Matrices and Transformation

Matrices of Transformation
Identifying Common Transformation Matrices
Finding the Matrix of a Transformation
Using the Unit Square Method

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

-Define transformation and identify types
-Recognize that matrices can represent transformations
-Apply 2×2 matrices to position vectors
-Relate matrix operations to geometric transformations

-Review transformation concepts from Form 2
-Demonstrate matrix multiplication using position vectors
-Plot objects and images on coordinate plane
-Practice identifying transformations from images

Exercise books
-Manila paper
-Ruler
-Pencils
-String
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 1-5

Matrices and Transformation

Successive Transformations
Matrix Multiplication for Combined Transformations
Single Matrix for Successive Transformations
Inverse of a Transformation
Properties of Inverse Transformations
Area Scale Factor and Determinant
Shear Transformations

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

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

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

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

KLB Secondary Mathematics Form 4, Pages 16-24

Matrices and Transformation
Statistics II
Statistics II

Stretch Transformations
Combined Shear and Stretch Problems
Isometric and Non-isometric Transformations
Introduction to Advanced Statistics
Working Mean Concept

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

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

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

Exercise books
-Rubber bands
-Manila paper
-Ruler
-Chalk/markers
-Paper cutouts
-Real data examples
-Sample datasets

KLB Secondary Mathematics Form 4, Pages 28-34

Statistics II

Mean Using Working Mean - Simple Data
Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean
Advanced Working Mean Techniques
Introduction to Quartiles, Deciles, Percentiles

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

-Calculate mean using working mean for ungrouped data
-Apply the formula: mean = working mean + mean of deviations
-Verify results using direct calculation method
-Solve problems with whole numbers

-Work through step-by-step examples on chalkboard
-Practice with student marks and heights data
-Verify answers using traditional method
-Individual practice with guided support

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

KLB Secondary Mathematics Form 4, Pages 42-48

Statistics II

Calculating Quartiles for Ungrouped Data
Quartiles for Grouped Data
Deciles and Percentiles Calculations
Introduction to Cumulative Frequency
Drawing Cumulative Frequency Curves (Ogives)

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

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

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

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

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Reading Values from Ogives
Applications of Ogives
Introduction to Measures of Dispersion
Range and Interquartile Range
Mean Absolute Deviation

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

-Read median from cumulative frequency curve
-Find quartiles using ogive
-Estimate any percentile from the curve
-Interpret readings in real-world context

-Demonstrate reading techniques on large ogive
-Practice finding median position (n/2)
-Read quartile positions systematically
-Students practice reading their own curves

Exercise books
-Manila paper
-Completed ogives
-Ruler
-Real problem datasets
-Comparative datasets
-Chalk/markers
-Student data
-Measuring tape
-Test score data

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II

Introduction to Variance
Variance Using Alternative Formula
Standard Deviation Calculations
Standard Deviation for Grouped Data
Advanced Standard Deviation Techniques

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

-Define variance as mean of squared deviations
-Calculate variance using definition formula
-Understand why deviations are squared
-Compare variance with other dispersion measures

-Work through variance calculation step by step
-Explain squaring deviations eliminates negatives
-Calculate variance for simple datasets
-Compare with mean absolute deviation

Exercise books
-Manila paper
-Simple datasets
-Chalk/markers
-Frequency data
-Exam score data
-Agricultural data
-Transformation examples

KLB Secondary Mathematics Form 4, Pages 65-70

Loci

Introduction to Loci
Basic Locus Concepts and Laws
Perpendicular Bisector Locus
Properties and Applications of Perpendicular Bisector
Locus of Points at Fixed Distance from a Point

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
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 73-75

Loci

Locus of Points at Fixed Distance from a Line
Angle Bisector Locus
Properties and Applications of Angle Bisector
Constant Angle Locus
Advanced Constant Angle Constructions

