 ,6 ,5 ,8, 7 ,3 ,2 ,7 , 8 ,9

Solution

Arranging in ascending order

2, 3, 5,5,6, 7,7,8,8,9,10

The median is 7

The lower quartile is the median of the first half, which is 5.

The upper quartile is the median of the second half, which is 8.

Median from cumulative frequency curve

Graph for cumulative frequency is called an ogive. We plot a graph of cumulative frequency against the upper class limit.

Example

Given the class interval of the measurement and the frequency,we first find the cumulative frequency as shown below.

Then draw the graph of cumulative frequency against upper class limit

Arm Span (cm)	Frequency (f)	Cumulative Frequency
140 ≤ x ‹ 145	3	3
145 ≤ x ‹ 150	1	4
150 ≤ x ‹ 155	4	8
155 ≤ x ‹ 160	8	16
160 ≤ x ‹ 165	7	23
165 ≤ x ‹ 170	5	28
170 ≤ x ‹ 175	2	30
Total:	30

Solution

Example

The table below shows marks of 100 candidates in an examination

1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
4	9	16	24	18	12	8	5	3	1

Marks

FRCY

Determine the median and the quartiles
If 55 marks is the pass mark, estimate how many students passed
Find the pass mark if 70% of the students are to pass

Determine the range of marks obtained by

(I) The middle 50 % of the students

(ii) The middle 80% of the students

Solution

1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
4	9	16	24	18	12	8	5	3	1

Marks

Frqcy

Cumulative 4 13 29 53 71 83 91 96 99 100

Frequency

Solution

Reading from the graph

The median = 39.5

The Lower quartile

The upper quartile

23 candidates scored 55 and over
Pass mark is 31 if 70% of pupils are to pass
(I) The middle 50% include the marks between the lower and the upper quartiles i.e. between 28.5 and 53.5 marks.

(II) The middle 80% include the marks between the first decile and the 9^th decile i.e between 18 and 69 marks

Measure of Dispersion

Range

The difference between the highest value and the lowest value

Disadvantage

It depends only on the two extreme values

Interquartile range

The difference between the lower and upper quartiles. It includes the middle 50% of the values

Semi quartile range

The difference between the lower quartile and upper quartile divided by 2.It is also called the quartile deviation.

Mean Absolute Deviation

If we find the difference of each number from the mean and find their mean , we get the mean Absolute deviation

Variance

The mean of the square of the square of the deviations from the mean is called is called variance or mean deviation.

Example

Deviation from mean(d)	+1	-1	+6	-4	-2	-11	+1	10
f_i	1	1	36	16	4	121	1	100

Sum

Variance =

The square root of the variance is called the standard deviation.It is also called root mean square deviation. For the above example its standard deviation =

Example

The following table shows the number of children per family in a housing estate

*Number of childred*	0	1	2	3	4	5	6
*Number of families*	1	5	11	27	10	4	2

Calculate

The mean number of children per family
The standard deviation

Solution

Number of children	Number of	fx	Deviations		f
(x)	Families (f)		d= x -m
o	1	0	– 3	9	9
1	5	5	– 2	4	20
2	11	22	-1	1	11
3	27	81	0	0	0
4 5 6	10 4 2	40 20 12	1 2 3	1 4 9	10 16 18
	Σf = 60				Σf= – 40

Mean =
Variance =

Example

The table below shows the distribution of marks of 40 candidates in a test

*Marks*	1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
*frequency*	2	2	3	9	12	5	2	3	1	1

Calculate the mean and standard deviation.

Marks	Midpoint ( x)	Frequency (f)	fx	d= x – m		f
1-10	5.5	2	11.0	– 39.5	1560.25	3120.5
11-20	15.5	2	31.0	-29.5	870.25	1740.5
21-30	25.5	3	76.5	-19.5	380.25	1140.75
31 -40	35.5	9	319.5	-9.5	90.25	812.25
41 -50	45.5	12	546.0	0.5	0.25	3.00
51-60	55.5	5	277.5	10.5	110.25	551.25
61- 70 71-80 81 -90 91 -100	65.5 75.5 85.5 95.5	2 3 1 1	131.0 226.5 85.5 95.5	20.5 30.5 40.5 50.5	420.25 930.25 1640.25 2550.25	840.5 2790.75 1640.25 2550.25
		Σf= 40	Σ**f x=1800**			Σf= 15190

Mean

Variance =

= 379.8

Standard deviation =

= 19.49

Note;

Adding or subtracting a constant to or from each number in a set of data does not alter the value of the variance or standard deviation.

More formulas

The formula for getting the variance

Example

The table below shows the length in centimeter of 80 plants of a particular species of tomato

length	152-156	157-161	162-166	167-171	172- 176	177-181
frequency	12	14	24	15	8	7

Calculate the mean and the standard deviation

Solution

Let A = 169

Length	Mid-point x	x-169	t=	f	ft
152 -156	154	-15	-3	12	-36	108
157 -161	159	-10	-2	14	-28	56
162 -166	164	-5	-1	24	-24	24
167 -171	169	0	0	15	0	0
172-176	174	5	1	8	8	8
177-181	179	10	2	7	14	28

Therefore

= -4.125 + 169

= 164.875 ( to 4 s.f)

Variance of t =

= 2.8 – 0.6806

= 2.119

Therefore , variance of x = 2.119 x

= 52.975

= 52.98 ( 4 s.f)

Standard deviation of x =

= 7.279

= 7.28 (to 2 d.p)

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic

Every week the number of absentees in a school was recorded. This was done for 39 weeks these observations were tabulated as shown below

Number of absentees	0.3	4 -7	8 -11	12 – 15	16 – 19	20 – 23
(Number of weeks)	6	9	8	11	3	2

Estimate the median absentee rate per week in the school

The table below shows high altitude wind speeds recorded at a weather station in a period of 100 days.

Wind speed ( knots)	0 – 19	20 – 39	40 – 59	60-79	80- 99	100- 119	120-139	140-159	160-179
Frequency (days)	9	19	22	18	13	11	5	2	1

(a) On the grid provided draw a cumulative frequency graph for the data

(b) Use the graph to estimate

(i) The interquartile range

(ii) The number of days when the wind speed exceeded 125 knots

Five pupils A, B, C, D and E obtained the marks 53, 41, 60, 80 and 56 respectively. The table below shows part of the work to find the standard deviation.

Pupil

Mark x

x – a

( x-a)²

-5

-17

-2

(a) Complete the table

(b) Find the standard deviation

In an agricultural research centre, the length of a sample of 50 maize cobs were measured and recorded as shown in the frequency distribution table below.

Length in cm

Number of cobs

8 – 10

11 – 13

14 – 16

17 – 19

20 – 22

23 – 25

Calculate

The mean
(i) The variance

(ii) The standard deviation

The table below shows the frequency distribution of masses of 50 new- born calves in a ranch

Mass (kg)Frequency

15 – 18 2

19- 22 3

23 – 26 10

27 – 30 14

31 – 34 13

35 – 38 6

39 – 42 2

(a) On the grid provided draw a cumulative frequency graph for the data

(b) Use the graph to estimate

(i) The median mass

(ii) The probability that a calf picked at random has a mass lying between 25 kg and 28 kg.

The table below shows the weight and price of three commodities in a given period

Commodity Weight Price Relatives

X 3 125

Y 4 164

Z 2 140

Calculate the retail index for the group of commodities.

The number of people who attended an agricultural show in one day was 510 men, 1080 women and some children. When the information was represented on a pie chart, the combined angle for the men and women was 216⁰. Find the angle representing the children.
The mass of 40 babies in a certain clinic were recorded as follows:

Mass in Kg No. of babies.

1.0 – 1.9 6

2.0 – 2.9 14

3.0 -3.9 10

4.0 – 4.9 7

5.0 – 5.9 2

6.0 – 6.9 1

Calculate

(a) The inter – quartile range of the data.

(b) The standard deviation of the data using 3.45 as the assumed mean.

The data below shows the masses in grams of 50 potatoes

Mass (g)	25- 34	35-44	45 – 54	55- 64	65 – 74	75-84	85-94
No of potatoes	3	6	16	12	8	4	1

(a) On the grid provide, draw a cumulative frequency curve for the data

(b) Use the graph in (a) above to determine

(i) The 60^th percentile mass

(ii) The percentage of potatoes whose masses lie in the range 53g to 68g

The histogram below represents the distribution of marks obtained in a test.

The bar marked A has a height of 3.2 units and a width of 5 units. The bar marked B has a height of 1.2 units and a width of 10 units

If the frequency of the class represented by bar B is 6, determine the frequency of the class represented by bar A.

A frequency distribution of marks obtained by 120 candidates is to be represented in a histogram. The table below shows the grouped marks. Frequencies for all the groups and also the area and height of the rectangle for the group 30 – 60 marks.

Marks	0-10	10-30	30-60	60-70	70-100
Frequency	12	40	36	8	24
Area of rectangle			180
Height of rectangle			6

(a) (i) Complete the table

(ii) On the grid provided below, draw the histogram

(b) (i) State the group in which the median mark lies

(ii) A vertical line drawn through the median mark divides the total area of the histogram into two equal parts

Using this information or otherwise, estimate the median mark

In an agriculture research centre, the lengths of a sample of 50 maize cobs were measured and recorded as shown in the frequency distribution table below

Length in cm

Number of cobs

8 – 10

11- 13

14 – 16

17- 19

20 – 22

23- 25

Calculate

(a) The mean

(b) (i) The variance

(ii) The standard deviation

The table below shows the frequency distribution of masses of 50 newborn calves in a ranch.

Mass (kg)

Frequency

15 – 18

19- 22

23 – 26

27 – 30

31- 34

35 – 38

39 – 42

(a) On the grid provided draw a cumulative frequency graph for the data

(b) Use the graph to estimate

(i) The median mass

(ii) The probability that a calf picked at random has a mass lying

between 25 kg and 28 kg

The table shows the number of bags of sugar per week and their moving averages

Number of bags per week	340	330	x	343	350	345
Moving averages		331	332	y	346

(a) Find the order of the moving average

(b) Find the value of X and Y axis

CHAPTER FIFTY EIGHT

Specific Objectives

By the end of the topic the learner should be able to:

(a) State the geometric properties of common solids;

(b) Identify projection of a line onto a plane;

(d) Calculate the length between two points in three dimensional geometry;

(e) Identify and calculate the angle between

(i) Two lines;

(ii) A line and a plane;

(ii) Two planes.

Content

(a) Geometrical properties of common solids

(b) Skew lines and projection of a line onto a plane

(d) The angle between

i) A line and a line
ii) A line a plane

iii) A plane and a plane

iv) Angles between skewlines.

Introduction

Geometrical properties of common solids

A geometrical figure having length only is in one dimension
A figure having area but not volume is in two dimension
A figure having vertices ( points),edges(lines) and faces (plans) is in three dimension

Examples of three dimensional figures

Rectangular Prism

A three-dimensional figure having 6 faces, 8 vertices, and 12 edges

Triangular Prism

A three-dimensional figure having 5 faces, 6 vertices, and 9 edges.

Cone

A three- dimensional figure having one face.

Sphere

A three- dimensional figure with no straight lines or line segments

Cube

A three- dimensional figure that is measured by its length, height, and width.

It has 6 faces, 8 vertices, and 12 edges

Cylinder

A three- dimensional figure having 2 circular faces

Rectangular Pyramid

A three-dimensional figure having 5 faces, 5 vertices, and 8 edges

Angle between a line and a plane

The angle between a line and a plane is the angle between the line and its projection on the plane

The angle between the line L and its projection or shadow makes angle A with the plan. Hence the angle between a line and a plane is A.

Example

The angle between a line, r, and a plane, π, is the angle between r and its projection onto π, r’.

height is 4 m

Example

Suppose r’ is 10 cm find the angle

Solution

To find the angle we use tan

Angle Between two planes

Any two planes are either parallel or intersect in a straight line. The angle between two planes is the angle between two lines, one on each plane, which is perpendicular to the line of intersection at the point

Example

The figure below PQRS is a regular tetrahedron of side 4 cm and M is the mid point of RS;

Show that PM is cm long, and that triangle PMQ is isosceles
Calculate the angle between planes PSR and QRS
Calculate the angle between line PQ and plane QRS

Solution

Triangle PRS is equilateral. Since M,is the midpoint of RS , PM is perpendicular bisector

= cm

Similar triangle MQR is right angled at M

= cm

The required angle is triangle PMQ .Using cosine rule
The required angle is triangle PQM

Since triangle PMQ is isosceles with triangle PMQ =

<PQM

(109.46)

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

The diagram below shows a right pyramid VABCD with V as the vertex. The base of the pyramid is rectangle ABCD, WITH ab = 4 cm and BC= 3 cm. The height of the pyramid is 6 cm.

(a) Calculate the

Length of the projection of VA on the base
Angle between the face VAB and the base

(b) P is the mid- point of VC and Q is the mid – point of VD.

Find the angle between the planes VAB and the plane ABPQ

The figure below represents a square based solid with a path marked on it.

Sketch and label the net of the solid.

The diagram below represents a cuboid ABCDEFGH in which FG= 4.5 cm, GH = 8 cm and HC = 6 cm

Calculate:

(a) The length of FC

(b) (i) The size of the angle between the lines FC and FH

(ii) The size of the angle between the lines AB and FH

The base of a right pyramid is a square ABCD of side 2a cm. The slant edges VA, VB, VC and VD are each of length 3a cm.

(a) Sketch and label the pyramid

(b) Find the angle between a slanting edge and the base

The triangular prism shown below has the sides AB = DC = EF = 12 cm. the ends are equilateral triangles of sides 10cm. The point N is the mid point of FC.

Find the length of:

(a) (i) BN

(ii) EN

(b) Find the angle between the line EB and the plane CDEF

CHAPTER FIFTY NINE

Specific Objectives

By the end of the topic the learner should be able to:

(a) Recall and define trigonometric ratios;

(b) Derive trigonometric identity sin2x+cos2x = 1;

(d) Solve simple trigonometric equations analytically and graphically;

(e) Deduce from the graph amplitude, period, wavelength and phase angles.

Content

(a) Trigonometric ratios

(b) Deriving the relation sin2x+cos2x =1

y = sin x y = cos x, y = tan x

y = a sin x, y = a cos x,

y = a tan x y = a sin bx,

y = a cos bx y = a tan bx

y = a sin(bx ± 9)

y = a cos(bx ± 9)

y = a tan(bx ± 9)

(d) Simple trigonometric equation

(e) Amplitude, period, wavelength and phase angle of trigonometric functions.

Introduction

Consider the right – angled triangle OAB

AB = r

OA = r

Since triangle OAB is right- angled

Divide both sides by gives

Example

If tanshow that;

Solution

Factorize the numerator gives and since

But

Therefore, =

Example

Show that

Removing the brackets from the expression gives

Using

Also

Therefore

Example

Given that

Solution using the right angle triangle below.

therefore=

Waves

Amplitude

This is the maximum displacement of the wave above or below the x axis.

Period

The interval after which the wave repeats itself

Transformations of waves

The graphs of y = sin x and y = 3 sin x can be drawn on the same axis. The table below gives the corresponding values of sin x and 3 sin x for

	30	60	90	120	150	180	210	240	270	300	330	360
Sin x	0.50	0.87	1.00	0.87	0.50	0	-0.50	-0.87	-0.50	-0.87	-0.50	0
3 sin x	1.50	2.61	3.00	2.61	1.50	0	-1.50	-2.61	-1.50	-2.61	-1.50	0

390	420	450	480	510	540	570	600	630	660	690	720
0.5	0.87	1.00	0.87	0.50	0	-0.50	-0.87	-1.00	-0.87	-0.50	0
1.50	2.61	3.00	2.61	1.50	0	-1.50	-2.61	-3.00	-2.61	-2.61	0

The wave of y = 3 sin x can be obtained directly from the graph of y = sin x by applying a stretch scale factor 3 , x axis invariant .

Note;

The amplitude of y= 3sinx is y =3 which is three times that of y = sin x which is y =1.
The period of the both the graphs is the same that is or 2

Example

Draw the waves y = cos x and y = cos . We obtain y = cos from the graph y = cos x by applying a stretch of factor 2 with y axis invariant.

Note;

The amplitude of the two waves are the same.
The period of y = cos is that is, twice the period of y = cos x

Trigonometric Equations

In trigonometric equations, there are an infinite number of roots. We therefore specify the range of values for which the roots of a trigonometric equation are required.

Example

Solve the following trigonometric equations:

Sin 2x = cos x, for
Tan 3x = 2, for

Solution

Sin 2 x = cos x

Sin 2x = sin (90 – x)

Therefore 2 x = 90 – x

X =

For the given range, x =.

Tan 3x = 2

From calculator

3x =.

In the given range;

Sin sin

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic

(a) Complete the table for the function y = 2 sin x

0⁰

10⁰

20⁰

30⁰

40⁰

50⁰

60⁰

70⁰

80⁰

90⁰

100⁰

110⁰

120⁰

Sin 3x

0.5000

-08660

1.00

-1.73

(b) (i) Using the values in the completed table, draw the graph of

y = 2 sin 3x for 0⁰ ≤ x ≤ 120⁰ on the grid provided

(ii) Hence solve the equation 2 sin 3x = -1.5

Complete the table below by filling in the blank spaces

X⁰

0⁰

30⁰

60⁰

90⁰

120⁰

150⁰

180⁰

210⁰

240⁰

270⁰

300⁰

330⁰

360⁰

Cos x⁰

1.00

0.50

-0.87

2 cos ½ x⁰

2.00

1.93

0.52

-1.00

-2.00

Using the scale 1 cm to represent 30⁰ on the horizontal axis and 4 cm to represent 1 unit on the vertical axis draw, on the grid provided, the graphs of y = cosx⁰ and y = 2 cos ½ x⁰ on the same axis.

(a) Find the period and the amplitude of y = 2 cos ½ x⁰

(b) Describe the transformation that maps the graph of y = cos x⁰ on the graph of y = 2 cos ¹/₂ x⁰

(a) Complete the table below for the value of y = 2 sin x + cos x.

X	0⁰	30⁰	45⁰	60⁰	90⁰	120⁰	135⁰	150⁰	180⁰	225⁰	270⁰	315⁰	360⁰
2 sin x	0		1.4	1.7	2	1.7	1.4	1	0		-2	-1.4	0
Cos x	1		0.7	0.5	0	-0.5	-0.7	-0.9	-1		0	0.7	1
Y	1		2.1	2.2	2	1.2	0.7	0.1	-1		-2	-0.7	1

(b) Using the grid provided draw the graph of y=2sin x + cos x for 0⁰. Take 1cm represent 30⁰ on the x- axis and 2 cm to represent 1 unit on the axis.

2 sin x cos x > 0.5

(a) Complete the table below, giving your values correct to 2 decimal places.

x	0	10	20	30	40	50	60	70
Tan x	0
2 x + 300	30	50	70	90	110	130	150	170
Sin ( 2x + 30⁰)	0.50			1

b) On the grid provided, draw the graphs of y = tan x and y = sin ( 2x + 30⁰) for 0⁰ ≤ x 70⁰

Take scale: 2 cm for 100 on the x- axis

4 cm for unit on the y- axis

Use your graph to solve the equation tan x- sin ( 2x + 30⁰ ) = 0.

(a) Complete the table below, giving your values correct to 2 decimal places

X⁰	0	30	60	90	120	150	180
2 sin x⁰	0	1		2		1
1 – cos x⁰			0.5	1

(b) On the grid provided, using the same scale and axes, draw the graphs of

y = sin x⁰ and y = 1 – cos x⁰ ≤ x ≤ 180⁰

Take the scale: 2 cm for 30⁰ on the x- axis

2 cm for I unit on the y- axis

(i) Solve equation

2 sin x^o + cos x⁰ = 1

Determine the range of values x for which 2 sin x^o> 1 – cos x⁰

(a) Given that y = 8 sin 2x – 6 cos x, complete the table below for the missing

values of y, correct to 1 decimal place.

X	0⁰	15⁰	30⁰	45⁰	60⁰	75⁰	90⁰	105⁰	120⁰
Y = 8 sin 2x – 6 cos x	-6	-1.8		3.8	3.9	2.4	0		-3.9

(b) On the grid provided, below, draw the graph of y = 8 sin 2x – 6 cos for

0⁰ ≤ x ≤ 120⁰

Take the scale 2 cm for 15⁰ on the x- axis

2 cm for 2 units on the y – axis

(i) The maximum value of y

(ii) The value of x for which 4 sin 2x – 3 cos x =1

Solve the equation 4 sin (x + 30⁰) = 2 for 0 ≤ x ≤ 360⁰

Find all the positive angles not greater than 180⁰ which satisfy the equation

Sin² x – 2 tan x = 0

Cos x

Solve for values of x in the range 0⁰ ≤ x ≤ 360⁰ if 3 cos² x – 7 cos x = 6

Simplify 9 – y² where y = 3 cos θ

Find all the values of Ø between 0⁰ and 360⁰ satisfying the equation 5 sin Ө = -4

Given that sin (90 – x) = 0.8. Where x is an acute angle, find without using mathematical tables the value of tan x⁰
Complete the table given below for the functions

y= -3 cos 2x⁰ and y = 2 sin (^3x/₂⁰ + 30) for 0 ≤ x ≤ 180⁰

X⁰	0⁰	20⁰	40⁰	60⁰	80⁰	100⁰	120⁰	140⁰	160⁰	180⁰
-3cos 2x⁰	-3.00	-2.30	-0.52	1.50	2.82	2.82	1.50	-0.52	-2.30	-3.00
2 sin (3 x⁰ + 30⁰)	1.00	1.73	2.00	1.73	1.00	0.00	-1.00	-1.73	-2.00	-1.73

Using the graph paper draw the graphs of y = -3 cos 2x⁰ and y = 2 sin (^3x/₂⁰ + 30⁰)

(a) On the same axis. Take 2 cm to represent 20⁰ on the x- axis and 2 cm to represent one unit on the y – axis

(b) From your graphs. Find the roots of 3 cos 2 x⁰ + 2 sin (^3x/₂⁰ + 30⁰) = 0

Solve the values of x in the range 0⁰ ≤ x ≤ 360⁰ if 3 cos²x – 7cos x = 6

Complete the table below by filling in the blank spaces

x⁰	0⁰	30⁰	60⁰	90	1⁰	150⁰	180	210	240	270	300	330	360
Cosx⁰	1.00		0.50			-0.87		-0.87
2cos ½ x⁰	2.00	1.93					0.5

Using the scale 1 cm to represent 30⁰ on the horizontal axis and 4 cm to represent 1 unit on the vertical axis draw on the grid provided, the graphs of y – cos x⁰ and y = 2 cos ½ x⁰ on the same axis

(a) Find the period and the amplitude of y =2 cos ½ x⁰

Ans. Period = 720⁰. Amplitude = 2

Describe the transformation that maps the graph of y = cos x⁰ on the graph of y = 2 cos ½ x⁰

CHAPTER SIXTY

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define the great and small circles in relation to a sphere (including the

Earth);

(b) Establish the relationship between the radii of small and great circles;

(d) Calculate the distance between two points along the great circles and small circles (longitude and latitude) in nautical miles (nm) an kilometers (km);

(e) Calculate time in relation to longitudes;

(f) Calculate speed in knots and kilometers per hour.

Content

(a) Latitude and longitude (great and small circles)

(b) The Equator and Greenwich Meridian

(d) Position of a place on the surface of the earth

(e) Distance between two points along the small and great circles in nautical miles and kilometers

(f) Distance in nautical miles and kilometres along a circle of latitude

(g) Time and longitude

(h) Speed in knots and Kilometres per hour.

Introduction

Just as we use a coordinate system to locate points on a number plane so we use latitude and longitude to locate points on the earth’s surface.

Because the Earth is a sphere, we use a special grid of lines that run across and down a sphere. The diagrams below show this grid on a world globe and a flat world map.

