Differentiation

Introduction to Rate of Change

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

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Average Rate of Change
Instantaneous Rate of Change

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

-Calculate average rate of change between two points
-Use formula: average rate = Δy/Δx
-Apply to distance-time and other practical graphs
-Understand limitations of average rate calculations

-Calculate average speed between two time points
-Find average rate of population change
-Use coordinate points to find average rates
-Compare average rates over different intervals

Exercise books
-Manila paper
-Calculators
-Graph paper
-Tangent demonstrations
-Motion examples

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Gradient of Curves at Points
Introduction to Delta Notation

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

-Find gradient of curve at specific points
-Use tangent line method for gradient estimation
-Apply limiting process to find exact gradients
-Practice with various curve types

-Draw tangent lines to curves on manila paper
-Estimate gradients using tangent slopes
-Use the limiting approach with chord sequences
-Practice with parabolas and other curves

Exercise books
-Manila paper
-Rulers
-Curve examples
-Delta notation examples
-Symbol practice

KLB Secondary Mathematics Form 4, Pages 178-182

Differentiation

The Limiting Process
Introduction to Derivatives

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

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

Derivative of Linear Functions
Derivative of y = x^n (Basic Powers)

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

-Find derivatives of linear functions y = mx + c
-Understand that derivative of linear function is constant
-Apply to straight line gradient problems
-Verify using limiting process

-Find derivative of y = 3x + 2 using definition
-Show that derivative equals the gradient
-Practice with various linear functions
-Verify results using first principles

Exercise books
-Manila paper
-Linear function examples
-Verification methods
-Power rule examples
-First principles verification

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Constant Functions
Derivative of Coefficient Functions
Derivative of Polynomial Functions

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

-Understand that derivative of constant is zero
-Apply to functions like y = 5, y = -3
-Explain geometric meaning of zero derivative
-Combine with other differentiation rules

-Show that horizontal lines have zero gradient
-Find derivatives of constant functions
-Explain why rate of change of constant is zero
-Apply to mixed functions with constants

Exercise books
-Manila paper
-Constant function graphs
-Geometric explanations
-Coefficient examples
-Rule combinations
-Polynomial examples
-Term-by-term method

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Applications to Tangent Lines
Applications to Normal Lines

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

-Find equations of tangent lines to curves
-Use derivatives to find tangent gradients
-Apply point-slope form for tangent equations
-Solve problems involving tangent lines

-Find tangent to y = x² at point (2, 4)
-Use derivative to get gradient at specific point
-Apply y - y₁ = m(x - x₁) formula
-Practice with various curves and points

Exercise books
-Manila paper
-Tangent line examples
-Point-slope applications
-Normal line examples
-Perpendicular concepts

KLB Secondary Mathematics Form 4, Pages 187-189

Differentiation

Introduction to Stationary Points
Types of Stationary Points

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

-Define stationary points as points where dy/dx = 0
-Identify different types of stationary points
-Understand geometric meaning of zero gradient
-Find stationary points by solving dy/dx = 0

-Show horizontal tangents at stationary points
-Find stationary points of y = x² - 4x + 3
-Identify maximum, minimum, and inflection points
-Practice finding where dy/dx = 0

Exercise books
-Manila paper
-Curve sketches
-Stationary point examples
-Sign analysis charts
-Classification examples

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Finding and Classifying Stationary Points
Curve Sketching Using Derivatives

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

-Solve dy/dx = 0 to find stationary points
-Apply systematic classification method
-Use organized approach for point analysis
-Practice with polynomial functions

-Work through complete stationary point analysis
-Use systematic gradient sign testing
-Create organized solution format
-Practice with cubic and quartic functions

Exercise books
-Manila paper
-Systematic templates
-Complete examples
-Curve sketching templates
-Systematic method

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Introduction to Kinematics Applications
Acceleration as Second Derivative

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

-Apply derivatives to displacement-time relationships
-Understand velocity as first derivative of displacement
-Find velocity functions from displacement functions
-Apply to motion problems

-Find velocity from s = t³ - 2t² + 5t
-Apply v = ds/dt to motion problems
-Practice with various displacement functions
-Connect to real-world motion scenarios

Exercise books
-Manila paper
-Motion examples
-Kinematics applications
-Second derivative examples
-Motion analysis

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Motion Problems and Applications
Introduction to Optimization

