Quadratic Expressions and Equations

Factorization of quadratic expressions
Completing squares
Completing squares
Solving quadratic expression by completing square
Solving quadratic expression by factorization

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

Factorize quadratic expressions
Write the perfect squares

Discussions
Solving
Demonstrating
Explaining

calculators
Calculators  
Calculators 

KLB Mathematics
Book Three
Pg 1

Quadratic Expressions and Equations
Approximations and Errors
Approximations and Errors
Approximations and Errors

The quadratic formula
Formation of quadratic equations
Graphs of quadratic functions
Graphs of quadratic functions
Graphical solutions of quadratic equation
Graphical solutions of quadratic equation
Graphical solutions of simultaneous equations
Further graphical solutions
Computing using calculators
Computing using calculators
Approximation

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

Solve quadratic expressions using the quadratic formula

Discussions
Solving
Demonstrating
Explaining

Calculators 
graph papers & geoboard
graph papers & geoboards

KLB Mathematics
Book Three
Pg 7-9

Approximations and Errors
Trigonometry (II)

Estimation
Accuracy and errors
Percentage error
Rounding off error and truncation error
Propagation of errors
Propagation of errors
Propagation of errors
Propagation of errors
Propagation of errors
Propagation of errors
Word problems
The unit circle

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

Approximate values by estimation

Discussions
Solving
Demonstrating
Explaining

Calculators 
Calculators
Protractor
Ruler
Pair of compasses

KLB Mathematics
Book Three
Pg 30

Trigonometry (II)

The unit circle
Trigonometric ratios of angles greater than 900
Trigonometric ratios of angles greater than 900
Trigonometric ratios of negative angles
Trigonometric ratios of angles greater than 3600
Use of mathematical tables
Use of mathematical tables
Use of calculators
Radian measure
Simple trigonometric graphs
Graphs of cosines

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

Solve problems using the unit circle

Discussions
Solving
Demonstrating
Explaining

Calculators
Protractor
Ruler
Pair of compasses
Calculators 
geo boards & graph books
mathematical tables

KLB Mathematics
Book Three
Pg 43-44

Trigonometry (II)
Surds
Surds
Surds
Surds
Surds
Surds
Surds
Surds

Graphs of tan
The sine rule
Cosine rule
Problem solving
Rational and irrational numbers
Surds
Addition of surds
Subtraction of surds
Multiplication of surds
Division of surds
Rationalizing the denominator
Solving problem

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

Further Logarithms
Commercial arithmetic
Commercial arithmetic

Introduction
Laws of logarithms
Laws of logarithms
Logarithmic equations and expressions
Logarithmic equations and expressions
Further computation using logarithms
Further computation using logarithms
Further computation using logarithms
Problem solving
Problem solving
Simple interest
Compound interest

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

Use calculators to find the logarithm of numbers

Discussions
Solving
Demonstrating
Explaining

Calculators 

KLB Mathematics
Book Three
Pg 89

Commercial arithmetic
Circles: Chords and tangents
Circles: Chords and tangents
Circles: Chords and tangents
Circles: Chords and tangents
Circles: Chords and tangents
Circles: Chords and tangents

Appreciation
Depreciation
Hire purchase
Income tax
P.A.Y.E
Length of an arc
Chords
Parallel chords
Equal chords
Intersecting chords
Intersecting chords

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

Calculate the appreciation value of items

Discussions
Solving
Demonstrating
Explaining

Calculators 
 ,calculator
income tax table ,calculator
Calculators s
Geometrical set,calculator
Geometrical set ,calculator

KLB Mathematics
Book Three
Pg 108

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
Contact of circles
Contact of circles
Problem solving
Angle in alternate segment
Angle in alternate segment
Circumscribed circle
Escribed circles

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

Construct a tangent to a circle

Discussions
Solving
Demonstrating
Explaining

Geometrical set ,calculator

KLB Mathematics
Book Three
Pg 139-140

Circles: Chords and tangents
Matrices
Matrices
Matrices
Matrices
Matrices
Matrices
Matrices
Matrices
Matrices
Matrices

