Free Maths schemes of work Form Four, Term 1-3
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FORM 4 MATHS SCHEMES OF WORK FOR TERM 1-3.
| SCHEME OF WORK FORM FOUR MATHEMATICS TERM ONE YEAR | |||||||
WKNO. |
L/NO | TOPIC / SUBTOPIC | LESSON / SPECIFIC
OBJECTIVES |
TEACHING / LEARNING
ACTIVITIES |
MATERIALS
/ RESOURCES |
REFERE-
NCES |
REMARKS |
| 1 | 1 | MATRICES & TRANSFORMA-TIONS
Definition of a transformation. Reflection in the y-axis. |
By the end of the lesson, the learner should be able to:
Define a transformation. Obtain image of an object by reflection in the y-axis. |
Questioning to review position vectors; Drawing objects and their images on the Cartesian plane; Inferring the matrix of transformation for reflection in the y-axis. Written exercise.
|
Geo – board, Graph papers, mirrors. |
KLB BK IV Pgs 1-2 |
|
| 2 | Reflection in the
x-axis. |
Obtain image of an object by reflection in the x-axis. | Drawing object and image on the Cartesian plane;
Inferring the matrix of transformation for reflection in the x-axis. Written exercise.
|
Geo – board, Graph papers, mirrors. |
KLB BK IV
Pgs 2 – 3 |
||
| 3 | Reflection in the
Lines y = x, y = – x and other lines. |
Obtain image of an object by reflection in a given line.
Obtain the object given its image and line of reflection.
|
Review equation of a line;
Draw the line y = x; Reflect an object in the line y = x; Infer the matrix of transformation Written exercise.
|
Geo – board, Graph papers, mirrors. |
KLB BK IV
Pgs 2-3 |
||
| 4 | Rotation matrix.
(positive angle) |
Obtain image of an object by rotation through a positive angle.
Obtain the object given its image and positive rotation angle.
|
Guided discovery;
Worked example; Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 3-4 |
||
| 5 | Rotation matrix.
(negative angle) |
Obtain image of an object by rotation through a negative angle.
|
Guided discovery;
Worked example; Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 3-4 |
||
| 6 | The unit circle. | Use the unit circle to identify a transformation represented by a given matrix. | Guided discovery;
Worked example; Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 9-13 |
||
| 7 | Finding matrix of transformation. | Find matrix of transformation given an object and image.
Describe the transformation fully. |
Review simultaneous equations and matrix multiplication;
Worked examples; Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 6-8 |
||
| 2 | 1 | Enlargement matrix. | Identify an enlargement matrix.
Perform operations involving enlargement matrices.
|
Review scale factor and centre of enlargement;
Worked examples; Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 11-12 |
|
| 2 | Two successive transformations. | Perform two successive transformations. | Guided discovery of order of operation;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 16-17 |
||
| 3 | Several successive transformations. | Perform several successive transformations. | Previous exercise review;
Guided discovery of order of operation; Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 16-17 |
||
| 4 | Combined matrix of transformations. | Find combined matrix of several transformations. | Previous exercise review;
Guided discovery of order of operation; Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 21-22 |
||
| 5 | Inverse of a transformation matrix. | Identify the identity matrix.
Determine the inverse of a transformation matrix. |
Worked examples using several methods;
Supervised practice; Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 24-26 |
||
| 6 | Inverse of several transformation matrices. | Determine the inverse of several combined transformation matrices. | Worked;
Supervised practice; Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 24-26 |
||
| 7 | A.S.F. and determinant of a transformation matrix. | State the relation between A.S.F. and determinant of a transformation matrix. | Finding area of object, image, ASF;
Guided discovery; Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 26-27 |
||
| 3 | 1 | Shear transformation.
(x-axis invariant) |
Identify a shear transformation. (x-axis invariant)
Describe a shear fully. |
Drawing object and image under a shear transformation;
Oral exercise; Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 28-32 |
|
| 2 | Shear transformation.
(y-axis invariant) |
Identify a shear transformation. (y-axis invariant)
Describe a shear fully. |
Drawing object and image under a shear transformation;
Oral exercise; Written exercise.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 28-31 |
||
| 3 | Finding shear matrix. | Find shear matrix given the object and image. | Worked examples;
Written exercise. |
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 31-2 |
||
| 4 | One-way stretch.