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

-Solve complete motion analysis problems
-Find displacement, velocity, acceleration relationships
-Apply to real-world motion scenarios
-Use derivatives for motion optimization

-Analyze complete motion of falling object
-Find when particle changes direction
-Calculate maximum height in projectile motion
-Apply to vehicle motion problems

Exercise books
-Manila paper
-Complete motion examples
-Real scenarios
-Optimization examples
-Real applications

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Geometric Optimization Problems
Business and Economic Applications
Advanced Optimization Problems

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

-Apply calculus to geometric optimization
-Find maximum areas and minimum perimeters
-Use derivatives for shape optimization
-Apply to construction and design problems

-Find dimensions for maximum area enclosure
-Optimize container volumes and surface areas
-Apply to architectural design problems
-Practice with various geometric constraints

Exercise books
-Manila paper
-Geometric examples
-Design applications
-Business examples
-Economic applications
-Complex examples
-Engineering applications

KLB Secondary Mathematics Form 4, Pages 201-204

Integration

Introduction to Reverse Differentiation
Basic Integration Rules - Power Functions
Integration of Polynomial Functions
Finding Particular Solutions

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

-Define integration as reverse of differentiation
-Understand the concept of antiderivative
-Recognize the relationship between gradient functions and original functions
-Apply reverse thinking to simple differentiation examples

-Q/A review on differentiation formulas and rules
-Demonstration of reverse process using simple examples
-Working backwards from derivatives to find original functions
-Discussion on why multiple functions can have same derivative
-Introduction to integration symbol ∫

Graph papers
-Differentiation charts
-Exercise books
-Function examples
Calculators
-Graph papers
-Power rule charts
-Algebraic worksheets
-Polynomial examples
-Calculators
-Curve examples

KLB Secondary Mathematics Form 4, Pages 221-223

Integration

Introduction to Definite Integrals
Evaluating Definite Integrals
Area Under Curves - Single Functions
Areas Below X-axis and Mixed Regions

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

-Define definite integrals using limit notation
-Understand the difference between definite and indefinite integrals
-Learn proper notation: ∫ₐᵇ f(x)dx
-Understand geometric meaning as area under curve

-Introduction to definite integral concept and notation
-Geometric interpretation using simple curves
-Comparison between ∫f(x)dx and ∫ₐᵇf(x)dx
-Discussion on limits of integration
-Basic examples with simple functions

Graph papers
-Geometric models
-Integration notation charts
-Calculators
Calculators
-Step-by-step worksheets
-Exercise books
-Evaluation charts
-Curve sketching tools
-Colored pencils
-Area grids
-Curve examples
-Colored materials

KLB Secondary Mathematics Form 4, Pages 226-228

Integration
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation
Matrices and Transformation

Area Between Two Curves
Matrices of Transformation
Identifying Common Transformation Matrices
Finding the Matrix of a Transformation
Using the Unit Square Method

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

-Calculate area between two intersecting curves
-Find intersection points as integration limits
-Apply method: Area = ∫ₐᵇ [f(x) - g(x)]dx
-Handle multiple intersection scenarios

-Method for finding curve intersection points
-Working examples: area between y = x² and y = x
-Step-by-step process for area between curves
-Practice with linear and quadratic function pairs
-Advanced examples with multiple intersections

Graph papers
-Equation solving aids
-Calculators
-Colored pencils
-Exercise books
Exercise books
-Manila paper
-Ruler
-Pencils
-String
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 233-235

Matrices and Transformation

Successive Transformations
Matrix Multiplication for Combined Transformations
Single Matrix for Successive Transformations
Inverse of a Transformation

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

-Understand the concept of successive transformations
-Apply transformations in correct order
-Recognize that order matters in matrix multiplication
-Perform multiple transformations step by step

-Demonstrate successive transformations with paper cutouts
-Practice applying transformations in sequence
-Compare results when order is changed
-Work through step-by-step examples

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

KLB Secondary Mathematics Form 4, Pages 16-24

Matrices and Transformation

Properties of Inverse Transformations
Area Scale Factor and Determinant
Shear Transformations

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

-Calculate determinants of 2×2 matrices
-Use determinant formula for matrix inverses
-Identify when inverse matrices exist
-Apply inverse matrix formula efficiently

-Practice determinant calculations on chalkboard
-Use formula: A⁻¹ = (1/det A) × adj A
-Identify singular matrices (det = 0)
-Solve systems using inverse matrices