Great and Small Circles

If you cut a ‘slice’ through a sphere, its shape is a circle. A slice through the centre of a sphere is called a great circle, and its radius is the same as that of the sphere. Any other slice is called a small circle, because its radius is smaller than that of a great circle.Hence great circles divides the sphere into two equal parts

Latitude

Latitudes are imaginary lines that run around the earth and their planes are perpendicular to the axis of the earth .The equator is the latitude tha divides the earth into two equal parts.Its the only great circles amoung the latitudes. The equator is , 0°.

The angle of latitude is the angle the latitude makes with the Equator at the centre, O, of the Earth. The diagram shows the 50°N parallel of latitude. Parallels of latitude range from 90°N (North Pole) to 90°S (South Pole).

The angle 5 subtended at the centre of the earth is the is the is the latitude of the circle passing through 5 north of equator.The maximum angle of latitude is 9 north or south of equator.

Longitudes /meridians

They are circles passing through the north and south poles

They can also be said that they are imaginary semicircles that run down the Earth. They are ‘half’ great circles that meet at the North and South Poles. The main meridian of longitude is the prime meridian, 0°. It is also called the Greenwich meridian since it runs through the Royal Observatory at Greenwich in London, England. The other meridians are measured in degrees east or west of the prime meridian.

The angle of longitude is the angle the meridian makes with the prime meridian at the centre, O, of the Earth. The diagram shows the 35°E meridian of longitude.

Meridians of longitude range from 180°E to 180°W. 180°E and

180°W are actually the same meridian, on the opposite side of the Earth to the prime meridian. It runs through the Pacific Ocean, east of Fiji.

Note

If P is north of the equator and Q is south of the quator , then the difference in latitude between them is given by
If P and Q are on the same side of the equator , then the difference in latitude is

Position Coordinates

Locations on the Earth are described using latitude (°N or °S) and longitude (°E or °W) in that order. For example, Nairobi has coordinates (1°S, 37°E), meaning it is position is 1° south of the Equator and 37° east of the prime meridian.

Great Circle Distances

Remember the arc length of a circle is where θ is the degrees of the central angle, and the radius of the earth is 6370 km approx.

On a flat surface, the shortest distance between two points is a straight line. Since the Earth’s surface is curved, the shortest distance between A and B is the arc length AB of the great circle that passes through A and B. This is called the great circle distance and the size of angle ∠AOB where O is the centre of the Earth is called the angular distance.

Note

The length of an arc of a great circle subtending an angle of (one minute) at the centre of the earth is 1 nautical mile nm.
A nautical mile is the standard international unit from measuring distances travelled by ships and aeroplanes 1 nautical mile (nm) = 1.853 km

If an arc of a great circle subtends an angle at the centre of the earth,the arcs length is nautical miles.

Example

Find the distance between points P() and Q and express it in;

Solution

Angle subtended at the centre is

Is subtended by 60 nm

Is subtended by; 60 x 60.5 = 3630 nm

The radius of the earth is 6370 km

Therefore, the circumference of the earth along a great circle is;

Angle between the points is .Therefore, we find the length of an arch of a circle which subtends an angle of at the centre is is subtended by arc whose length is

Therefore, 60. Is subtended by ;

Example

Find the distance between points A ( and express it in ;

Solution

The two points lie on the equator, which is great circle. Therefore ,we are calculating distance along a great circle.

Angle between points A and B is (

Distance in km =

Distance along a small Circle (circle of latitude)

The figure below ABC is a small circle, centre X and radius r cm.PQST is a great circle ,centre O,radius R cm.The angle is between the two radii.

From the figure, XC is parallel to OT. Therefore, angle COT = angle XCO=.Angle CXO =9 (Radius XC is perpendicular to the axis of sphere).

Thus, from the right- angled triangle OXC

Therefore, r = R cos

This expression can be used to calculate the distance between any two points along the small circle ABC, centre X and radius r.

Example

Find the distance in kilometers and nautical miles between two points (.

Solution

Figure a shows the position of P and Q on the surface of the earth while figure b shows their relative positions on the small circle is the centre of the circle of latitude with radius r.

The angle subtended by the arc PQ centre C is .So, the length of PQ

The length of PQ in nautical miles

In general, if the angle at the centre of a circle of latitude then the length of its arc is 60 where the angle between the longitudes along the same latitude.

Shortest distance between the two points on the earths surface

The shortest distance between two points on the earths surface is that along a great circle.

Example

P and Q are two points on latitude They lie on longitude respectively. Find the distance from P to Q :

Along a parallel of latitude
Along a great circle

Solution

The positions of P and Q on earths surface are as shown below

The length of the circle parallel of latitude is 2 km, which is 2.The difference in longitude between P and Q is

The required great circle passes via the North Pole. Therefore, the angle subtended at the centre by the arc PNQ is;

– 2 x

Therefore the arc PNQ

Note;

Notice that the distance between two points on the earth’s surface along a great circle is shorter than the distance between them along a small circle

Longitude and Time

The earth rotates through 36 about its axis every 24 hours in west – east direction. Therefore for every change in longitude there is a corresponding change in time of 4 minutes, or there is a difference of 1 hour between two meridians apart.

All places in the same meridian have the same local time. Local time at Greenwich is called Greenwich Mean Time .GMT.

All meridians to the west of Greenwich Meridian have sunrise after the meridian and their local times are behind GMT.

All meridian to the east of Greenwich Meridian have sunrise before the meridian and their local times are ahead of GMT. Since the earth rotates from west to east, any point P is ahead in time of another point Q if P is east of Q on the earth’s surface.

Example

Find the local time in Nairobi ( ), when the local time of Mandera (Nairobi ( ) is 3.00 pm

Solution

The difference in longitude between Mandera and Nairobi is (, that is Mandera is .Therefore their local time differ by; 4 x 5 = 20 min.

Since Nairobi is in the west of Mandera, we subtract 20 minutes from 3.00 p.m. This gives local time for Nairobi as 2.40 p.m.

Example

If the local time of London ( ), IS 12.00 noon, find the local time of Nairobi ( ),

Solution

Difference in longitude is ( ) =

So the difference in time is 4 x 37 min = 148 min

= 2 hrs. 28 min

Therefore , local time of Nairobi is 2 hours 28 minutes ahead that of London that is,2.28 p.m

Example

If the local time of point A () is 12.30 a.m, on Monday,Find the local time of a point B ( ).

Solution

Difference in longitude between A and B is

In time is 4 x 340 = 1360 min

= 22 hrs. 40 min.

Therefore local time in point B is 22 hours 40 minutes behind Monday 12:30 p.m. That is, Sunday 1.50 a.m.

Speed

A speed of 1 nautical mile per hour is called a knot. This unit of speed is used by airmen and sailors.

Example

A ship leaves Mombasa (and sails due east for 98 hours to appoint K Mombasa (in the indian ocean.Calculate its average speed in;

Km/h
Knots

Solution

The length x of the arc from Mombasa to the point K in the ocean

Therefore speed is

The length x of the arc from Mombasa to the point K in the ocean in nautical miles

Therefore , speed =

= 25.04 knots

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

An aeroplane flies from point A (1⁰ 15’S, 37⁰ E) to a point B directly North of A. the arc AB subtends an angle of 45⁰ at the center of the earth. From B, aeroplanes flies due west two a point C on longitude 23⁰ W.)

(Take the value of π ²²/ ₇ as and radius of the earth as 6370km)

(a) (i) Find the latitude of B

(ii) Find the distance traveled by the aeroplane between B and C

(b) The aeroplane left at 1.00 a.m. local time. When the aeroplane was leaving B, what was the local time at C?

The position of two towns X and Y are given to the nearest degree as X (45⁰ N, 10⁰W) and Y (45⁰ N, 70⁰W)

Find

(a) The distance between the two towns in

Kilometers (take the radius of the earth as 6371)
Nautical miles (take 1 nautical mile to be 1.85 km)

(b) The local time at X when the local time at Y is 2.00 pm.

A plane leaves an airport A (38.5⁰N, 37.05⁰W) and flies dues North to a point B on latitude 52⁰N.

(a) Find the distance covered by the plane

(b) The plane then flies due east to a point C, 2400 km from B. Determine the position of C

Take the value π of as ²²/₇ and radius of the earth as 6370 km

A plane flying at 200 knots left an airport A (30⁰S, 31⁰E) and flew due North to an airport B (30⁰N, 31⁰E)

(a) Calculate the distance covered by the plane, in nautical miles

(b) After a 15 minutes stop over at B, the plane flew west to an airport C (30⁰N, 13⁰E) at the same speed.

Calculate the total time to complete the journey from airport C, though airport B.

Two towns A and B lie on the same latitude in the northern hemisphere.

When its 8 am at A, the time at B is 11.00 am.

a) Given that the longitude of A is 15⁰ E find the longitude of B.
b) A plane leaves A for B and takes 3¹/₂ hours to arrive at B traveling along a parallel of latitude at 850 km/h. Find:

(i) The radius of the circle of latitude on which towns A and B lie.

(ii) The latitude of the two towns (take radius of the earth to be 6371 km)

Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 118⁰W and the longitude of B is 133⁰ E. The shorter distance between A and B measured along the circle of latitude is 5422 nautical miles.

Find, to the nearest degree, the latitude on which A and B lie

(a) A plane flies by the short estimate route from P (10⁰S, 60⁰ W) to Q (70⁰ N,

120⁰ E) Find the distance flown in km and the time taken if the aver age speed is 800 km/h.

(b) Calculate the distance in km between two towns on latitude 50⁰S with long longitudes and 20⁰ W. (take the radius of the earth to be 6370 km)

Calculate the distance between M (30⁰N, 36⁰E) and N (30⁰ N, 144⁰ W) in nautical miles.

(i) Over the North Pole

(ii) Along the parallel of latitude 30⁰ N

(a) A ship sailed due south along a meridian from 12⁰ N to 10⁰30’S. Taking

the earth to be a sphere with a circumference of 4 x 10⁴ km, calculate in km the distance traveled by the ship.

(b) If a ship sails due west from San Francisco (37⁰ 47’N, 122⁰ 26’W) for distance of 1320 km. Calculate the longitude of its new position (take the radius of the earth to be 6370 km and π = 22/7).

CHAPTER SIXTY ONE

Specific Objectives

By the end of the topic the learner should be able to:

(a) Form linear inequalities based on real life situations;

(b) Represent the linear inequalities on a graph;

(d) Apply linear programming to real life situations.

Content

(a) Formation of linear inequalities

(b) Analytical solutions of linear inequalities

(d) Optimisation (include objective function)

(e) Application of quadratic equations to real life situations.

Forming linear inequalities

In linear programing we are going to form inequalities representing given conditions involving real life situation.

Example

Esha is five years younger than his sister. The sum of their age is less than 36 years. If Esha’s age is x years, form all the inequalities in x for this situation.

Solution

The age of Esha’s sister is x +5 years.

Therefore, the sum of their age is;

X + (x +5) years

Thus;

2x +5 < 36

2x < 31

X > 15.5

X > 0 ( age is always positive)

Linear programming

Linear programming is the process of taking various linear inequalities relating to some situation, and finding the “best” value obtainable under those conditions. A typical example would be taking the limitations of materials and labor, and then determining the “best” production levels for maximal profits under those conditions.

In “real life”, linear programming is part of a very important area of mathematics called “optimization techniques”. This field of study are used every day in the organization and allocation of resources. These “real life” systems can have dozens or hundreds of variables, or more. In algebra, though, you’ll only work with the simple (and graph able) two-variable linear case.

The general process for solving linear-programming exercises is to graph the inequalities (called the “constraints”) to form a walled-off area on the x,y-plane (called the “feasibility region”). Then you figure out the coordinates of the corners of this feasibility region (that is, you find the intersection points of the various pairs of lines), and test these corner points in the formula (called the “optimization equation”) for which you’re trying to find the highest or lowest value.

Example

Suppose a factory want to produce two types of hand calculators, type A and type B. The cost, the labor time and the profit for every calculator is summarized in the following table:

Type	Cost	Labor Time	Profit
A	Sh 30	1 (hour)	Sh 10
B	Sh 20	4 (hour)	Sh 8

Suppose the available money and labors are ksh 18000 and 1600 hours. What should the production schedule be to ensure maximum profit?

Solution

Suppose is the number of type A hand calculators and is the number of type B hand calculators and y to be the cost. Then, we want to maximize subject to

whereis the total profit.

Solution by graphing

Solutions to inequalities formed to represent given conditions can be determined by graphing the inequalities and then reading off the appropriate values ( possible values)

Example

A student wishes to purchase not less than 10 items comprising books and pens only. A book costs sh.20 and a pen sh.10.if the student has sh.220 to spend, form all possible inequalities from the given conditions and graph them clearly, indicating the possible solutions.

Solution

Let the number of books be x and the number of pens then, the inequalities are;

This simplifies to

All the points in the unshaded region represent possible solutions. A point with co-ordinates ( x ,y) represents x books and y pens. For example, the point (3, 10 ) means 3 books and 10 pens could be bought by the students.

Optimization

The determination of the minimum or the maximum value of the objective function ax + by is known as optimization. Objective function is an equation to be minimized or maximized .

Example

A contractor intends to transport 1000 bags of cement using a lorry and a pick up. The lorry can carry a maximum of 80 bags while a pick up can carry a maximum of 20 bags. The pick up must make more than twice the number of trips the lorry makes and the total number of trip to be less than 30.The cost per trip for the lorry is ksh 2000, per bag and ksh 900 for the pick up.Find the minimum expenditure.

Solution

If we let x and y be the number of trips made by the lorry and the pick up respectively. Then the conditions are given by the following inequalities;

The total cost of transporting the cement is given by sh 2000x + 900y.This is called the objective function.

The graph below shows the inequalities.

From the graph we can identify 7 possibilities

Note;

Co-ordinates stands for the number of trips. For example (7, 22) means 7 trips by the lorry and 22 trips by the pickup. Therefore the possible amount of money in shillings to be spent by the contractor can be calculated as follows.

We note that from the calculation that the least amount the contractor would spend is sh.32200.This is when the lorry makes 8 trips and the pick- up 18 trips. When possibilities are many the method of determining the solution by calculation becomestedious. The alternative method involves drawing the graph of the function we wish to maximize or minimize, the objective function. This function is usually of the form ax +by , where a and b ar constants.

For this ,we use the graph above which is a convenient point (x , y) to give the value of x preferably close to the region of the possibilities. For example the point ( 5, 10) was chosen to give an initial value of thus ,2000x + 900y = 19000.we now draw the line 2000x + 900y=19000.such a line is referred to us a search line.

Using a ruler and a set square, slide the set square keeping one edge parallel to until the edge strikes the feasible point nearest ( see the dotted line ) From the graph this point is (8,18 ),which gives the minimum expenditure as we have seen earlier.The feasible point furthest from the line gives the maximum value of the objective function.

The determination of the minimum or the maximum value of the objective function ax + by is known as optimization.

Note;

The process of solving linear equations are as follows

Forming the inequalities satisfying given conditions
Formulating the objective function .
Graphing the inequalities
Optimizing the objective function

This whole process is called linear programming .

Example

A company produces gadgets which come in two colors: red and blue. The red gadgets are made of steel and sell for ksh 30 each. The blue gadgets are made of wood and sell for ksh 50 each. A unit of the red gadget requires 1 kilogram of steel, and 3 hours of labor to process. A unit of the blue gadget, on the other hand, requires 2 board meters of wood and 2 hours of labor to manufacture. There are 180 hours of labor, 120 board meters of wood, and 50 kilograms of steel available. How many units of the red and blue gadgets must the company produce (and sell) if it wants to maximize revenue?

Solution

The Graphical Approach

Step 1. Define all decision variables.

Let: x₁ = number of red gadgets to produce (and sell)

x₂ = number of blue gadgets to produce (and sell)

Step 2. Define the objective function.

Maximize R = 30 x₁+ 50 x₂ (total revenue in ksh)

Step 3. Define all constraints.

(1) x₁ £ 50 (steel supply constraint in kilograms)

(2) 2 x₂ £120 (wood supply constraint in board meters)

(3) 3 x₁ + 2 x₂£ 180 (labor supply constraint in man hours)

x₁ , x₂³ 0 (non-negativity requirement)

Step 4. Graph all constraints.

Then determine area of feasible study

Note;

The area under the line marked blue is the needed area or area of feasible solutions.
We therefore shade the unwanted region out the trapezium marked blue

Optimization

List all corners (identify the corresponding coordinates), and pick the best in terms of the resulting value of the objective function.

(1) x₁ = 0 x₂ = 0 R = 30 (0) + 50 (0) = 0

(2) x₁ = 50 x₂ = 0 R = 30 (50) + 50 (0) = 1500

(3) x₁ = 0 x₂ = 60 R = 30 (0) + 50 (60) = 3000

(4) x₁ = 20 x₂ = 60 R = 30 (20) + 50 (60) = 3600 (the optimal solution)

(5) x₁ = 50 x₂ = 15 R = 30 (50) + 50 (15) = 2250

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

A school has to take 384 people for a tour. There are two types of buses available, type X and type Y. Type X can carry 64 passengers and type Y can carry 48 passengers. They have to use at least 7 buses.

(a) Form all the linear inequalities which will represent the above information.

(b) On the grid [provide, draw the inequalities and shade the unwanted region.

Type X: Ksh 25,000

Type Y Ksh 20,000

Use your graph to determine the number of buses of each type that should be hired to minimize the cost.

An institute offers two types of courses technical and business courses. The institute has a capacity of 500 students. There must be more business students than technical students but at least 200 students must take technical courses. Let x represent the number of technical students and y the number of business students.

(a) Write down three inequalities that describe the given conditions

(b) On the grid provided, draw the three inequalities

(c) If the institute makes a profit of Kshs 2, 500 to train one technical students and Kshs 1,000 to train one business student, determine

The number of students that must be enrolled in each course to maximize the profit
The maximum profit.

A draper is required to supply two types of shirts A and type B.

The total number of shirts must not be more than 400. He has to supply more type A than of type B however the number of types A shirts must be more than 300 and the number of type B shirts not be less than 80.

Let x be the number of type A shirts and y be the number of types B shirts.

Write down in terms of x and y all the linear inequalities representing the information above.
On the grid provided, draw the inequalities and shade the unwanted regions
The profits were as follows

Type A: Kshs 600 per shirt

Type B: Kshs 400 per shirt

Use the graph to determine the number of shirts of each type that should be made to maximize the profit.
Calculate the maximum possible profit.

A diet expert makes up a food production for sale by mixing two ingredients N and S. One kilogram of N contains 25 units of protein and 30 units of vitamins. One kilogram of S contains 50 units of protein and 45 units of vitamins. The food is sold in small bags each containing at least 175 units of protein and at least 180 units of vitamins. The mass of the food product in each bag must not exceed 6kg.

If one bag of the mixture contains x kg of N and y kg of S

Write down all the inequalities, in terms of x and representing the information above ( 2 marks)
On the grid provided draw the inequalities by shading the unwanted regions ( 2 marks)

(c) If one kilogram of N costs Kshs 20 and one kilogram of S costs Kshs 50, use the graph to determine the lowest cost of one bag of the mixture.

Esha flying company operates a flying service. It has two types of aeroplanes. The smaller one uses 180 litres of fuel per hour while the bigger one uses 300 litres per hour.

The fuel available per week is 18,000 litres. The company is allowed 80 flying hours per week.

(a) Write down all the inequalities representing the above information

(b) On the grid provided on page 21, draw all the inequalities in (a) above by

shading the unwanted regions

bigger one is Kshs. 6000 per hour. Use your graph to determine the maximum profit that the company made per week.

A company is considering installing two types of machines. A and B. The information about each type of machine is given in the table below.

Machine	Number of operators	Floor space	Daily profit
A	2	5m²	Kshs 1,500
B	5	8m²	Kshs 2,500

The company decided to install x machines of types A and y machines of type B

(a) Write down the inequalities that express the following conditions

The number of operators available is 40
The floor space available is 80m²

The company is to install not less than 3 type of A machine

The number of type B machines must be more than one third the number of type A machines

(b) On the grid provided, draw the inequalities in part (a) above and shade the

unwanted region.

type that should be installed to maximize the daily profit.

CHAPTER SIXTY TWO

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define Locus;

(b) Describe common types of Loci;

i) Loci involving inequalities;
ii) Loci involving chords;

iii) Loci involving points under given conditions;

iv) Intersecting loci.

Content

(a) Common types of Loci

(b) Perpendicular bisector loci

(d) Angle bisector loci

(e) Other loci under given condition including intersecting loci

(f) Loci involving inequalities

(g) Loci involving chords (constant angle loci).

Introduction

Locus is defined as the path, area or volume traced out by a point, line or region as it moves according to some given laws

In construction the opening between the pencil and the point of the compass is a fixed distance, the length of the radius of a circle. The point on the compass determines a fixed point. If the length of the radius remains the same or unchanged, all of the point in the plane that can be drawn by the compass from a circle and any points that cannot be drawn by the compass do not lie on the circle. Thus the circle is the set of all points at a fixed distance from a fixed point. This set is called a locus.

Common types of Loci

Perpendicular bisector locus

The locus of a point which are equidistant from two fixed points is the perpendicular bisector of the straight line joining the two fixed points. This locus is called the perpendicular bisector locus.

So to find the point equidistant from two fixed points you simply find the perpendicular bisector of the two points as shown below.

Q is the mid-point of M and N.

In three Dimensions

In three dimensions, the perpendicular bisector locus is a plane at right angles to the line and bisecting the line into two equal parts. The point P can lie anywhere in the line provided its in the middle.

The Locus of points at a Given Distance from a given straight line.

In two Dimensions

In the figure below each of the lines from the middle line is marked a centimeters on either side of the given line MN.

The ‘a’ centimeters on either sides from the middle line implies the perpendicular distance.

The two parallel lines describe the locus of points at a fixed distance from a given straight line.

In three Dimensions

In three dimensions the locus of point ‘a’ centimeters from a line MN is a cylindrical shell of radius ‘a’ c, with MN as the axis of rotation.

Locus of points at a Given Distance from a fixed point.

In two Dimension

If O is a fixed point and P a variable point‘d’ cm from O,the locus of p is the circle O radius ‘d’ cm as shown below.

All points on a circle describe a locus of a point at constant distance from a fixed point. In three dimesion the locus of a point ‘d’ centimetres from a point is a spherical shell centre O and radius d cm.

Angle Bisector Locus

The locus of points which are equidistant from two given intersecting straight lines is the pair of perpendicular lines which bisect the angles between the given lines.

Conversely ,a point which lies on a bisector of given angle is equidistant from the lines including that angle.P C

Line PB bisect angle ABC into two equal parts.

Example

Construct triangle PQR such that PQ= 7 cm, QR = 5 cm and angle PQR = .Construct the locus L of points equidistant from RP and RQ.

Solution

L is the bisector of Angle PRQ.

Constant angle loci

A line PQ is 5 cm long, Construct the locus of points at which PQ subtends an angle of .

Solution

Draw PQ = 5 cm
Construct TP at P such that angle QPT =
Draw a perpendicular to TP at P( radius is perpendicular to tangent)
Construct the perpendicular bisector of PQ to meet the perpendicular in (iii) at O
Using O as the centre and either OP or OQ as radius, draw the locus
Transfer the centre on the side of PQ and complete the locus.
Transfer the centre on the opposite sides of PQ and complete the locus as shown below.
To are of the same radius,
Angle subtended by the same chord on the circumference are equal ,
This is called the constant angle locus.

Intersecting Loci

Construct triangle PQR such that PQ =7 cm, OR = 5 cm and angle PQR = 3
Construct the locus of points equidistant from P and Q to meet the locus of points equidistant from Q and R at M .Measure PM

Solution

In the figure below

is the perpendicular bisector of PQ
is the perpendicular bisector of PQ
By measurement, PM is equal to 3.7 cm

Loci of inequalities

An inequality is represented graphically by showing all the points that satisfy it.The intersection of two or more regions of inequalities gives the intersection of their loci.

