Integration

Introduction to Reverse Differentiation

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

KLB Secondary Mathematics Form 4, Pages 221-223

Integration

Basic Integration Rules - Power Functions
Integration of Polynomial Functions

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

-Apply power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + c
-Understand the constant of integration and why it's necessary
-Integrate simple power functions where n ≠ -1
-Practice with positive, negative, and fractional powers

-Derivation of power rule through reverse differentiation
-Multiple examples with different values of n
-Explanation of arbitrary constant using family of curves
-Practice exercises with various power functions
-Common mistakes discussion and correction

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

KLB Secondary Mathematics Form 4, Pages 223-225

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

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

KLB Secondary Mathematics Form 4, Pages 226-230

Integration

Areas Below X-axis and Mixed Regions
Area Between Two Curves

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

-Handle negative areas when curve is below x-axis
-Understand absolute value consideration for areas
-Calculate areas of regions crossing x-axis
-Apply integration to mixed positive/negative regions

-Demonstration of negative integrals and their meaning
-Working with curves that cross x-axis multiple times
-Finding total area vs net area
-Practice with functions like y = x³ - x
-Problem-solving with complex area calculations

Graph papers
-Calculators
-Curve examples
-Colored materials
-Exercise books
-Equation solving aids
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 230-235

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

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

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Advanced Line-Plane Angle Problems

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

-Solve complex angle problems systematically
-Apply coordinate geometry methods where helpful
-Use multiple right-angled triangles in solutions
-Verify answers using different approaches

-Practice with tent and roof angle problems
-Solve ladder against wall problems in 3D
-Work through architectural angle calculations
-Use real-world engineering applications

Exercise books
-Manila paper
-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

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

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

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

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Understanding Longitude

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

-Define longitude and its measurement
-Identify Greenwich Meridian as 0° longitude reference
-Understand East and West longitude designations
-Recognize that longitude ranges from 0° to 180°

-Mark longitude lines on globe using string
-Show Greenwich Meridian as reference line
-Demonstrate measurement East and West from Greenwich
-Practice identifying longitude positions

Exercise books
-Globe
-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

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

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Advanced Distance Calculations

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

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

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

Exercise books
-Manila paper
-Calculator
-Surveying examples

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

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

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

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

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

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

Loci

Introduction to Loci
Basic Locus Concepts and Laws

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

-Define locus and understand its meaning
-Distinguish between locus of points, lines, and regions
-Identify real-world examples of loci
-Understand the concept of movement according to given laws

-Demonstrate door movement to show path traced by corner
-Use string and pencil to show circular locus
-Discuss examples: clock hands, pendulum swing
-Students trace paths of moving objects

Exercise books
-Manila paper
-String
-Chalk/markers
-Real objects

KLB Secondary Mathematics Form 4, Pages 73-75

Loci

Perpendicular Bisector Locus

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

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

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

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Properties and Applications of Perpendicular Bisector

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

-Understand perpendicular bisector in 3D space
-Apply perpendicular bisector to find circumcenters
-Solve practical problems using perpendicular bisector
-Use perpendicular bisector in triangle constructions

-Find circumcenter of triangle using perpendicular bisectors
-Solve water pipe problems (equidistant from two points)
-Apply to real-world location problems
-Practice with various triangle types

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Locus of Points at Fixed Distance from a Point

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

-Define circle as locus of points at fixed distance from center
-Construct circles with given radius using compass
-Understand sphere as 3D locus from fixed point
-Solve problems involving circular loci

-Construct circles of different radii
-Demonstrate with string of fixed length
-Discuss radar coverage, radio signal range
-Students create circles with various measurements

Exercise books
-Manila paper
-Compass
-String

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Locus of Points at Fixed Distance from a Line

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

-Define locus of points at fixed distance from straight line
-Construct parallel lines at given distances
-Understand cylindrical surface in 3D
-Apply to practical problems like road margins

-Construct parallel lines using ruler and set square
-Mark points at equal distances from given line
-Discuss road design, river banks, field boundaries
-Practice with various distances and orientations