Exercise books
-Manila paper
-Ruler
-Chalk/markers
det A
-Cardboard pieces

KLB Secondary Mathematics Form 4, Pages 24-26

Matrices and Transformation

Stretch Transformations
Combined Shear and Stretch Problems

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

-Define stretch transformation and scale factors
-Distinguish between one-way and two-way stretches
-Construct matrices for stretch transformations
-Apply stretch transformations to solve problems

-Demonstrate stretch using rubber bands and paper
-Practice with x-axis and y-axis invariant stretches
-Construct stretch matrices systematically
-Compare stretches with enlargements

Exercise books
-Rubber bands
-Manila paper
-Ruler
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 28-34

Matrices and Transformation
Statistics II

Isometric and Non-isometric Transformations
Introduction to Advanced Statistics

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

-Distinguish between isometric and non-isometric transformations
-Classify transformations based on shape and size preservation
-Identify isometric transformations from matrices
-Apply classification to solve problems

-Compare congruent and non-congruent images using cutouts
-Classify transformations systematically
-Practice identification from matrices
-Discuss real-world applications of each type

Exercise books
-Paper cutouts
-Manila paper
-Ruler
-Real data examples
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 35-38

Statistics II

Working Mean Concept
Mean Using Working Mean - Simple Data

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

-Define working mean (assumed mean)
-Explain why working mean simplifies calculations
-Identify appropriate working mean values
-Apply working mean to reduce calculation errors

-Demonstrate calculation difficulties with large numbers
-Show how working mean simplifies arithmetic
-Practice selecting suitable working means
-Compare results with and without working mean

Exercise books
-Manila paper
-Sample datasets
-Chalk/markers
-Student data

KLB Secondary Mathematics Form 4, Pages 39-42

Statistics II

Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean

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

-Calculate mean using working mean for frequency data
-Apply working mean to discrete frequency distributions
-Use the formula with frequencies correctly
-Solve real-world problems with frequency data

-Demonstrate with family size data from local community
-Practice calculating fx and fd systematically
-Work through examples step-by-step
-Students practice with their own collected data

Exercise books
-Manila paper
-Community data
-Chalk/markers
-Real datasets

KLB Secondary Mathematics Form 4, Pages 42-48

Statistics II

Advanced Working Mean Techniques
Introduction to Quartiles, Deciles, Percentiles

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

-Apply coding techniques with working mean
-Divide by class width to simplify further
-Use transformation methods efficiently
-Solve complex grouped data problems

-Demonstrate coding method on chalkboard
-Show how dividing by class width helps
-Practice reverse calculations to get original mean
-Work with economic data from Kenya

Exercise books
-Manila paper
-Economic data
-Chalk/markers
-Student height data
-Measuring tape

KLB Secondary Mathematics Form 4, Pages 42-48

Statistics II

Calculating Quartiles for Ungrouped Data
Quartiles for Grouped Data
Deciles and Percentiles Calculations

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

-Find lower quartile, median, upper quartile for raw data
-Apply the position formulas correctly
-Arrange data in ascending order systematically
-Interpret quartile values in context

-Practice with test scores from the class
-Arrange data systematically on chalkboard
-Calculate Q1, Q2, Q3 step by step
-Students work with their own datasets

Exercise books
-Manila paper
-Test score data
-Chalk/markers
-Grade data
-Performance data

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Introduction to Cumulative Frequency
Drawing Cumulative Frequency Curves (Ogives)

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

-Construct cumulative frequency tables
-Understand "less than" cumulative frequencies
-Plot cumulative frequency against class boundaries
-Identify the characteristic S-shape of ogives

-Create cumulative frequency table with class data
-Plot points on manila paper grid
-Join points to form smooth curve
-Discuss properties of ogive curves

Exercise books
-Manila paper
-Ruler
-Class data
-Pencils

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II

Reading Values from Ogives
Applications of Ogives

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

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II

Introduction to Measures of Dispersion
Range and Interquartile Range

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

-Define dispersion and its importance
-Understand limitations of central tendency alone
-Compare datasets with same mean but different spread
-Identify different measures of dispersion

-Compare test scores of two classes with same mean
-Show how different spreads affect interpretation
-Discuss variability in real-world data
-Introduce range as simplest measure

Exercise books
-Manila paper
-Comparative datasets
-Chalk/markers
-Student data
-Measuring tape