Remember we shed the unwanted region

Example

Draw the locus of point ( x, y) such that x + y < 3 , y – x and y > 2.

Solution

Draw the graphs of x + y = 3 ,y –x =4 and y = 2 as shown below.

The unwanted regions are usually shaded. The unshaded region marked R is the locus of points ( x ,y ), such that x + y < 3 , y – X 4 and y > 2.

The lines of greater or equal to ad less or equal to ( ) are always solid while the lines of greater or less (<>) are always broken.

Example

P is a point inside rectangle ABCD such that APPB and Angle DAP Angle BAP. Show the region on which P lies.

Solution

A B

Draw a perpendicular bisector of AP=PB and shade the unwanted region. Bisect <DAB (< DAP = < BAP) and shade the unwanted region lies in the unshaded region.

Example

Draw the locus of a point P which moves that AP 3 cm.

Solution

Draw a circle, centre A and radius 3 cm
Shade the unwanted region.

Locus involving chords

The following properties of chords of a circle are used in construction of loci

(I)Perpendicular bisector of any chord passes through the centre of the circle.

(ii) The perpendicular drawn from a centre of a circle bisects the chord.

(III) If chords of a circle are equal, they are equidistant from the centre of the circle and vice -versa

(IV) In the figure below, if chord AB intersects chord CD at O, AO = x ,BO = y, CO = m and DO =n then

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

Using a ruler and a pair of compasses only,
Construct a triangle ABC such that angle ABC = 135^oC, AB = 8.2cm and BC = 9.6cm
Given that D is a position equidistant from both AB and BC and also from B and C
Locate D
Find the area of triangle DBC.

(a) Using a ruler, a pair of compasses only construct triangle XYZ such that XY = 6cm,

YZ = 8cm and ÐXYZ = 75^o

(b) Measure line XZ and ÐXZY

(d) A point M moves such that it is always equidistant from Y and Z. construct the locus of M and define the locus

(a) (i) Construct a triangle ABC in which AB=6cm, BC = 7cm and angle ABC = 75^o

Measure:-

(i) Length of AC

(ii) Angle ACB

(b) Locus of P is such that BP = PC. Construct P

BQC = 30^o

(d) (i) Locus of P and locus of Q meet at X. Mark x

(ii) Construct locus R in which angle BRC 120^o

(iii) Show the locus S inside triangle ABC such that XS ³ SR

Use a ruler and compasses only for all constructions in this question.
a) i) Construct a triangle ABC in which AB=8cm, and BC=7.5cm and ÐABC=112½°
ii) Measure the length of AC
b) By shading the unwanted regions show the locus of P within the triangle ABC such that
i) AP ≤ BP
ii) AP >3cm

Mark the required region as P

c) Construct a normal from C to meet AB produced at D
d) Locate the locus of R in the same diagram such that the area of triangle ARB is ¾ the area of the triangle ABC.
On a line AB which is 10 cm long and on the same side of the line, use a ruler and a pair of compasses only to construct the following.
a) Triangle ABC whose area is 20 cm² and angle ACB = 90^o
b) (i) The locus of a point P such that angle APB = 45^o.

(ii) Locate the position of P such that triangle APB has a maximum area and calculate this area.

A garden in the shape of a polygon with vertices A, B, C, D and E. AB = 2.5m, AE = 10m,

ED = 5.2M and DC=6.9m. The bearing of B from A is 030º and A is due to east of E

whileD is due north of E, angle EDC = 110º,

a) Using a scale of 1cm to represent 1m construct an accurate plan of the garden
b) A foundation is to be placed near to CD than CB and no more than 6m from A,
i) Construct the locus of points equidistant from CB and CD.
ii) Construct the locus of points 6m from A
c) i) shade and label R ,the region within which the foundation could be placed in the garden
ii) Construct the locus of points in the garden 3.4m from AE.

iii) Is it possible for the foundation to be 3.4m from AE and in the region?

a) Using a ruler and compasses only construct triangle PQR in which QR= 5cm, PR = 7cm and angle PRQ = 135°
b) Determine < PQR
c) At P drop a perpendicular to meet QR produced at T d) Measure PT
e) Locate a point A on TP produced such that the area of triangle AQR is equal to one- and – a – half times the area of triangle PQR
f) Complete triangle AQR and measure angle AQR
Use ruler and a pair of compasses only in this question.

(a) Construct triangle ABC in which AB = 7 cm, BC = 8 cm and ∠ABC = 60⁰.

(b) Measure (i) side AC (ii) ∠ ACB

(d) Construct ∆ PBC such that P is on the same side of BC as point A and ∠ PCB = ½ ∠ ACB,∠ BPC = ∠ BAC measure ∠ PBC.

Without using a set square or a protractor:-

(a) Construct triangle ABC in which BC is 6.7cm, angle ABC is 60^o and ÐBAC is 90^o.

(b) Mark point D on line BA produced such that line AD =3.5cm

(i) A circle that touches lines AC and AD

(ii) A tangent to this circle parallel to line AD

Use a pair of compasses and ruler only in this question;

(a) Draw acute angled triangle ABC in which angle CAB = 37½ ^o, AB = 8cm and CB = 5.4cm. Measure the length of side AC (hint 37½ ^o = ½ x 75^o)

(b) On the triangle ABC below:

(i) On the same side of AC as B, draw the locus of a point X so that angle Ax C = 52½ ^o

(ii) Also draw the locus of another point Y, which is 6.8cm away from AC and on the same side as X

P is not less than 6.8cm away from AC

CHAPTER SIXTY THREE

Specific Objectives

By the end of the topic the learner should be able to:

(a) Find average rates of change and instantaneous rates of change;

(b) Find the gradient of a curve at a point using tangent;

(d) Find the gradient function of a function of the form y = x n (n is a positive

Integer);

(e) Define derivative of a function, derived function of a polynomial anddifferentiation;

(f) Determine the derivative of a polynomial;

(g) Find equations of tangents and normal to the curves;

(h) Sketch a curve;

(i) Apply differentiation in calculating distance, velocity and acceleration;

(j) Apply differentiation in finding maxima and minima of a function.

Content

(a) Average and instantaneous rates of change

(b) Gradient of a curve at a point

(d) Delta notation ( A ) or 5

(e) Derivative of a polynomial

(f) Equations of tangents and normals to the curve

(g) Stationery points

(h) Curve sketching

(i) Application of differentiation in calculation of distance, velocity andacceleration

(j) Maxima and minima

Introduction

Differentiation is generally about rate of change

Example

If we want to get the gradient of the curve y = at a general point ( x ,y ).We note that a general point on the curve y = will have coordinates of the form ( x )The gradient of the curve y= at a general point ( x, y ) can be established as below.

If we take a small change in x , say h. This gives us a new point on the curve with co-ordinates

[(x +h), (x + h]. So point Q is [(x +h), (x + h] while point P is ( x ).

To find the gradient of PQ =

Change in y = (x + h

Change in x = ( x + h ) – x

Gradient =

= 2x + h

By moving Q as close to p as possible, h becomes sufficiently small to be ignored. Thus, 2x +h becomes2x.Therefore, at general point ( x,y)on the curve y =,the gradient is 2x.

2x is called the gradient function of the curve y = .We can use the gradient function to determine the gradient of the curve at any point on the curve.

In general, the gradient function of y = is given by ,where n is a positive integer. The gradient function is called the derivative or derived function and the process of obtaining it is called differentiation.

The function

Delta Notation

A small increase in x is usually denoted bysimilarly a small increase in y is denoted by .Let us consider the points P ( x ,y ) and Q [ (x + ),(y + ) on the curve y =

Note;

X is a single quantity and not a product of and x .similarly is a single quantity.

The gradient of PQ, =

= 2x +

As tends to zero;

can be ignored
gives the derivative which is denoted by
thus

When we find , we say we are differentiating with respect to x, For example given y =; then

In general the derivatives of y = e.g. y =

Derivative of a polynomial.

A polynomial in x is an expression of the form where are constants

To differentiate a polynomial function, all you have to do is multiply the coefficients of each variable by their corresponding exponents/powers, subtract each exponent/powers by one , and remove any constants.

Steps involved in solving polynomial areas follows

Identify the variable terms and constant terms in the equation.

A variable term is any term that includes a variable and a constant term is any term that has only a number without a variable. Find the variable and constant terms in this polynomial function: y = 5x³ + 9x² + 7x + 3

The variable terms are 5x³, 9x², and 7x
The constant term is 3

Multiply the coefficients of each variable term by their respective powers.

Their products will form the new coefficients of the differentiated equation. Once you find their products, place the results in front of their respective variables. For example:

5×3 = 5 x 3 = 15
9×2 = 9 x 2 = 18
7x = 7 x 1 = 7

Lower each exponent by one.

To do this, simply subtract 1 from each exponent in each variable term. Here’s how you do it:

Replace the old coefficients and old exponents/powers with their new counterparts.

To finish differentiating the polynomial equation, simply replace the old coefficients with their new coefficients and replace the old powers with their values lowered by one. The derivative of constants is zero so you can omit 3, the constant term, from the final result.

The derivative of the polynomial y =

In general, the derivative of the sum of a number of terms is obtained by differentiating each term in turn.

Examples

Find the derived function of each of the following

S=t ) A =

Solution

Equations of tangents and Normal to a curve.

The gradient of a curve is the same as the gradient of the tangent to the curve at that point. We use this principle to find the equation of the tangent to a curve at a given point.

Find the equation of the tangent to the curve;

Solution

At the point the gradient is 3 x + 2 = 5

We want the equation of straight line through (1, 4) whose gradient is 5.

Thus

A normal to a curve at appoint is the line perpendicular to the tangent to the curve at the given point.

In the example above the gradient of the tangent of the tangent to the curve at (1, 4) is 5. Thus the gradient of the normal to the curve at this point is.

Therefore, equation of the normal is:

5(y – 4) = – 1( x – 1 )

Example

Find the equation of the normal to the curve y =

Solution

At the point ( 1,-2) gradient of the tangent line is 1.Therefore the gradient of the normal is -1.the required equation is

The equation of the normal is y = -x -1

Stationary points

Note;

In each of the points A ,B and C the tangent is horizontal meaning at these points the gradient is zero.so .
Any point at which the tangent to the graph is horizontal is called a stationary point. We can locate stationary points by looking for points at which = 0.

Turning points

The point at which the gradient changes from negative through zero to positive is called minimum point while the point which the gradient changes from positive through zero to negative is called maximum point .In the figure above A is the maximum while B is the minimum.

Minimum point .

Gradient moves from negative through zero to positive.

Maximum point

Gradient moves from positive through zero to negative.

The maximum and minimum points are called turning points.

A point at which the gradient changes from positive through zero to positive or from negative zero to negative is called point of inflection.

Example

Identify the stationary points on the curve y =for each point, determine whether it is a maximum, minimum or a point of inflection.

Solution

At stationary point,

Thus

Therefore, stationary points are ( -1 , 4 ) and (1 ,0).

Consider the sign of the gradient to the left and right of x = 1

x	0	1	2
	-3	0	9
Diagrammatic representation	\		/

Therefore ( 1 , 0 ) is a minimum point.

Similarly, sign of gradient to the left and right of x = -1 gives

x	-2	-1	0
	9	0	-3
Diagrammatic representation	/	___	\

Therefore ( -1 , 4 ) is a maximum point.

Example

Identify the stationary points on the curve y =.Determine the nature of each stationary point.

Solution

y =

At stationary points,

Stationary points are (0, 1) and (3, 28)

Therefore (0, 1) is a point of inflection while (3, 28) is a maximum point.

Application of Differentiation in calculation of velocity and acceleration.

Velocity

If the displacement, S is expressed in terms of time t, then the velocity is v =

Example

The displacement, S metres, covered by a moving particle after time, t seconds, is given by

S =.Find:

Velocity at :
t= 3

Instant at which the particle is at rest.

Solution

S =

The gradient function is given by;

V =

velocity
at t = 2 is ;

v =

= 24 + 16 – 8

=32m/s

at t = 3 is ;

v =

= 54 + 24 – 8

=70m/s

the particle is at rest when v is zero

It is not possible to have t = -2

The particle is therefore at rest at seconds

Acceleration

Acceleration is found by differentiating an equation related to velocity. If velocity v , is expressed in terms of time, t , then the acceleration, a, is given by a =

Example

A particle moves in a straight line such that is its velocity v m after t seconds is given by

v = 3 + 10 t – .

Find

the acceleration at :
t =1 sec
t =3 sec
the instant at which acceleration is zero

Solution

At t = 1 sec a = 10 – 2 x 1

At t = 3 sec a = 10 – 2 x 3

Acceleration is zero when

Therefore, 10 – 2t = 0 hence t = 5 seconds

Example

A closed cylindrical tin is to have a capacity of 250π ml. if the area of the metal used is to be minimum, what should the radius of the tin be?

Solution

Let the total surface area of the cylinder be A ,radius r cm and height h cm.

Then, A = 2

Volume = 2

Making h the subject, h =

Put h = in the expression for surface area to get;

A = 2

For minimum surface area,

= 5

Therefore the minimum area when r = 5 cm

Example

A farmer has 100 metres of wire mesh to fence a rectangular enclosure. What is the greatest area he can enclose with the wire mesh?

Solution

Let the length of the enclosure be x m. Then the width is

Then the area A of the rectangle is given by;

A = x (50 –x)

= 50x –

For maximum or minimum area,

Thus, 50 – 2x = 0

The area is maximum when x = 25 m

That is A = 50 X 25 – (25

= 625 .

CHAPTER SIXTY FOUR

Specific Objectives

By the end of the topic the learner should be able to:

(a) Carry out the process of differentiation;

(b) Interpret integration as a reverse process of differentiation;

(d) Integrate a polynomial;

(e) Apply integration in finding the area under a curve,

(f) Apply integration in kinematics.

Content

(a) Differentiation

(b) Reverse differentiation

(d) Indefinite and definite integrals

(e) Area under a curve by integration

(f) Application in kinematics.

Introduction

The process of finding functions from their gradient (derived) function is called integration

Suppose we differentiate the function y=x². We obtain

Integration reverses this process and we say that the integral of 2x is .

From differentiation we know that the gradient is not always a constant. For example, if = 2x, then this comes from the function of the form y=, Where c is a constant.

Example

Find y if is:

Solution

Then, y =

Note;

To integrate we reverse the rule for differentiation. In differentiation we multiply by the power of x and reduce the power by 1.In integration we increase the power of x by one and divide by the new power.

If ,then, where c is a constant and n.since c can take any value we call it an arbitrary constant.

Example

Integrate the following expression

2x +4

Solution

Then, y =

B.)

Then, y =

= –

C.) 2x +4

Then, y =

Example

Find the equation of a line whose gradient function is and passes through (0,1)

Solution

Since ,the general equation is y =.The curve passes through ( 0,1).Substituting these values in the general equation ,we get 1 = 0 + 0 + c

1 = c

Hence, the particular equation is y =

Example

Find v in terms of h if and V =9 when h=1

Solution

The general solution is

V =

V= 9 when h= 1.Therefore

9 = 5 + c

4 = C

Hence the particular solution is ;

Definite and indefinite integrals

It deals with finding exact area.

Estimate the area shaded beneath the curve shown below

The area is divided into rectangular strips as follows.

The shaded area in the figure above shows an underestimated and an overestimated area under the curve. The actual area lies between the underestimated and overestimated area. The accuracy of the area can be improved by increasing the number of rectangular strips between x = a and x = b.

The exact area beneath the curve between x = a and b is given by

The symbol

Thus means integrate the expression for y with respect to x.

The expression ,where a and b are limits , is called a definite integral. ‘a’ is called the lower limit while b is the upper limit. Without limits, the expression is called an indefinite integral.

Example

The following steps helps us to solve it

Integrate with respect to x , giving
Place the integral in square brackets and insert the limits, thus
Substitute the limits ;

X = 6 gives

x = 6 gives

Subtract the results of the lower limit from that of upper limit, that is;

(162 + c) – (

We can summarize the steps in short form as follows:

=150

Example

Find the indefinite integral

Evaluate

Solution

Evaluate

4 + 10 -4 ) – ( -)

= (27 – 18 +15) – (8 – 8 +10)

= 14

Area under the curve

Find the exact area enclosed by the curve y = ,the axis, the lines x = 2 and x = 4

Solution

2 4

The area is given by;

Example

Find the area of the region bounded by the curve , the x axis x = 1 and x = 2

Solution

The area is given by;

= (4 – 8 + 4) – (

= 0 – =

Note;

The negative sign shows that the area is below the x – axis. We disregard the negative sign and give it as positive as positive .The answer is .

Example

Find the area enclosed by the curvethe x – axis and the lines x = 4 and x =10.

Solution

The required area is shaded below.

Area =

Example

Find the area enclosed by the curve y and the line y =x.

Solution

The required area is

To find the limits of integration, we must find the x co-ordinates of the points of intersection when;

The required area is found by subtracting area under y = x from area under y =

The required area =

Application in kinematics

The derivative of displacement S with respect to time t gives velocity v, while the derivative of velocity with respect to time gives acceleration, a

Differentiation. Integration

Displacement. displacement

Velocity. Velocity

Acceleration. Acceleration

Note;

Integration is the reverse of differentiation. If we integrate velocity with respect to time we get displacement while if velocity with respect to time we get acceleration.

Example

A particle moves in a straight line through a fixed point O with velocity ( 4 – 1)m/s.Find an expression for its displacement S from this point, given that S = when t = 0.

Solution

Since

S =

Substituting S = 4, t = 0 to get C;

4 = C

Therefore.

Example

A ball is thrown upwards with a velocity of 40 m s

Determine an expression in terms of t for
Its velocity
Its height above the point of projection
Find the velocity and height after:
2 seconds
5 seconds
8 seconds
Find the maximum height attained by the ball. (Take acceleration due to gravity to be 10 m/.

Solution

= -10 ( since the ball is projected upwards)

Therefore, v =-10 t + c

When t = 0, v = 40 m/s

Therefore, 40 = 0 + c

40 = c

The expression for velocity is v = 40 – 10t
Since

When t = 0 , S = 0

C = 0

The expression for displacement is ;

Since v = 40 – 10t
When t = 2

v = 40 – 10 (2)

= 40 – 20

= 20 m/s

S =40t –

= 40 (2) – 5 (

= 80 – 20

= 60 m

When t = 5

V = 40 – 10 (5)

= -10 m/s

= 75 m

When t = 8

V = 40

= 320 – 320

= 0

Maximum height is attained when v = 0.

Thus , 40 – 10t = 0

t= 4

Maximum height S = 160 – 80

= 80 m

Example

The velocity v of a particle is 4 m/s. Given that S = 5 when t =2 seconds:

Find the expression of the displacement in terms of time.
Find the :
Distance moved by the particle during the fifth second.
Distance moved by the particle between t =1 and t =3.

Solution

S=4t + c

Since S = 5 m when t =2;

5 = 4 (2) + C

5 – 8 = C

-3 = C

Thus, S =4t – 3

)

II.)

CHAPTER SIXTY FIVE

Specific Objectives

By the end of the topic the learner should be able to:

(a) Approximate the area of irregular shapes by counting techniques;

(b) Derive the trapezium rule;

(d) Apply trapezium rule to estimate areas under curves;

(e) Derive the mid-ordinate rule;

(f) Apply mid-ordinate rule to approximate area under curves.

Content

(a) Area by counting techniques

(b) Trapezium rule

(d) Mid-ordinate

(e) Area by the mid-ordinate rule

Introduction

Estimation of areas of irregular shapes such as lakes, oceans etc. using counting method. The following steps are followed

Copy the outline of the region to be measured on a tracing paper
Put the tracing on a one centimeter square grid shown below

Count all the whole squares fully enclosed within the region
Count all the partially enclosed squares and take them as half square centimeter each
Divide the number of half squares by two and add it to the number of full squares.

Number of compete squares = 4

Number of half squares = 16/ 2 = 8

Therefore the total number of squares = 25 + 8

= 33

The area of the land mass on the paper is therefore 33

Note;

The smaller the subdivisions, the greater the accuracy in approximating area.

Approximating Area by Trapezium Method.

Find the area of the region shown, the region may be divided into six trapezia of uniform as shown

The area of the region is approximately equal to the sum of the areas of the six trapezia.

Note;

The width of each trapezium is 2 cm, and 4 and 3.5 are the lengths of the parallel sides of the first trapezium.

The area of the trapezium A =

Area of the trapezium B =

Area of the trapezium C =

Area of the trapezium D =

Area of the trapezium E =

Area of the trapezium F =

Therefore, the total area of the region is

If the lengths of the parallel sides of the trapezia (ordinates) are

Note;

In trapezium rule, except for the first and last lengths, each of the other lengths is counted twice. Therefore, the expression for the area can be simplified to:

In general, the approximate area of a region using trapezium method is given by:

;

Where h is the uniform width of each trapezium, are the first and last length respectively. This method of approximating areas of irregular shape is called trapezium rule.

Example

A car start from rest and its velocity is measured every second from 6 seconds.

Time (t)	0	1	2	3	4	5	6
Velocity v ( m/s	0	12	24	35	41	45	47

Use the trapezium rule to calculate distance travelled between t = 1 and t = 6

Note;

The area under velocity – time graph represents the distance covered between the given times.

To find the required displacement, we find the area of the region bounded by graph, t =1 and t =6

0 1 2 3 4 5 6

Solution

Divide the required area into five trapezia, each of with 1 unit. Using the trapezium rule;

;

The required displacement =

Example

Estimate the area bounded by the curve y = , the x – axis, the line x =1 and x = 5 using the trapezium rule.

Solution

To plot the graph y = , make a table of values of x and the corresponding values of y as follows:

x	0	1	2	3	4	5
Y =	5	5.5	7	9.5	13	17.5

By taking the width of each trapezium to be 1 unit, we get 4 trapezium .A, B , C and D .The area under curve is approximately;

= sq.units

The Mid- ordinate Rule

The area OPQR is estimated:

The area of OPQR is estimated as follows

Divide the base OR into a number of strips, each of their width should be the same .In the example we have 5 strips where h =
From the midpoints of OE ,EF ,FG ,GH and HR , draw vertical lines ( mid- ordinates) to meet the curve PQ as shown above
Label the mid-ordinates
We take the area of each trapezium to be equal to area of a rectangle whose width is the length of interval (h) and the length is the value of mid –ordinates. Therefore, the area of the region OPQR is given by;

This the mid –ordinate rule.

Note:

The mid-ordinate rule for approximating areas of irregular shapes is given by ;

Area = (width of interval) x (sum of mid – ordinates)

Example

Estimate the area of a semi-circle of radius 4 cm using the mid – ordinate rule with four equal strips, each of width 2 cm.

Solution

The above shows a semicircle of radius 4 cm divided into 4 equal strips, each of width 2 cm. The dotted lines are the mid-ordinates whose length are measured.

By mid- ordinate rule;

= 2 (2.6 + 3.9 + 3.9 + 2.6)

= 2 x 13

= 26

The actual area is

= 25.14 to 4 s.f

Example

Estimate the area enclosed by the curve y = and the x – axis using the mid-ordinate rule.

Solution

Take 3 strips. The dotted lines are the mid – ordinate and the width of each of the 3 strips is 1 unit.

By calculation, are obtained from the equation;

y =

When x = 0.5,

When x = 1.5,

When x = 2.5,

Using the mid ordinate rule the area required is

A = 1

= 1 (1.125 + 2.125 + 4.125)

= 7.375 square units

End of topic

Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic.

