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

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

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Additional Trigonometric Identities

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

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

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

Exercise books
-Manila paper
-Identity reference sheet
-Calculators

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Introduction to Waves
Sine and Cosine Waves

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

-Define amplitude and period of waves
-Understand wave characteristics and properties
-Identify amplitude and period from graphs
-Connect waves to trigonometric functions

-Use physical demonstrations with string/rope
-Draw simple wave patterns on manila paper
-Measure amplitude and period from wave diagrams
-Discuss real-world wave examples (sound, light)

Exercise books
-Manila paper
-String/rope
-Wave diagrams
-Rulers
-Graph paper (if available)

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Transformations of Sine Waves

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

-Understand effect of coefficient on amplitude
-Plot graphs of y = k sin x for different values of k
-Compare transformed waves with basic sine wave
-Apply amplitude changes to real situations

-Plot y = 2 sin x, y = 3 sin x on manila paper
-Compare amplitudes with y = sin x
-Demonstrate stretching effect of coefficient
-Apply to sound volume or signal strength examples

Exercise books
-Manila paper
-Colored pencils
-Rulers

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Period Changes in Trigonometric Functions

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

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Combined Amplitude and Period Transformations
Phase Angles and Wave Shifts

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

-Plot graphs of y = a sin(bx) functions
-Identify both amplitude and period changes
-Solve problems with multiple transformations
-Apply to complex wave phenomena

-Plot y = 2 sin(3x), y = 3 sin(x/2) on manila paper
-Calculate both amplitude and period for each function
-Compare multiple transformed waves
-Apply to radio waves or tidal patterns

Exercise books
-Manila paper
-Rulers
-Transformation examples
-Colored pencils
-Phase shift examples

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

General Trigonometric Functions

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

-Work with y = a sin(bx + c) functions
-Identify amplitude, period, and phase angle
-Plot complex trigonometric functions
-Solve problems involving all transformations

-Plot y = 2 sin(3x + 60°) step by step
-Identify all transformation parameters
-Practice reading values from complex waves
-Apply to real-world periodic phenomena

Exercise books
-Manila paper
-Rulers
-Complex function examples

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Cosine Wave Transformations

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

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Introduction to Trigonometric Equations
Solving Basic Trigonometric Equations

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

-Understand concept of trigonometric equations
-Identify that trig equations have multiple solutions
-Solve simple equations like sin x = 0.5
-Find all solutions in given ranges

-Demonstrate using unit circle or graphs
-Show why sin x = 0.5 has multiple solutions
-Practice finding principal values
-Use graphs to identify all solutions in range

Exercise books
-Manila paper
-Unit circle diagrams
-Trigonometric tables
-Calculators
-Solution worksheets

KLB Secondary Mathematics Form 4, Pages 109-112

Trigonometry III

Quadratic Trigonometric Equations

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

-Solve equations like sin²x - sin x = 0
-Apply factoring techniques to trigonometric equations
-Use substitution methods for complex equations
-Find all solutions systematically

-Demonstrate substitution method (let y = sin x)
-Factor quadratic expressions in trigonometry
-Solve resulting quadratic equations
-Back-substitute to find angle solutions

Exercise books
-Manila paper
-Factoring techniques
-Substitution examples

KLB Secondary Mathematics Form 4, Pages 109-112

Trigonometry III

Equations Involving Multiple Angles

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

KLB Secondary Mathematics Form 4, Pages 109-112

Trigonometry III

Using Graphs to Solve Trigonometric Equations
Trigonometric Equations with Identities

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

-Solve equations graphically using intersections
-Plot trigonometric functions on same axes
-Find intersection points as equation solutions
-Verify algebraic solutions graphically

-Plot y = sin x and y = 0.5 on same axes
-Identify intersection points as solutions
-Use graphical method for complex equations
-Compare graphical and algebraic solutions

Exercise books
-Manila paper
-Rulers
-Graphing examples
-Identity reference sheets
-Complex examples

KLB Secondary Mathematics Form 4, Pages 109-112

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

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

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

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
Practical Applications of Plane Angles

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
-Real engineering data
-Construction examples

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Understanding Skew Lines

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

-Define skew lines and their properties
-Distinguish skew lines from parallel/intersecting lines
-Identify skew lines in 3D models
-Understand that skew lines exist only in 3D

-Use classroom edges to show skew lines
-Demonstrate with two rulers in space
-Identify skew lines in building frameworks
-Practice recognition in various 3D shapes

Exercise books
-Manila paper
-Rulers
-Building frameworks

KLB Secondary Mathematics Form 4, Pages 128-135

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
Distance Calculations in 3D

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

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

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

Exercise books
-Manila paper
-Engineering examples
-Structure diagrams
-Distance calculation charts
-3D coordinate examples

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Volume and Surface Area Applications

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

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry

Coordinate Geometry in 3D

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

KLB Secondary Mathematics Form 4, Pages 115-135

Three Dimensional Geometry
Longitudes and Latitudes

Integration with Trigonometry
Introduction to Earth as a Sphere

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
-Globe/spherical ball
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 115-135