KLB Secondary Mathematics Form 4, Pages 60-65

Statistics II

Mean Absolute Deviation
Introduction to Variance

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

-Calculate mean absolute deviation
-Use absolute values correctly in calculations
-Understand concept of average distance from mean
-Apply MAD to compare variability in datasets

-Calculate MAD for class test scores
-Practice with absolute value calculations
-Compare MAD values for different subjects
-Interpret MAD in context of data spread

Exercise books
-Manila paper
-Test score data
-Chalk/markers
-Simple datasets

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II

Variance Using Alternative Formula
Standard Deviation Calculations
Standard Deviation for Grouped Data

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

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II
Longitudes and Latitudes

Advanced Standard Deviation Techniques
Introduction to Earth as a Sphere

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

-Apply transformation properties of standard deviation
-Use coding with class width division
-Solve problems with multiple transformations
-Verify results using different methods

-Demonstrate coding transformations
-Show how SD changes with data transformations
-Practice reverse calculations
-Verify using alternative methods

Exercise books
-Manila paper
-Transformation examples
-Chalk/markers
-Globe/spherical ball

KLB Secondary Mathematics Form 4, Pages 65-70

Longitudes and Latitudes

Great and Small Circles
Understanding Latitude

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

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Properties of Latitude Lines
Understanding Longitude

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

-Understand that latitude lines are parallel circles
-Recognize that latitude lines are small circles (except equator)
-Calculate radii of latitude circles using trigonometry
-Apply formula r = R cos θ for latitude circle radius

-Demonstrate parallel nature of latitude lines
-Calculate radius of latitude circle at 60°N
-Show relationship between latitude and circle size
-Use trigonometry to find circle radii

Exercise books
-Globe
-Calculator
-Manila paper
-String
-World map

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Properties of Longitude Lines
Position of Places on Earth

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

-Understand that longitude lines are great circles
-Recognize that all longitude lines pass through poles
-Understand that longitude lines converge at poles
-Identify that opposite longitudes differ by 180°

-Show longitude lines converging at poles
-Demonstrate that longitude lines are great circles
-Find opposite longitude positions
-Compare longitude and latitude line properties

Exercise books
-Globe
-String
-Manila paper
-World map
-Kenya map

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Latitude and Longitude Differences
Introduction to 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

KLB Secondary Mathematics Form 4, Pages 139-143

Longitudes and Latitudes

Distance Along Great Circles
Distance Along Small Circles (Parallels)
Shortest Distance Problems

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

-Calculate distances along meridians (longitude lines)
-Calculate distances along equator
-Apply formula: distance = angle × 60 nm
-Convert distances between nautical miles and kilometers

-Calculate distance from Nairobi to Cairo (same longitude)
-Find distance between two points on equator
-Practice conversion between units
-Apply to real geographical examples

Exercise books
-Manila paper
-Calculator
-Real examples
-African city examples
-Flight path examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Advanced Distance Calculations
Introduction to Time and Longitude

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

-Solve complex distance problems with multiple steps
-Calculate distances involving multiple coordinate differences
-Apply to surveying and mapping problems
-Use systematic approaches for difficult calculations

-Work through complex multi-step distance problems
-Apply to surveying land boundaries
-Calculate perimeters of geographical regions
-Practice with examination-style problems

Exercise books
-Manila paper
-Calculator
-Surveying examples
-Globe
-Light source
-Time zone examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Local Time Calculations
Greenwich Mean Time (GMT)

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

-Calculate local time differences between places
-Understand that places east are ahead in time
-Apply rule: 4 minutes per degree of longitude
-Solve time problems involving East-West positions

-Calculate time difference between Nairobi and London
-Practice with cities at various longitudes
-Apply East-ahead, West-behind rule consistently
-Work through systematic time calculation method

Exercise books
-Manila paper
-World time examples
-Calculator
-World map
-Time zone charts

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Complex Time Problems
Speed Calculations

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

-Solve time problems involving date changes
-Handle calculations crossing International Date Line
-Apply to travel and communication scenarios
-Calculate arrival times for international flights

-Work through International Date Line problems
-Calculate flight arrival times across time zones
-Apply to international communication timing
-Practice with business meeting scheduling

Exercise books
-Manila paper
-International examples
-Travel scenarios
-Calculator
-Navigation examples