The shaded region below represents a forest. The region has been drawn to scale where 1 cm represents 5 km. Use the mid – ordinate rule with six strips to estimate the area of forest in hectares. (4 marks)

Find the area bounded by the curve y=2x³ – 5, the x-axis and the lines x=2 and x=4.
Complete the table below for the function y=3x² – 8x + 10 (1 mk)

x	0	2	4	6	8	10
y	10	6		70		230

Using the values in the table and the trapezoidal rule, estimate the area bounded by the curve y= 3x² – 8x + 10 and the lines y=0, x=0 and x=104. Use the trapezoidal rule with intervals of 1 cm to estimate the area of the shaded region below

(a) Find the value of x at which the curve y= x- 2x² – 3 crosses the x- axis

(b) Find ò(x² – 2x – 3) dx

The graph below consists of a non- quadratic part (0 ≤ x ≤ 2) and a quadrant part (2 ≤ x 8). The quadratic part is y = x² – 3x + 5, 2 ≤ x ≤ 8

(a) Complete the table below

x	2	3	4	5	6	7	8
y	3

(1mk)

(b) Use the trapezoidal rule with six strips to estimate the area enclosed by the

curve, x = axis and the line x = 2 and x = 8 (3mks)

(d) If the trapezoidal rule is used to estimate the area under the curve between

x = 0 and x = 2, state whether it would give an under- estimate or an over- estimate. Give a reason for your answer.

Find the equation of the gradient to the curve Y= (x^‑2 + 1) (x – 2) when x = 2
The distance from a fixed point of a particular in motion at any time t seconds is given by

S = t³ – 5t² + 2t + 5

2t²

Find its:

(a) Acceleration after 1 second

(b) Velocity when acceleration is Zero

The curve of the equation y = 2x + 3x², has x = -2/3 and x = 0 and x intercepts.

The area bounded by the axis x = -2/3 and x = 2 is shown by the sketch below.

Find:

(a) (2x + 3 x²) dx

(b) The area bounded by the curve x – axis, x = – ²/₃ and x =2

A particle is projected from the origin. Its speed was recorded as shown in the table below

Time (sec)	0	5	10	15	20	25	39	35
Speed (m/s)	0	2.1	5.3	5.1	6.8	6.7	4.7	2.6

Use the trapezoidal rule to estimate the distance covered by the particle within the 35 seconds.

(a) The gradient function of a curve is given by dy = 2x² – 5

Find the equation of the curve, given that y = 3, when x = 2

(b) The velocity, vm/s of a moving particle after seconds is given:

v = 2t³ + t² – 1. Find the distance covered by the particle in the interval 1 ≤ t ≤ 3

Given the curve y = 2x³ + ¹/₂x² – 4x + 1. Find the:
i) Gradient of curve at {1, –¹/₂}
ii) Equation of the tangent to the curve at {1, – ¹/₂}

The diagram below shows a straight line intersecting the curve y = (x-1)² + 4

At the points P and Q. The line also cuts x-axis at (7, 0) and y axis at (0, 7)

a) Find the equation of the straight line in the form y = mx +c.
b) Find the coordinates of p and Q.
c) Calculate the area of the shaded region.
The acceleration, a ms^-2, of a particle is given by a =25 – 9t², where t in seconds after the particle passes fixed point O.

If the particle passes O, with velocity of 4 ms^-1, find

(a) An expression of velocity V, in terms of t

(b) The velocity of the particle when t = 2 seconds

A curve is represented by the function y = ¹/₃ x³+ x² – 3x + 2

(a) Find: dy

(b) Determine the values of y at the turning points of the curve

y =¹/₃x³ + x² – 3x + 2

A circle centre O, ha the equation x² + y² = 4. The area of the circle in the first quadrant is divided into 5 vertical strips of width 0.4 cm

(a) Use the equation of the circle to complete the table below for values of y

correct to 2 decimal places

X	0	0.4	0.8	1.2	1.6	2.0
Y	2.00			1.60		0

(b) Use the trapezium rule to estimate the area of the circle

A particle moves along straight line such that its displacement S metres from a given point is S = t³ – 5t² + 4 where t is time in seconds

Find

(a) The displacement of particle at t = 5

(b) The velocity of the particle when t = 5

(d) The acceleration of the particle when t = 2

The diagram below shows a sketch of the line y = 3x and the curve y = 4 – x² intersecting at points P and Q.

(a) Find the coordinates of P and Q

(b) Given that QN is perpendicular to the x- axis at N, calculate

(i) The area bounded by the curve y = 4 – x2, the x- axis and the line QN (2 marks)

(ii) The area of the shaded region that lies below the x- axis

(iii) The area of the region enclosed by the curve y = 4-x², the line

y – 3x and the y-axis.

The gradient of the tangent to the curve y = ax³ + bx at the point (1, 1) is -5

Calculate the values of a and b.

2007

The diagram on the grid below represents as extract of a survey map showing

two adjacent plots belonging to Kazungu and Ndoe.

The two dispute the common boundary with each claiming boundary along different smooth curves coordinates (x, y) and (x, y₂) in the table below, represents points on the boundaries as claimed by Kazungu Ndoe respectively.

X	1	2	3	4	5	6	7	8	9
Y₁	4	5.7	6.9	8	9	9.8	10.6	11.3	12
Y₂	0.2	0.6	1.3	2.4	3.7	5.3	7.3	9.5	12

(a) On the grid provided above draw and label the boundaries as claimed by Kazungu and Ndoe.

(b) (i) Use the trapezium rule with 9 strips to estimate the area of the

section of the land in dispute

(ii) Express the area found in b (i) above, in hectares, given that 1 unit on each axis represents 20 metres

The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point (-4, 6);

(a) Find:

(i) The equation of the curve

(ii) The vales of x, at which the curve cuts the x- axis

(b) Determine the area enclosed by the curve and the x- axis

A particle moves in a straight line through a point P. Its velocity v m/s is given by v= 2 -t, where t is time in seconds, after passing P. The distance s of the particle from P when t = 2 is 5 metres. Find the expression for s in terms of t.
Find the area bonded by the curve y=2x – 5 the x-axis and the lines x=2 and x = 4.
Complete the table below for the function

Y = 3x² – 8 x + 10

X	0	2	4	6	8	10
Y	10	6	–	70	–	230

Using the values in the table and the trapezoidal rule, estimate the area bounded by the curve y = 3x² – 8x + 10 and the lines y – 0, x = 0 and x = 10

(a) Find the values of x which the curve y = x² – 2x – 3 crosses the axis

(b) Find (x² – 2 x – 3) dx

lines x = 2 and x = 4

Find the equation of the tangent to the curve y = (x + 1) (x- 2) when x = 2
The distance from a fixed point of a particle in motion at any time t seconds is given by s = t – ⁵/₂t² + 2t + s metres

Find its

(a) Acceleration after t seconds

(b) Velocity when acceleration is zero

The curve of the equation y = 2x + 3x², has x = – ²/₃ and x = 0, as x intercepts. The area bounded by the curve, x – axis, x = –²/₃ and x = 2 is shown by the sketch below.

(a) Find ò(2x + 3x²) dx

(b) The area bounded by the curve, x axis x = –²/₃ and x = 2

A curve is given by the equation y = 5x³ – 7x² + 3x + 2

Find the

(a) Gradient of the curve at x = 1

(b) Equation of the tangent to the curve at the point (1, 3)

The displacement x metres of a particle after t seconds is given by x = t² – 2t + 6, t> 0

(a) Calculate the velocity of the particle in m/s when t = 2s

(b) When the velocity of the particle is zero,

Calculate its

(i) Displacement

(ii) Acceleration

The displacement s metres of a particle moving along a straight line after t seconds is given by s = 3t + ³/₂t² – 2t³

(a) Find its initial acceleration

(b) Calculate

(i) The time when the particle was momentarily at rest.

(ii) Its displacement by the time it comes to rest momentarily when

t = 1 second, s = 1 ½ metres when t = ½ seconds

Teachers' Resources

ENGLISH FORM 2 OPENER EXAM PLUS ANSWERS FREE

October 5, 2025 Hillary Kangwana Leave a comment

NAME…………………………………………………………………………………………….CLASS…………….ADM…………..

JOINT EVALUATION

FORM 2 ENGLISH

FORM 2 OPENER EXAM

DURATION: 1 HOUR 45 MINUTES

INSTRUCTIONS

This paper consists of six sections as follows:-

SECTION A: WRITING (15mks) SECTION B: CLOZE TEST (10mks)

SECTION C: ORAL SKILLS (10mks) SECTION D: GRAMMAR (20mks)

SECTION E: ORAL LITERATURE (15mks)

Ensure that you answer all questions in the spaces provide

SECTION A: WRITING (15MKS)

Your friend in primary school is in form one in Bidii Secondary of P.O Box 341, Kisimani. She has written to you telling you about her new school. She has also requested you to carry your end of term one examinations for comparative analysis. Write your reply to her.

SECTION B: CLOSE TEST (10MKS)

A neighbor had left (1) _______________________ store un attended (2) ____________________ she heeded the cries of her (3) _________________________ baby. Her kitchen caught fire, and the flames (4) ________________ to the neighboring shacks in (5) _______________________. There was no (6) _______________________________ available and no fire (7) __________________________ for the people to call. (8)_____________________________ that the assembled crowd of hundreds (9)__________________________ do was gather buckets of sand and (10)_______________________ into the flame.

SECTION C: ORAL SKILLS (15MKS)

For each of the following words, write a word that is pronounced the same way (5mks)
Principle ……………………………………..
Dye …………………………………….

Weak …………………………………….

Stationery …………………………………….
Sent …………………………………….
You have noted that your desk mate Vivian has a poor handwriting. State two factors that might have contributed to this (2mks)

In Form One, one makes new friends. Write three things that you can do when introducing yourself to a new person, so as to appear friendly (3mks)

SECTION D: GRAMMAR (20MKS)

Fill in the blank spaces in the following passage with the most appropriate article (4mks)

___________________________ banana tree is _______________________________ strange looking plant. It grows very quickly and in less than _____________________________ year will reach a height of seven meters or more. Usually, pruning needs to be done and one can take more than ______________________________ hour to finish an acre.

Choose the correct word from the ones in bracket and use it to fill in the blank spaces (4mks)
“I am sorry for the ________________________,” said my friend. (loose, loss)
Why have you ________________________ to eat raw bananas while we have ripe ones in the store? (chose, chosen)
We ___________________ for our president each time we get an opportunity. (pray, prays)
Who ____________________ the bell this morning? (rang, rung)

Complete the sentences below using appropriate reflexive pronouns. (4mks)

The boy was beside___________________________ with fury for missing the penalty.
Let us not deceive ____________________ that life is a bed of roses.
When one faces challenges, one has to encourage __________________________ that things will just be fine.
A house divided against ____________________________ cannot stand.
Use the plural forms of the words in brackets to fill in the blank spaces. (4mks)
You surely do not need three ___________________________. (radio)
Remember to buy grandmother some _______________________ .(potato)
The two ________________________ met so that they could make strategic plans for their locations. (Chief).
The two _____________________ disappeared into the nearby bush. (deer)
Use the most appropriate word to fill in the blank spaces so as to form questions. (4mks)
____________________________ is your mother? Is she a nurse or a teacher?
_______________________________ did you find at the shop? Tom or Mary?
____________________ of these bags is yours? The red one or the green one?
________________________ pen is this? Is it Wilson’s or Kennedy’s?

SECTION E: ORAL LITERATURE (20MKS)

Read the following story and answer the questions that follow

The Monkey and The Crocodile

A long long time ago. Monkey and Crocodile were very good friends. The Monkey’s house was close to a river and there were many fruit trees on the banks of this river.

Usually monkey would sit on the branches of the fruit trees and chat with his friend Crocodile who would be basking on the banks of the river. Their friendship continued for a long time until they decided it was time to introduce their wives to this friendship. “We have been friends for a long time and you don’t even know my house, Crocodile began.

“Neither do you know mine,” Monkey replied. “It is easier for you to come to my-house that it is for me to visit you since I cannot swim and your house is beyond the water.”

“That is not a problem. I can always carry you on my back,” responded crocodile. “Let us visit my house first. My wife is a very good cook,” Monkey argued. “No” replied Crocodile “My wife has had a baby and there is plenty to eat in the house.”

“Let us not argue about this,” Monkey said. “If we go to my house first, my wife will not be anxious when I tell her I am going across the waters to visit you.” They agreed that they would visit Monkey’s house first. Though at first Monkey’s wife was afraid of crocodile, she later realized that Crocodile was very friendly. She did not have problems with her husband visiting him. In fact she wished she would join him.

Monkey was very excited the following day when he got to the banks of the river and found Crocodile waiting for him. This was going to be Monkey’s first trip across the waters and he could not hide his excitement. He jumped onto Crocodile’s back and Crocodile swiftly swam towards the deep waters.

When they were in the middle of the river, crocodile slowed down and began, laughing.

“Why are you laughing?” Monkey asked in surprise “You fool. Did you think I would take you to my house? I have waited for that heart of yours for a long time. Today I have it.”

Immediately Monkey knew he was in deep trouble. He started thinking of a way out of his predicament. “Poor you, my friend: Why didn’t you tell me this earlier?” Monkey calmly asked. “What do you mean?” asked Crocodile in surprise “It is not difficult for me to give you my heart. If you had asked when we were at my house. I would even have given you my wife’s heart too,” Monkey replied. Crocodile was confused.

“Then why don’t you give it to me now?” Crocodile asked.

You see my friend; Monkeys have a tradition of leaving their hearts at home when they are going for a long journey. I therefore left mine on my favorite tree.” Crocodile was even more confused.

“We can go and visit your wife first, and then I will give you my heart when you take me back,” Monkey suggested.

“No,” cried crocodile “I will take you back first. When 1 have your heart, we can then visit my wife.”

Quickly, Crocodile headed back to the bank of the river. When they got there, monkey jumped from Crocodile’s back onto his favorite tree. He asked crocodile to open is mouth wide to receive the heart. Monkey then picked the biggest of the mangoes on the tree and threw it into Crocodile’s open mouth. It fell in with a thud, breaking four of Crocodile’s teeth. Crocodile was so upset but there was nothing he could do as Monkey jumped from tree to tree insulting him.

From that day Monkey and Crocodile have remained enemies. And that is the end of my story and may I not end like it.

Questions

Classify this narrative and give reasons for your classification (3mks)

……………………………………………………………………………………………………………………………………………………………………………………………………………………

Name two characters found in this story (2mks)

a) Using an adjective, describe monkey’s character trait that enabled him save his life from the crocodile (1mk)

…………………………………………………………………………………………………………

b) Illustrate your answer (2mks)

…………………………………………………………………………………………………………………………………………………………………………………………………………………….

What economic activity is practiced by the people from whom this narrative was collected? (2mks)

Write a proverbs that summarizes the narrative and explain how this proverb applies to the narrative

(3mks)

Apart from your answer in A1 above, name two other types of narratives that you know of

(3mks)

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

ENGLISH 101

MARKING SCHEME

FORM 2 OPENER EXAM

TIME: 1 HOURS 45 MINUTES

SECTION A: WRITING (15MKS)

FORMAT : Address (2mks)

: Date (1mk)

: Salutation (1mk)

: Valediction (1mk)

: Name (1mk)

Total (6mks)

CONTENT : Introduction/greetings (2mks)

: Acknowledge receiving a letter (2mks)

: Comment anything about the friend’s school (1mks)

: Carrying of exam papers (2mks)

: Conclusion (2mks)

LANGUAGE (4MKS)

A – 4mks

B – 3mks

C – 2mks

D – 1mk

NOTE:

If student writes the address of Bidii Secondary deny marks for address. Deny mark for half punctuated address.
Salutation should contain one name and must be punctuated with a comma.
The name at the end of the letter should be one, or a short form, not a full name.

Sample

Ufanisi High School,

P.O Box 1362,

Embu.

28^th February, 2014

Dear Sue,

I send my warm greetings hoping that you are fine. I am happy to tell you that I am now settled in my new school.

I received your letter last Friday. It reminded me of the days we had in Primary School when you would send me messages using your mother’s phone. I was surprised that your school has three buses. Ours has got only a van. I also noted that you wanted us to compare our end of term exams. I will carry the exam papers.

I wish you all the best in your new school remember to keep good company. See you over the holidays.

Your friend,

Ann.

SECTION B: CLOZE TEST (10MKS)

her water
while brigade
young All – ‘A’ must be capital
spread could
minutes Throw

SECTION C: ORAL SKILLS (15MKS)

i) Principal
Die

Week

Stationary
Scent, cent
Poor sitting posture when writing

Holding the pen in the wrong way
Shaping letters in the wrong way/poor spacing of work
Writing carelessly and in hurry
Poor training in primary school (2 x 1 = 2mks)
Shaking hands
Smiling at them
Maintaining eye contact
Using phrases like “pleasure to meet you”
Using phrases like “ happy to be your friend”
Nodding of the head where appropriate (3 x 1 = 3mks)

SECTION D: GRAMMAR (20MKS)

The – ‘T’ must be capital

a) loss
b) chosen
c) pray
d) rang

a) himself

b) ourselves
c) oneself
d) itself
a) radios
b) potatoes
c) chiefs
d) deer
a) What
b) Whom
c) Which
d) Whose

SECTION F: ORAL LITERATURE (20MKS)

Fable √(1) – The main characters are animals √(1)

The crocodile and the monkey √(1)

Trickster – The crocodile tricks the monkey to visit his home yet he wants to eat his heart √(2)

Or The monkey tricks the crocodile that her left his heart on top of a tree √(2)

The crocodile √(1)

The monkey √(1)

NB: If candidate does not mention the names

Or simply says “animals” deny mark

Clever √(1) – He tricked the crocodile that he had left his heart on top of the tree √(2)

Note: Accept any other appropriate answer e.g. intelligent

Fishermen √(1) – presence of the river√(1)

Farmers √(1) – grew mangoes√(1)

Identification (1mk)

Illustration (1mk)

1 mk for an appropriate proverbs

2mks for appropriate explanation

Examples of proverbs

The best of friend must part
An ounce of blood is worth more than a pound of friendship
A friend in need is a friend to be avoided
Your closest friend may turn out to be your greatest enemy
Friends are like roses, you have to look out for the thorns
An open enemy is better than a false friend

Legends

Myths
Dilemma stories
Spirit tales
Human stories
Allegorical stories
Ogre/monster stories (2 x 1 = 2mks)

Teachers' Resources

English High School Oral Literature Best Notes

October 5, 2025 Hillary Kangwana Leave a comment

ORAL LITERATURE STUDY GUIDE

UNIT ONE

DEFINITION OF ORAL LITERATURE

Several definitions of our oral literature have been advances but many of them are way above the secondary school students.

A simple yet all inclusive definition of oral literature shows take into account the following aspects:-

Mode of transmission.
Inter-generation transmission

Content of what it transmits.

To start with, we note that the mode of transmission of oral literature is oral. The word oral means by word of mouth secondly the transmission is from one generation to another. Thirdly, what is transmitted is the content of oral literature, that is: oral narratives, songs, proverbs, riddles and tongue twisters.

Thus a simple definition of oral literature would be;

The oral narratives,

Songs,

Proverbs,

Riddles

And tongue twisters

[These were composed and transmitted orally from one generation to another

However, this definition has changed slightly because of the mode transmission which, has broadened to include other modes like the written. However, the above definitions would suffice for oral literature.

FUNCTIONS OF ORAL LITERATURE

The introduction of oral literature into the secondary school syllabus was done in the view of the role or usefulness it serves to those who study it. So function refers to the reasons as to why oral literature is studied.

Different forms or oral literature may perform different functions but generally, the following are functions of oral literature:

Oral literature is a source of entertainment. People derive amusement or fun from such aspects of oral literature as cultural songs E.g. as they are performed in wedding, Harambee meeting and other communal gathering. Oral narratives help people to pass time and derive enjoyment.
Oral literature teaches or educates people on moral values or good behaviour; songs for instance communicate a direct message and attack immorality. Proverbs also speak a direct moral message which narrative lead to moral lesson.
Oral literature sensitizes people on social and communal values. Virtues upheld by the community are taught through oral literature. On the importance of unity for instance a community would have proverbs like “Unity is Strength” Kidole Kimoja Hakivunji chawa’ (one finger alone cannot kill a louse)
Oral Literature teaches about culture is a peoples way of life and it is well reflected in oral literature for example, the way people were governed, their form of religion, division of labour, rites of passage, mode of dressing e.t.c
Having learned about culture, this gives people confidence in their culture as they get to understand why a community lives the way it does.
Closely related to this is that we get to learn about our history or heritage. The study of oral literature provides a useful links with our roots. For example, myth of origin tells the community’s origin and progress up to present.
This means the world of our ancestors is laid bare for present generations to see.
Such a link with the past enables us to understand ourselves. The present is a product of the past to understand where we are and where we are heading to, we first know the past. Today many young people know their names that seem to tie them to a certain past name of their clan and tribes.
Having understood our culture forms of good background for us to know other people’s culture. This fosters good neighborliness and the spirit of nationalism as we understand and appreciate other people.
The study of oral literature provides as with heroes from the past for us to emulate. We get to know of courageous women like Wangu wa Makeri and Mekatilili, Brave men like Wang’ombe wa ihura and Lwanda Magere.

Such heroes provide an aspiration for present generations as we see the way they struggled and made a name for themselves.

Oral literature helps to develop language skills, sense of creativity, wit and even to sharpen speech.

Skill of speaking and listening can be enhanced for example; one would know how to be eloquent by appropriate use of proverbs.

This means that Oral literature is an important tool for shaping the individual into an all round character who can fit into the family, community and nation at large.

CLASSIFICATION OF ORAL LITERATURE

In every community’s oral literature exists in various forms or groups or categories that are referred to in academic jargon as genres of oral literature. It is not the academicians who classify oral literature rather it is the individual communities that do this classification.

The following are the main genres of oral literature.

oral narratives
songs or oral poetry
proverbs and wise sayings
riddles
Tongue twisters or verbal play.

The last three are sometimes put into a broad category called the short fixed forms or oral short forms. This includes the oral literary forms that are brief and compact in comparison to the songs and narratives. This broad category of oral literature would include genres like puns, jokes, and idioms e.t.c.

However, it is important to confine ourselves to the fire classes or divisions of oral literature to avoid confusion. Each of these five genres will be looked at in detail.

UNIT TWO

ORAL NARRATIVES

Where did our Oral narrative come?

An obvious answer to this question would be from our ancestors. But, where did the ancestors get them? I believe from their ancestors and the endless tale of timeless past.

The following are some of the theories put forward to explain the origin of oral narratives:

The existence of oral artists in society
these are the men or women with creative prowess who are able to spin stories and recreate existing ones afresh. These are the people who created the stories we pass from one generation to another.
Group work. Groups of people relaxing together spin a story to logical conclusion. Even today, a class can create a story by simply asking one student to start any way and others creative can on in turns until they are a logical story.
It is also possible that some stories may be have been deliberated created in those in authority to valid existing order of things. Elders for example would spin a story to force compliance.
Some ordinary happens become distorted and exaggerations such that in them they rich epic and fictional. Proportions. Many of the legends are likely to have been created this way.
The fear of mystery and the unknown could have lead to generation of related stories. That is the reason why the communities living near forest had stories about ogres/giants e.t.c. Those living near large rivers and masses of water had stories of mermaids while those living near deserts would imagine of formidable reptiles. To a creative eye and mind, nature has phenomena that naturally raises curiosity and can easily render itself to a story. The very nature of a tortoise is that way. It is for this reason that different accounts on the same phenomenon are available. Whatever theory is put forward on the origin of the stories is acceptable for at the end day it is these stories that passed on from one generation to another.

MODE OF STORY – TELLING

In most of the communities, stories were told in the evening around the fire- place as a recreational activity. It was a taboo to tell stories during the day. This was done in the realization that stories can go captivating that they would disrupt work. So, story-telling sessions were held in the evening to help pass time as people were waiting for the evening meal.

These sessions would involve either

Adults telling stories to children
Adults telling stories to both children and adults
Children telling stories to both children.
Children telling story to a mixed group of children and adults.
In telling stories there was convectional style of announcing the intention to tell a story. The narrator or storyteller would call attention as follows.

Narrator: I would like to tell you a story

(Kiswahili Hadithi Hadithi)

Audience: Tell us
(Kiswahili Hadithi Njoo).

Different communities would put it into different ways but the concept is the same.