Centroid
Orthocenter
Matrix representation and order of matrix
Addition of matrix
Subtraction of matrices
Combined addition and subtraction of matrices
Matrix multiplication
Matrix multiplication
Identity matrix
Determinant of a 2
Inverse of a 2
Inverse of a 2

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

Construct centroid

Discussions
Solving
Demonstrating
Explaining

Geometrical set ,calculator
Chart showing tabular data
Calculator
Calculators 

KLB Mathematics
Book Three
Pg 166

Matrices
Formulae and variations
Formulae and variations
Formulae and variations
Formulae and variations
Formulae and variations
Formulae and variations
Sequences and series
Sequences and series
Sequences and series

Solutions of simultaneous equations by matrix method
Problem solving
Formulae
Direct variation
Inverse variation
Partial variation
Joint variation
Joint variation
Sequences
Arithmetic sequences
Geometric sequence

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

Sequences and series
Vectors II
Vectors II
Vectors II
Vectors II
Vectors II
Vectors II
Vectors II
Vectors II

Arithmetic series
Geometric series
Geometric series
Coordinates in two dimensions
Coordinates in three dimensions
Column vectors
Position vector
Unit vectors
Unit vectors
Magnitude of a vector in three dimensions
Parallel vectors

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

Find the nth term of a given arithmetic series

Discussions
Solving
Demonstrating
Explaining

Wire mesh in 3 dimensions
calculators
Geoboard

KLB Mathematics
Book Three
Pg 214-215

Vectors II

Collinear points
Proportion division of a line
Proportion division of a line
Proportion division of a line
Ratio theorem
Ratio theorem
Mid-point
Ratio theorem
Ratio theorem
Applications of vectors
Applications of vectors

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

Binomial expansion
Probability
Probability
Probability
Probability
Probability
Probability

Binomial Expansion up to power four
Pascal
Pascal
Pascal
Applications to numerical cases
Applications to numerical cases
Experimental probability
Experimental probability
Range of probability measure
Probability space
Probability space
Combined events

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

Expand binomial function up to power four

Discussions
Solving
Demonstrating
Explaining

 calculators
Calculators
Calculators, charts

KLB Mathematics
Book Three
Pg 256

Probability
Compound proportions and rate of work
Compound proportions and rate of work
Compound proportions and rate of work
Compound proportions and rate of work

Combined events
Independent events
Independent events
Independent events
Tree diagrams
Tree diagrams
Tree diagrams
Compound proportions
Compound proportions
Proportional parts
Rates of work

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
Calculators 

KLB Mathematics
Book Three
Pg 273-274

Compound proportions and rate of work
Graphical methods
Graphical methods
Graphical methods
Graphical methods
Graphical methods
Graphical methods
Graphical methods
Graphical methods
Graphical methods
Graphical methods

Rates of work
Tables of given relations
Graphs of given relations
Graphical solution of cubic equations
Graphical solution of cubic equations
Average rates of change
Rate of change at an instant
Empirical graphs
Reduction of non-linear laws to linear form
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:

Calculate the rate of work

Discussions
Solving
Demonstrating
Explaining

Calculators 
Geoboard & graph books
Geoboard & graph bookss

KLB Mathematics
Book Three
Pg 295-296

Graphical methods
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation

Equation of a circle
Matrices of Transformation
Identifying Common Transformation Matrices
Finding the Matrix of a Transformation
Using the Unit Square Method
Successive Transformations
Matrix Multiplication for Combined Transformations
Single Matrix for Successive Transformations
Inverse of a Transformation
Properties of Inverse Transformations

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
Exercise books
-Manila paper
-Ruler
-Pencils
-String
-Chalk/markers
-Coloured pencils

KLB Mathematics
Book Three
Pg 325-326

Matrices and Transformation

Area Scale Factor and Determinant
Shear Transformations
Stretch Transformations
Combined Shear and Stretch Problems
Isometric and Non-isometric Transformations

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

-Establish relationship between area scale factor and determinant
-Calculate area scale factors for transformations
-Apply determinant to find area changes
-Solve problems involving area transformations