KLB Secondary Mathematics Form 4, Pages 156-161

Trigonometry III

Review of Basic Trigonometric Ratios
Deriving the Identity sin²θ + cos²θ = 1

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

-Recall sin, cos, tan from right-angled triangles
-Apply Pythagoras theorem with trigonometry
-Use basic trigonometric ratios to solve problems
-Establish relationship between trigonometric ratios

-Review right-angled triangle ratios from Form 2
-Practice calculating unknown sides and angles
-Work through examples using SOH-CAH-TOA
-Solve simple practical problems

Exercise books
-Manila paper
-Rulers
-Calculators (if available)
-Unit circle diagrams
-Calculators

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Applications of sin²θ + cos²θ = 1
Additional Trigonometric Identities
Introduction to Waves

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

-Solve problems using the fundamental identity
-Find missing trigonometric ratios given one ratio
-Apply identity to simplify trigonometric expressions
-Use identity in geometric problem solving

-Work through examples finding cos when sin is given
-Practice simplifying complex trigonometric expressions
-Solve problems involving unknown angles
-Apply to real-world navigation problems

Exercise books
-Manila paper
-Trigonometric tables
-Real-world examples
-Identity reference sheet
-Calculators
-String/rope
-Wave diagrams

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Sine and Cosine Waves
Transformations of Sine Waves

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

-Plot graphs of y = sin x and y = cos x
-Identify amplitude and period of basic functions
-Compare sine and cosine wave patterns
-Read values from trigonometric graphs

-Plot sin x and cos x on same axes using manila paper
-Mark key points (0°, 90°, 180°, 270°, 360°)
-Measure and compare wave characteristics
-Practice reading values from completed graphs

Exercise books
-Manila paper
-Rulers
-Graph paper (if available)
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Period Changes in Trigonometric Functions
Combined Amplitude and Period Transformations

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

-Understand effect of coefficient on period
-Plot graphs of y = sin(bx) for different values of b
-Calculate periods of transformed functions
-Apply period changes to cyclical phenomena

-Plot y = sin(2x), y = sin(x/2) on manila paper
-Compare periods with y = sin x
-Calculate period using formula 360°/b
-Apply to frequency and musical pitch examples

Exercise books
-Manila paper
-Rulers
-Period calculation charts
-Transformation examples

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Phase Angles and Wave Shifts
General Trigonometric Functions

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

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Cosine Wave Transformations
Introduction to Trigonometric Equations

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

-Apply transformations to cosine functions
-Plot y = a cos(bx + c) functions
-Compare cosine and sine transformations
-Use cosine functions in modeling

-Plot various cosine transformations on manila paper
-Compare with equivalent sine transformations
-Practice identifying cosine wave parameters
-Model temperature variations using cosine

Exercise books
-Manila paper
-Rulers
-Temperature data
-Unit circle diagrams
-Trigonometric tables

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Solving Basic Trigonometric Equations
Quadratic Trigonometric Equations

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

-Solve equations of form sin x = k, cos x = k
-Find all solutions in specified ranges
-Use symmetry properties of trigonometric functions
-Apply inverse trigonometric functions

-Work through sin x = 0.6 step by step
-Find all solutions between 0° and 360°
-Use calculator to find inverse trigonometric values
-Practice with multiple basic equations

Exercise books
-Manila paper
-Calculators
-Solution worksheets
-Factoring techniques
-Substitution examples

KLB Secondary Mathematics Form 4, Pages 109-112

Trigonometry III

Equations Involving Multiple Angles
Using Graphs to Solve Trigonometric Equations
Trigonometric Equations with Identities

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

KLB Secondary Mathematics Form 4, Pages 109-112

Three Dimensional Geometry

Introduction to 3D Concepts
Properties of Common Solids

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

-Distinguish between 1D, 2D, and 3D objects
-Identify vertices, edges, and faces of 3D solids
-Understand concepts of points, lines, and planes in space
-Recognize real-world 3D objects and their properties

-Use classroom objects to demonstrate dimensions
-Count vertices, edges, faces of cardboard models
-Identify 3D shapes in school environment
-Discuss difference between area and volume

Exercise books
-Cardboard boxes
-Manila paper
-Real 3D objects
-Cardboard
-Scissors
-Tape/glue

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Understanding Planes in 3D Space
Lines in 3D Space

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

-Define planes and their properties in 3D
-Identify parallel and intersecting planes
-Understand that planes extend infinitely
-Recognize planes formed by faces of solids