(x-axis invariant) |
Describe a one-way stretch.
(x-axis invariant) Find the scale factor of a stretch. |
Guided discovery;
Worked examples and discussion.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 32-34 |
||
| 5 | One-way stretch.
(y-axis invariant) |
Describe a one-way stretch.
(y-axis invariant). Find the scale factor of a stretch. |
Guided discovery;
Worked examples and discussion.
|
Geo – board,
Graph papers.
|
KLB BK IV
Pgs 32-34 |
||
| 6 | Isometric and non-isometric transformation. | Classify transformations as either isometric or non-isometric. | Review types of transformations;
Probing questions on size and shape of objects and images.
|
KLB BK IV
Pg 35 |
|||
| 7 | Test / mixed exercise. | Past exam papers. | |||||
| 4 | 1 | STATISTICS II
Mean and assumed mean. (frequency 1) |
Find mean of ungrouped data using an assumed mean. (frequency 1) |
Simple worked examples;
Exposition of method involving an assumed mean; Written exercise.
|
Calculator. | KLB BK IV
Pgs 38-39 |
|
| 2 | Mean and assumed mean.
(frequency > 1) |
Find mean of ungrouped data using an assumed mean.
(frequency > 1) |
Simple worked examples;
Written exercise.
|
Calculator. | KLB BK IV
Pg 40 |
||
| 3 | Mean of grouped data. | Find mean of grouped data. | Review previous exercise;
Completing table; Worked examples. |
Calculator. | KLB BK IV
Pgs 40-41 |
||
| 4 | Mean of grouped data.
(alternative methods) |
Find mean of grouped data.
(alternative methods) |
Completing table;
Worked examples. Written exercise. |
Calculator. | KLB BK IV
Pgs 40-46 |
||
| 5 | Median. | Find median of grouped data. | Worked examples;
Written exercise. |
Calculator. | KLB BK IV
Pgs 46-7 |
||
| 6 | Quartiles. | Find upper and lower quartiles. | Exposition;
Worked examples; Written exercise. |
Calculator. | KLB BK IV
Pgs 47-8 |
||
| 7 | Deciles and Percentiles. | Define a decile and percentile.
Find nth decile / percentile. |
Exposition;
Worked examples; Written exercise. |
Calculator. | KLB BK IV
Pgs 47-8 |
||
| 5 | 1 | Cumulative frequency curve. | Draw a cumulative frequency curve. | Q/A to review upper and lower limits of class boundaries;
Complete a table by finding cumulative totals; Draw an ogive.
|
Calculator, graph papers. | KLB BK IV
Pgs 38-40 |
|
| 2 | Median and quartiles from an ogive. | Estimate median and quartiles from an ogive. | Probing questions to make inferences from an ogive.
|
Calculator, graph papers. | KLB BK IV
Pgs 48-50 |
||
| 3 | Deciles and percentiles from an ogive. | Estimate deciles and percentiles from an ogive. | Probing questions to make inferences from an ogive.
|
Calculator, graph papers. | KLB BK IV
Pgs 53-55 |
||
| 4 | Range, inter-quartile range and quartile deviation. | Find range and inter-quartile range of a set of data. | Exposition and oral exercise. | Calculator. | KLB BK IV
Pgs 55-56 |
||
| 5 | Mean absolute deviation. | Determine mean absolute deviation. | Exposition;
Worked examples. |
Calculator. | KLB BK IV
Pgs 56-7 |
||
| 6 | Variance. | Define variance.
Determine variance of a set of data. |
Exposition;
Worked examples. |
Calculator. | KLB BK IV
Pgs 57-59 |
||
| 7 | Standard deviation. | Determine standard deviation of a set of data. | Exposition;
Worked examples; Written exercise. |
Calculator. | KLB BK IV
Pgs 59-60 |
||
| 6 | 1-4 | Formulae for standard deviation. | Use various methods of finding std deviation. | Exposition;
Worked examples; Written exercise. |
Calculator. | KLB BK IV
Pgs 60-3 |
|
| 5 | LOCI
Definition of a locus. |
Define locus of a point. |
Illustrative examples; Exposition of meaning of locus of a point.
|
Door, clock, see saw, etc. |
KLB BK IV
Pgs 66-7 |
||
| 6 | Sketching locus of a point. | Sketch locus of a point. | Oral exercise;
Supervised practice; Written exercise. |
KLB BK IV
Pgs 67-8 |
|||
| 7 | Perpendicular bisector locus.