-Measure areas of objects and images using grid paper
-Calculate determinants and compare with area ratios
-Practice with various transformation types
-Verify the relationship: ASF =

det A
Exercise books
-Cardboard pieces
-Manila paper
-Ruler
-Rubber bands
-Chalk/markers
-Paper cutouts

Statistics II

Introduction to Advanced Statistics
Working Mean Concept
Mean Using Working Mean - Simple Data
Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean
Advanced Working Mean Techniques

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

-Review measures of central tendency from Form 2
-Identify limitations of simple mean calculations
-Understand need for advanced statistical methods
-Recognize patterns in large datasets

-Review mean, median, mode from previous work
-Discuss challenges with large numbers
-Examine real data from Kenya (population, rainfall)
-Q&A on statistical applications in daily life

Exercise books
-Manila paper
-Real data examples
-Chalk/markers
-Sample datasets
-Student data
-Community data
-Real datasets
-Economic data

KLB Secondary Mathematics Form 4, Pages 39-42

Statistics II

Introduction to Quartiles, Deciles, Percentiles
Calculating Quartiles for Ungrouped Data
Quartiles for Grouped Data
Deciles and Percentiles Calculations
Introduction to Cumulative Frequency
Drawing Cumulative Frequency Curves (Ogives)

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

-Define quartiles, deciles, and percentiles
-Understand how they divide data into parts
-Explain the relationship between these measures
-Identify their importance in data analysis

-Use physical demonstration with student heights
-Arrange 20 students by height to show quartiles
-Explain percentile ranks in exam results
-Discuss applications in grading systems

Exercise books
-Manila paper
-Student height data
-Measuring tape
-Test score data
-Chalk/markers
-Grade data
-Performance data
-Ruler
-Class data
-Pencils

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Reading Values from Ogives
Applications of Ogives
Introduction to Measures of Dispersion
Range and Interquartile Range
Mean Absolute Deviation
Introduction to Variance

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

-Read median from cumulative frequency curve
-Find quartiles using ogive
-Estimate any percentile from the curve
-Interpret readings in real-world context

-Demonstrate reading techniques on large ogive
-Practice finding median position (n/2)
-Read quartile positions systematically
-Students practice reading their own curves

Exercise books
-Manila paper
-Completed ogives
-Ruler
-Real problem datasets
-Comparative datasets
-Chalk/markers
-Student data
-Measuring tape
-Test score data
-Simple datasets

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II
Loci
Loci

Variance Using Alternative Formula
Standard Deviation Calculations
Standard Deviation for Grouped Data
Advanced Standard Deviation Techniques
Introduction to Loci
Basic Locus Concepts and Laws

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

-Apply the formula: σ² = (Σx²/n) - x̄²
-Use alternative variance formula efficiently
-Compare computational methods
-Solve variance problems for frequency data

-Demonstrate both variance formulas
-Show computational advantages of alternative formula
-Practice with frequency tables
-Students choose efficient method

Exercise books
-Manila paper
-Frequency data
-Chalk/markers
-Exam score data
-Agricultural data
-Transformation examples
-String
-Real objects

KLB Secondary Mathematics Form 4, Pages 65-70

Loci

Perpendicular Bisector Locus
Properties and Applications of Perpendicular Bisector
Locus of Points at Fixed Distance from a Point
Locus of Points at Fixed Distance from a Line
Angle Bisector Locus
Properties and Applications of Angle Bisector

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

-Define perpendicular bisector locus
-Construct perpendicular bisector using compass and ruler
-Prove that points on perpendicular bisector are equidistant from endpoints
-Apply perpendicular bisector to solve problems

-Construct perpendicular bisector on manila paper
-Measure distances to verify equidistance property
-Use folding method to find perpendicular bisector
-Practice with different line segments

Exercise books
-Manila paper
-Compass
-Ruler
-String
-Set square
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Constant Angle Locus
Advanced Constant Angle Constructions
Introduction to Intersecting Loci
Intersecting Circles and Lines
Triangle Centers Using Intersecting Loci
Complex Intersecting Loci Problems