Exercise books
-Manila paper
-Ruler
-Set square

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Angle Bisector Locus

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

-Define angle bisector locus
-Construct angle bisectors using compass and ruler
-Prove equidistance property of angle bisector
-Apply angle bisector to find incenters

-Construct angle bisectors for various angles
-Verify equidistance from angle arms
-Find incenter of triangle using angle bisectors
-Practice with acute, obtuse, and right angles

Exercise books
-Manila paper
-Compass
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Properties and Applications of Angle Bisector

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

-Understand relationship between angle bisectors in triangles
-Apply angle bisector theorem
-Solve problems involving inscribed circles
-Use angle bisectors in geometric constructions

-Construct inscribed circle using angle bisectors
-Apply angle bisector theorem to solve problems
-Find external angle bisectors
-Solve practical surveying problems

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Constant Angle Locus
Advanced Constant Angle Constructions

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

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

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

Exercise books
-Manila paper
-Compass
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Introduction to Intersecting Loci

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

-Understand concept of intersecting loci
-Identify points satisfying multiple conditions
-Find intersection points of two loci
-Apply intersecting loci to solve practical problems

-Demonstrate intersection of two circles
-Find points equidistant from two points AND at fixed distance from third point
-Solve simple two-condition problems
-Practice identifying intersection points

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Intersecting Circles and Lines

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

-Find intersections of circles with lines
-Determine intersections of two circles
-Solve problems with line and circle combinations
-Apply to geometric construction problems

-Construct intersecting circles and lines
-Find common tangents to circles
-Solve problems involving circle-line intersections
-Apply to wheel and track problems

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Triangle Centers Using Intersecting Loci

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

-Find circumcenter using perpendicular bisector intersections
-Locate incenter using angle bisector intersections
-Determine centroid and orthocenter
-Apply triangle centers to solve problems

-Construct all four triangle centers
-Compare properties of different triangle centers
-Use triangle centers in geometric proofs
-Solve problems involving triangle center properties

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Complex Intersecting Loci Problems

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

-Solve problems with three or more conditions
-Find regions satisfying multiple constraints
-Apply intersecting loci to optimization problems
-Use systematic approach to complex problems

-Solve treasure hunt type problems
-Find optimal locations for facilities
-Apply to surveying and engineering problems
-Practice systematic problem-solving approach

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

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Introduction to Loci of Inequalities

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

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

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

Exercise books
-Manila paper
-Ruler
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Distance Inequality Loci

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

-Represent distance inequalities graphically
-Solve problems with "less than" and "greater than" distances
-Find regions satisfying distance constraints
-Apply to safety zone problems

-Shade regions inside and outside circles
-Solve exclusion zone problems
-Apply to communication range problems
-Practice with multiple distance constraints

Exercise books
-Manila paper
-Compass
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Combined Inequality Loci
Advanced Inequality Applications

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

-Solve problems with multiple inequality constraints
-Find intersection regions of inequality loci
-Apply to optimization and feasibility problems
-Use systematic shading techniques

-Find feasible regions for multiple constraints
-Solve planning problems with restrictions
-Apply to resource allocation scenarios
-Practice systematic region identification

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

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Introduction to Loci Involving Chords

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

-Review chord properties in circles
-Understand perpendicular bisector of chords
-Apply chord theorems to loci problems
-Construct equal chords in circles

-Review chord bisector theorem
-Construct chords of given lengths
-Find centers using chord properties
-Practice with chord intersection theorems

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 92-94

Loci

Chord-Based Constructions

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

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

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

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 92-94

Loci

Advanced Chord Problems
Integration of All Loci Types

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

-Solve complex problems involving multiple chords
-Apply power of point theorem
-Find loci related to chord properties
-Use chords in circle geometry proofs

-Apply intersecting chords theorem
-Solve problems with chord-secant relationships
-Find loci of points with equal power
-Practice with tangent-chord angles

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 92-94