(two dimensions) |
Describe perpendicular bisector locus.
(two dimensions) |
Geometrical construction;
Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pgs 68-9 |
||
| 7 | 1 | Perpendicular bisector locus.
(three dimensions) |
Describe perpendicular bisector locus.
(three dimensions) |
Geometrical construction;
Guided discovery; Supervised practice; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 69 |
|
| 2 | Locus of points at a given distance from a fixed point.
(two dim) |
Describe locus of points at a given distance from a fixed point. | Geometrical construction;
Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 70 |
||
| 3 | Locus of points at a given distance from a fixed point.
(three dim) |
Describe locus of points at a given distance from a fixed point. | Geometrical construction;
Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 71 |
||
| 4 | Locus of points at a given distance from a line.
(two dim) |
Describe locus of points at a given distance from a fixed point. | Geometrical construction;
Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 69 |
||
| 5 | Locus of points at a given distance from a line.
(three dim) |
Describe locus of points at a given distance from a fixed point. | Geometrical construction;
Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 70 |
||
| 6 | Angle bisector locus. | Construct the angle bisector locus. | Geometrical construction;
Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 70 |
||
| 7 | Constant angle locus. | Construct constant angle locus. | Probing questions to review angle properties of a circle;
Geometrical construction; Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pgs 72-4 |
||
| 8 | 1 | Constant angle locus.
(contd) |
Construct constant angle locus. | Probing questions to review previous exercise;
Geometrical construction; Guided discovery; Written exercise. |
Geometrical sets. | KLB BK IV
Pgs 72-4 |
|
| 2 | Intersecting loci involving lines and angles. | Construct intersecting loci involving lines and angles. | Geometrical construction;
Supervised practice; Written exercise. |
Geometrical sets. | KLB BK IV
Pgs 72-4 |
||
| 3 | Circumcircle locus. | Construct a circumcircle. | Geometrical construction;
Supervised practice; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 78 |
||
| 4 | In-circle locus. | Construct an in-circle locus. | Geometrical construction;
Supervised practice; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 78 |
||
| 5 | Ex-circle locus. | Construct an ex-circle locus. | Geometrical construction;
Supervised practice; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 78 |
||
| 6 | Intersecting loci in plane figures. | Construct intersecting loci in plane figures. | Problem solving. | Geometrical sets. | KLB BK IV
Pgs 79-81 |
||
| 7 | Loci of inequalities. | Draw locus of points that satisfy various inequalities. | Q/A to review simple and compound inequalities;
Worked examples; Written exercise. |
Geometrical sets. | KLB BK IV
Pgs 81-2 |
||
| 9 | 1 | Loci of inequalities.
(contd) |
Draw locus of points that satisfy various inequalities. | Review previous exercise;
Further worked examples; Written exercise. |
Geometrical sets. | KLB BK IV
Pg 83 |
|
| 2 | Locus involving chords. | Construct locus involving chords. | Worked examples;
Written exercise.
|
Geometrical sets. | KLB BK IV
Pgs 96-97 |
||
| 3 | TRIGONOMETRY
III
Some trigonometric ratios. |
Rearrange trigonometric expressions.
|
Exposition and worked examples; Written exercise. |
Geometrical sets. |
KLB BK IV Pgs 90-91 |
||
| 4 | Trigonometric identities. | Prove some trigonometric identities. | Problem solving. | Geometrical sets. | KLB BK IV
Pgs 100-1 |
||
| 5 | Period and amplitude of waves. | Determine period and amplitude of waves. | Exposition and worked examples. | Geometrical sets. | KLB BK IV
94-5 |
||
| 6 | Tables for trigonometric functions. | Complete tables for trigonometric functions.
|
Exposition and worked examples. | Calculator.
|
KLB BK IV
Pgs 96-7 |
||
| 7 | Graphs for trig. functions. | Plot graphs for trigonometric functions.