THE ROLE OF THE AUDIENCE

The audience refers to those who listen to the story. They are as important as the storyteller or the narrator. They act as a stimulus or the catalyst to the creating and imagination of the narrator. The mood of the audience directly affects the narrator. They urge the narrator. There are two types of audiences.

Active Audience.

These are the listeners who are lively during the performance. They remain active throughout the performance. Through such action as laughing, nodding, clapping, asking questions, joining in the repetition or singing showing the appropriate emotion e.t.c.

Passive audience.

These listeners are attentive but they remain dormant. They keenly engage their ears and eyes but do not play any role in enhancing the liveliness of the performance.

QUALITIES OF A GOOD STORY TELLER:

A storyteller should possess certain qualities/abilities/characteristics in order to stand before the audience and tell a story and captivate the audience throughout the narrative.

The following are qualities of a good storyteller.

A good storyteller should be bold in order to stand before the audience, face them and tell the story freely. A fearful person would shy away from the audience thus; his story would not be interesting. Eye contact in any communication is vital for effectiveness rapport building and for the purpose of registering the response of the audience.
A good storyteller would have a good memory in order to recall details of the story many of the stories told are adaptations of the old ones and it is important to remember the plots of the story.
A good storyteller would be creative and imaginative in order to make the story interesting. When an old story is re-told imaginatively, it sounds new, fresh and interesting. A creative storyteller reads the mood of the audience and adapts the story appropriately for example one would introduce a song in order to involve the audience. This requires a lot of creativity.
A good storyteller should be interested in various cultures. Stories, like all literature, reflect the culture of a people. For a story teller to be effective he should be well versed in a variety of culture so that his stories are within cultural contents of the community in question
A good storyteller should know about the past of his people and also a keen observer of what is happening today so that his stories are dynamic and can appeal to present generations. The artist in society is a bridge between the world of yesterday, today and tomorrow.
A good storyteller should be sensitive in order to ensure that he does offend or embarrass the audience. To be sensitive is to be careful about other people’s feeling in a mixed audience in terms of age, sex, and ethnic background, the artist must be very careful not to sound rude or obscene. In certain instances, she will employ euphemism instead of use of the taboo words.
A good storyteller should be a teacher of morality so as to inculcate the necessary values and practices in the evidence. Besides entertainment, oral narratives are expected to teach good morality in society.
A good storyteller should be a good actor in order to keep the audience attentive throughout the performance. Accordingly, he will employ narrative techniques such as dramatization, gestures, facial expressions e.t.c.

TECHNIQUES OF STORY-TELLING

To make the story interesting and to keep the audience attentive throughout the performance, the storyteller should employ certain techniques.

They includes:-

Dramatization: –
certain aspects of the story or even parts can be re-enacted by reproducers by the narrator for the audience to have a visual insight into how they happened. E.g. the narrator would sit up the way they had done in a meeting.
Use of gestures: –
this refers t the use of hands to demonstrate actions within an oral narrative. The hands can be used to demonstrate cutting down a tree, throwing objects, lifting e.t.c.
Facial expressions: –
the face can be used to capture very many feelings and moods like shock, anger, joy, pain, disgust, suspicion e.t.c. The narrator should use his face to show the audience the feeling of various characters in the story.
Tonal variation: –
the intensity of sound and projection can reflect different tones and moods; the voice can portray urgency, fear, and excitement e.t.c.

Mimicry: –
this is the ability to imitate people or animals for the purpose of making fun. The story teller mimics the character in the story in order to make the story interesting.
Involvement of the audience:-
The story teller should ensure that the audience is active throughout the story through being involved in such areas as the opening formulas, repetition, singing, asking questions and any other area that they can come into the story
Use of costumes and decorations
this involves the use of objects to drive home the message. Where for instance, the hare has glued horns to his head in order to attend a meeting of animals with horns, the narrator can use small sticks to show these horns.
The use of dramatic pause: –
At a strategic point in the story, the narrator can pause for effect. Dramatic pause can work best where there is heightened feeling like shock, surprise and unbelief.
These techniques re married together and used where appropriate to make the story real and lively for the audience to enjoy, follow and understand.

CLASSIFICATIONS OF ORAL NARRATIVES

Oral narratives can be sub-divided into various sub-genres as follows: –

Tricksters stories
Ogre/Monster stories
Explanatory/etiological/why stories
Dilemma
Myths
Legen

TRICKSTER STORIES:

The stories involve trickery where one character, the tricksters, uses his wit to undo another dupe. The trickster is presented as a wise and cunning character while the dupe is usually foolish and gullible.

Each community tends to have its tricksters and dupes. Common tricksters include the hare, the squirrel, Chameleon, tortoise, spider, and monkey e.t.c. The most common dupe is the hyena. There is a trend where smaller and weaker animals seem to outdo the stronger and the bigger ones. Is this done despise the bigger characters?

No, this is done with the following reasons: –

To pass a moral message that might not always be right.
To encourage children that they can also excel in spite of their size.

To encourage the weak in society to fight for their rights in spite of their disadvantages

To show the importance of being wise in society. Sometimes the dupe is depicted as evil and his defeat is a celebration of good over evil.
However, the trickster occasionally finds himself outwitted. This serves as a warning to those who are sly in the society for they could get a taste of their own medicine. Besides, no community would like to encourage slyness and deceit as ways of survival.

EXPLANATORY/AETIOLOGICAL STORIES:

They are called why stories because they attempt to explain the origin of phenomena. These stories usually ends with “and they is why…………………”

It is important to clarify that they do not explain the origin of the universe and communities (myths) rather they pick on the specific trend or aspect of life and explain its origin. They may explain physical attributes of animals and nature and trace the origin of present relationships.

Examples – why the hyena limps, why the hare has a short tail, why the zebra has stripes, how the dog became a domestic animal, why women do not own animals, how the hawk and the hen became perpetual enemies.

OGRE/MONSTER NARRATIVES:

Ogres are characters that are half human and half animal. They are super to change from human characters that have the ability to change from human beings to animals. They feed on human beings and have the ability to devour everything that comes to sight. In many of the stories, they appear in human gatherings as perfect human being for example, very handsome young men but late they old turn to ugly man-eating creatures.

Ogres are an embodiment of evil that successfully camouflages as good among human beings only to reveal itself later. Ogre stories serve to caution human beings to be careful and on the look out for evil that could be camouflaged around us. Children were especially warned against strangers.

DILEMMA STORIES:

A dilemma is a situation where a character is torn between two things and cannot decide what to do and the listener or reader is left to look for the solution. The two or more choices that fact the character or community are usually of a moral nature requiring critical judgement.

The dilemma is meant to test our wit in critical issues of life, initiate debate among listeners or readers and to prepare us for such moments in life.

LEGENDS/HERO STORIES:

Legends are stories of human characters that lived in the past and exhibited extra –ordinary qualities. These characters are of super human nature and their exploits are of epic proportions. The belief among the respective communities is that these heroes are historical figures. What happens is that unique individuals are celebrated by society and with time, their prowess is exaggerated down the line to reach epic proportions.

There is a legend among the Kikuyu known as Wamugumo who was famous to eat volumes and volumes of food. A research I carried out on the same revealed that this man did exist like you and I; he was a very hardworking man and his food consumption was definitely commensurate with his volume of work. To ordinary mortals, this was too much food and his culinary tendencies spread from hill to hill with each making an addition to the abilities. Eventually what emerges today is a figure that could eat a whole will and ask for a second helping while performing work for a hundred ordinary men.

Legends provide us with heroes to copy or emulate for they excelled in various fields e.g. Wangu wa Makeri of the Agikuyu excelled in leadership which was previously a domain of men. Lwanda Magere of the Luo was ideal examples of bravery during the times of inter – clan and tribal wars.

MYTHS

Myths are creation stories that trace the origin of communities and the universe in general as having come through supernatural powers.

The difference between myths and legends is that myths involve the activities of the supernatural or gods while legends are main about human beings but who have super – human qualities.

The function of myths is to explain the origin of mankind and the Bio-physical universe. Thus, myths validate social systems and authority and educate or socialize community members. Each community has its myth though quite a number seem to be similar

OTHER STORIES:

Students should also familiarize themselves with the following other categories of oral narrative.

This is a story that involves the use of animals as the main character with the main with the aim of delivering a moral message.
There is a story about the hyena that went out looking for food during famine after many days of starvation he came across a carcass and ate and ate until he died. This story is neither of the six categories above it is fable.
HUMAN TALES.
These are the stories where human beings are the main character. Sometimes they may interact with animals but it is they (men) who are his focus of the story.

We have other stories about girls seeking beauty and becoming jealous of the most beautiful one among them whom the unsuccessfully try to eliminate leading to their punishments. Such is a human tale.

STORIES ABOUT SPIRIT
we also have stories that highlight the work of spirits among men; the way they live among men influence and control the lives men and generally their existence in the human world.

STYLE IN ORAL NARRATIVES

Oral narratives employ certain feature forms or qualities to deliver their message. Style has to do with the way language is fashioned or used artistically to communicate.

These features of styles includes: –

OPENING FORMULAE
this is when the story begins with word; along time ago, Long long time ago or once a upon a time. When a story begins this way it achieves certain effects or functions including.
It marks the beginning of the story.
The person who utters those words is immediately identified as the narrator.

These words call for attention from the audience as the story has started.

The words clearly indicates that we are moving away from the natural world and entering the fictional world of the narrator since we are dealing with long time – ago the infinite past.

NB: However not all stories start with the opening formulae myths and legend for instance do not start with it for they are believed to be true by their respective communities.

2. CLOSING FORMULAE

This is when the story ends with the words; there ends my story and that is my story of similar words.

This kind of ending has its effects or functions.

It marks the end of the story.
Since the story has ended the audience is removed from the narrative fiction world and released from concentration.

The audience is also free to participate by reflecting on the story or asking questions.

The present narrator makes way for another narrator or presentation

TIMELESSNESS

The time when the events of the narrative took place is not specified. The story is said to take place. Long time ago, one day, at that time, those days e.t.c.

Timelessness enhances the fictional quality of the narrative as there is no reference time. The story becomes believable since it did not take place yesterday but infinite past when those things were possible. So the narrative becomes time in the content of the time.
4. FANTASY.
This refers to elements, situations, events or happenings in the story that are impossible in ordinary day life. Fantasy is the opposite of reality. Example of such includes characters dying and coming back to life. Animals changing into human beings and vice versa: plants and the inanimate objects acquiring human nature e.t.c.

However, the use of the animal characters not fantasy for it is nature of oral narratives. Animals are characters just like human beings.

Fantasy is a source of humour in the story. It also helps to enhance plots by providing for the impossible.

PERSONIFICATION/USE OF ANIMAL CHARACTERS

Personification goes beyond the use of animal characters as other forms of life may be given human attributes as well. The use of animal characters is almost synonymous with oral narratives animals are in deed the characters in the narrative.

Why are animals characters used in the oral narratives?

To create humour: – the imagination of why the animals are able to do is a great source of humour.
To achieve in direct castigation or to avoid directly attacking human beings. This is the principle purpose so as to make human beings see their folly in behaving as those animals do.
This leads to passing a moral message. Animals are used to teach us.
The universal nature of animals helps to universalize the issue at hand. The use of certain objects may tend to localize the message but animals have a universe appeal and their use send the message across various divides.

REPITITION:

Words or phases may be repeated in a story. A common repetition is they went and went, they worked and worked, They ate and ate.

Such repetition serves the following functions:

It creates some rhythm or regularity.
It is a source of humour.

It emphasizes or stresses what is being talked about.

It may serve to show a sense of continuation or cumulative e.g. They walked and walked indicates they walked for a long time and covered a long distance.
Repetition may also indicate a tone or set of moods of the narrative. When a sad phrase is repeated severally, it creates the mood of sadness.

RHETORICAL QUESTIONS

This is a question asked but whose answer is not provided or needed rather it is left up to the audience to think in search of the answer.

The function of such a song includes: –

It entertains the audience and breaks the monopoly of narration. The song provides a good opportunity for the audience to participate in the narration.
It enhances plot development by prolonging the story and joining up different episode in the story.

It captures the mood of the moment as it can express joy or sadness. This cases or relief tension in the story.

A song creates suspense in the story and can be used to anticipate the climax of the story.
A song may become a source of communication between characters in the song. E.g. a bird may deliver a message in a song. A song may help character development when it exposes aspect of character.
DIALOGUE:

This refers to a conversation between two or more characters in the story. Dialogue enhances plot development it may help in character exposition and bring realism into the story.

HUMOUR/COMIC RELIEF

Some elements of a story elicit light moments and laughter from the audience. Humour helps create interest in the audience and keep them glued to the story. Humour also breaks away tension among the audience.

FIGURATIVE LANGUAGE/FIGURES OF SPEECH.

These like imagery, refer in a narrow sense to the use of simile and metaphors. Similes are images that directly compare two or more things using words like as, than: as black as charcoal, black like coal, black than darkness itself. A metaphor is a comparison in which one thing is called another. She is peacock.

These comparisons help to create a mental image of what is being described by making what is abstract become concrete. Some comparisons can be source of humour. Note that figurative language or imagery can broadly include similes, metaphors, personification, symbolism and exaggerations.

EXAGGERATION/HYPERBOLE:

Some elements of reality are deliberated blown out of proportion such that they look large than life.

This creates humour and occasions help us to visualize issues through magnifying them.

SYMBOLISM.

This refers to the use of a person, animal or object to represent an ideal or something else. In life, we have come to see a cross as a symbol of Christianity. Some animals also seem to carry a certain idea e.g. a dove usually represents peace.

However, students should be cautioned against symbol hunting, the tendency to read symbols behind everything they read.

SUSPENSE

Like humour, it is both a style and effect of other style. Suspense is a state of poised anticipation or expectation. It arises from delayed activities that we look forward to a successful story should carry suspense throughout the story so as to whet the appetite of the audience as they eagerly look forward to what happens next.
14. USE OF PROVERBS AND WISE SAYING.

Proverbs can be used in oral narrative to convey a message. They carry both literal and metaphorical interpretations.

IRONY

This refers to a deliberate misrepresentation of the truth. A mode of communication where meaning is expressed through deliberately expressing the opposite of what is intended in the hope that the audience (or reader) will decipher the true meaning it can thus be called honest deception.

Irony also accrues from situations where what happens is the opposite of what seemed obvious. In a story a jealous step – mother puts poison in food expecting to kill a step-son but it is an ironic twist, the food is eaten by her own son who dies.

IDEOPHONES:
These are sound produced by man, Animals and nature that have been coded into words. The barking of the Dog gugugu!, the hissing of the snake sssh!, mooing of the cow Moooh!, Laugh, Kwa! Kwa! Kwa! Or hehehe! Or Waaah!.

To help create realism in the story, break monotony of story and may be a source of humour.
17. ONOMATOPOEA
Certain words or expressions are derived from their natural sound or ideophones. Consider the following

ONOMATOPOEIA

IDEOPHONE

Moo

Mew/miaow

Howl

Bang

Croak

Zoom

Gong

Hiss

Boom

hum

Moooh! Moooh! Moooh!

Miaoh! Miaoh! Miaoh!

Hooo! Hooo! Hooo!

Ba! Ba! Ba!

Croo! Croo! Croo!

Zoo! Zoo! Zoo!

Ngo! Ngo! Ngo!

Ssssssh! Ssssssh! Ssssssh!

Booo! Booo! Booo!

Mmmm! Mmmm! Mmmm!

LESSONS LEARNT FROM NARRATIVES

Each moral oral narrative is meant to pass a moral message to the audience.

In fact, at the end of the narrative the narrator is supposed to lead the group into deducing the moral lessons of the narrative

A moral lesson has a given structure.

It is supposed to be positive when we want to teach something we put it positively as opposed to commandments that is put negatively.
We should not ……….. (commandments not a moral lesson)
A moral lesson should imply consequences. These consequences are either a reward or punishment. This means that when we advice we tell what to do and the benefits or the repercussions of doing so. E.g. we should be careful in choosing our friends for some can be deceitful and mislead.
The most ideal moral lesson is the fourth commandments. Unlike other commandments that are negative and do not imply consequence. It is well formulated positively and with consequences for instance obey your father and mother so that your days on earth may increase.
After stating a moral lesson it should be explained in the context of the narrative. This means that the relevance of moral lesson to the narrative must be traced. In a very simple language. The moral should be illustrated from the story. This is because the moral is derived from the story.
Sometimes a proverb can capture a moral lesson such a proverb must be both positive and implying a consequence. Examples of such proverbs includes:-
a) Pride comes before a fall.
b) Mtaka yote hukosa yote. (He who desires all loses all)
c) Unity is strength.
d) Mtegemea cha nduguye hufa maskini (whoever relies on his siblings dies poor).

However, it is important to know that each story has its own moral lessons and there are no moral lessons that can apply to all stories

ECONOMIC ACTIVITIES

These are activities through which a community meets its basic needs and wants as you listen to or read a story you notice activities that are geared towards meeting the needs and wants of the community.

They may include cultivation of crops, keeping of livestock, hunting, gathering, fishing, blacksmithing, trade or commerce wearing e.t.c.

SOCIAL-CULTURAL ACTIVITIES

This is the peoples way of life and as we listen to or read a story we get to see trends of a community set up in terms of religion rites of passage, division of labour, mode governance. Food, housing, education, solid set-ups, celebrations and festivals e.t.c

UNIT THREE

SONGS/ORAL POETRY

What is poetry? – Poetry refers to the message that is arranged in verse as opposed to prose. When these words are rendered in a musical form they become a song or oral poetry, in deed any poem can become a song if appropriate music or melodies are added.

PERFORMANCE OF SONGS

Man is a singing being. All is life is marked and permitted with song and dance. The African is particularly more musical and virtually all his life is accompanied by song and dance, working leisure, rites of passage, religion e.t.c.

Most of the singing is done in given rhythm and accompanied by dancing.

This dancing range from simple nodding of the head, tapping of the feet and clapping of the hand to vigorous body movements and group formations

The performance is usually led by a single person, the soloist or a group leads the rest. Sometimes instrumentation’s accompanies singing and dancing. In some communities songs are performed according to age and sex though there are instances where all comes together in song and dance.

On the whole the versatile nature of songs allowed for a variety of performance and there seems to be no boundaries or limit of creativity.

CLASSIFICATION OF SONGS

In some communities, songs are classified along gender and age such that we have songs for boys, girl’s e.t.c. But this classification is a bit isolated and the more common one is done accordingly to the functions.

The main functions of songs, of course entertainment but each category has it specific functions. These classes are as follows.

LULLABIES
These are songs that are sung by mother and by sisters to soothe babies to sleep or quiet crying babies
Lullabies are simple songs that involve monosyllabic words that are constantly repeated. They have a soft tone and smooth rocking rhythm for effect.
CHILDREN PLAY SONGS
Children everywhere in the world tend to have a variety of songs to enhance their play activity. These songs can further be sub-divided as follows.
Singing games.
These are songs as part of the play activity. The singing is an integral part of the game. A common one is the song sung by small girls s the jump around a rope.
Nonsense songs:
These songs pick on a particular petty thing or issue and sing about it and saying nothing in particular. They are used by children to bring out their childishness. In such songs children would sing about such things as frogs and cats.
Naughty songs
each age has its secret naughty things that they want to do or say only in the context of their age-mates. For children they would taunt one another and occasional they may border on the absence. Sometimes nursery school children have naughty songs taunting their teacher though in a light note.
Tongue –twisting rhymes/catch rhymes
These are songs based on attempts to articulate difficult sounds especially those sounds with similar pronunciation
Trick – verse.
This involves two groups engaged in a battle of wits using words in a song. Each group would represent an idea, object or specific group trying to prove to the other their supremacy. One group could represent cats while the other represents dogs and each would try to show the other how he is adored by men
Round songs.

Several groups would be singing the same song but in a rotational form such that while the first is singing in the second line, the second starts the first line and so on. Its intention is to ensure that the members of each concentrate so that they are not outdone or overshadowed by the other.

g] Nursery chants

This is a modern category of songs sung in elementary schools to enhance the learning process.

INITIATION SONGS:

These are sometimes narrowly perceived circumcision songs. They are sung when youngsters are being initiated into adults.
Their function is to educate the initiate or such things are tribal history, immorality expectations in adulthood. Sometimes they can be used to encourage the initiates praise the fearless ones and ridicule cowardice.

LOVE/NUPTIALS/WEDDING SONGS
They express strong feeling of love and intention to marry. Besides expressions of feeling they also teach in morality and the expectations of the society in matter pertaining to marriage.
FUNERAL DIRGES
These are songs sung during burial ceremonies to express sorrow and hopelessness at man’s liability to overcome death. These songs may be used to praise the dead and the legacy they have left behind
WORK SONGS.
They are sung to accompany work. They help those working to relax as they do work, enhance the work, create harmony among workers, praise the virtue of hard-work and ridicule laziness and reflect generally on work.

There are quite a number of songs serving very specific purposes. Others include.

War songs
Political songs/patriotic songs
Praise/epic songs
Beer songs
Satirical songs
Child-naming songs.

FEATURES OF STYLE IN SONG

Consider the following work song or satirical song

These men of Kaaria.

He has hardly thrown into Jembes
when he says
aai! I want to go to the bush
I might have eaten a bad thing
in that village of Ndumbi
the people of Ndumbi
the people of Ndumbi cannot be trusted
they are frequent visitors of Gaturi

And he goes dragging his feet
these men of Kaaria
they all have steel backs
but very sweet words to cover
their inability to bend in the shamba

I ask

Where do they get food?

And when the women approach
with pots and Calabashes
he hurriedly rushes in from the bush
he has not even done his clothes well
to be the first to dip his hands there
aai. You men of Kaaria
don’t you even have shame?
(Anonymous)

The following are some of the features of style in songs

It functions in the same way as in oral narratives only that in songs there is usually a lot of repetition for musicality.
DIRECT TRANSLATIONS.
Songs are rendered in their original language and they have to be translated into English. Very thorough translation would lose the real meaning and humour of the song so a lose translation is given. Sometimes the translation is so direct that only those familiar with the original language can grasp the real meaning.

Direct translation ensures that the translation text remains as close as possible to the original text. It also traces the origin of the song and can be source of humour. The first line of the above song is a direct translation from the Kikuyu version “Gukia icembe” where digging is referred as throwing a Jembe.

DIRECT ADDRESS
Most of the songs have a specific target audience. The singer will directly mention the address. This creates a dramatic effect since somebody is being referred to it also given the message context as the audience is known. In the sixth line of the third stanza there is direct address – “You men of Kaaria”.
TRADITIONAL SETTING.
The setting of the song in terms of social cultural traits may trace directly to traditional practices. You can clearly tell that you are dealing with practices of the pre-modern society.
In the third line of the first stanza, the young man says he want to go to the bush for he must have eaten some bad food. This refers to going to the toilet which is traditional times was the bush.
CLASS MORAL JUDGEMENT.
Under normal circumstances we judge individual moral conduct but occasionally a singer backing in the glory of poetic license.
In the song, the young men of Kaaria are said to have no shame in the last line of the poem.
ELEMENTS THAT CAN BE DRAMATIZED
It is said that there is no song without dance. As you look through the song, you notice that it has areas that can be rendered through action.
In the last stanza of the song the young man is said to rush into be the first to clip his hand in pots. This can be brought out through action.
EXTREME CHARACTERISATION

Again due poetic licence a singer can cast characters in the extreme for humour and to pass a moral message through ridicule.

The young man of Kaaria are said to have no shame in the rhetorical questions appearing in the last line of the poem. They are also said to have steel backs in the second stanza implying that they cannot bend to do work. This is a bit extreme.

In other works of literature like prose and drama, messages are expressed in an implicit manner such that it is upto the reader or audience to deduce the message, but in songs this is done in didactic manner and so we have direct address, class moral judgement and extreme characterization.

ANONYMITY

This feature of style refer to instances where in place of composer’s name we have the word “anonymous” meaning that the composer is not known.

An anonymous composition might indicate that the song is a communal property having been composed and transmitted orally by the community. So even as the singer sings, the message is communally owned giving it great validity.

