REVISION

Paper 1 Revision
Paper 1 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past Paper 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision
paper 2 Revision

Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– integrate knowledge to solve mixed short questions – apply logical reasoning and time management – identify common errors and correct them

Timed practice with mixed short-answer questions Class discussion of solutions

Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes

Students’ Notes, Revision Texts
paper 1 question paper

paper 2 Revision
Paper 1 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions
Section I: Short Answer Questions

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past Paper 1 exams, Marking Schemes

KLB Math Bk 1–4
paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– practice a variety of short-answer styles – apply problem-solving strategies – build confidence in tackling compulsory questions

Teacher demonstrates approaches Students work in pairs and discuss solutions

Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

KLB Math Bk 1–4, paper 2 question paper

Paper 1 Revision

Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice
Section II: Structured Questions

By the end of the lesson, the learner should be able to:
– attempt compulsory short-answer questions – show clear working for full marks – apply speed and accuracy in solving problems

Students attempt selected questions individually Peer-marking and teacher correction

Past Paper 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes
Past Paper 1s, Marking Schemes

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision
paper 2 Revision
paper 2 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions
Section I: Mixed Question Practice

By the end of the lesson, the learner should be able to:
– practice extended problem solving – interpret and use graphs, diagrams and data – present answers clearly for maximum marks

Students attempt structured questions under timed conditions Peer review and corrections

Graph Papers, Geometry Sets, Past Papers
Past paper 2 exams, Marking Schemes
Chalkboard, Past Papers, Calculators
Past Papers, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision
Paper 1 Revision
Integration
Integration

Section II: Structured Questions
Section I: Short Answer Questions
Introduction to Reverse Differentiation
Basic Integration Rules - Power Functions

By the end of the lesson, the learner should be able to:
– develop detailed structured responses – organize answers step by step – apply concepts in real-life problem settings

Group brainstorming on selected structured questions Teacher gives feedback on presentation

Past Paper 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers
Past Paper 1 exams, Marking Schemes
Graph papers
-Differentiation charts
-Exercise books
-Function examples
Calculators
-Graph papers
-Power rule charts

KLB Math Bk 1–4
paper 2 question paper

Integration

Integration of Polynomial Functions
Finding Particular Solutions
Introduction to Definite Integrals
Evaluating Definite Integrals

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

-Integrate polynomial functions with multiple terms
-Apply linearity: ∫[af(x) + bg(x)]dx = a∫f(x)dx + b∫g(x)dx
-Handle constant coefficients and addition/subtraction
-Solve integration problems requiring algebraic simplification

-Step-by-step integration of polynomials like 3x² + 5x - 7
-Working with coefficients and constants
-Integration of expanded expressions: (x+2)(x-3)
-Practice with mixed positive and negative terms
-Exercises from textbook Exercise 10.1

Calculators
-Algebraic worksheets
-Polynomial examples
-Exercise books
Graph papers
-Calculators
-Curve examples
-Geometric models
-Integration notation charts
-Step-by-step worksheets
-Evaluation charts

KLB Secondary Mathematics Form 4, Pages 223-225

Integration
Matrices and Transformations
Matrices and Transformations

Area Under Curves - Single Functions
Areas Below X-axis and Mixed Regions
Area Between Two Curves
Transformation on a Cartesian plane
Basic Transformation Matrices

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

-Understand integration as area calculation tool
-Calculate area between curve and x-axis
-Handle regions bounded by curves and vertical lines
-Apply definite integrals to find exact areas

-Geometric demonstration of area under curves
-Drawing and shading regions on graph paper
-Working examples: area under y = x², y = 2x + 3, etc.
-Comparison with approximation methods from Chapter 9
-Practice finding areas of various regions

Graph papers
-Curve sketching tools
-Colored pencils
-Calculators
-Area grids
-Curve examples
-Colored materials
-Exercise books
-Equation solving aids
Square boards
-Peg boards
-Graph papers
-Mirrors
-Rulers
-Protractors

KLB Secondary Mathematics Form 4, Pages 230-233

Matrices and Transformations

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 transformation matrix from object and image coordinates
-Identify type of transformation from given matrix
-Use algebraic methods to find unknown matrices
-Classify transformations based on matrix properties

-Worked examples finding matrices from coordinate pairs
-Analysis of matrix elements to identify transformation type
-Solving simultaneous equations to find matrix elements
-Practice with various transformation identification problems
-Discussion on matrix patterns for each transformation