-Use books/boards to represent planes
-Demonstrate parallel planes using multiple books
-Show intersecting planes using book corners
-Identify planes in classroom architecture

Exercise books
-Manila paper
-Books/boards
-Classroom examples
-Rulers/sticks
-3D models

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Introduction to Projections
Angle Between Line and Plane - Concept

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

-Understand concept of projection in 3D geometry
-Find projections of points onto planes
-Identify foot of perpendicular from point to plane
-Apply projection concept to shadow problems

-Use light source to create shadows (projections)
-Drop perpendiculars from corners to floor
-Identify projections in architectural drawings
-Practice finding feet of perpendiculars

Exercise books
-Manila paper
-Light source
-3D models
-Protractor
-Rulers/sticks

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Calculating Angles Between Lines and Planes
Advanced Line-Plane Angle Problems

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

-Calculate angles using right-angled triangles
-Apply trigonometry to 3D angle problems
-Use Pythagoras theorem in 3D contexts
-Solve problems involving cuboids and pyramids

-Work through step-by-step calculations
-Use trigonometric ratios in 3D problems
-Practice with cuboid diagonal problems
-Apply to pyramid and cone angle calculations

Exercise books
-Manila paper
-Calculators
-3D problem diagrams
-Real scenarios
-Problem sets

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Introduction to Plane-Plane Angles
Finding Angles Between Planes
Complex Plane-Plane Angle Problems

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

-Define angle between two planes
-Understand concept of dihedral angles
-Identify line of intersection of two planes
-Find perpendiculars to intersection line

-Use two books to demonstrate intersecting planes
-Show how planes meet along an edge
-Identify dihedral angles in classroom
-Demonstrate using folded paper

Exercise books
-Manila paper
-Books
-Folded paper
-Protractor
-Building examples
-Complex 3D models
-Architecture examples

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Practical Applications of Plane Angles
Understanding Skew Lines

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

-Apply plane angles to real-world problems
-Solve engineering and construction problems
-Calculate angles in roof structures
-Use in navigation and surveying contexts

-Calculate roof pitch angles
-Solve bridge construction angle problems
-Apply to mining and tunnel excavation
-Use in aerial navigation problems

Exercise books
-Manila paper
-Real engineering data
-Construction examples
-Rulers
-Building frameworks

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Angle Between Skew Lines
Advanced Skew Line Problems

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

-Understand how to find angle between skew lines
-Apply translation method for skew line angles
-Use parallel line properties in 3D
-Calculate angles by creating intersecting lines

-Demonstrate translation method using rulers
-Translate one line to intersect the other
-Practice with cuboid edge problems
-Apply to framework and structure problems

Exercise books
-Manila paper
-Rulers
-Translation examples
-Engineering examples
-Structure diagrams

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Distance Calculations in 3D
Volume and Surface Area Applications

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

-Calculate distances between points in 3D
-Find shortest distances between lines and planes
-Apply 3D Pythagoras theorem
-Use distance formula in coordinate geometry

-Calculate space diagonals in cuboids
-Find distances from points to planes
-Apply 3D distance formula systematically
-Solve minimum distance problems

Exercise books
-Manila paper
-Distance calculation charts
-3D coordinate examples
-Volume formulas
-Real containers

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Coordinate Geometry in 3D
Integration with Trigonometry

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

-Extend coordinate geometry to three dimensions
-Plot points in 3D coordinate system
-Calculate distances and angles using coordinates
-Apply vector concepts to 3D problems

-Set up 3D coordinate system using room corners
-Plot simple points in 3D space
-Calculate distances using coordinate formula
-Introduce basic vector concepts

Exercise books
-Manila paper
-3D coordinate grid
-Room corner reference
-Trigonometric tables
-Astronomy examples

KLB Secondary Mathematics Form 4, Pages 115-135

Linear Programming

Introduction to Linear Programming
Forming Linear Inequalities from Word Problems

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

-Understand the concept of optimization in real life
-Identify decision variables in practical situations
-Recognize constraints and objective functions
-Understand applications of linear programming

-Discuss resource allocation problems in daily life
-Identify optimization scenarios in business and farming
-Introduce decision-making with limited resources
-Use simple examples from student experiences

Exercise books
-Manila paper
-Real-life examples
-Chalk/markers
-Local business examples
-Agricultural scenarios

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Types of Constraints
Objective Functions
Complete Problem Formulation