EUPHEMISM

This is a manner of expression that employs more socially acceptable and less direct language for something that would otherwise have been unpleasant, vulgar or taboo. In nursery schools, children are taught very basic euphemism. Instead of going to the toilet, it is, “may I go out”.

MORAL LESSON

As argued above, songs communicate in a didactic manner. The singer opts to preach his message directly. Where this happens it is a moral lesson.

A singer, for instance would sing “work hard young men for hard work pays”.

This is a common feature of oral narratives where the message is put very explicitly.

PARALLELISM

The use images to compare or contrast ideas. Such pair of images can be characters, expressions, experiences or ideas that stand out in the song as mutually exclusive.

ALLUSION

This refers to the use of names of people, place, things or Events that the listener or reader is automatically assigned to know about or is familiar with. In choosing the word, the writer or singer makes the basic assumption that its implications are well known.

In the song above, the singer says the man of Kaaria could have visited Gaturi. This is a rude reference to use of poison. Gaturi among the Kikuyu was believed to be a place where people used witchcraft.

Other features include

Imagery/ figurative language
Idiophones
Personification
Rhetorical questions
Irony
Use of proverbs and wise sayings

UNIT FOUR

PROVERBS

DEFINITIONS

A proverb is a short statement of wisdom accepted by a community as an expression of truth and wisdom.

Overtime a community develops short statement that reflects its experience, belief, philosophy of life, world view and tested opinion.

This statement is passed down the generations in form of wise sayings or proverbs.

CLASSIFICATION OF PROVERBS

There are several ways of classifying proverbs. Some of these includes: –

Alphabetic classification

In quite a number of books where proverbs are recorded this is done in alphabetical order. This is done in the realization that classification of proverbs is not as easy as obvious as that of songs and narratives.

Classification according to the subject, matter, contents or themes

This way, themes would be grouped on what they are talking about. We would therefore have proverbs on poverty, family, patriotism, unity, religion, wisdom, readership, handwork, honesty, greed friendship, obedience, death, wealth and poverty etc.

Classification according to style

This is a more complex academic exercise where proverbs are classified according to style they employ for example a certain experience event or story would be summarized to form a single statement that becomes a proverb. Such is an anecdote proverb.

According to style, we would have proverbs like aphorisms, allusions, satirical, epigrams etc.

Classification according to functions

For secondary school students this appears to be the most appropriate since it is simple. We note that a single proverb can serve several functions.

The following are some of the functions of the proverbs and their classifications

Advisory and advising proverbs

E.g. Mtaka cha mvunguni sharti ainame

(If you want something, you must work hard)

Cautionary or cautioning or warning proverb

E.g. Bad Company ruins morals

Educative e.g. Mtoto umleavyo ndivyo akuavyo

(The child grows up the way you bring him up)

Satirical proverbs e.g. Nyani haoni kundule

(The monkey does not see its ugly buttocks)

Encouraging proverbs e.g. Success does not come on a silver plate.
They are incorporated into ordinary conversation as sign of eloquence

They are used in deciding a case e.g. among the Luos there is a proverb that says “blame both the world cat and the chicken” while the Kikuyu says “both the thief and the witness are equally guilty”.
They express a worldview of a given people of issues of life like sickness, poverty, wisdom etc.

Summarizing a situation e.g. Charity begins at home.
Proverbs also express or capture the contradictions of life e.g. if you want peace prepare for war.

It is important to note that classification according to function is not rigid since one proverb can be used for various functions.

CHARACTERISRICS OF PROVERBS (STYLES)

Proverbs are usually short in form. In company with other genres like songs and narrative proverbs are short.
They are metaphorical or referential. The language of proverbs employs images and pictures to compare experiences. Therefore, a proverb has literal and metaphoric meanings.
They are compressed/compact/concise/pithy. The message of the proverb is delivered using very few words but which are loaded with meaning.
Proverbs are fixed/static
the statement does not change with time and remains the same as it is handled down the generations. However the relevance of the proverbs transcends the boundaries of time and space.
Proverbs are situational and contextual.
The nature of proverbs is such that they have to be conceived in a particular context. One proverb can be used to contradict another.
NB: at a more advanced level, the style of proverbs can be analyzed and found to employ such features of style as parallelism/juxtaposition, contrast. Imagery, idiophones, allusion, humours and sounds patterns.

UNIT FIVE

RIDDLES

Definitions

This is a simple form of phrase or statement referring to an analogy of some well- known objects or reality that a challenger pauses to the respondent.

In very simple language, a riddle is puzzle put forward by a challenger for the respondent to try and un-raffle.

PERFOMANCE OF RIDDLES

Traditionally riddles were performed in the evening, alongside other genres as a way of passing time although they were mainly passed down from older people. The performance of riddles was a domain of children.

Today riddles are performed in school as part of learning process. This means that they have become quite dynamic.

The process of performance of riddle normally takes the following form:

The challenger declares a wish to place a riddle
English : I throw a riddle
Kiswahili : Kitendawili

The respondents accept the challenge
English : We take it

Kiswahili : tega

The challenger poses the riddle.
Respondents make the attempt until they get the correct answer.
If the correct answer is not forthcoming the challenger proudly asks for a reward in order to reveal it. The reward is mere token applicable only within the context of the riddling process. The token/rewards depend on the creativity of the participants. So they offer rewards until the challenger accepts one.
Then the correct answer is given and the respondents marvel at the genius of the challenger.

CLASSIFICATION OF RIDDLES:

There are several ways of classifying riddles. They include:-

According to the imagery employed:
This classification looks at the object mentioned in the riddles and classifies them thus,
example riddles on wild animals, plants, domestic, animals, people, natural phenomenon, traditional objects, modern technology, cooking, utensils e.t.c.
According to style and
Like other forms of literature, riddles also employ style to communicate the message.
Accordingly we have:-
Homologues / idiophonic riddles.
These rely on sound. The relationship between the puzzle and the answer lies in the ability to relate to the sound to particular objects.
For example among the Kikuyu “Shi na Shi” refers to a needle. The sound “Shi” imitates the process of needling in and out
Declarative riddles
the styles employed are description. A description of the object is provided. They match so perfectly that the respondent can guess.
Challenger : A European standing on one
Respondent : a mushroom.

Interrogative riddles.
This is presence in a question form
Challenger : Wanicheka nimekufanya nini (what have I done that you may laugh at me)
Respondent : kioo
(mirror)

Epigrams
the style is puzzling. This is done by presenting a series of logically connected puzzles that allude to a process or an object.
g.
Challenger : Ting ting kaleta tang tang na

tang tang kaleta ting ting
(Ting ting brings tang tang and

tang tang brings ting ting).

Respondent : Kuku kataga mayai na mayai huleta kuku.

Analogue (coinage]
This is a sub-group of the epigram. The style here is comparison. The riddle is a comparison between the object and the expected answer.
E.g.
Challenger : Two carrying two driving four to the paa.
Answer : A woman carrying the baby taking a

Cow to the river

Narrative riddle.
The style is narration. The challenger begins by telling as short story that has elements of ambiguity or that which presents a difficult problem to be solved or that which underlies some hidden facts and that asks a question which requires an analysis of the story.

E.g. a man was going on a journey carrying the goat, a leopard and some sweet potato vines. He came he came to a river that he could only cross by a boat but only which could only carry two items at a time. How did he carry the three items across the river.

FUNCTIONS OF A RIDDLE

Entertainment/leisure/amusement/passing time.
Test and develops Children’s wit/intelligence.
They help children to be observant of the environment.
They enhance socialization. Sometimes children would exchange riddles with adults.

SIMILARITIES BETWEEN RIDDLES AND PROVERBS

They are both short in form.
They both employ metaphorical/figurative referential language.
They are used for the purpose of oral communication.
They embody the culture (values, beliefs, practices, artifacts) of a particular community.
They are distinct to a particular community or environment

DIFFERENCES BETWEEN RIDDLES AND PROVERBS

While a proverb is a short statement of wisdom, a riddle is a language game.
The proverb is a single statement while a riddle has a formula requiring a coders and decoder/challenger and a respondent. So they have a different form.
A proverb is a static statement that does not change in time and space but riddles are dynamic as they are influenced by time and space to change.
Proverbs are usually used by adults while riddles are a domain of children.

UNIT SIX

TONGUE TWISTERS

DEFINITION

This is a phrase containing a number of words that are very similar in pronounciation and which are difficult to articulate in a single breath. A group of similar yet difficult words are systematically put in succession to provide a sound puzzle.

CHARACTERISTICS

Tongue twisters rely on sound patterns like alteration, assonance, consonance, rhyme and repetition.
Meaning not a necessary component. The meaning of those statements is not considered since many of them are meaningless.
The main aim at auditory discrimination the ability to tell the difference between similar sounds.

FUNCTIONS OF TONGUE TWISTERS

They help to articulate words. They are said to ‘lighten’ the tongue.
They sharpen wits in an attempt to coin them or articulate them.
They enhance the harmony between what is heard and what is said.
They can be said to have an educational value as they aid in language development

EXAMPLES

Wale watu saba walipewa siku saba kutafuta shamba lakini siku saba hazikutosha kupata shaba kwani shaba haiwezi kupatikana kwa siku saba
Faith faithfully facilitated fairly fort night for the fair at the former factory facing famous fairly fait.
Kwa sababu alikiwa shababu, shaaban alisahau kuwa maisha ya shababu ni hatari sana kwa sababu shababu isipochunga huweza kupotoshwa ma mashababu mengine bila sababu maalum.

UNIT SEVEN

FIELDWORK

In spite of heavy classrooms, work load students are expected to have time for field work.

What is field work?

This is a systematic fact finding mission whereby students go out to collect oral material. This is done with a view of recording and analyzing this information.

TERMS USED FIELDWORK

FIELD – This does not refer to any physically designated area

It is any place that a researcher (students) goes to collect oral literature material

RESEARCH – The process of gathering, recording and

Analyzing oral literature material

DATA – Information gathered in a research.

INFORMANT – Any person who provides information to the researcher in the process of field work also known as the respondent.

INTERVIEWER –The researcher as he asks questions

INTERVIEWEE – The person responding to those questions (informant).

RAPPORT – a cordial relationship between the researcher and the informant

TRANSCRIPTION – Writing down oral material in the original language of performance exactly as it is rendered without any alteration or directly from a tape recorder.

TRANSLATIONS – Giving meaning in another language to what is said or recorder

IMPORTANCE OF FIELDWORK

Fieldwork is done with a very clear purpose or objectives. They include.

Provide students with an opportunity experience oral literature. What is written in book becomes meaningful once students get first hand bit through seeing, hearing and participating in the performances in the field.
Students are able to relate what they learn with real life situations. What is learnt in class is no longer rote learning but reality.
Field work provides an opportunity to detect ant new trends even as students confirm what is there. Oral literature dynamic and students should be kept a breast of any change.
It helps students sharpen skills of observation, recording and analysis. Furthermore field work is a continuous process throughout academia.
Oral literature is a performed art that can only be fully appreciated in the context of a performance.
There is still a lot of oral literature material in the areas of songs, narratives, proverbs, riddles and tongue twisters that is yet to be collected recorded and analyzed. This is the work researchers like students.

Field work provides students with a moment of relaxation and enjoyment outside the classroom situation. Students also enhance their ability to socialize and interact with people and also to make independent and important decisions.
STAGES IN FIELD WORK

The process of carrying out field work involves five stages:-

Preparations
Collecting data
Recording the data
Processing the data
Analyzing and interpreting the data.
PREPARATIONS

This involves the following:

Logically the first thing to do is to decide on what is to be researched.
Researcher then identifies the catchment’s area location of the study.

It is important to seek official permission from the authorities.

A pre-visit is important visiting before hand gives the researcher an insight into the physical and social environment of the field.
It is important to do library research on the topic of research so as to establish a research gap.
Prepare material for recording and any necessary equipment.

It is vital to work out an estimation of time and money required for a successful completion of the study.

COLLECTING DATA.

This is the process of gathering and acquiring the information being sought for. Here the main issue establishing contact with the informant, establish rapport and using certain techniques to get the information. These techniques are the methods of collecting information include listening, observation, participation, and interview. These methods are not used in isolation. A good researcher will harmonize the use of several of these.

A keen listener will gather lot information from what is a said.

b) Observation

The researcher stands aside and uses his eyes and ears to follow what is effective as one can get wrong perceptions of what is going on. Furthermore you cannot get insights into what is going on while you stand aloof.

c) Participation.

It is also called participant observation. The researcher becomes part and parcel of what is going on. He observes from within. This way first hand information is gathered without the prejudice of the respondents.

However there can be problem of getting answers to set questions.

Interview can be used to get information even from illiterate people. The researcher guides the discussions towards getting answers to set questions.

Interviews can be used to get information even from illiterate people. The researcher has a chance to gauge the feelings of the respondents and probe further if needed be also important is that instant answers are provided.

But interviewees can put up a show thus mislead the interview suffer memory lapse or deliberately till lies when using a translate there could be distortions

d) Questionnaires

This is the set of prepared questions that a respondent id given to write down the answers.

The following questionnaire has been prepared by a researcher gathering information on the same.

SAMPLE QUESTIONNAIRE

BACKGROUND OF THE INFORMANT

Name …………………………………………………………

Sex …………………………………………………………….

Age …………………………………………………………….

Place of birth ………………………………………………….

District …………………………………………………………

Province ……………………………………………………….

Tribe …………………………………………………………

Marital status ……………………………………………….

Occupation …………………………………………………

INFORMATION OF THE SONG

How did you learn the song that you are singing………………………………………………………………………………………………………………………
When were these songs usually sung and by who?
………………………………………………………………………………………………………………………………
What functions did they serve?
…………………………………………………………………………………………………………………………….
Were there roles governing the way songs were sung?
………………………………………………………………………………………………………………………………
Have these songs undergone any change today?
………………………………………………………………………………………………………………………………
Comments on songs in general
………………………………………………………………………………………………………………………………
The questionnaires can cover a wide range of information using one or a few researchers. The researcher just gets the kind of information he seeks and the respondents feel free. But they are limited to the literate people. No opportunity to probe further and the respondents can deliberately give misleading information.

NOTE:

To overcome these problems of inaccurate information, the researcher should use various methods to reinforce each other and also increase on the number of respondents so as to compare notes

RECORDING DATA.

In practice both data collection and recording goes on simultaneously. The two may be done by the same person but some methods require a different person for recording.

The methods of recording includes:- memory recording, writing, type recording, photography or filming or video recording

Memory recording
this is sometimes called foreteller method as it was the sole method through which our fore father stored oral literature for later transmission to the next generation.
However, a lot of oral literature faded out this way as it never got to the next person sometimes it was forgotten and distorted.

This method is largely responsible for literally transmission. Written records are accessible to a wide audience across time and space. However it is only accessible for those who are literate furthermore this method is slow in recording a performance and may lead to inaccurate recording. It also leaves out the visual details of performance.

Tape recording
this accurately records verbatim. The proceedings of the performance. It can even be concealed to avoid interfering with the performance.

This can later be Tran scripted and translated
however, it is expensive as it requires at least a radio it also leaves out the visual details of the performance.

Photographing
photographs are also a means of keeping visual accounts of the performance. Such physical detail as costume and décor. The performance and the setting can be captured.
But this is narrow for it only records a few details. Besides it is very expensive and requires some expertise.
Filming or video recording
it is an all round recording for it takes accounts all details; it is audio visual. But the cost can be prohibited while it might require somebody with technical know-how.
NOTE:
As in the methods of collecting data the recording methods can be combined where possible to improve efficiency.
PROCESSING THE DATA
in view of the variety of recording techniques it is important to make a written copy of the findings. Both transcription and translation will be carried out to produce a fair copy of the findings.
ANALYSIS AND INTERPRETATION OF THE DATA
after a fair copy is obtained the researcher can no classify the material into genres and make comments and conclusions based on the findings. Here the success of the mission is measured in view of the objectives laid down at the beginning of the research.
Sometimes a researcher finds it important to point out areas left out that other researcher could venture into.

PROBLEMS ENCOUNTERED IN FIELDWORK.

Language barrier
some respondents are only familiar with their vernacular which the researcher may to be familiar with. This calls for the use of interpreter.
Unreliable informants
some informants may suffer memory lapse or provide untrue information. Sometimes this may be as a result of ignorance.
The research has to use a lot of informants and also probe and ask supplementary questions to the informants.
Failure to establish rapport.
Sometimes it is difficult to get the informants to corporate and provide information. Some will even be hostile. The researcher should make a pre-visit to do the ground work sometimes a researcher has to carry token gifts but it is good. Public relations on the part of the researcher that carries the day
Transport and accommodation problems.
Some parts of the country are not easily accessible and accommodation becomes a problem. A pre-visit gives the researcher an insight into what to expect and prepare accordingly.
Bad weather and environmental problems.
Researcher should be prepared for difficult conditions and adverse weather conditions.
Breakdown of research equipment
in the course of transportation and movement the researcher may lose or damage some equipment. This calls for care and adjustment on the part of the research. If a radio breaks down, he may have to record everything in writing.
This happens if the researcher had not prepared well. You arrive in the filed to find that the performance is through or does not happen that season. A good example is the circumcision ceremony which only takes place at a certain time in the year. Failure to prepare well would have the researcher missing the performance
Cultural shock
cultures are different and have different stands. In some areas a man cannot alone interview a woman such situations calls for creativity in complying with the standards and ensures that the research goes on. Researcher must be sensitive towards such practices as greetings, dressing, relationships across sexes and other sensitive cultural practice. A researcher goes out to understand and respect other cultures but not trying and challenge them or change them.

ORAL LITERATURE TODAY

Oral literature continues to be perpetuated today through the following ways

School curriculum
the incorporation of oral literature in the secondary school syllabus is a very important factor in consolidating the bright future of oral literature. This is even more so as English subject under which oral literature is taught is a compulsory subject and tested in Kenya Certificate of Secondary Education (K.C.S.E)
Availability of resources
there are quite a number of resources in terms of written materials, video tapes, regalia e.t.c that have recorded oral literature ensuring posterity.
Institutions
some institutions like the Bomas of Kenya museum e.t.c provide for presentation of oral literature materials.
Inter-school festivals
the music and drama festivals provide an opportunity for exposure to oral literature
Cultural festivals
some communities and institutions prepare very popular cultural festivals that help to perpetuate oral literature.
Oral literature for public entertainment.
Songs, dances and narratives continue to be part and parcel of public entertainment in gathering and mass media

@ENGLISH DEPARTMENT

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Health Education Grade 7 CBC Free Schemes of Work

