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## FORM 4 MATHS SCHEMES OF WORK FOR TERM 1-3.

SCHEME OF WORK               FORM  FOUR  MATHEMATICS              TERM  ONE  YEAR

# WK

NO.

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