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Mathematics
Form 4 2025
TERM II
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WK LSN TOPIC SUB-TOPIC OBJECTIVES T/L ACTIVITIES T/L AIDS REFERENCE REMARKS
1

Opening and Revision

2 1
Quadratic Expressions and Equations
Factorization of quadratic expressions
By the end of the lesson, the learner should be able to:

Factorize quadratic expressions
Write the perfect squares
Discussions
Solving
Demonstrating
Explaining
calculators
KLB Mathematics
Book Three
Pg 1
2 2
Quadratic Expressions and Equations
Completing squares
Solving quadratic expression by completing square
By the end of the lesson, the learner should be able to:

Factorize quadratic expression by completing square method
Discussions
Solving
Demonstrating
Explaining
calculators
Calculators  
KLB Mathematics
Book Three
Pg 1-2
2 3
Quadratic Expressions and Equations
Solving quadratic expression by factorization
The quadratic formula
The quadratic formula
Formation of quadratic equations
By the end of the lesson, the learner should be able to:

Factorize quadratic expressions
Solve quadratic expressions by factorization
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 7
2 4
Quadratic Expressions and Equations
Graphs of quadratic functions
Graphical solutions of quadratic equation
By the end of the lesson, the learner should be able to:

Draw a table of the quadratic functions
Draw graphs of quadratic functions
Discussions
Solving
Demonstrating
Explaining
graph papers & geoboard
KLB Mathematics
Book Three
Pg 12-15
2 5
Quadratic Expressions and Equations
Graphical solutions of quadratic equation
Graphical solutions of simultaneous equations
Further graphical solutions
By the end of the lesson, the learner should be able to:

Draw graphs of quadratic functions
Solve quadratic equations using the graphs
Discussions
Solving
Demonstrating
Explaining
graph papers & geoboard
graph papers & geoboards
KLB Mathematics
Book Three
Pg 17-19
2 6
Approximations and Errors
Computing using calculators
Approximation
By the end of the lesson, the learner should be able to:

Solve basic operations using calculators
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 24-26
2 7
Approximations and Errors
Estimation
Accuracy and errors
Percentage error
Rounding off error and truncation error
By the end of the lesson, the learner should be able to:

Approximate values by estimation
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 30
3 1
Approximations and Errors
Propagation of errors
By the end of the lesson, the learner should be able to:

Find the propagation of errors in addition and subtraction
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 35-36
3 2
Approximations and Errors
Propagation of errors
By the end of the lesson, the learner should be able to:

Find the propagation of errors in multiplication
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 36-37
3 3
Approximations and Errors
Trigonometry (II)
Trigonometry (II)
Trigonometry (II)
Word problems
The unit circle
The unit circle
Trigonometric ratios of angles greater than 900
By the end of the lesson, the learner should be able to:

Find the propagation of errors of a word problem
Discussions
Solving
Demonstrating
Explaining
Calculators 
Calculators
Protractor
Ruler
Pair of compasses
KLB Mathematics
Book Three
Pg 39-40
3 4
Trigonometry (II)
Trigonometric ratios of angles greater than 900
Trigonometric ratios of negative angles
Trigonometric ratios of angles greater than 3600
By the end of the lesson, the learner should be able to:

Find the trigonometric values of angles
Discussions
Solving
Demonstrating
Explaining
Calculators 
geo boards & graph books
KLB Mathematics
Book Three
Pg 46-47
3 5
Trigonometry (II)
Use of mathematical tables
Use of calculators
By the end of the lesson, the learner should be able to:

Use mathematical tables to find sine and cosine
Discussions
Solving
Demonstrating
Explaining
mathematical tables
calculators
KLB Mathematics
Book Three
Pg 51-55
3 6
Trigonometry (II)
Radian measure
Simple trigonometric graphs
Graphs of cosines
By the end of the lesson, the learner should be able to:

Convert degrees to radians and vice versa
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 58-61
3 7
Trigonometry (II)
Graphs of tan
The sine rule
Cosine rule
Problem solving
By the end of the lesson, the learner should be able to:

Draw tables for tan of values
Draw graphs of tan functions
Discussions
Solving
Demonstrating
Explaining
Calculators 
Calculators                                                       
KLB Mathematics
Book Three
Pg 64-65
4 1
Surds
Rational and irrational numbers
Surds
Addition of surds
By the end of the lesson, the learner should be able to:

Classify numbers as rational and irrational numbers
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 78
4 2
Surds
Subtraction of surds
Multiplication of surds
Division of surds
By the end of the lesson, the learner should be able to:

Subtract surds
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 80
4 3
Surds
Further Logarithms
Rationalizing the denominator
Solving problem
Introduction
By the end of the lesson, the learner should be able to:

Rationalize the denominator
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 85-87
4 4
Further Logarithms
Laws of logarithms
Logarithmic equations and expressions
Logarithmic equations and expressions
By the end of the lesson, the learner should be able to:

State the laws of logarithms
Use laws of logarithms to solve problems
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 90-93
4 5
Further Logarithms
Further computation using logarithms
By the end of the lesson, the learner should be able to:

Solve problems involving logarithms
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 95-96
4 6
Further Logarithms
Commercial arithmetic
Problem solving
Simple interest
By the end of the lesson, the learner should be able to:

Solve problems involving logarithms
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 97
4 7
Commercial arithmetic
Compound interest
Appreciation
Depreciation
Hire purchase
By the end of the lesson, the learner should be able to:

Calculate the compound interest
Discussions
Solving
Demonstrating
Explaining
Calculators 
 ,calculator
KLB Mathematics
Book Three
Pg 102-106
5 1
Commercial arithmetic
Circles: Chords and tangents
Income tax
P.A.Y.E
Length of an arc
By the end of the lesson, the learner should be able to:

Calculate the income tax
Discussions
Solving
Demonstrating
Explaining
income tax table ,calculator
Calculators s
Geometrical set,calculator
KLB Mathematics
Book Three
Pg 112-114
5 2
Circles: Chords and tangents
Chords
Parallel chords
Equal chords
By the end of the lesson, the learner should be able to:

Calculate the length of a chord
Discussions
Solving
Demonstrating
Explaining
Geometrical set ,calculator
KLB Mathematics
Book Three
Pg 126-128
5 3
Circles: Chords and tangents
Intersecting chords
Tangent to a circle
By the end of the lesson, the learner should be able to:

Calculate the length of intersecting chords
Discussions
Solving
Demonstrating
Explaining
Geometrical set ,calculator
KLB Mathematics
Book Three
Pg 132-135
5 4
Circles: Chords and tangents
Tangent to a circle
Properties of tangents to a circle from an external point
Tangents to two circles
Tangents to two circles
By the end of the lesson, the learner should be able to:

Calculate the length of tangent
Calculate the angle between tangents
Discussions
Solving
Demonstrating
Explaining
Geometrical set ,calculator
KLB Mathematics
Book Three
Pg 141-142
5 5
Circles: Chords and tangents
Contact of circles
Problem solving
By the end of the lesson, the learner should be able to:

Calculate the radii of contact circles
Discussions
Solving
Demonstrating
Explaining
Geometrical set ,calculator
KLB Mathematics
Book Three
Pg 151-153
5 6
Circles: Chords and tangents
Angle in alternate segment
Circumscribed circle
By the end of the lesson, the learner should be able to:

Calculate the angles in alternate segments
Discussions
Solving
Demonstrating
Explaining
Geometrical set ,calculator
KLB Mathematics
Book Three
Pg 157-160
5 7
Circles: Chords and tangents
Escribed circles
Centroid
Orthocenter
By the end of the lesson, the learner should be able to:

Construct escribed circles
Discussions
Solving
Demonstrating
Explaining
Geometrical set ,calculator
KLB Mathematics
Book Three
Pg 165-166
6 1
Matrices
Matrix representation and order of matrix
Addition of matrix
Subtraction of matrices
Combined addition and subtraction of matrices
By the end of the lesson, the learner should be able to:

Represent matrix
State the order of a matrix
Discussions
Solving
Demonstrating
Explaining
Chart showing tabular data
KLB Mathematics
Book Three
Pg 168-170
6 2
Matrices
Matrix multiplication
Identity matrix
By the end of the lesson, the learner should be able to:

Multiply matrices
Discussions
Solving
Demonstrating
Explaining
Chart showing tabular data
KLB Mathematics
Book Three
Pg 174-175
6 3
Matrices
Determinant of a 2
Inverse of a 2
Inverse of a 2
By the end of the lesson, the learner should be able to:

Find the determinant of a 2
Discussions
Solving
Demonstrating
Explaining
Calculator
Calculators 
KLB Mathematics
Book Three
Pg 183
6 4
Matrices
Formulae and variations
Solutions of simultaneous equations by matrix method
Problem solving
Formulae
By the end of the lesson, the learner should be able to:

Solve simultaneous equations by matrix method
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 188-190
6 5
Formulae and variations
Direct variation
Inverse variation
Partial variation
By the end of the lesson, the learner should be able to:

Solve problems involving direct variations
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 194-196
6 6
Formulae and variations
Sequences and series
Joint variation
Sequences
By the end of the lesson, the learner should be able to:

Solve problems involving join variations
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 204-205
6 7
Sequences and series
Arithmetic sequences
Geometric sequence
Arithmetic series
By the end of the lesson, the learner should be able to:

Find the nth term of a given arithmetic sequence
Discussions
Solving
Demonstrating
Explaining
KLB Mathematics
Book Three
Pg 209-210
7 1
Sequences and series
Vectors II
Vectors II
Geometric series
Coordinates in two dimensions
Coordinates in three dimensions
By the end of the lesson, the learner should be able to:

Find the nth term of a given geometric series
Discussions
Solving
Demonstrating
Explaining
Wire mesh in 3 dimensions
KLB Mathematics
Book Three
Pg 216-219
7 2
Vectors II
Column vectors
Position vector
Unit vectors
By the end of the lesson, the learner should be able to:

Find a displacement and represent it in column vector
Discussions
Solving
Demonstrating
Explaining
Wire mesh in 3 dimensions
KLB Mathematics
Book Three
Pg 223-224
7 3
Vectors II
Unit vectors
Magnitude of a vector in three dimensions
Parallel vectors
By the end of the lesson, the learner should be able to:

Express vectors in terms of unit vectors
Discussions
Solving
Demonstrating
Explaining
calculators
Geoboard
KLB Mathematics
Book Three
Pg 226-228
7 4
Vectors II
Collinear points
Proportion division of a line
By the end of the lesson, the learner should be able to:

Show that points are collinear
Discussions
Solving
Demonstrating
Explaining
Geoboard
Geoboard, calculators
KLB Mathematics
Book Three
Pg 232
7 5
Vectors II
Proportion division of a line
Ratio theorem
Ratio theorem
By the end of the lesson, the learner should be able to:

Divide a line externally in the given ratio
Discussions
Solving
Demonstrating
Explaining
Geoboard, calculators
KLB Mathematics
Book Three
Pg 238
7 6
Vectors II
Mid-point
Ratio theorem
Ratio theorem
By the end of the lesson, the learner should be able to:

Find the mid-points of the given vectors
Discussions
Solving
Demonstrating
Explaining
Geoboard, calculators
KLB Mathematics
Book Three
Pg 243
7 7
Vectors II
Binomial expansion
Applications of vectors
Binomial Expansion up to power four
By the end of the lesson, the learner should be able to:

Use vectors to show the diagonals of a parallelogram
Discussions
Solving
Demonstrating
Explaining
Geoboard, calculators
 calculators
KLB Mathematics
Book Three
Pg 248-249
8

Midterm break

9 1
Binomial expansion
Pascal
Applications to numerical cases
By the end of the lesson, the learner should be able to:

Use Pascal
Discussions
Solving
Demonstrating
Explaining
 calculators
KLB Mathematics
Book Three
Pg 256-257
9 2
Binomial expansion
Probability
Probability
Applications to numerical cases
Experimental probability
Experimental probability
By the end of the lesson, the learner should be able to:

Use binomial expansion to solve numerical problems
Discussions
Solving
Demonstrating
Explaining
Calculators
KLB Mathematics
Book Three
Pg 259-260
9 3
Probability
Range of probability measure
Probability space
Probability space
By the end of the lesson, the learner should be able to:

Calculate the range of probability measure
Discussions
Solving
Demonstrating
Explaining
Calculators
Calculators, charts
KLB Mathematics
Book Three
Pg 265-266
9 4
Probability
Combined events
Independent events
By the end of the lesson, the learner should be able to:

Find the probability of a combined events
Discussions
Solving
Demonstrating
Explaining
Calculators, charts
KLB Mathematics
Book Three
Pg 272-273
9 5
Probability
Independent events
Tree diagrams
Tree diagrams
By the end of the lesson, the learner should be able to:

Find the probability of independent events
Discussions
Solving
Demonstrating
Explaining
Calculators, charts
KLB Mathematics
Book Three
Pg 276-277
9 6
Probability
Compound proportions and rate of work
Compound proportions and rate of work
Tree diagrams
Compound proportions
Compound proportions
By the end of the lesson, the learner should be able to:

Use tree diagrams to find probability
Discussions
Solving
Demonstrating
Explaining
Calculators, charts
Calculators 
KLB Mathematics
Book Three
Pg 283-285
9 7
Compound proportions and rate of work
Proportional parts
Rates of work
Rates of work
By the end of the lesson, the learner should be able to:

Calculate the proportional parts
Discussions
Solving
Demonstrating
Explaining
Calculators 
KLB Mathematics
Book Three
Pg 291-293
10 1
Compound proportions and rate of work
Graphical methods
Graphical methods
Rates of work
Tables of given relations
Graphs of given relations
By the end of the lesson, the learner should be able to:

Calculate the rate of work
Discussions
Solving
Demonstrating
Explaining
Calculators 
Geoboard & graph books
KLB Mathematics
Book Three
Pg 295-296
10 2
Graphical methods
Graphical solution of cubic equations
Average rates of change
Rate of change at an instant
By the end of the lesson, the learner should be able to:

Draw tables of cubic functions
Discussions
Solving
Demonstrating
Explaining
Geoboard & graph books
KLB Mathematics
Book Three
Pg 301
10 3
Graphical methods
Empirical graphs
Reduction of non-linear laws to linear form
Reduction of non-linear laws to linear form
By the end of the lesson, the learner should be able to:

Draw the empirical graphs
Discussions
Solving
Demonstrating
Explaining
Geoboard & graph books
KLB Mathematics
Book Three
Pg 315-316
10 4
Graphical methods
Reduction of non-linear laws to linear form
Equation of a circle
Equation of a circle
By the end of the lesson, the learner should be able to:

Draw the graphs of reduction of non-linear laws to linear form
Discussions
Solving
Demonstrating
Explaining
Geoboard & graph bookss
Geoboard & graph books
KLB Mathematics
Book Three
Pg 318-321
10 5
Graphical methods
Trigonometry
Trigonometry
Equation of a circle
Trigonometric ratios
Deriving the relation Sin2 0 + Cos2 0 = 1
By the end of the lesson, the learner should be able to:

Find the equation of a circle
Discussions
Solving
Demonstrating
Explaining
Geoboard & graph books
Chart illustrating
Trigonometric ratios
Charts illustrating the
unit circle and right
KLB Mathematics
Book Three
Pg 327-328
10 6
Trigonometry
Trigonometric ratios of the form y = sin x y = tan x y = cos x
Graphs of Trigonometric relations y = a sin x y = a cos x y = a tan x
By the end of the lesson, the learner should be able to:


Draw graphs of trigonometric ratios of
the form y = sin x
y = tan x
y = cos x

Practice exercise
KLB Pg 4, Ex. 4.3
Advancing BK 4,
Ex. 4.4 and 4.5
Patel BK 4, Ex. 4.2
Square boards
Graph papers
- K.M, Advancing in
Math F4 Pg 59-64
- KLB Bk4 Pg 96-99 
10 7
Trigonometry
Simple trigonometric equations, amplitudes, period, wavelength and phase angle of trigonometric function
Trigonometry y = a sin (bx + 0)
By the end of the lesson, the learner should be able to:


Deduce from the graphs
y = sin x
y = tan x
y = cos x
The amplitude, wavelength and phase
angle




Practice exercise
Trigonometric relations
Graphs
Square boards
Graph papers
- K.M, Advancing in
Math F4 Pg 59-63 
11 1
Trigonometry
Trigonometry y = a cos (bx + 0) y = a tan (bx + 0)
Amplitude, period, wavelength and phase Phase angles of trigonometric function
By the end of the lesson, the learner should be able to:


Draw graphs of trigonometric ratios of
the form y = a cos (bx + 0)
y = a tan (bx + 0)

Drawing graphs
Square boards
Graph papers
Trigonometric relations
Graphs
- K.M, Advancing in
Math F4 Pg 59-64
11 2
Trigonometry
Three Dimensional Geometry
Three Dimensional Geometry
Three Dimensional Geometry
Solution to simple Trigonometric equations
Geometrical properties of common solids
Skew lines projection of a line onto a plane
Length of a line in 3D geometry
By the end of the lesson, the learner should be able to:


Solve simple trigonometric equations
analytically and graphically


Practice exercise
KLB Pg 4, Ex. 4.3
Advancing BK 4,
Ex. 4.6
Patel BK 4, Ex. 4.4
Trigonometric relations
Graphs
3-D models
- K.M, Advancing in
Math F4 Pg 65-67
- KLB BK 4
Pg 100-102 
11 3
Three Dimensional Geometry
Angle between a line and a line
A line and a plane
A plane and a plane
By the end of the lesson, the learner should be able to:


Identify and calculate the angle between
a line and a line

Practice exercise
Advancing BK 4,
Ex. 5.4
3-D models
- K.M, Advancing in
Math F4 Pg 77-80
11 4
Three Dimensional Geometry
Longitudes and Latitudes
Angles between skew lines
Latitudes and longitudes (great and small circle)
By the end of the lesson, the learner should be able to:


Identify and calculate the angle
between skew lines

Practice exercise
Advancing BK 4,
Ex. 5.4
KLB Pg 4, Ex. 5.2
3-D models
Globe
Ball
- K.M, Advancing in
Math F4 Pg 78-80
- KLB BK 4
Pg 118-119 
11 5
Longitudes and Latitudes
The equator and Greenwich meridian
Longitudes and Latitudes Position of a place on the surface of the earth
By the end of the lesson, the learner should be able to:


Define the great and small circle in
relation to a sphere (including the earth)

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1
Globe
Ball
- K.M, Advancing in
Math F4 Pg 83
- KLB BK 4
Pg 126-127 
11 6
Longitudes and Latitudes
Radii of small and great circles
Distance between two points along the small and great circle in nautical miles and kilometres
Distance in nautical miles and kilometers along a circle of latitude
By the end of the lesson, the learner should be able to:


Establish the relationship between the
radii of small and great circles

Practice exercise
Advancing BK 4,
Ex. 6.4
KLB Pg 4, Ex. 6.2
Globe
Ball
Calculators
- K.M, Advancing in
Math F4 Pg 89
- KLB BK 4
Pg 133-134 
11 7
Longitudes and Latitudes
Time and longitude
By the end of the lesson, the learner should be able to:


Calculate time in relation to kilometers
per hour

Practice exercise
Advancing BK 4,
Ex. 6.5
KLB Pg 4, Ex. 6.3

Globe
Ball
Calculators
- K.M, Advancing in
Math F4 Pg 91-92
- KLB Bk4Pg141-142 
12 1
Longitudes and Latitudes
Linear Programming
Speed in knots and kilometer per hour
Formation of linear Inequalities
By the end of the lesson, the learner should be able to:


Calculate speed in knots and
kilometer per hour

Practice exercise
Advancing BK 4,
Ex. 6.6
KLB Pg 4, Ex. 6.3
Real life situation
Inequalities
- K.M, Advancing in
Math F4 Pg 96-98
- KLB BK 4 Pg 150 
12 2
Linear Programming
Analytical solutions of linear inequalities
Solutions of linear inequalities by graph
By the end of the lesson, the learner should be able to:


Analyze solutions of linear inequalities

Practice exercise
Advancing BK 4,
Ex. 7.1
KLB BK 4, Ex. 7.2
Square boards
Graph papers
- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155 
12 3
Linear Programming
Optimization (include objective)
By the end of the lesson, the learner should be able to:


Solve and interpret the optimum
solution of the linear inequalities

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3


Graph paper
- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155
12 4
Linear Programming
Differentiation
Application of linear programming to real life situation
Average and instantaneous rates of change
By the end of the lesson, the learner should be able to:


Solve and interpret the optimum
solution of the linear programming to
real life situations

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3
Real life situations
Square boards
Graph paper
- K.M, Advancing in
Math F4 Pg 99-100
- KLB BK 4
Pg 157-159 
12 5
Differentiation
Differentiation Gradient of a curve at a point
By the end of the lesson, the learner should be able to:


Find the gradient of a curve at a point
using tangent

Practice exercise
Advancing BK 4,
Ex. 8.2
KLB BK 4, Ex. 8.1


Square boards
Graph paper
- K.M, Advancing in
Math F4 Pg 109
- KLB BK 4
Pg 162-163 
12 6
Differentiation
Gradient of y = xn where n is a positive interger
Delta notation (?)
Derivation of a Polynomial
Equations of tangents And normal to the Curve
By the end of the lesson, the learner should be able to:


Find the gradient function of the form
y = xn (n = positive interger)

Practice exercise
Advancing BK 4,
Ex. 8.2 and 8.3
KLB BK 4, Ex. 8.1
Square boards
Graph paper
Polynomials
- K.M, Advancing in
Math F4 Pg 110
- KLB BK 4
Pg 164-167 
12 7
Differentiation
Stationery point
Curve sketching
Application of differentiation to calculation of distance velocity and acceleration
Maxima and minima
By the end of the lesson, the learner should be able to:


Sketch a sketch

Practice exercise
Advancing BK 4,
Ex. 8.6
KLB BK 4, Ex. 8.3
Square boards
Graph paper
- K.M, Advancing in
Math F4 Pg118-120
- KLB BK 4
Pg 174-179 
13-14

End term examination and closing


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