October 5, 2025 Hillary Kangwana Leave a comment

GRADE 7 SPOTLIGHT HEALTH EDUCATION SCHEMES OF WORK TERM 3

NAME OF THE TEACHER SCHOOL YEAR TERM III

Week	LSN	strand	Sub-strand	Specific Learning Outcomes	Key Inquiry Question(s)	Learning Experiences	Learning Resources	Assessment Methods	Ref
1	1	ENVIRONMENTAL HEALTH AND SANITATION	Meaning and Importance of Environmental Health	By the end of the lesson the learner should be able to: a) explain the meaning of the term environmental health and sanitation b) discuss the importance of environmental health for healthy living c) Appreciate the importance of a healthy environment for promotion of the well-being of self and others.	1. Why is environmental health important? 2. How do you control environmental factors affecting health?	The learner is guided to: ● brainstorm on the meaning of the term environmental health and sanitation	Resource person, digital devices, video clips, print reference materials, realia, tree seedlings, posters, pictures, cleaning materials and equipment *Spotlight health education T.G pg. 66-68* *Spotlight health education P.B pg.* 98-100	Graded observation of group work activities ● Written test ● Oral assessment
	2		environmental factors that affect human health	By the end of the lesson the learner should be able to: a) identify environmental factors that affect human health b) watch a video clip of environmental factors affecting human health c) Appreciate the importance of a healthy environment for promotion of the well-being of self and others.	1. Why is environmental health important? 2. How do you control environmental factors affecting health?	The learner is guided to: ● participate in activities to control environmental factors affecting human health (planting trees, environmental cleanup, sensitization and advocacy). ● investigate environmental factors affecting human health and report their findings	Resource person, digital devices, video clips, print reference materials, realia, tree seedlings, posters, pictures, cleaning materials and equipment *Spotlight health education T.G pg. 68-69* *Spotlight health education P.B pg.* 101-102	Graded observation of group work activities ● Written test ● Oral assessment
2	1		Measure for controlling environmental affecting human health	By the end of the lesson the learner should be able to: a) identify the importance of a healthy environment b) apply measures for control of environmental factors affecting health c) Appreciate the importance of a healthy environment for promotion of the well-being of self and others.	1. Why is environmental health important? 2. How do you control environmental factors affecting health?	The learner is guided to: ● participate in activities to control environmental factors affecting human health (planting trees, environmental cleanup, sensitization and advocacy). ● investigate measures taken to control environmental factors affecting health	Resource person, digital devices, video clips, print reference materials, realia, tree seedlings, posters, pictures, cleaning materials and equipment *Spotlight health education T.G pg. 68-69* *Spotlight health education P.B pg.* 103-105	Graded observation of group work activities ● Written test ● Oral assessment
	2	Environmental contaminants	Types of environmental contaminants	By the end of the lesson the learner should be able to: a) identify types of environmental contaminants that affect human health b) Watch a video clip on different environmental contaminants c) Develop curiosity in identifying environmental contaminants.	Why maintain a healthy environment?	The learner is guided to: ● discuss types of environmental contaminants that affect human health, and make presentations (biological contaminants, chemical contaminants, gases and heavy metals)	Digital resources, reference materials, realia, pictures, charts, photos *Spotlight health education T.G pg. 70-72* *Spotlight health education P.B pg.* 106-107	● Written assignment ● Oral assessment ● Self and peer assessment
3	1		effects of environmental contamination	By the end of the lesson the learner should be able to: a) state the types of environmental contaminants that affect human health b) outline the effects of environmental contamination on human health c) Develop curiosity in identifying environmental contaminants.	Why maintain a healthy environment?	The learner is guided to: ● research and discuss the effects of exposure to environmental contamination on human health.	Digital resources, reference materials, realia, pictures, charts, photos *Spotlight health education T.G pg. 73* *Spotlight health education P.B pg.* 108-109	● Written assignment ● Oral assessment ● Self and peer assessment
	2		Importance of an environment free from contaminants	By the end of the lesson the learner should be able to: a) list the effects of environmental contamination on human health b) control environmental contamination for a healthy environment c) Value an environment free from contamination for healthy living.	Why maintain a healthy environment?	The learner is guided to: ● explore on ways of preventing and controlling environmental contamination	Digital resources, reference materials, realia, pictures, charts, photos *Spotlight health education T.G pg. 74* *Spotlight health education P.B pg.* 110-111	● Written assignment ● Oral assessment ● Self and peer assessment
4	1	Infection Prevention and Control	Equipment’s for infection prevention	By the end of the lesson the learner should be able to: a) explain the meaning of infection prevention and control for health promotion b) outline personal protective equipment used for infection prevention c) value infection prevention and control for healthy life	1. How do we prevent and control infection? 2. What is the difference between cleaning and disinfection?	The learner is guided to: ● brainstorm on the meaning of infection prevention and control ● use digital devices and reference materials to search for information on commonly used personal protective equipment	Realia, Pictures, charts, posters, digital resources, print materials, reference books, video clips, digital devices, resource person, cleaning equipment and disinfecting materials *Spotlight health education T.G pg. 75-77* *Spotlight health education P.B pg.* 112-113	● Graded observation of learner demonstrations ● Written assignment ● Oral assessment ● projects
	2		Improvising a personal protective equipment	By the end of the lesson the learner should be able to: a) list personal protective equipment used for infection prevention b) make personal protective equipment using locally available materials c) value infection prevention and control for healthy life	1. How do we prevent and control infection? 2. What is the difference between cleaning and disinfection?	The learner is guided to: ● improvise personal protective equipment using locally available resources	Realia, Pictures, charts, posters, digital resources, print materials, reference books, video clips, digital devices, resource person, cleaning equipment and disinfecting materials *Spotlight health education T.G pg. 77-78* *Spotlight health education P.B pg.* 114	● Graded observation of learner demonstrations ● Written assignment ● Oral assessment ● projects
5	1		Proper usage of personal protective equipment	By the end of the lesson the learner should be able to: a) explain the meaning of infection prevention and control for health promotion b) illustrate correct use of personal protective equipment for infection prevention and control c) value infection prevention and control for healthy life	1. How do we prevent and control infection? 2. What is the difference between cleaning and disinfection?	The learner is guided to: ● demonstrate proper use of personal protective equipment (face masks, gloves, gumboots, gowns, goggles, face shield, head gear)	Realia, Pictures, charts, posters, digital resources, print materials, reference books, video clips, digital devices, resource person, cleaning equipment and disinfecting materials *Spotlight health education T.G pg. 78-79* *Spotlight health education P.B pg.* 115-116	● Graded observation of learner demonstrations ● Written assignment ● Oral assessment ● projects
	2		Difference between cleaning and disinfection of surfaces	By the end of the lesson the learner should be able to: a) differentiate cleaning and disinfection of equipment and surfaces for infection control b) apply infection prevention and control measures for promotion of health c) value infection prevention and control for healthy life	1. How do we prevent and control infection? 2. What is the difference between cleaning and disinfection?	The learner is guided to: ● practice different measures for infection prevention and control (use of protective gear, respiratory hygiene and cough etiquette, hand hygiene, cleaning and disinfection of equipment and surfaces, safe handling and disposal of wastes) ● watch a video clip or demonstration on the process of cleaning and disinfecting equipment and surfaces	Realia, Pictures, charts, posters, digital resources, print materials, reference books, video clips, digital devices, resource person, cleaning equipment and disinfecting materials *Spotlight health education T.G pg. 78-79* *Spotlight health education P.B pg.* 117-120	● Graded observation of learner demonstrations ● Written assignment ● Oral assessment ● projects
6	1	HUMAN REPRODUCTIVE HEALTH	Pubertal growth and development	By the end of the lesson the learner should be able to: a) identify changes occurring in boys and girls at puberty b) discuss personal hygiene needs during puberty c) appreciate puberty as a stage in personal growth and development	1. What changes occur in boys and girls at puberty? 2. Which are the personal hygiene needs associated with puberty?	The learner is guided to: ● discuss and classify changes occurring in boys and girls at puberty (physical, emotional and social changes)	video clips, digital devices, resource person, pictures, charts, digital and print reference materials *Spotlight health education T.G pg. 80-82* *Spotlight health education P.B pg.* 121-122	● Written tests ● Oral assessment ● Peer assessment
	2		Personal hygiene needs during puberty and management measures	By the end of the lesson the learner should be able to: a) Apply measures for management of menstrual hygiene for personal health. b) discuss personal hygiene needs during puberty c) appreciate puberty as a stage in personal growth and development	1. What changes occur in boys and girls at puberty? 2. Which are the personal hygiene needs associated with puberty?	● make online research for information on personal hygiene needs associated with onset of puberty and discuss in class ● discuss measures for managing menstrual hygiene for personal health	video clips, digital devices, resource person, pictures, charts, digital and print reference materials *Spotlight health education T.G pg. 82-83* *Spotlight health education P.B pg.* 123-124	● Written tests ● Oral assessment ● Peer assessment
7	1		Myths and misconceptions of menstrual experiences stages of identifying intersex persons	By the end of the lesson the learner should be able to: a) outline stages of identifying intersex persons for intervention b) identify myths and misconceptions on menstrual experience in the community c) appreciate puberty as a stage in personal growth and development	1. What changes occur in boys and girls at puberty? 2. Which are the personal hygiene needs associated with puberty?	The learner is guided to: ● explore on myths and misconception on menstrual experience within their community	video clips, digital devices, resource person, pictures, charts, digital and print reference *Spotlight health education T.G pg. 83-84* *Spotlight health education P.B pg.* 126-129	● Written tests ● Oral assessment ● Peer assessment
	2	Reproductive Health	Importance of reproductive health in the community	By the end of the lesson the learner should be able to: a) discuss importance of reproductive health in the community b) State the meaning of reproductive health c) Embrace positive reproductive health practices for a healthy community.	1. What is reproductive health? 2. How is reproductive health affected by cultural practices?	The learner is guided to: ● brainstorm on importance of reproductive health to the community ● watch a documentary on practices that are harmful to reproductive health	Video clips/ Documentaries, digital devices, reference books, post *Spotlight health education T.G pg. 84-86* *Spotlight health education P.B pg.* 130-131	● Graded observation of group discussions ● Written test ● Oral assessment
8	1		Practices that enhance reproductive health	By the end of the lesson the learner should be able to: a) list practices that enhance reproductive health b) explain practices that adversely affect reproductive health c) Embrace positive reproductive health practices for a healthy community.	1. What is reproductive health? 2. How is reproductive health affected by cultural practices?	The learner is guided to: ● research on practices that enhance reproductive health and share their findings ● research using digital and print materials on practices that affect reproductive health (early marriages and female genital mutilation among others)	Video clips/ Documentaries, digital devices, reference books, posters, charts *Spotlight health education T.G pg. 86-87* *Spotlight health education P.B pg.* 131-133	● Graded observation of group discussions ● Written test ● Oral assessment
	2		Myths and misconceptions of reproductive health	By the end of the lesson the learner should be able to: a) explain practices that adversely affect reproductive health b) identify myths and misconceptions about reproductive health in the community c) Embrace positive reproductive health practices for a healthy community.	1. What is reproductive health? 2. How is reproductive health affected by cultural practices?	The learner is guided to: ● discuss with a resource person on effects of harmful practices on reproductive health (sexually transmitted infections, excessive bleeding, fistula) ● brainstorm to distinguish facts from misconceptions associated with culture on reproductive health and share with peers	Video clips/ Documentaries, digital devices, reference books, posters, charts *Spotlight health education T.G pg. 87-88* *Spotlight health education P.B pg.* 134-138	● Graded observation of group discussions ● Written test ● Oral assessment
9	END TERM ASSESSMENT/CLOSING

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Grade 7 Free Exams and Marking Schemes

October 5, 2025 Hillary Kangwana

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GRADE-7-PRETECHNICAL-PP2-1 (2)

GRADE-7-SOCIAL-STUDIES (2)

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October 5, 2025 Hillary Kangwana Leave a comment

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Teachers' Resources

444/1 KCSE Woodwork Revision Exams plus Answers

October 5, 2025 Hillary Kangwana Leave a comment

NAME:………………………………………………….…………………………………………… ADMISSION NO:…………………….

CANDIDATE SIGNATURE:……………………. DATE :…………………..

444/1

WOODWORK

PAPER 1

TIME:2 HOURS 30 MINUTES

MECS JOINT EXAMINATION

Kenya Certificate of Secondary Education

WOODWORK

PAPER 1

Instructions to candidates

Write your name and admission number in the spaces provided above

Sign and write the date of the examination in the spaces provided

You should the following for the exam

Drawing instruments

A3 drawing paper

Answer all the questions in the space provided

SECTION A (40MARKS)

State four factors that determine the appearance of grains in timber. (2mks)

b) List four characteristic of trees that produce hardwoods. (4mks)

Name two tasks that can be performed using each of the following tools. (4mks)
Back saw.

Hand saw

b) Using a labelled sketch, give the meaning of the term ‘’saw Kerf’’. (3mks)

Name four measuring tools that may be used in a workshop. (2mks)

Sketch and label the pictorial view of ta mortice gauge. (4mks)

a) Make sketches to show the following methods of matching veneers. (6mks)
Side to side pattern.

Slip match pattern.

‘’v’’ match pattern.

State two safety precautions to be observed while using contact glue. (2mks)

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

Name four characteristics of polyvinyl glue. (4mks)

State three precautions to be observed to ensure there is no damage of a saw blade when in use. (3mks)

Outline four measures to be taken to ensure efficient planning when using a bench plane. (4mks)

Sketch an exploded pictorial view of an open corner bridle joint. (3mks)

SECTION B (60MKS)

11.Below is a sketch of polygon ABCDE. Given that AB =45 BC=30 CD=35 DE=35 EA=30, angle EAB=90° and angle ABC=130°. Draw the polygon and hence reduce it in the ratio 2:3 using A as the center of reduction. 15 MKS

12a) Other than food, state and explain two favourable conditions for fungal growth in timber. (4mks)

b) Using sketches (labelled) show the difference between an auger bit and twist drill bit. (6mks)

c) Name five sources of business capital. (5mks)

With the aid of sketches describe the ripping and cross cutting operations on a piece of timber. (8mks)

b) State two advantages and two disadvantages of quarter sawing method of timber. (4mks)

c) List three precautions to be observed to prevent splitting the work piece when marking a hole using a chisel. (3mks)

List six items that should be in a first Aid Kit and state each its use. (6mks)

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

b) State five characteristics of timber that has been attacked by dry rot. (5mks)

c) The time taken for timber to season in open air seasoning depends on various reasons state four of these reasons (4mks)

……………………………………………………………………………………………………………………………………..

Describe the oven dry method of determining the percentage moisture content of a piece of timber. (6mks)

b) Outline the procedure of making a groove in a work piece using a plough plane. (7mks)

c) State two precautions to be observed when using a steel tape measure. (2MKS)

Teachers' Resources

KICD HISTORY & GOVERNMENT SYLLABUS FREE PDF

October 5, 2025 Hillary Kangwana Leave a comment

KENYA SECONDARY SCHOOL HISTORY AND government

Knec Kcse History Syllabus

HISTORY & GOVERNMENT Examination Syllabus * FORM 1

INTRODUCTION TO HISTORY AND GOVERNMENT

The meaning of History

The meaning of Government

Sources of information on History and Government

Importance of studying History and Government.

EARLY MAN

Ori of man

Evolution of man

Cultural and economic practices of Early Man

DEVELOPMENT OF AGRICULTURE

Development of early agriculture

Early agriculture in:

Egypt

Mesopotamia

The Agrarian Revolution in

Britain 2. U.S.A 4. The food situation in Africa and the rest of the Third World

Remedies of food shortages

THE PEOPLE OF KENYA UP TO THE 19th CENTURY

Ori migration and settlement of the people of Kenya 1. Bantu 2. Nilotes 3. Cushites 4. Results of the migration and settlement of the people of Kenya

SOCIAL,ECONOMIC AND POLITICAL ORGANIZATION OF KENYAN SOCIETIES IN THE 19th CENTURY

Bantu 1. Agikuyu 2. Ameru 3. Akamba 4. Abagusii 5. Mijikenda

Nilotes

Luo

Nandi

Maasai

Cushites

Borana

Somali

CONTACTS BETWEEN EAST AFRICA AND THE OUTSIDE WORLD UP TO THE 19th CENTURY

Early visitors to the East African Coast up to 1500

Trade between the East African Coast and the outside World

Development of the trade

Organization of the trade

Impact of the trade on the people of East Africa

The coming of the Portuguese

Reasons for their coming to East Africa

Their conquest and rule

The decline of Portuguese power

Establishment and Impact of Omani Rule: 1. Seyyidd Said and the development of plantation Agriculture

Development,Organization and Consequence of

The spread of Christianity:

Reasons for the coming of Christian missionaries

Missionary activities and challenges

Effects of missionary activities

CITIZENSHIP

Kenya citizenship

Rights of a citizen

Responsibilities of a citizen

Elements of good citizenship

NATIONAL INTEGRATION

National Integration 1. Meaning 2. Importance

National Unity

Factors promoting national unity

Factors limiting national unity

Conflict Resolution

Meaning of the term ‘conflict’

Methods of resolving conflicts

Process of resolving conflicts

* FORM 2 1. TRADE

Definition of trade

Methods of trade

Barter

Currency

Types of trade

Local trade 2. Regional trade (Trans-Saharan Trade) 3. International Trade (Trans-Atlantic Trade) 2. DEVELOPMENT OF TRANSPORT AND COMMUNICATION

Definition of transport and communication

Traditional forms of Transport

Land

Water

Development in modern means of transport

Road transport

Rail transport

Water transport

Air transport

Space exploration

Impact of modern means of transport

Traditional forms of communication

Smoke signals

Drum beats

Messengers

Horn blowing

Written messages on scrolls and stone tablets

Developments in modern means of communication

Telecommunication

Print media

DEVELOPMENT OF INDUSTRY

Early source of energy 1. wood 2. Wind 3. Water

Uses of metals in Africa

Bronze

Gold

Copper

Iron

The Industrial Revolution in Europe

Uses of various sources of energy

Uses of Iron and steel

Industrial inBritain

Industrialization in Continental Europe

Effects of the Industrial Revolution in Europe

The Scientific Revolution

Scientific inventions

Impact of science inventions on

Emergences of selection World industrial powers

USA

Germany

Japan

Industrialization in the Third World

South Africa

Brazil

India

URBANIZATION

Meaning of urbanization

Early Urbanization in: 1. Africa

Europe

Emergence of modern urban center in Africa

Nairobi

Johannesburg

Impact pf agrarian and industrial development on Urbanization

SOCIAL ,ECONOMIC AND POLITICAL ORGANIZATION OF AFRICA SOCIETIES IN THE 19th CENTURY

The Social Economic and Political organization of Africa society with reference to

The Baganda

The Ashanti /Asante

The Shona

CONSTITUTION AND CONSTITUTION MARKING

Types of constitutions 1. Written 2. Unwritten

The independence Constitution

The Kenya constitution

Constitution making process

Constitutional amendments since independence

Feature of the Kenyan constitution

DEMOCRACY AND HUMAN RIGHTS

Democracy 1. Definition of democracy 2. Types of democracy 3. Principel of democracy

Human Rights

Defination of Human Rights

The Bills of Human

U.N Charter on Human Rights

The rights of the child

classification of Human Rights

* FORM 3

EUROPEAN INVASION OF AFRICA AND THE PROCESS OF COLONIZATION

The Scramble for and Partition of Africa 1. Definition of the terms ”scramble” and ”partition” 2. Methods used by Europeans to acquire colonies in Africa 3. Factors that led to the scramble for colonies in Africa 4. The process of partition 5. Impact of partition

African Reactions to European Colonization

Resistance

Collaboration

Mixed Reactions

ESTABLISHMENT OF COLONIAL RULE IN KENYA

Background to the Scramble and Partition of East Africa

British occupation of Kenya

The response of the peoples of Kenya to the British

invasion and occupation

Resistance

Collaboration

COLONIAL ADMINISTRATION

Indirect Rule: 1. The British in Kenya 2. The British in Nigeria

Direct Rule: 1. The British in Zimbambwe (Southern Rhodesia) 3. Assimilation: 1. The French in Senegal

SOCIAL AND ECONOMIC DEVELOPMENTS DURING THE COLONIAL PERIOD IN KENYA

The Uganda Railway

Settler farming in kenya

Colonial land policies

The Devonshire White Paper

Urbanization

and

POLITICAL DEVELOPMENTS AND THE STRUGGLE FOR INDEPENDENCE IN

KENYA (1919-1963) 1. Early Political Organization in Kenya up to 1939 1. East Africa Association 2. Kikuyu Central Association 3. Kavirondo Tax Payer and Welfare Association 4. Ukamba Members Association 5. Coast African Association 6. Taita Hills Association

Emergence of Independent Churches and 3. Political organization and movements after 1945

Kenya Africa Study Union (K.A.S.U.)

Kenya African Union (K.A.U)

Mau Mau

Kenya Africa National Union (K.A.N.U)

Kenya Africa Democratic Union (K.A.D.U)

African People Party (A.P.P)

Trade Union Movement

Africa Workers Federation

Kenya Federation of Labour

Role of women in the struggle for independence 6. Constitutional changes leading to independence

African representation in the Legco

Lyttleton Constitution

Lennox-Boyd Constitution

Lancaster House Conferences

RISE OF AFRICAN NATIONALISM 1. Rise and growth of African Nationalism in: 1. Ghana 2. Mozambique 3. South Africa

LIVES AND CONTRIBUTION OF KENYAN LEADERS

Jomo Kenyatta

Daniel arap Moi

Oga Odinga

Tom Mboya

Ronald Ngala

THE FORMATION AND FUNCTION OF THE GOVERNMENT OF KENYA

Electoral Process

Function of the Electoral Commission of Kenya

Formation of Government

Structure and Function of the Government of Kenya

Legislature

Executive

The Judiciary

The role of Law

The Concept Natural Justice

* FORM 4

WORLD WARS

The First World War(1914-1918) 1. Causes 2. Course 3. Results

The League of Nations

Formation

Organization

Performance

The second World War (1939-1945)

Causes

Course

Results

INTERNATIONAL RELATIONS

The United Nations 1. Formation 2. Organization 3. Performance and challenges

The Commonwealth

Formation

Membership

Functions

Challenges

The Non-Aligned Movement

Formation

Perfomance and challenges

The Cold War (Vietnam, Cuba, Europe, Angola)

Causes

Course

Effects

CO-OPERATION IN AFRICA

Pan-Africanism 1. Oris 2. Development 3. Perfomance

Organisation of African Unity (OAU)

Formation

Charter

Perfomance and challenges

African Union

Formation

Charter

East African community

Formation

Organization

Challenges up to 1977

Rebirth of the East African Community -2001

Economic Community of West African State (ECOWAS)

Formation

Organization

Perfomance and challenges

The Common Market for Eastern and Southern Africa (COMESA)

Formation

Functions

Perfomance and challenges

NATIONAL PHILOSOPHIES (KENYA)

Africa Socialism

Harambee

Nyayoism

Impact of National Philosophies

SOCIAL, ECONOMIC AND POLITICAL DEVELOPMENTS AND CHALLENGES IN KENYA SINCE INDEPENDENCE

Political developments 1. Developments from 1963-1991 2. Multi-party democracy in kenya 3. challenges of multi-party democracy 4. The role of political parties in Government and nation building

Economic development and challenges

Land policies

Industry

Social developments and challenges

and sports

SOCIAL, ECONOMIC AND POLITICAL DEVELOPMENT AND CHALLENGES IN AFRICA SINCE INDEPENDENCE

Social, Economic and Political developments in selected African countries

Democratic Republic of Congo -DRC

Tanzania

Social, Economic and Political challenges in Africa since independence

LOCAL AUTHORITIES IN KENYA

Types of local authorities

Function of local authorities

Relationship between local authorities and the central

government 4. Challenges facing local authorities

GOVERNMENT REVENUE AND EXPENDITURE IN KENYA

National budget

Sources of government revenue

Control of public finance

THE ELECTORAL PROCESS AND FUNCTION OF GOVERNMENTS IN OTHER PARTS OF THE WORLD

USA

Britain

India

101 Knec English Syllabus 102 Knec Kiswahili Syllabus 121 Knec Syllabus 231 Knec Biology Syllabus 232 Knec Physics Syllabus 233 Knec Chemistry Syllabus 311 Knec History & Govt.Syllabus 312 Knec Geography Syllabus 313 Knec C.R.E. Syllabus 314 Knec I.R.E. Syllabus 441 Knec Syllabus 441 Knec Woodwork Syllabus 442 Knec Art and Design Syllabus 443 Knec Agriculture Syllabus 448 Knec Electricity Syllabus 451 Knec Computer Studies Syllabus 501 Knec French Syllabus 502 Knec German Syllabus 511 Knec Music Syllabus 565 Knec Studies Syllabus

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* Introduction

* General Objectives

* Form One History and Government

* Form Two History and Government

* Form Three History and Government

* Form Four History and Government

* Suggested Learning/Teaching resources

* Suggested Assessment Methods.

INTRODUCTION HISTORY AND GOVERNMENT

History and Government is an important discipline because it plays a key role in the development of society. Knowledge of the past is critical to the understanding of the present and to planning for the future. It is through the study of the subject that the youth of a nation acquire knowledge about the past and the present so as to develop positive attitudes about the future. Thus, learners are able to recognize the relationship between the events of today and the world of tomorrow.

This syllabus addresses key themes in history such as the social, economic and political organizations of African societies during the colonial period, European colonization, the rise of African nationalism, developments in trade, transport and communication, industry, agriculture and urbanization. It also covers the issues of morality, responsible citizenship, good governance, national integration, conflict resolution and international cooperation.

A number of themes which address individual honesty, health and integrity have been selected to enable the learners cope with the challenges of the day, e.g. HIV/AIDS, drug abuse and corruption. It is hoped that the knowledge gained will enable the learner to develop into a socially and economically useful member of the society.

The various approaches to searching for, and investigating historical knowledge have been highlighted in the syllabus. Emphasis has been put towards developing in learners independent group and individual study habits, production, manipulation and use of a variety of learning resources.

With consistent and resourceful use of study approaches such as visitations, report writing, research and use of resource persons, the syllabus promises vibrant class discourse.

GENERAL OBJECTIVES- KCSE HISTORY AND GOVERNMENT

By the end of the course the learner should be able to:

recognize and appreciate the importance of studying History and Government
acquire knowledge, ability and show appreciation for critical historical analysis of socio-economic and political organization of African societies
understand and show appreciation of the rights, privileges and obligations of oneself and others for promotion of a just and peaceful society
promote a sense of nationalism, patriotism and national unity
encourage and sustain moral and mutual social responsibility
identify, assess and appreciate the rich and varied cultures of the Kenyan people and other peoples
promote a sense of awareness and need for a functional democracy of the Kenyan people and other nations
promote an understanding and appreciation of intra—national and international consciousness and relationships
derive through the study of History and Government an interest in further learning.

FORM I – KCSE HISTORY AND GOVERNMENT INDEX

1.0.0 Introduction to History and Government

2.0.0 Early Man

3.0.0 Development of Agriculture

4.0.0 The People of Kenya Up to the 19th Century

5.0.0 Social, Economic and Political Organization of Kenyan Societies in the 19 Century

6.0.0 Contacts between East Africa and the Outside World up to the 19th Century

7.0.0 Citizenship

8.0.0 National Integration

1.00 INTRODUCTION TO HISTORY AND GOVERNMENT

1.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) explain the meaning of the term History
b) explain the meaning of the term Government
c) identify the sources of information on History and Government
d) explain the importance of studying History and Government

1.2.1 The meaning of History

1.2.2 The meaning of Government

1.2.3 Sources of information on History and Government

1.2.4 Importance of studying History and Government

2.0.0 EARLY MAN

2.1.0 Specific Objective

By the end of the topic the learner should be able to:

a) explain the origin of man
b) identify the stages through which man evolved during the Stone Age Period
e) describe the cultural and economic practices of Early Man

2.2.1 Origin of man

2.2.2 Evolution of man

2.2.3 Cultural and economic practices of Early Man.

3.00 DEVELOPMENT OF AGRICULTURE

3.10 Specific Objective

By the end of the topic the learner should be able to:

a) identify the factors that led to the development of early agriculture
b) explain the development of agriculture in Egypt and Mesopotamia
c) describe the Agrarian Revolution in Britain and the USA
d) identify the causes of food in Africa and the rest of the Third World
e) discuss the effects and remedies of food shortages in Africa and the rest of the Third World

3.2.1 Development of early agriculture

3.2.2 Early agriculture in:

a) Egypt
b) Mesopotamia

3.2.3 The Agrarian Revolution in:

a) Britain
b) S.A

3.2.4 The food situation in Africa and the rest of the Third World

3.2.5 Remedies of food shortages

4.00 THE PE0PLE OF KENYA UP TO THE 19TH CENTURY

4.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) state the origins of the Bantu, Nilotes and Cushites
b) trace and describe the migration and settlement of the Bantu, Nilotes and Cushites
c) discuss the results of the migration and settlement of the people of Kenya

4.2.1 Origin, migration and settlement of the people of Kenya

a) Bantu
Western Bantu
Eastern Bantu
b) Nilotes
River-Lake Nilotes
Plains Nilotes

iii. Highland Nilotes

c) Cushites
Eastern Cushites
Southern Cushites

4.2.2 Results of the migration and settlement of the people of Kenya.

5.00 SOCIAL, ECONOMIC AND POLITICAL ORGANIZATION OF KENYAN SOCIETIES IN THE 19 CENTURY

5.1.0 Specific objectives

By the end of the topic, the learner should be able to discuss the Social, Economic and Political organization of the Bantu, the Nilotes and the Cushites.