|
Drawing graphs; supervised practice; make inferences from the graphs. | Geometrical sets, graph papers. | KLB BK IV
Pgs 96-7 |
||
| 10 | 1 | Further graphs for trig. functions. | Plot graphs for trigonometric functions.
|
Drawing graphs; supervised practice; make inferences from the graphs. | Geometrical sets, graph papers. | KLB BK IV
Pgs 96-7 |
|
| 2 | Transformations of waves. | Describe some transformations of waves. | Supervised practice;
Exposition and worked examples; Written exercise. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 96-97 |
||
| 3 | Waves with a phase angle.
(positive) |
Determine the phase angle (positive) for two waves. | Guided discovery;
Written exercise. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 97-8 |
||
| 4 | Waves with a phase angle.
(negative) |
Determine the phase angle (negative) for two waves. | Guided discovery;
Written exercise. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 97-8 |
||
| 5 | Trigonometric equations. | Solve trigonometric equations. | Q/A to review trig. ratios for complementary angles;
Worked examples; Supervised practice; Written exercise. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 100-3 |
||
| 6 | Further trig. equations. | Solve trigonometric equations. | Exercise review;
Problem solving. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 100-3 |
||
| 7 | Graph of a trig. function and a line. | Draw the graph of a trig. function and a line to solve an equation. | Worked examples;
Supervised practice; Written exercise. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 100-3 |
||
| 11 | 1 | Graphs of two trig. functions. | Draw graphs of two trig. functions to solve some equations. | Worked examples;
Supervised practice; Written exercise. |
Geometrical sets, graph papers. | KLB BK IV
Pgs 100-3 |
|
| 2 | THREE DIMENSIONAL GEOMETRY
Dimensions of figures. |
State the dimensions of figures. Identify faces, edges, and vertices of common figures. |
Probing questions; Oral exercise. |
Common planes and solids. |
KLB BK IV Pgs 104-6 |
||
| 3 | Angle between a line and a plane. | Identify the angle between a line and a plane. | Exposition;
Oral exercise. |
Cuboid wire mesh. | KLB BK IV
Pgs 106-7 |
||
| 4 | Finding the angle between a line and a plane. | Find the angle between a line and a plane. | Guided discovery;
Worked examples; Written exercise.
|
Models of solids. | KLB BK IV
Pgs 107-113 |
||
| 5 | Finding the angle between a line and a plane.
(contd) |
Find the angle between a line and a plane. | Problem solving. | Models of solids. | KLB BK IV
Pgs 107-113 |
||
| 6 | Angle between two planes. | Identify the angle between two planes. | Q/A counting planes;
Exposition.
|
Models of solids. | KLB BK IV
Pgs 113-118 |
||
| 7 | Angle between two planes.
(contd) |
Find the angle between two planes. | Exposition;
Guided discovery; Worked examples; Written exercise.
|
Models of solids. | KLB BK IV
Pgs 113-118 |
||
| 12
13 |
END OF TERM EXAMS | ||||||
| SCHEME OF WORK FORM FOUR MATHEMATICS TERM TWO YEAR | |||||||||||||||
| 1 | 1 | Angle between two planes.
(contd) |
Find the angle between two planes. | Problem solving. | Models of solids. | KLB BK IV
Pgs 113-118 |
|||||||||
| 2 | Length between two points in three dimensions. | Determine length between two points in three dimensions. | Supervised practice,
Problem solving. |
Models of solids. | KLB BK IV
Pgs 119-124 |
||||||||||
| 3 | Length between two points on nets of solids. | Determine length between two points on nets of solids. | Making nets of solids;
Supervised practice, Problem solving. |
Manilla off-cuts, scissors/ Models of solids. | KLB BK IV
Pg 118 |
||||||||||
| 4 | Angle between skew lines. | Find the angle between skew lines. | Exposition;
Guided discovery; Worked examples; Written exercise |
Models of solids. | KLB BK IV
Pgs 142-8 |
||||||||||
|
|
5 | LONGITUDES AND LATITUDES
Great and small circles |
Identify great and small circles from on a globe. |
Probing questions; Oral exercise. |
Globe, atlas. | KLB BK IV
Pgs 125-7 |
|||||||||
|
|
6 | Difference in longitudes and latitudes. | Find the difference in longitudes and latitudes. | Probing questions;
Oral exercise.
|
Wire globe. | KLB BK IV
Pgs 128-9, 131-141 |
|||||||||
| 7 | Distance along a great circle.