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

-Understand constant angle locus concept
-Construct constant angle loci using arc method
-Apply circle theorems to constant angle problems
-Solve problems involving angles in semicircles

-Demonstrate constant angle using protractor
-Construct arc passing through two points
-Use angles in semicircle property
-Practice with different angle measures

Exercise books
-Manila paper
-Compass
-Protractor
-Ruler
-Real-world scenarios

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Introduction to Loci of Inequalities
Distance Inequality Loci
Combined Inequality Loci
Advanced Inequality Applications
Introduction to Loci Involving Chords

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

-Understand graphical representation of inequalities
-Identify regions satisfying inequality conditions
-Distinguish between boundary lines and regions
-Apply inequality loci to practical constraints

-Shade regions representing simple inequalities
-Use broken and solid lines appropriately
-Practice with distance inequalities
-Apply to real-world constraint problems

Exercise books
-Manila paper
-Ruler
-Colored pencils
-Compass
-Real problem data

KLB Secondary Mathematics Form 4, Pages 89-92

Loci
Trigonometry III
Trigonometry III
Trigonometry III

Chord-Based Constructions
Advanced Chord Problems
Integration of All Loci Types
Review of Basic Trigonometric Ratios
Deriving the Identity sin²θ + cos²θ = 1
Applications of sin²θ + cos²θ = 1

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

-Construct circles through three points using chords
-Find loci of chord midpoints
-Solve problems with intersecting chords
-Apply chord properties to geometric constructions

-Construct circles using three non-collinear points
-Find locus of midpoints of parallel chords
-Solve chord intersection problems
-Practice with chord-tangent relationships

Exercise books
-Manila paper
-Compass
-Ruler
-Rulers
-Calculators (if available)
-Unit circle diagrams
-Calculators
-Trigonometric tables
-Real-world examples

KLB Secondary Mathematics Form 4, Pages 92-94

Trigonometry III

Additional Trigonometric Identities
Introduction to Waves
Sine and Cosine Waves
Transformations of Sine Waves
Period Changes in Trigonometric Functions
Combined Amplitude and Period Transformations

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

-Derive and apply tan θ = sin θ/cos θ
-Use reciprocal ratios (sec, cosec, cot)
-Apply multiple identities in problem solving
-Verify trigonometric identities algebraically

-Demonstrate relationship between tan, sin, cos
-Introduce reciprocal ratios with examples
-Practice identity verification techniques
-Solve composite identity problems

Exercise books
-Manila paper
-Identity reference sheet
-Calculators
-String/rope
-Wave diagrams
-Rulers
-Graph paper (if available)
-Colored pencils
-Period calculation charts
-Transformation examples

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Phase Angles and Wave Shifts
General Trigonometric Functions
Cosine Wave Transformations
Introduction to Trigonometric Equations
Solving Basic Trigonometric Equations
Quadratic Trigonometric Equations

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

-Understand concept of phase angle
-Plot graphs of y = sin(x + θ) functions
-Identify horizontal shifts in wave patterns
-Apply phase differences to wave analysis

-Plot y = sin(x + 45°), y = sin(x - 30°)
-Demonstrate horizontal shifting of waves
-Compare leading and lagging waves
-Apply to electrical circuits or sound waves

Exercise books
-Manila paper
-Colored pencils
-Phase shift examples
-Rulers
-Complex function examples
-Temperature data
-Unit circle diagrams
-Trigonometric tables
-Calculators
-Solution worksheets
-Factoring techniques
-Substitution examples

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III
Three Dimensional Geometry
Three Dimensional Geometry
Three Dimensional Geometry

Equations Involving Multiple Angles
Using Graphs to Solve Trigonometric Equations
Trigonometric Equations with Identities
Introduction to 3D Concepts
Properties of Common Solids
Understanding Planes in 3D Space

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

-Solve equations like sin(2x) = 0.5
-Handle double and triple angle cases
-Find solutions for compound angle equations
-Apply to periodic motion problems

-Work through sin(2x) = 0.5 systematically
-Show relationship between 2x solutions and x solutions
-Practice with cos(3x) and tan(x/2) equations
-Apply to pendulum and rotation problems

