Three Dimensional Geometry

Introduction to 3D Concepts

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

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Properties of Common Solids
Understanding Planes in 3D Space

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

-Identify properties of cubes, cuboids, pyramids
-Count faces, edges, vertices systematically
-Apply Euler's formula (V - E + F = 2)
-Classify solids by their geometric properties

-Make models using cardboard and tape
-Create table of properties for different solids
-Verify Euler's formula with physical models
-Compare prisms and pyramids systematically

Exercise books
-Cardboard
-Scissors
-Tape/glue
-Manila paper
-Books/boards
-Classroom examples

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Lines in 3D Space

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

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Introduction to Projections

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

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Angle Between Line and Plane - Concept

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

-Define angle between line and plane
-Understand that angle is measured with projection
-Identify the projection of line on plane
-Recognize when line is perpendicular to plane

-Demonstrate using stick against book (plane)
-Show that angle is with projection, not plane itself
-Use protractor to measure angles with projections
-Identify perpendicular lines to planes

Exercise books
-Manila paper
-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

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

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Finding Angles Between Planes

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

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Complex Plane-Plane Angle Problems

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

-Solve advanced dihedral angle problems
-Apply to frustums and compound solids
-Use systematic approach for complex shapes
-Verify solutions using geometric properties

-Work with frustum of pyramid problems
-Solve wedge and compound shape angles
-Practice with architectural applications
-Use geometric reasoning to check answers

Exercise books
-Manila paper
-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

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

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Advanced Skew Line Problems

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

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Distance Calculations in 3D

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

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Volume and Surface Area Applications
Coordinate Geometry in 3D

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

-Connect 3D geometry to volume calculations
-Apply angle calculations to surface area problems
-Use 3D relationships in optimization
-Solve practical volume and area problems

-Calculate slant heights using 3D angles
-Find surface areas of pyramids using angles
-Apply to packaging and container problems
-Use in architectural space planning

Exercise books
-Manila paper
-Volume formulas
-Real containers
-3D coordinate grid
-Room corner reference

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Integration with Trigonometry

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

-Apply trigonometry extensively to 3D problems
-Use multiple trigonometric ratios in solutions
-Combine trigonometry with 3D geometric reasoning
-Solve complex problems requiring trig and geometry

-Work through problems requiring sin, cos, tan
-Use trigonometric identities in 3D contexts
-Practice angle calculations in pyramids
-Apply to navigation and astronomy problems

Exercise books
-Manila paper
-Trigonometric tables
-Astronomy examples

KLB Secondary Mathematics Form 4, Pages 115-135

Integration

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

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

KLB Secondary Mathematics Form 4, Pages 221-223

Integration

Finding Particular Solutions
Introduction to Definite Integrals

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

-Use initial conditions to find specific values of constant c
-Solve problems involving boundary conditions
-Apply integration to find equations of curves
-Distinguish between general and particular solutions

-Working examples with given initial conditions
-Finding curve equations when gradient function and point are known
-Practice problems from various contexts
-Discussion on why particular solutions are important
-Problem-solving session with curve-finding exercises

Graph papers
-Calculators
-Curve examples
-Exercise books
-Geometric models
-Integration notation charts

KLB Secondary Mathematics Form 4, Pages 223-225

Integration

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:

-Apply Fundamental Theorem of Calculus
-Evaluate definite integrals using [F(x)]ₐᵇ = F(b) - F(a)
-Understand why constant of integration cancels
-Practice numerical evaluation of definite integrals

-Step-by-step evaluation process demonstration
-Multiple worked examples showing limit substitution
-Verification that constant c cancels out
-Practice with various polynomial and power functions
-Exercises from textbook Exercise 10.2

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

KLB Secondary Mathematics Form 4, Pages 226-230

Integration

Area Between Two Curves

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

KLB Secondary Mathematics Form 4, Pages 233-235

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

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

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Objective Functions

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

-Define objective functions for maximization problems
-Define objective functions for minimization problems
-Understand profit, cost, and other objective measures
-Connect objective functions to real-world goals

-Form profit maximization functions
-Create cost minimization functions
-Practice with revenue and efficiency objectives
-Apply to business and production scenarios

Exercise books
-Manila paper
-Business examples
-Production scenarios

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Complete Problem Formulation

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

-Combine constraints and objective functions
-Write complete linear programming problems
-Check formulation for completeness and correctness
-Apply systematic approach to problem setup

-Work through complete problem formulation process
-Practice with multiple constraint types
-Verify problem setup using logical reasoning
-Apply to comprehensive business scenarios

Exercise books
-Manila paper
-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

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

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

Introduction to Optimization

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

-Understand concept of optimal solution
-Recognize that optimal solution occurs at corner points
-Learn to evaluate objective function at corner points
-Compare values to find maximum or minimum