(in nm) |
Calculate the distance along a great circle.
(in nm) |
Exposition;
Guided discovery; Worked examples; Written exercise |
Wire globe, calculator. | KLB BK IV
Pgs 130-3, 131-141 |
||||||||||
| 2 | 1 | Distance along a great circle.
(in km) |
Calculate the distance along a great circle.
(in nm) |
Exposition;
Guided discovery; Worked examples; Written exercise |
Wire globe, calculator. | KLB BK IV
Pgs 130-3, 131-141 |
|||||||||
| 2 | Distance along a small circle.
(in nm) |
Calculate the distance along a great circle.
(in nm) |
Exposition;
Guided discovery; Worked examples; Written exercise |
Wire globe, calculator. | KLB BK IV
Pgs 130-3, 131-141 |
||||||||||
| 3 | Distance along a small circle.
(in km) |
Calculate the distance along a great circle.
(in nm) |
Review previous exercise;
Worked examples; Written exercise |
Wire globe, calculator. | KLB BK IV
Pgs 133-7 |
||||||||||
|
|
4 | Shortest distance between two points on the earth’s surface. | Determine the shortest distance between two points on the earth’s surface. | Review previous exercise;
Worked examples; Written exercise |
Wire globe, calculator. | KLB BK IV
Pgs 137-9 |
|||||||||
| 5 | Longitudes and time. | Relate longitudes with local time. | Probing questions;
Worked examples; Written exercise. |
Wire globe, calculator. | KLB BK IV
Pgs 141-2 |
||||||||||
| 6 | Speed (in km/h) | Calculate speed given distance and time. | Probing questions;
Worked examples; Written exercise. |
Wire globe, calculator. | KLB BK IV
Pgs 142 |
||||||||||
| 7 | Speed (in knots) | Calculate speed given distance in nm and time. | Review previous exercise;
Probing questions; Worked examples; Written exercise. |
Wire globe, calculator. | KLB BK IV
Pgs 142 |
||||||||||
| 3 | 1 | LINEAR PROGRAMMING
Forming inequalities. |
Form inequalities from given situations. |
Q/A to review inequalities; Worked examples; Written exercise.
|
Graph papers. |
KLB BK 1V Pgs 150-1 |
|||||||||
| 2 | Forming inequalities. | Form inequalities from given situations. | Review previous exercise.
Problem solving.
|
Graph papers. | KLB BK IV
Pgs 150-1 |
||||||||||
| 3 | Solutions of linear inequalities. | Solve linear inequalities. | Probing questions;
Worked examples; Written exercise.
|
Graph papers. | KLB BK IV
Pgs 151-2 |
||||||||||
| 4 | Graphs of linear inequalities. | Represent situations graphically with inequalities.
|
Worked examples;
Supervised practice; Written exercise.
|
Graph papers. | KLB BK IV
Pgs 188-90 |
||||||||||
| 5 | Graphs of linear inequalities.
(contd) |
Represent situations graphically with inequalities.
|
Exercise review;
Supervised practice; Written exercise.
|
Graph papers. | KLB BK IV
Pgs 188-90 |
||||||||||
| 6 | Objective function. | Formulate the objective function.
|
Probing questions;
Oral exercise. |
Graph papers. | KLB BK IV
Pgs 191-4 |
||||||||||
| 7 | Optimization. | Obtain the optimum solution to inequalities. | Exposition;
Guided discovery. Written exercise.
|
Graph papers. | KLB BK IV
Pgs 194-7 |
||||||||||
| 4 | 1 | Further Optimization. | Obtain the optimum solution to inequalities. | Guided discovery.
Written exercise.
|
Graph papers. | KLB BK IV
Pgs 197-201 |
|||||||||
| 2 | DIFFERENTI–
ATION
Average rate of change.
|
Define average rate of change. Determine average rate of change.
|
Filling in a table of values for a curve; Plotting the curve; Finding average rate of change. Written exercise. |
Graph papers, calculaors. |
KLB BK IV Pgs 162-3 |
||||||||||
| 3 | Instantaneous rate of change. | Define instantaneous rate of change.