Exercise books
-Manila paper
-Multiple angle examples
-Real applications
-Rulers
-Graphing examples
-Identity reference sheets
-Complex examples
-Cardboard boxes
-Real 3D objects
-Cardboard
-Scissors
-Tape/glue
-Books/boards
-Classroom examples

KLB Secondary Mathematics Form 4, Pages 109-112

Three Dimensional Geometry

Lines in 3D Space
Introduction to Projections
Angle Between Line and Plane - Concept
Calculating Angles Between Lines and Planes
Advanced Line-Plane Angle Problems
Introduction to Plane-Plane Angles

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

-Understand different types of lines in 3D
-Identify parallel, intersecting, and skew lines
-Recognize that skew lines don't intersect and aren't parallel
-Find examples of different line relationships

-Use rulers/sticks to demonstrate line relationships
-Show parallel lines using parallel rulers
-Demonstrate skew lines using classroom edges
-Practice identifying line relationships in models

Exercise books
-Rulers/sticks
-3D models
-Manila paper
-Light source
-Protractor
-Calculators
-3D problem diagrams
-Real scenarios
-Problem sets
-Books
-Folded paper

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Finding Angles Between Planes
Complex Plane-Plane Angle Problems
Practical Applications of Plane Angles
Understanding Skew Lines
Angle Between Skew Lines

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

-Construct perpendiculars to find plane angles
-Apply trigonometry to calculate dihedral angles
-Use right-angled triangles in plane intersection
-Solve angle problems in prisms and pyramids

-Work through construction method step-by-step
-Practice finding intersection lines first
-Calculate angles in triangular prisms
-Apply to roof and building angle problems

Exercise books
-Manila paper
-Protractor
-Building examples
-Complex 3D models
-Architecture examples
-Real engineering data
-Construction examples
-Rulers
-Building frameworks
-Translation examples

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry
Longitudes and Latitudes

Advanced Skew Line Problems
Distance Calculations in 3D
Volume and Surface Area Applications
Coordinate Geometry in 3D
Integration with Trigonometry
Introduction to Earth as a Sphere

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

-Solve complex skew line angle calculations
-Apply to engineering and architectural problems
-Use systematic approach for difficult problems
-Combine with other 3D geometric concepts

-Work through power line and cable problems
-Solve bridge and tower construction angles
-Practice with space frame structures
-Apply to antenna and communication tower problems

Exercise books
-Manila paper
-Engineering examples
-Structure diagrams
-Distance calculation charts
-3D coordinate examples
-Volume formulas
-Real containers
-3D coordinate grid
-Room corner reference
-Trigonometric tables
-Astronomy examples
-Globe/spherical ball
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 128-135

Longitudes and Latitudes

Great and Small Circles
Understanding Latitude
Properties of Latitude Lines
Understanding Longitude
Properties of Longitude Lines
Position of Places on Earth

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

-Define great circles and small circles on a sphere
-Identify properties of great and small circles
-Understand that great circles divide sphere into hemispheres
-Recognize examples of great and small circles on Earth

-Demonstrate great circles using globe and string
-Show that great circles pass through center
-Compare radii of great and small circles
-Identify equator as the largest circle

Exercise books
-Globe
-String
-Manila paper
-Tape/string
-Protractor
-Calculator
-World map
-Kenya map

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Latitude and Longitude Differences
Introduction to Distance Calculations
Distance Along Great Circles
Distance Along Small Circles (Parallels)
Shortest Distance Problems
Advanced Distance Calculations

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

-Calculate latitude differences between two points
-Calculate longitude differences between two points
-Understand angular differences on same and opposite sides
-Apply difference calculations to navigation problems

-Calculate difference between Nairobi and Cairo
-Practice with points on same and opposite sides
-Work through systematic calculation methods
-Apply to real navigation scenarios

Exercise books
-Manila paper
-Calculator
-Navigation examples
-Globe
-Conversion charts
-Real examples
-African city examples
-Flight path examples
-Surveying examples