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

-Identify non-negativity constraints
-Understand resource constraints and their implications
-Form demand and supply constraints
-Apply constraint formation to various industries

-Practice with non-negativity constraints (x ≥ 0, y ≥ 0)
-Form material and labor constraints
-Apply to manufacturing and service industries
-Use school resource allocation examples

Exercise books
-Manila paper
-Industry examples
-School scenarios
-Business examples
-Production scenarios
-Complete examples
-Systematic templates

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Introduction to Graphical Solution Method
Plotting Multiple Constraints

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

-Understand graphical representation of inequalities
-Plot constraint lines on coordinate plane
-Identify feasible and infeasible regions
-Understand boundary lines and their significance

-Plot simple inequality x + y ≤ 10 on graph
-Shade feasible regions systematically
-Distinguish between ≤ and < inequalities
-Practice with multiple examples on manila paper

Exercise books
-Manila paper
-Rulers
-Colored pencils
-Different colored pencils

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

Properties of Feasible Regions
Introduction to Optimization

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

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

The Corner Point Method
The Iso-Profit/Iso-Cost Line Method

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

-Apply systematic corner point evaluation method
-Create organized tables for corner point analysis
-Identify optimal corner point efficiently
-Handle cases with multiple optimal solutions

-Create systematic evaluation table
-Work through corner point method step-by-step
-Practice with various objective functions
-Identify and handle tie cases

Exercise books
-Manila paper
-Evaluation templates
-Systematic approach
-Rulers
-Sliding technique

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming
Matrices and Transformations

Comparing Solution Methods
Business Applications - Production Planning
Transformation on a Cartesian plane

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

-Compare corner point and iso-line methods
-Understand when each method is most efficient
-Verify solutions using both methods
-Choose appropriate method for different problems

-Solve same problem using both methods
-Compare efficiency and accuracy of methods
-Practice method selection based on problem type
-Verify consistency of results

Exercise books
-Manila paper
-Method comparison
-Verification examples
-Manufacturing examples
-Kenyan industry data
Square boards
-Peg boards
-Graph papers
-Mirrors
-Rulers

KLB Secondary Mathematics Form 4, Pages 172-176

Matrices and Transformations

Basic Transformation Matrices
Identification of transformation matrix
Two Successive Transformations
Complex Successive Transformations
Single matrix of transformation for successive transformations

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

-Determine matrices for reflection in x-axis, y-axis, and y=x
-Find matrices for 90°, 180°, 270° rotations about origin
-Calculate translation using column vectors
-Apply enlargement matrices with different scale factors

-Step-by-step derivation of reflection matrices
-Demonstration of rotation matrices using unit square
-Working examples with translation vectors
-Practice calculating images under each transformation
-Group exercises on matrix identification

Square boards
-Peg boards
-Graph papers
-Protractors
-Calculators
Graph papers
-Exercise books
-Matrix examples
-Colored pencils
-Rulers
Calculators
-Matrix multiplication charts

KLB Secondary Mathematics Form 4, Pages 1-16

Matrices and Transformations

Matrix Multiplication Properties
Identity Matrix and Transformation
Inverse of a matrix

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

-Understand that matrix multiplication is not commutative (AB ≠ BA)
-Apply associative property: (AB)C = A(BC)
-Calculate products of 2×2 matrices accurately
-Solve problems involving multiple matrix operations

-Detailed demonstration showing AB ≠ BA with examples
-Practice calculations with various matrix pairs
-Associativity verification with three matrices
-Problem-solving session with complex matrix products
-Individual practice from textbook exercises

Calculators
-Exercise books
-Matrix worksheets
-Formula sheets
-Graph papers
-Matrix examples

KLB Secondary Mathematics Form 4, Pages 21-24

Matrices and Transformations

Determinant and Area Scale Factor
Area scale factor and determinant relationship
Shear Transformation
Stretch Transformation and Review

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

-Calculate determinant of 2×2 matrix
-Understand relationship between determinant and area scaling
-Apply formula: area scale factor =

det(matrix)

-Solve problems involving area changes under transformations
Calculators
-Graph papers
-Formula sheets
-Area calculation tools
Square boards
-Flexible materials
-Rulers
-Calculators
Graph papers
-Elastic materials
-Comparison charts
-Review materials

-Determinant calculation practice
-Demonstration using shapes with known areas
-Establishing that area scale factor =