Determine instantaneous rate of change.
|
Drawing a tangent to a curve;
Supervised working; Written exercise.
|
KLB BK IV
Pg 163 |
|||||||||||
| 4 | Gradient of a curve at a point. | Find gradient of a curve at a point. | Q/A to review gradient of a line;
Exposition of gradient of a curve; Worked examples.
|
KLB BK IV
Pgs 163-4 |
|||||||||||
| 5 | Gradient of a curve.
(first principles) |
Determine gradient of a curve.
(first principles) |
Exposition;
Probing questions. |
KLB BK IV
Pgs 164-6 |
|||||||||||
| 6 | Derivative of a function. (first principles) | Obtain derivative of a function. (first principles) | Exposition;
Probing questions. |
KLB BK IV
Pgs 167-9 |
|||||||||||
| 7 | Meaning of differentiation. | Recall the process of differentiation. | Exposition;
Worked examples; Supervised practice; Written exercise. |
KLB BK IV
Pgs 166-7 |
|||||||||||
| 5 | 1 | Derivative of a polynomial. | Differentiate a polynomial. | Exposition;
Worked examples; Supervised practice; Written exercise. |
KLB BK IV
Pgs 170-2 |
||||||||||
| 2 | Derivative of a polynomial with a denominator. | Differentiate a polynomial having a denominator. | Exposition;
Worked examples; Supervised practice; Written exercise. |
KLB BK IV
Pgs 170-2 |
|||||||||||
| 3 | Derivative of a quadratic function. | Differentiate a quadratic function. | Exposition;
Worked examples; Supervised practice; Written exercise. |
KLB BK IV
Pgs 170-2 |
|||||||||||
| 4 | Obtaining gradient from gradient function. | Obtain gradient from gradient function. | Worked examples;
Supervised practice; Written exercise. |
KLB BK IV
Pgs 170-2 |
|||||||||||
| 5 | Equation of a tangent to a curve at a point. | Find equation of a tangent to a curve at a point. | Q/A review gradient function;
Worked examples; Written exercise.
|
KLB BK IV
Pgs 173-4 |
|||||||||||
| 6 | Equation of a normal to a curve at a point. | Find equation of a normal to a curve at a point. | Q/A review gradient function and gradients of perpendicular lines;
Worked examples; Supervised practice; Written exercise.
|
KLB BK IV
Pgs 173-4 |
|||||||||||
| 7 | Stationary point ((minimum) | Determine minimum point of a curve. | Filling in a table of gradients at various points;
Probing questions; Discussion. |
Graph books. | KLB BK IV
Pgs 174-5 |
||||||||||
| 6 | 1 | Stationary point ((maximum) | Determine maximum point of a curve. | Filling in a table of gradients at various points;
Probing questions; Discussion. |
Graph books. | KLB BK IV
Pgs 175-6 |
|||||||||
| 2 | Stationary point (point of inflexion +ve to +ve)
|
Determine a point of inflexion on a curve. | Filling in a table of gradients at various points;
Probing questions; Discussion. |
Graph books. | KLB BK IV
Pgs 176-7 |
||||||||||
| 3 | Stationary point (point of inflexion -ve to -ve)
|
Determine a point of inflexion on a curve. | Filling in a table of gradients at various points;
Probing questions; Discussion. |
Graph books. | KLB BK IV
Pgs 176-7 |
||||||||||
| 4 | Features of a curve. | Identify points on a curve.