5.2.1 Bantu

a) Agikuyu
b) Ameru
c) Akamba
d) Abagusii
e) Mijikenda

5.2.2 Nilotes

a) Luo
b) Nandi
c) Maasai

5.2.3 Cushites

a) Borana

b)Somali

6.00 CONTACTS BETWEEN EAST AFRICA AND THE OUTSIDE WORLD UP TO THE 19TH CENTURY

6.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) identify the origin of the early visitors to the East African Coast
b) explain the development of trade between the East African Coast and the outside World
c) discuss the effects of the contact between the East African Coast and the outside world
d) identify reasons for the coming of the Portuguese
e) trace the Portuguese conquest of the East African Coast
f) discuss the decline and effects of the Portuguese rule
g) discuss the establishment and impact of Omani rule
h) explain the reasons for the coming of the Christian missionaries
i) describe missionary activities and challenges
j) discuss the effects of missionary activities

6.2.1 Early visitors to the East African Coast up to 1500.

6.2.2 Trade between the East African Coast and the outside World.

a) Development of the trade
b) Organization of the trade
c) Impact of the trade on the peoples of East Africa

6.2.3 The corning of the Portuguese

a) Reasons for their coming to East Africa
b) Their conquest and rule
c) The decline of Portuguese power
d) Impact of Portuguese rule

6.2.4 Establishment and impact of Omani rule:

a) Seyyid Said and the development of plantation agriculture
b) Development, organisation and consequences of:
i) Long distance trade
ii) International trade

6.2.5 The spread of Christianity:

a) Reasons for the coming of Christian missionaries
b) Missionary activities and challenges
c) Effects of missionary activities

7.0.0 CITIZENSHIP

7.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) state ways of becoming a Kenyan citizen
b) state the rights and responsibilities of a Kenyan citizen
c) discuss the elements of good citizenship

7.2.1 Kenyan citizenship

7.2.2 Rights of a citizen

7.2.3 Responsibilities of a citizen

7.2.4 Elements of good citizenship

8.00 NATIONAL INTEGRATION

8.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) explain the meaning and importance of national integration
b) describe factors promoting and limiting national unity
c) identify methods of resolving conflicts
d) describe the process of resolving conflicts.

8.2.I National Integration

Meaning

Importance

8.2.2 National Unity

Factors promoting national unity

Factors limiting national unity

8.2.3 Conflict Resolution

Meaning of the term conflict

Methods of resolving conflicts

Process of resolving conflicts.

FORM II – HISTORY AND GOVERNMENT INDEX

9.0.0 Trade

10.0.0 Development of Transport and Communication

11.0.0 Development of Industry

12.0.0 Urbanisation

13.0.0 Social, Economic and Political Organization of African Societies In the 19th Century

14.0.0 Constitutions and Constitution Making

15.0.0 Democracy and Human Rights

9.00 TRADE

9.1.0 Specific Objectives

By the end of the topic the learner should be able to:

a) define the term trade
b) explain methods of trade
c) identify types of trade
d) discuss the origin, development, organization and impact of different types of trade.

9.2.1 Definition of Trade

9.2.2 Methods of Trade

* Barter

* Currency

9.2.3 Types of Trade

a) Local trade

* Origin

* Development

* Organization

* Impact

b) Regional trade (Trans-Saharan Trade)

* Origin

* Development

* Organization

* Impact

c) International Trade (Trans-Atlantic Trade)

* Origin

* Development

* Organization

* Impact

10.00 DEVELOPMENT OF TRANSPORT AND COMMUNICATION

10.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) define the terms transport and communication
b) explain the traditional and modern means of transport
c) describe the traditional and modern means of communication
d) analyse the impact of modern means of transport and communication

10.2.1 Definitions of transport arid communication.

I 0.2.2 Traditional forms of transport

a) Land
b) Water

I 0.2.3 Developments in modern means of transport.

a) Road transport
b) Rail transport
c) Water transport
d) Air transport
e) Space exploration

10.2.4 Impact of modern means of transport.

10.2.5 Traditional forms of communication

a) Smoke signals
b) Drum beats
e) Messengers
d) Horn blowing
c) Written messages on scrolls and stone tablets

10.2.6 Development in modern means communication

a) Telecommunication

* Telephone and cell phone

* Television

* Radio

* Telegraph

* Electronic mail (E-mail)

* Facsimile transreceiver (fax)

* Telex

* Pager

* Internet

b) Print media

* Newspapers

* Magazines

* Journals

* Periodicals

11.00 DEVELOPMENT OF INDUSTRY

11.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

* identify early sources of energy

* explain the uses of metals in Africa

* trace and describe the development of the Industrial Revolution in Europe

* discuss the Scientific Revolution and its effects on agriculture, industry and medicine

* describe the emergence of selected world industrial powers

* explain the development of industry in the Third World.

11.2.1 Early sources of energy

a) Wood
b) Wind
c) Water

11.2.2 Uses of metals in Africa

a) Bronze
b) Gold
c) Copper
d) Iron

11.2.3 The Industrial Revolution in Europe

a) Uses of various sources of energy

* Coal

* Oil

* Steam

* Electricity

b) Uses of iron and steel
c) Industrialization in Britain
d) Industrialization in Continental Europe
e) Effects of the Industrial Revolution in Europe

11.2.4 The Scientific Revolution

a) Scientific inventions
b) Impact of scientific inventions on:

* Agriculture

* Industry

* Medicine

11.2.5 Emergence of selected World industrial powers

a) USA
b) Germany
c) Japan

11.2.6 Industrialization in the Third World.

a) South Africa
b) Brazil
c) India

12.00 URBANISATION

12.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

* define the term urbanization

* describe Early Urbanization in Africa and Europe

* describe the emergence of modern urban centres in Africa

* discuss the impact of agrarian and industrial developments on urbanization.

By the end of the topic, the learner should be able to:

* define the term urbanization

* describe Early Urbanization in Africa and Europe

* describe the emergence of modern urban centres in Africa

* discuss the impact of agrarian and industrial developments on urbanization.

12.2.1 Meaning of urbanization

12.2.2 Early Urbanization in:

a) Africa

* Cairo

* Merowe/Meroe

* Kilwa

b) Europe

* London

* Athens

12.2.3 Emergence of modern urban centres in Africa

a) Nairobi
b) Johannesburg

12.2.4 Impact of agrarian and industrial developments on Urbanization.

13.0.0 SOCIAL, ECONOMIC AND POLITICAL ORGANIZATION OF AFRICAN SOCIETIES IN THE 19TH CENTURY

13.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

* describe the social and economic organization of African societies in the 19th century

* discuss the political organization of African societies in the 19th century.

13.2.1 The Social, Economic and Political organization of African societies with reference to the Baganda

13.2.2 The Social, Economic and Political organization of African societies with reference to the Shona

13.2.3 The Social, Economic and Political organization of African societies with reference to the Ashanti/Asante

14.0.0 CONSTITUTIONS AND CONSTITUTION MAKING

14.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

* identify the difference between written and unwritten constitutions

* discuss aspects of the Independence Constitution of Kenya

* trace and describe the constitutional changes in Kenya since independence

* explain the constitution making process in Kenya.

14.2.1 Types of constitutions

a) Written
b) Unwritten

14.2.2 The Independence Constitution

14.2.3 The Kenya constitution

a) Constitution making process
b) Constitutional amendments since independence
c) Features of the Kenyan constitution

15.00 DEMOCRACY AND HUMAN RIGHTS

15.1.0 Specific Objectives

By the end of the topic, the learner should he able to:

a) define the terms Democracy and Human Rights
b) identify types of democracy
c) discuss the principles of democracy
d) classify and discuss Human Rights
e) identify the rights of a child

15.2.1 Democracy

a) Definition of democracy
b) Types of democracy
c) Principles of democracy

15.2.2 Human Rights

a) Definition of Human Rights
b) The Bill of Rights
c) U.N. Charter on Human Rights
d) The rights of the child
e) Classification of Human Rights.

FORM III – HISTORY AND GOVERNMENT INDEX

16.0.0 European Invasion of Africa and the Process of Colonization

17.0.0 Establishment of Colonial Rule in Kenya

18.0.0 Colonial Administration

19.0.0 Social and Economic Developments during the Colonial Period in Kenya

20.0.0 Political Developments and Smuggle For Independence in Kenya (1919-1963)

21.0.0 Rise of African Nationalism

22.0.0 Lives and Contributions of Kenyan Leaders

23.0.0 The Formation, Structure and Functions of the Government of Kenya

16.00 EUROPEAN INVASION OF AFRICA AND THE PROCESS OF COLONIZATION

16.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) define the terms scramble and partition
b) identify the methods used by Europeans to acquire colonies in Africa
c) discuss the factors that led to the scramble for colonies in Africa in the 19th Century
d) describe the process of partition
e) analyse the impact of the partition
f) discuss the African reaction to European colonization.

16.2.1 The Scramble for and Partition of Africa

a) Definitions of the terms scramble and partition
b) Methods used by Europeans to acquire colonies in Africa
c) Factors that led to the scramble for colonies in Africa
d) The Process of partition
e) Impact of partition

16.2.2 African Reactions to European Colonization

a) Resistance
Maji Maji
Mandinka – Samori Toure

iii. Ndebele – Lobengula

b) Collaboration
Baganda
Lozi – Lewanika

17.00 ESTABLISHMENT OF COLONIAL RULE IN KENYA

17.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) explain factors for European invasion of Kenya
b) describe the process of British occupation of Kenya
e) explain African response to British invasion
d) analyse the process of colonial administration in Kenya.

17.2.1 Background to the Scramble and Partition of East Africa

17.2.2 British occupation of Kenya

17.2.3 The response of the peoples of Kenya to the British invasion and occupation

a) Resistance

* Nandi

* Agiryama

* Bukusu

* Somali

b) Collaboration

* Maasai

* The Wanga

c) Mixed Reactions

* Akamba

* Agikuyu

* Luo

18.00 COLONIAL ADMINISTRATION

18.1.0 Specific Objective

By the end of the topic, the learner should be able to identify and analyse the colonial systems of administration with special reference to:

a) Indirect rule
b) Direct rule
c) Assimilation.

18.2.1 Indirect Rule:

a) The British in Kenya
b) The British in Nigeria

18.2.2 Direct Rule:

The British in Zimbabwe (Southern Rhodesia)

18.2.3 Assimilation:

The French in Senegal

19.00 SOCIAL. AND ECONOMIC DEVELOPMENTS DURING THE COLONIAL PERIOD IN KENYA

19.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) explain the social changes that took place in Kenya during the colonial period
b) identify and explain the main economic developments in Kenya during the colonial

19.2.1 The Uganda Railway

19.2.2 Settler farming in Kenya

19.2.3 Colonial land policies

19.2.4 The Devonshire White Paper

19.2.5 Urbanization

19.2.6 Education and Health

20.0.0 POLITICAL DEVELOPMENTS AND SMUGGLE FOR INDEPENDENCE IN KENYA (1919-1963)

20.1.0 Specific Objectives

By the end of the topic, the learner should be able in:

a) Identify and explain the origins, organization and effects of political movements up to 1939
b) Trace the origins of the independent churches and schools
c) Discuss political organizations and movements up to 1945
d) describe the role of trade unionism in the struggle of independence
e) discuss the role of women in the struggle for independence
f) describe the constitutional changes leading to independence.

20.2.1 Early Political Organizations in Kenya up to 1939

a) East Africa Association
b) Kikuyu Central Association
c) Kavirondo Tax Payers and Welfare Association
d) Ukamba Members Association
e) Coast African Association
f) Taita Hills Association

20.2.2 Emergence of Independent Churches and Schools

20.2.3 Political organizations and movements after 1945

a) Kenya African Study Union (K.A.S.U)
b) Kenya African Union (K.A.U)
e) Mau Mau
d) Kenya African National Union (K.A.N.U)
e) Kenya African Democratic Union (K.A.D.U)
f) African Peoples Party (APP)

20.2.4 Trade Union Movement

a) African Workers Federation
b) Kenya Federation of Labour

20.2.5 Role of women in lie struggle for independence

20.2.6 Constitutional changes leading to independence

a) African representation in the Legco
b) Lyttleton Constitution
c) Lennox – Boyd Constitution
d) Lancaster House Conferences

21.0.0 RISE OF AFRICAN NATIONALISM

21.10 Specific Objective

By the end of the topic, the learner should be able to discuss the rise and growth of African Nationalism in selected African countries.

21.2.1 Rise and growth of African Nationalism in:

a) Ghana
b) Mozambique
c) South Africa

22.0.0 LIVES AND CONTRIBUTIONS OF KENYAN LEADERS

22.1.0 Specific Objective

By the end of the topic, the learner should be able to analyse the lives and contributions of selected Kenyan leaders.

22.2.1 Kenyan leaders.

22.2.3 Jomo Kenyatta

22.2.4 Daniel arap Moi

22.2.5 Oginga Odinga

22.2.6 Tom Mboya

23.0.0 THE FORMATION, STRUCTURE AND FUNCTIONS OF THE GOVERNMENT OF KENYA

23.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) describe the electoral process in Kenya
b) state the functions of the Electoral Commission of Kenya
c) explain the process of the formation of government
d) describe the structure and functions of the three arms of the Government of Kenya
e) state the functions of the Armed forces, police and prisons departments in Kenya
f) Analyse the challenges facing the police and prisons departments in Kenya
g) Analyse the concepts of the Rule of Law and Natural Justice

23.2.1 Electoral Process

23.2.2 Functions of the Electoral Commission of Kenya

23.2.3 Formation of Government

23.2.4 Structure and Functions of the Government of Kenya

a) Legislature

* Composition

* Functions

* Process of law making

* Parliamentary Supremacy

b) The Executive

* Powers and function the President

* Composition and functions of the Cabinet

* Composition and functions of the Civil Service

* Provincial administration

* Functions of the:

* armed forces

* police

* prisons department

Challenges facing the police and prisons departments in Keny
c) The Judiciary

* Chief Justice

* Attorney General

* Structure and functions of the Court System in Kenya

* Importance of the Independence of the Judiciary

c) The Judiciary
d) The Rule of Law
e) The Concept of Natural Justice

FORM IV – HISTORY AND GOVERNMENT INDEX

24.0.0 World Wars

25.0.0 International Relations

26.0.0 Co-Operation in Africa

27.0.0 National Philosophies (Kenya)

28.0.0 Social, Economic and Political Developments and Challenges in Kenya Since Independence

29.0.0 Social, Economic and Political Developments and Challenges in Africa Since Independence

30.0.0 Local Authorities in Kenya

31.1.1 Government Revenue and expenditure in Kenya

32.0.0 The Electoral Process and Functions of Governments in Other Parts of The World.

24.0.0 WORLD WARS

24.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) explain the causes of the First and the Second World Wars
b) describe the course of the First and the Second World Wars
c) discuss the results of the First and the Second World Wars
d) explain the reasons for the formation of the League of Nations
e) describe the organisation of the League of Nations
f) analyse the performance of the League of Nations.

24.2.1 The First World War (1914 -1918)

a) Causes
b) Course
c) Results

24.2.2 The League of Nations

a) Formation
b) Organization
c) Performance

24.2.3 The Second World War (1939- 1945)

a) Causes
b) Course
c) Results

25.0.0 INTERNATIONAL RELATIONS

25.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) analyse the reasons for the formation of major international organizations
b) describe the structure of major international organizations
c) discuss the functions of major international organizations
d) analyse the performance of major international organizations
e) explain the causes of the Cold War
f) describe the course of the Cold War
g) discuss the effects of the Cold War

25.2.1 International organisations: The United Nations

a) Formation
b) Organization
c) Performance and challenges

25.2.2 International organisations: The Commonwealth

a) Formation
b) Membership
c) Functions
d) Challenges

25.2.3 International organisations: The Non-Aligned Movement

a) Formation
b) Performance and challenges

25.2.4 The Cold War (Vietnam, Cuba, Europe, Angola)

a) Causes
b) Course
c) Effects

26.0.0 CO-OPERATION IN AFRICA

26.1.0 Specific Objectives

By the end of the topic, the learner should be able to:

a) explain the origin and development of selected regional organizations in Africa
b) discuss the performance and challenges of the respective organizations.

26.2.1 Pan-Africanism

a) Origins
b) Development
c) Performance

26.2.2 Organization of African Unity (OAU)

a) Formation
b) Charter
c) performance and challenges

26.2.3 African Union

a) Formation
b) Charter

26.2.4 East African community

a) Formation
b) Organization
c) Challenges up to 1977
d) Rebirth of the East African Community -2001
Formation
Organization

iii. Challenges

26.2.5 Economic Community of West African States (ECOWAS)

a) Formation
b) Organization
c) Performance and challenges

26.2.6 The Common Market for Eastern and Southern Africa (COMESA)

a) Formation
b) Functions
c) Performance and challenges

27.0.0 NATIONAL PHILOSOPHIES (KENYA)

27.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) explain the origin and development of National Philosophies
b) analyse the impact of National Philosophies.

27.2.1 African Socialism.

27.2.2 Harambee

27.2.3 Nyayoism

27.2.4 Impact of National Philosophies

28.0.0 SOCIAL, ECONOMIC AND POLITICAL DEVELOPMENTS AND CHALLENGES IN KENYA SINCE INDEPENDENCE(I)

28.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) discuss the political developments in Kenya since independence
b) discuss the social and economic developments in Kenya since independence
c) analyse the political, social and economic challenges in Kenya since Independence.

28.2.1 Political developments

a) Developments from 1963-1991
b) Multi-party democracy in Kenya
c) Challenges of multi-party democracy
d) The role of political parties in Government and nation building

28.2.2 Economic developments and challenges

a) Land policies
b) Industry

28.2.3 Social developments and challenges

a) Education
b) Health
c) Culture and sports

29.0.0 SOCIAL, ECONOMIC AND POLITICAL DEVELOPMENTS AND CHALLENGES IN AFRICA SINCE INDEPENDENCE

29.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) discuss the political, social and economic developments in selected African countries since independence
b) analyse the political, social and economic challenges in Africa since independence.

29.2.1 Social, Economic and Political developments in selected African countries

a) Democratic Republic of Congo – DRC
b) Tanzania

29.2.2 Social, Economic and Political challenges in Africa since independence

30.0.0 LOCAL AUTHORITIES IN KENYA

30.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) describe types of local authorities in Kenya
b) discuss the functions of local authorities
c) analyse the relationship between local authorities and the Central Government
d) discuss the challenges facing local authorities in Kenya.

30.2.1 Types of local authorities

30.2.2 Functions of local authorities

30.2.3 Relationship between local authorities and the central government

30.2.4 Challenges facing local authorities

31.0.0 GOVERNMENT REVENUE AND EXPENDITURE IN KENYA

31.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) identify and discuss sources of government revenue
b) explain the expenditure of government revenue
c) discuss how the government controls public finance.

31.2.1 National budget

31.2.2 Sources of government revenue

31.2.3 Control of public finance

32.0.0 THE ELECTORAL PROCESS AND FUNCTIONS OF GOVERNMENTS IN OTHER PARTS OF THE WORLD

32.1.0 Specific objectives

By the end of the topic, the learner should be able to:

a) explain the electoral process of governments in selected countries
b) discuss the functions of governments of the respective countries.

32.2.1 USA

32.2.2 Britain

32.2.3 India

	PRESENTATION MGN
1.	PRESENTATION – Work well pressed ( ½ ) and folded( ½ ) – Label firmly (1) fixed on a single (1) layer of fabric. – Pins and unnecessary tackings removed. (1) – Made up LEFT HALF (1)
2	CUTTING OUT MGN – CB/CF smoothly cut. (1) – Fabric cut on straight grain. (2) – BF (½) BB ((½)) Bindering (½) Facing (½) – Lower edge of blouse well cut. (1)
3	WORKING ON DOUBLE POINTED DART MGN – Correctly positioned dart (1) – Straight stitching (1) – Tapering to nothing on both ends (1) – Correct length of dart ( ½ ) (with 2 mm) – Firmly secured points ( ½ ) – Darts pressed towards C.F. (1) – Middle of double dart snipped (1) to lie flat on both sides. (1)
4	SHOULDER SEAM (FRENCH SEAM) (AWARD ZERO IF NOT FRENCH SEAM) MGN – Good straight stitching. (1) – Correct width of seam (1) (0.5 – 06 cm) – Evenness in width (1) – Self neatened raw edges all enclosed.. (1) – Good knife edge produced.. (1) – Seam pressed flat. (1)
5	SIDE SEAM (NEATENED OPEN SEAM) MGN (AWARD ZERO IF OT OPEN SEAM) – Good straight stitchery.(1) – Evenness of both sides. (1) – Flatness at the armhole joint. (1) – Correct size of seam (1) (0.8 – 1.2 cm each side) correctly neatened with edge stitching. (1) – Presses open. (1)
6	NECKLINE FACING MGN – Facing correctly joined (1) to back facing using plain seam. (1) – Free edge of facing correctly. (1) – And neatly neatened (1)
	ATTACHMENT TO FACING (Front Facing and Back Facing) MGN – Correct (½) placing of facing to neckline. – Good stitchery (1) (Back Front flatness of facing. (½) – Smoothness of neckline. (½) – Facing firmly fixed. (1) – Facing under stitched (½) from Top of neckline correctly produced.
7	CUTTING AND REPAIR OF HEDGE TEAR USING DARNING MGN – Correctly (1) cut triangular hedge tear repair using hand darning. (½) – Marked the vent of the tear. (½) – Used fish boned (1) – stitches to bring edges together. – Darn extending beyond vent. (½) – Threads firmly secured. (½) – Raw edges completely enclosed. (1)
8	BINDING ARMHOLE – Joining the binding piece. (1) – Correctly joined to armhole. (1) – Evenness of binding on both sides.(1) – Correct final stitching. (1)

JESMA CLASS 8 EXAMS PLUS ANSWERS- LATEST

Set 1

Set 2

Set 3

Set 4

Set 5

Set 6

Set 7

Set 8

Set 9

Set 10

FREE FORM FOUR MATHEMATICS NOTES

Specific Objectives

You see my friend; Monkeys have a tradition of leaving their hearts at home when they are going for a long journey. I therefore left mine on my favorite tree.” Crocodile was even more confused.

“We can go and visit your wife first, and then I will give you my heart when you take me back,” Monkey suggested.

“No,” cried crocodile “I will take you back first. When 1 have your heart, we can then visit my wife.”

From that day Monkey and Crocodile have remained enemies. And that is the end of my story and may I not end like it.

FUNCTIONS OF ORAL LITERATURE

CLASSIFICATION OF ORAL LITERATURE

MODE OF STORY – TELLING

THE ROLE OF THE AUDIENCE

CLASSIFICATIONS OF ORAL NARRATIVES

MYTHS

STYLE IN ORAL NARRATIVES

LESSONS LEARNT FROM NARRATIVES

ECONOMIC ACTIVITIES

SOCIAL-CULTURAL ACTIVITIES

PERFORMANCE OF SONGS

CLASSIFICATION OF SONGS

FEATURES OF STYLE IN SONG

PROVERBS

CLASSIFICATION OF PROVERBS

PERFOMANCE OF RIDDLES

SIMILARITIES BETWEEN RIDDLES AND PROVERBS

DIFFERENCES BETWEEN RIDDLES AND PROVERBS

CHARACTERISTICS

What is field work?

TERMS USED FIELDWORK

IMPORTANCE OF FIELDWORK

b) Observation

SAMPLE QUESTIONNAIRE

BACKGROUND OF THE INFORMANT

INFORMATION OF THE SONG

ORAL LITERATURE TODAY

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