-Evaluate objective function at each corner point
-Compare values to identify optimal solution
-Practice with both maximization and minimization
-Verify optimal solution satisfies all constraints

Exercise books
-Manila paper
-Calculators
-Evaluation tables

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming

The Corner Point 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

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming

The Iso-Profit/Iso-Cost Line Method
Comparing Solution Methods

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

-Understand concept of iso-profit and iso-cost lines
-Draw family of parallel objective function lines
-Use slope to find optimal point graphically
-Apply sliding line method for optimization

-Draw iso-profit lines for given objective function
-Show family of parallel lines with different values
-Find optimal point by sliding line to extreme position
-Practice with both maximization and minimization

Exercise books
-Manila paper
-Rulers
-Sliding technique
-Method comparison
-Verification examples

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming

Business Applications - Production Planning

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

-Apply linear programming to production problems
-Solve manufacturing optimization problems
-Handle resource allocation in production
-Apply to Kenyan manufacturing scenarios

-Solve factory production optimization problem
-Apply to textile or food processing examples
-Use local manufacturing scenarios
-Calculate optimal production mix

Exercise books
-Manila paper
-Manufacturing examples
-Kenyan industry data

KLB Secondary Mathematics Form 4, Pages 172-176

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

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

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Instantaneous Rate of Change
Gradient of Curves at Points

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

-Understand concept of instantaneous rate
-Recognize instantaneous rate as limit of average rates
-Connect to tangent line gradients
-Apply to real-world motion problems

-Demonstrate instantaneous speed using car speedometer
-Show limiting process using smaller intervals
-Connect to tangent line slopes on curves
-Practice with motion and growth examples

Exercise books
-Manila paper
-Tangent demonstrations
-Motion examples
-Rulers
-Curve examples

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Introduction to Delta Notation

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

-Understand delta (Δ) notation for small changes
-Use Δx and Δy for coordinate changes
-Apply delta notation to rate calculations
-Practice reading and writing delta expressions

-Introduce delta as symbol for "change in"
-Practice writing Δx, Δy, Δt expressions
-Use delta notation in rate of change formulas
-Apply to coordinate geometry problems

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

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

The Limiting Process

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

KLB Secondary Mathematics Form 4, Pages 182-184

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)

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

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Constant 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

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Coefficient 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

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Polynomial Functions
Applications to Tangent Lines

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

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Applications to Normal Lines

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

-Find equations of normal lines to curves
-Use negative reciprocal of tangent gradient
-Apply to perpendicular line problems
-Practice with normal line calculations

-Find normal to y = x² at point (2, 4)
-Use negative reciprocal relationship
-Apply perpendicular line concepts
-Practice normal line equation finding

Exercise books
-Manila paper
-Normal line examples
-Perpendicular concepts

KLB Secondary Mathematics Form 4, Pages 187-189

Differentiation

Introduction to 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

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Types of Stationary Points

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

-Distinguish between maximum and minimum points
-Identify points of inflection
-Use first derivative test for classification
-Apply gradient analysis around stationary points

-Analyze gradient changes around stationary points
-Use sign analysis of dy/dx
-Classify stationary points by gradient behavior
-Practice with various function types

Exercise books
-Manila paper
-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

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

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Acceleration as Second Derivative

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

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Motion Problems and Applications

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

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

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

KLB Secondary Mathematics Form 4, Pages 201-204

Differentiation
Paper 1 Revision

Advanced Optimization Problems
Section I: Mixed Question Practice

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

-Solve complex optimization with multiple constraints
-Apply systematic optimization methodology
-Use calculus for engineering applications
-Practice with advanced real-world problems

-Solve complex geometric optimization problems
-Apply to engineering design scenarios
-Use systematic optimization approach
-Practice with multi-variable situations

Exercise books
-Manila paper
-Complex examples
-Engineering applications
Past Papers, Marking Schemes

KLB Secondary Mathematics Form 4, Pages 201-204

REVISION

Paper 1 Revision
Paper 1 Revision

Section II: Structured Questions

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 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

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

KLB Math Bk 1–4, paper 2 question paper

paper 2 Revision

Section II: Structured Questions

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

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

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

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision

Section II: Structured Questions

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 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

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

KLB Math Bk 1–4, paper 2 question paper

paper 2 Revision

Section II: Structured Questions

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

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

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

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision

Section II: Structured Questions

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 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

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

KLB Math Bk 1–4, paper 2 question paper

paper 2 Revision

Section II: Structured Questions

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

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

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

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision

Section II: Structured Questions

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 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

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

KLB Math Bk 1–4, paper 2 question paper

paper 2 Revision

Section II: Structured Questions

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

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

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

KLB Math Bk 1–4, paper 1 question paper

Paper 1 Revision

Section II: Structured Questions

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 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

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

KLB Math Bk 1–4, paper 2 question paper