Identify stationary points of a curve. |
Probing questions;
Oral exercise. |
Graph books. | KLB BK IV
Pgs 180-1 |
||||||||||
| 5 | Curve sketching | Sketch curves. | Supervised practice;
Written exercise. |
Graph books. | KLB BK IV
Pgs 180-2 |
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| 6 | Displacement time graphs. | Sketch and interpret displacement time graphs. | Q/A to review relation between displacement and velocity;
Supervised practice; Discussion. |
KLB BK IV
Pgs 182-3 |
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| 7 | Velocity from displacement function. | Determine velocity from a displacement function. | Worked examples;
Written exercise.
|
KLB BK IV
Pgs 182-3 |
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| 7 | 1 | Velocity time graphs. | Sketch and interpret velocity time graphs. | Q/A to review relation between velocity and acceleration;
Supervised practice; Discussion. |
KLB BK IV
Pgs 184-6 |
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| 2 | Acceleration from velocity function. | Determine velocity from a displacement function. | Worked examples;
Written exercise.
|
KLB BK IV
Pgs 184-6 |
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| 3 | Acceleration from displacement function. | Determine acceleration from a displacement function. | Probing questions;
Worked examples; Written exercise.
|
KLB BK IV
Pgs 184-6 |
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| 4 | Maxima and minima. | Apply differentiation to find maxima and minima. | Exposition;
Worked examples; Written exercise.
|
KLB BK IV
Pgs 186-9 |
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| 5 | Maxima and minima (contd) | Apply differentiation to find maxima and minima. | Exercise review;
Problem solving. |
KLB BK IV
Pgs 186-9 |
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| 6 | INTEGRATION
Reverse the process of differentiation. |
Reverse the process of differentiation. |
Probing questions; Worked examples; Written exercise.
|
KLB BK IV Pgs 207-9 |
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| 7 | Finding y given gradient function. | Find y given gradient function. | Probing questions;
Worked examples; Written exercise.
|
KLB BK IV Pgs 209-12 |
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| 1 | Indefinite integral. | Obtain an indefinite integral. | Exposition;
Worked examples; Written exercise.
|
KLB BK IV Pgs 212-6 |
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| 8 | 1 | Definite integral. | Obtain a definite integral. | Exposition;
Worked examples; Written exercise.
|
KLB BK IV Pgs 212-6 |
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| 2 | Area bounded by a curve above x-axis. | Determine area bounded by a curve and x-axis. | Exposition;
Worked examples; Written exercise.
|
KLB BK IV Pgs 217-8 |
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| 3 | Area bounded by a curve below x-axis. | Determine area bounded by a curve and x-axis. | Exposition;
Worked examples; Written exercise.
|
KLB BK IV Pgs 218-9 |
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| 4 | Area bounded by a curve and a line. | Determine area bounded by a curve and a straight line. | Exposition;
Worked examples; Written exercise.
|
KLB BK IV Pg 220 |
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| 5 | Displacement from velocity function. | Obtain displacement from a velocity function. | Probing questions;
Worked examples; Written exercise.
|
KLB BK IV Pgs 223-4 |
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| 6 | Velocity from acceleration function. | Obtain velocity from a acceleration function. | Probing questions;
Worked examples; Written exercise.
|
KLB BK IV Pgs 223-4 |
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| 7 | Exercise on kinematics. | Apply integration and differentiation in kinematics. | Exercises review;
Problem solving. |
KLB BK IV Pgs 225-231 |
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| 9 | 1 | AREA APPROXIMATION
Trapezium rule. |
Derive the trapezium rule. |
Divide area under a graph into several trapezia; Guided derivation of the trapezium rule. |
Copies of area under a curve. |
KLB BK IV Pgs 196-7 |
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| 2 | Application of trapezium rule. | Apply trapezium rule in problem solving. | Worked examples;
Written exercise. |
KLB BK IV Pgs 197-201 |
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| 3 | Application of trapezium rule. | Apply trapezium rule in problem solving. | Written exercise review.
Problem solving. |
KLB BK IV Pgs 197-201 |
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| 4 | The mid-ordinate rule. | Derive the mid-ordinate rule. | Divide area under a graph into several strips;
Guided derivation of the trapezium rule. |
KLB BK IV Pgs 202-3 |
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| 5 | Application of mid-ordinate rule. | Apply mid-ordinate rule.in problem solving. | Worked examples;
Written exercise. |
KLB BK IV Pgs 203-6 |
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| 6-7 | Application of mid-ordinate rule. | Apply mid-ordinate rule in problem solving. | Review exercises;
Problem solving. |
KLB BK IV Pgs 203-6 |
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| 10-13 | MOCK K.C.S.E EXAM | ||||||||||||||
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