KLB Secondary Mathematics Form 4, Pages 139-143

Longitudes and Latitudes
Linear Programming

Introduction to Time and Longitude
Local Time Calculations
Greenwich Mean Time (GMT)
Complex Time Problems
Speed Calculations
Introduction to Linear Programming

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

-Understand relationship between longitude and time
-Learn that Earth rotates 360° in 24 hours
-Calculate that 15° longitude = 1 hour time difference
-Understand concept of local time

-Demonstrate Earth's rotation using globe
-Show how sun position determines local time
-Calculate time differences for various longitudes
-Apply to understanding sunrise/sunset times

Exercise books
-Globe
-Light source
-Time zone examples
-Manila paper
-World time examples
-Calculator
-World map
-Time zone charts
-International examples
-Travel scenarios
-Navigation examples
-Real-life examples
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 156-161

Linear Programming

Forming Linear Inequalities from Word Problems
Types of Constraints
Objective Functions
Complete Problem Formulation
Introduction to Graphical Solution Method
Plotting Multiple Constraints

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

-Translate real-world constraints into mathematical inequalities
-Identify decision variables in word problems
-Form inequalities from resource limitations
-Use correct mathematical notation for constraints

-Work through farmer's crop planning problem
-Practice translating budget constraints into inequalities
-Form inequalities from production capacity limits
-Use Kenyan business examples for relevance

Exercise books
-Manila paper
-Local business examples
-Agricultural scenarios
-Industry examples
-School scenarios
-Business examples
-Production scenarios
-Complete examples
-Systematic templates
-Rulers
-Colored pencils
-Different colored pencils

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Properties of Feasible Regions
Introduction to Optimization
The Corner Point Method
The Iso-Profit/Iso-Cost Line Method
Comparing Solution Methods
Business Applications - Production Planning

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

-Understand that feasible region is convex
-Identify corner points (vertices) of feasible region
-Understand significance of corner points
-Calculate coordinates of corner points

-Identify all corner points of feasible region
-Calculate intersection points algebraically
-Verify corner points satisfy all constraints
-Understand why corner points are important

Exercise books
-Manila paper
-Calculators
-Algebraic methods
-Evaluation tables
-Evaluation templates
-Systematic approach
-Rulers
-Sliding technique
-Method comparison
-Verification examples
-Manufacturing examples
-Kenyan industry data

KLB Secondary Mathematics Form 4, Pages 166-172

Differentiation

Introduction to Rate of Change
Average Rate of Change
Instantaneous Rate of Change
Gradient of Curves at Points
Introduction to Delta Notation

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

-Understand concept of rate of change in daily life
-Distinguish between average and instantaneous rates
-Identify examples of changing quantities
-Connect rate of change to gradient concepts

-Discuss speed as rate of change of distance
-Examine population growth rates
-Analyze temperature change throughout the day
-Connect to gradients of lines from coordinate geometry

Exercise books
-Manila paper
-Real-world examples
-Graph examples
-Calculators
-Graph paper
-Tangent demonstrations
-Motion examples
-Rulers
-Curve examples
-Delta notation examples
-Symbol practice

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

The Limiting Process
Introduction to Derivatives
Derivative of Linear Functions
Derivative of y = x^n (Basic Powers)
Derivative of Constant Functions
Derivative of Coefficient Functions

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

-Understand concept of limit in differentiation
-Apply "as Δx approaches zero" reasoning
-Use limiting process to find exact derivatives
-Practice systematic limiting calculations

-Demonstrate limiting process with numerical examples
-Show chord approaching tangent as Δx → 0
-Calculate limits using table of values
-Practice systematic limit evaluation

Exercise books
-Manila paper
-Limit tables
-Systematic examples
-Derivative notation
-Function examples
-Linear function examples
-Verification methods
-Power rule examples
-First principles verification
-Constant function graphs
-Geometric explanations
-Coefficient examples
-Rule combinations

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

Derivative of Polynomial Functions
Applications to Tangent Lines
Applications to Normal Lines
Introduction to Stationary Points
Types of Stationary Points
Finding and Classifying Stationary Points

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

-Find derivatives of polynomial functions
-Apply term-by-term differentiation
-Practice with various polynomial degrees
-Verify results using first principles