Longitudes and Latitudes

Great and Small Circles

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

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Understanding Latitude

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

-Define latitude and its measurement
-Identify equator as 0° latitude reference
-Understand North and South latitude designations
-Recognize that latitude ranges from 0° to 90°

-Mark latitude lines on globe using tape
-Show equator as reference line (0°)
-Demonstrate measurement from equator to poles
-Practice identifying latitude positions

Exercise books
-Globe
-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

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

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Position of Places on Earth

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

-Express position using latitude and longitude coordinates
-Use correct notation for positions (e.g., 1°S, 37°E)
-Identify positions of major Kenyan cities
-Locate places given their coordinates

-Find positions of Nairobi, Mombasa, Kisumu on globe
-Practice writing coordinates in correct format
-Locate cities worldwide using coordinates
-Use maps to verify coordinate positions

Exercise books
-Globe
-World map
-Kenya map

KLB Secondary Mathematics Form 4, Pages 139-143

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

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

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Distance Along Small Circles (Parallels)

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

-Understand that parallel distances use different formula
-Apply formula: distance = longitude difference × 60 × cos(latitude)
-Calculate radius of latitude circles
-Solve problems involving parallel of latitude distances

-Derive formula using trigonometry
-Calculate distance between Mombasa and Lagos
-Show why latitude affects distance calculations
-Practice with various latitude examples

Exercise books
-Manila paper
-Calculator
-African city examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Shortest Distance Problems
Advanced Distance Calculations

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

-Understand that shortest distance is along great circle
-Compare great circle and parallel distances
-Calculate shortest distances between any two points
-Apply to navigation and flight path problems

-Compare distances: parallel vs great circle routes
-Calculate shortest distance between London and New York
-Apply to aircraft flight planning
-Discuss practical navigation implications

Exercise books
-Manila paper
-Calculator
-Flight path examples
-Surveying examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Introduction to Time and Longitude

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

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

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

Exercise books
-Globe
-Light source
-Time zone examples

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Local Time Calculations

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

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Greenwich Mean Time (GMT)
Complex Time Problems

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

-Understand Greenwich as reference for world time
-Calculate local times relative to GMT
-Apply GMT to solve international time problems
-Understand time zones and their practical applications

-Use Greenwich as time reference point
-Calculate local times for cities worldwide
-Apply to international business scenarios
-Discuss practical applications of GMT

Exercise books
-Manila paper
-World map
-Time zone charts
-International examples
-Travel scenarios

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Speed Calculations

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

-Define knot as nautical mile per hour
-Calculate speeds in knots and km/h
-Apply speed calculations to navigation problems
-Solve problems involving time, distance, and speed

-Calculate ship speeds in knots
-Convert between knots and km/h
-Apply to aircraft and ship navigation
-Practice with maritime and aviation examples

Exercise books
-Manila paper
-Calculator
-Navigation examples

KLB Secondary Mathematics Form 4, Pages 156-161

Linear Programming

Introduction to Linear Programming

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

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Forming Linear Inequalities from Word Problems
Types of Constraints

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

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

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

Exercise books
-Manila paper
-Local business examples
-Agricultural scenarios
-Industry examples
-School scenarios

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
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

Comparing Solution Methods

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

KLB Secondary Mathematics Form 4, Pages 172-176

Linear Programming
Paper 1 Revision

Business Applications - Production Planning
Section I: Short Answer Questions

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
Past Paper 1 exams, Marking Schemes

KLB Secondary Mathematics Form 4, Pages 172-176

REVISION

Paper 1 Revision
Paper 1 Revision
Paper 1 Revision

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:
– 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

KLB Math Bk 1–4
paper 1 question paper

Paper 1 Revision
paper 2 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

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

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Mixed Question Practice
Section II: Structured 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 2s, Marking Schemes

Students’ Notes, Revision Texts
Paper 2 question paper

paper 2 Revision
Paper 1 Revision
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

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 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4
paper 2 question paper

Paper 1 Revision

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:
– 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

Students’ Notes, Revision Texts
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

paper 2 Revision

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:
– 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 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

Students’ Notes, Revision Texts
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
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer 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
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

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

KLB Math Bk 1–4
paper 1 question paper

Paper 1 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer 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
Past paper 2 exams, Marking Schemes

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

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:
– 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

KLB Math Bk 1–4
paper 2 question paper

paper 2 Revision
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer Questions

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 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

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

KLB Math Bk 1–4
paper 1 question paper

Paper 1 Revision
paper 2 Revision
paper 2 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

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

KLB Math Bk 1–4
paper 1 question paper

paper 2 Revision

Section I: Mixed Question Practice
Section II: Structured 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 2s, Marking Schemes

Students’ Notes, Revision Texts
Paper 2 question paper

paper 2 Revision
Paper 1 Revision
Paper 1 Revision

Section II: Structured Questions
Section I: Short Answer Questions
Section I: Short Answer Questions

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 1 exams, Marking Schemes
Chalkboard, Past Papers, Calculators

KLB Math Bk 1–4
paper 2 question paper

Paper 1 Revision

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:
– 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

Students’ Notes, Revision Texts
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

paper 2 Revision

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:
– 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 2s, Marking Schemes
Graph Papers, Geometry Sets, Past Papers

Students’ Notes, Revision Texts
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