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

KLB Secondary Mathematics Form 4, Pages 6-16

Matrices and Transformations

Matrix Multiplication Properties
Identity Matrix and Transformation
Inverse of a matrix
Determinant and Area Scale Factor

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
-Solve problems involving area changes under transformations

KLB Secondary Mathematics Form 4, Pages 21-24

Matrices and Transformations

Area scale factor and determinant relationship
Shear Transformation

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

-Establish mathematical relationship between determinant and area scaling
-Explain why absolute value is needed
-Apply relationship in various transformation problems
-Understand orientation change when determinant is negative

-Mathematical proof of area scale factor relationship
-Examples with positive and negative determinants
-Discussion on orientation preservation/reversal
-Practice problems from textbook Ex 1.5
-Verification through direct area calculations

Calculators
-Graph papers
-Formula sheets
-Area calculation tools
Square boards
-Flexible materials
-Rulers
-Calculators

KLB Secondary Mathematics Form 4, Pages 26-27

Matrices and Transformations
Differentiation

Stretch Transformation and Review
Introduction to Rate of Change

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

-Define stretch transformation and its matrices
-Calculate effect of stretch on areas and lengths
-Compare and contrast shear and stretch
-Review all transformation types and their properties

-Demonstration using elastic materials
-Finding matrices for stretch in x and y directions
-Comparison table: isometric vs non-isometric transformations
-Comprehensive review of all transformation types
-Problem-solving session covering entire unit

Graph papers
-Elastic materials
-Calculators
-Comparison charts
-Review materials
Exercise books
-Manila paper
-Real-world examples
-Graph examples

KLB Secondary Mathematics Form 4, Pages 28-38

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
The Limiting Process

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
-Limit tables
-Systematic examples

KLB Secondary Mathematics Form 4, Pages 178-182

Differentiation

Introduction to Derivatives
Derivative of Linear Functions

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

-Define derivative as limit of rate of change
-Use dy/dx notation for derivatives
-Understand derivative as gradient function
-Connect derivatives to tangent line slopes

-Introduce derivative notation dy/dx
-Show derivative as gradient of tangent
-Practice derivative concept with simple functions
-Connect to previous gradient work

Exercise books
-Manila paper
-Derivative notation
-Function examples
-Linear function examples
-Verification methods

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

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

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

-Find derivatives of power functions
-Apply the rule d/dx(x^n) = nx^(n-1)
-Practice with x², x³, x⁴, etc.
-Verify using first principles for simple cases

-Derive d/dx(x²) = 2x using first principles
-Apply power rule to various functions
-Practice with x³, x⁴, x⁵ examples
-Verify selected results using definition

Exercise books
-Manila paper
-Power rule examples
-First principles verification
-Constant function graphs
-Geometric explanations

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Coefficient Functions
Derivative of Polynomial Functions

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

-Find derivatives of functions like y = ax^n
-Apply constant multiple rule
-Practice with various coefficient values
-Combine coefficient and power rules

-Find derivative of y = 5x³
-Apply rule d/dx(af(x)) = a·f'(x)
-Practice with negative coefficients
-Combine multiple rules systematically

Exercise books
-Manila paper
-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
Finding and Classifying 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
-Systematic templates
-Complete examples

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Curve Sketching Using Derivatives
Introduction to Kinematics Applications

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

KLB Secondary Mathematics Form 4, Pages 195-197

Differentiation

Acceleration as Second Derivative
Motion Problems and Applications

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

-Understand acceleration as derivative of velocity
-Apply a = dv/dt = d²s/dt² notation
-Find acceleration functions from displacement
-Apply to motion analysis problems

-Find acceleration from velocity functions
-Use second derivative notation
-Apply to projectile motion problems
-Practice with particle motion scenarios

Exercise books
-Manila paper
-Second derivative examples
-Motion analysis
-Complete motion examples
-Real scenarios

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Introduction to Optimization
Geometric Optimization Problems

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

-Apply derivatives to find maximum and minimum values
-Understand optimization in real-world contexts
-Use calculus for practical optimization problems
-Connect to business and engineering applications

-Find maximum area of rectangle with fixed perimeter
-Apply calculus to profit maximization
-Use derivatives for cost minimization
-Practice with geometric optimization

Exercise books
-Manila paper
-Optimization examples
-Real applications
-Geometric examples
-Design applications

KLB Secondary Mathematics Form 4, Pages 201-204

Differentiation

Business and Economic Applications
Advanced Optimization Problems

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

KLB Secondary Mathematics Form 4, Pages 201-204