-Differentiate y = x³ + 2x² - 5x + 7
-Apply rule to each term separately
-Practice with various polynomial types
-Check results using definition for simple cases

Exercise books
-Manila paper
-Polynomial examples
-Term-by-term method
-Tangent line examples
-Point-slope applications
-Normal line examples
-Perpendicular concepts
-Curve sketches
-Stationary point examples
-Sign analysis charts
-Classification examples
-Systematic templates
-Complete examples

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Curve Sketching Using Derivatives
Introduction to Kinematics Applications
Acceleration as Second Derivative
Motion Problems and Applications
Introduction to Optimization
Geometric Optimization Problems

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

-Use derivatives to sketch accurate curves
-Identify key features: intercepts, stationary points
-Apply systematic curve sketching method
-Combine algebraic and graphical analysis

-Sketch y = x³ - 3x² + 2 using derivatives
-Find intercepts, stationary points, and behavior
-Use systematic curve sketching approach
-Verify sketches using derivative information

Exercise books
-Manila paper
-Curve sketching templates
-Systematic method
-Motion examples
-Kinematics applications
-Second derivative examples
-Motion analysis
-Complete motion examples
-Real scenarios
-Optimization examples
-Real applications
-Geometric examples
-Design applications

KLB Secondary Mathematics Form 4, Pages 195-197

Differentiation
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations
Matrices and Transformations

Business and Economic Applications
Advanced Optimization Problems
Transformation on a Cartesian plane
Basic Transformation Matrices
Identification of transformation matrix
Two Successive Transformations
Complex Successive Transformations
Single matrix of transformation for successive transformations
Matrix Multiplication Properties
Identity Matrix and Transformation

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

-Apply derivatives to profit and cost functions
-Find marginal cost and marginal revenue
-Use calculus for business optimization
-Apply to Kenyan business scenarios

-Find maximum profit using calculus
-Calculate marginal cost and revenue
-Apply to agricultural and manufacturing examples
-Use derivatives for business decision-making

Exercise books
-Manila paper
-Business examples
-Economic applications
-Complex examples
-Engineering applications
Square boards
-Peg boards
-Graph papers
-Mirrors
-Rulers
-Protractors
-Calculators
Graph papers
-Exercise books
-Matrix examples
-Colored pencils
Calculators
-Matrix multiplication charts
-Matrix worksheets
-Formula sheets

KLB Secondary Mathematics Form 4, Pages 201-204

Matrices and Transformations
Integration
Integration
Integration
Integration
Integration
Integration
Integration
Integration
Integration

Inverse of a matrix
Determinant and Area Scale Factor
Area scale factor and determinant relationship
Shear Transformation
Stretch Transformation and Review
Introduction to Reverse Differentiation
Basic Integration Rules - Power Functions
Integration of Polynomial Functions
Finding Particular Solutions
Introduction to Definite Integrals
Evaluating Definite Integrals
Area Under Curves - Single Functions
Areas Below X-axis and Mixed Regions
Area Between Two Curves

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

-Calculate inverse of 2×2 matrix using formula
-Understand that AA⁻¹ = A⁻¹A = I
-Determine when inverse exists (det ≠ 0)
-Apply inverse matrices to find inverse transformations

-Formula for 2×2 matrix inverse derivation
-Multiple worked examples with different matrices
-Practice identifying singular matrices (det = 0)
-Finding inverse transformations using inverse matrices
-Problem-solving exercises Ex 1.5

Calculators
-Exercise books
-Formula sheets
-Graph papers
-Solve problems involving area changes under transformations
-Area calculation tools
Square boards
-Flexible materials
-Rulers
-Calculators
Graph papers
-Elastic materials
-Comparison charts
-Review materials
-Differentiation charts
-Function examples
-Power rule charts
-Algebraic worksheets
-Polynomial examples
-Curve examples
-Geometric models
-Integration notation charts
-Step-by-step worksheets
-Evaluation charts
-Curve sketching tools
-Colored pencils
-Area grids
-Colored materials
-Equation solving aids

KLB Secondary Mathematics Form 4, Pages 14-15, 24-26