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
-Compass
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Introduction to Intersecting Loci
Intersecting Circles and Lines
Triangle Centers Using Intersecting Loci
Complex Intersecting Loci Problems
Introduction to Loci of Inequalities

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
-Real-world scenarios
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Distance Inequality Loci
Combined Inequality Loci
Advanced Inequality Applications
Introduction to Loci Involving Chords
Chord-Based Constructions

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
-Ruler
-Real problem data

KLB Secondary Mathematics Form 4, Pages 89-92

Loci
Trigonometry III
Trigonometry III
Trigonometry III

Advanced Chord Problems
Integration of All Loci Types
Review of Basic Trigonometric Ratios
Deriving the Identity sin²θ + cos²θ = 1
Applications of sin²θ + cos²θ = 1

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
-Rulers
-Calculators (if available)
-Unit circle diagrams
-Calculators
-Trigonometric tables
-Real-world examples

KLB Secondary Mathematics Form 4, Pages 92-94

Trigonometry III

Additional Trigonometric Identities
Introduction to Waves
Sine and Cosine Waves
Transformations of Sine Waves
Period Changes in Trigonometric Functions

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
-String/rope
-Wave diagrams
-Rulers
-Graph paper (if available)
-Colored pencils
-Period calculation charts

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Combined Amplitude and Period Transformations
Phase Angles and Wave Shifts
General Trigonometric Functions
Cosine Wave Transformations
Introduction to Trigonometric Equations

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
-Complex function examples
-Temperature data
-Unit circle diagrams
-Trigonometric tables

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Solving Basic Trigonometric Equations
Quadratic Trigonometric Equations
Equations Involving Multiple Angles
Using Graphs to Solve Trigonometric Equations
Trigonometric Equations with Identities

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

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

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

Exercise books
-Manila paper
-Calculators
-Solution worksheets
-Factoring techniques
-Substitution examples
-Multiple angle examples
-Real applications
-Rulers
-Graphing examples
-Identity reference sheets
-Complex examples

KLB Secondary Mathematics Form 4, Pages 109-112

Three Dimensional Geometry

Introduction to 3D Concepts
Properties of Common Solids
Understanding Planes in 3D Space
Lines in 3D Space
Introduction to Projections

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

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

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

Exercise books
-Cardboard boxes
-Manila paper
-Real 3D objects
-Cardboard
-Scissors
-Tape/glue
-Books/boards
-Classroom examples
-Rulers/sticks
-3D models
-Light source

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Angle Between Line and Plane - Concept
Calculating Angles Between Lines and Planes
Advanced Line-Plane Angle Problems
Introduction to Plane-Plane Angles
Finding Angles Between Planes

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
-Calculators
-3D problem diagrams
-Real scenarios
-Problem sets
-Books
-Folded paper
-Building examples

KLB Secondary Mathematics Form 4, Pages 115-123

Three Dimensional Geometry

Complex Plane-Plane Angle Problems
Practical Applications of Plane Angles
Understanding Skew Lines
Angle Between Skew Lines
Advanced Skew Line 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
-Real engineering data
-Construction examples
-Rulers
-Building frameworks
-Translation examples
-Engineering examples
-Structure diagrams

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry
Longitudes and Latitudes

Distance Calculations in 3D
Volume and Surface Area Applications
Coordinate Geometry in 3D
Integration with Trigonometry
Introduction to Earth as a Sphere

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

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

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

Exercise books
-Manila paper
-Distance calculation charts
-3D coordinate examples
-Volume formulas
-Real containers
-3D coordinate grid
-Room corner reference
-Trigonometric tables
-Astronomy examples
-Globe/spherical ball
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 115-135

Longitudes and Latitudes

Great and Small Circles
Understanding Latitude
Properties of Latitude Lines
Understanding Longitude
Properties of Longitude Lines

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

-Define great circles and small circles on a sphere
-Identify properties of great and small circles
-Understand that great circles divide sphere into hemispheres
-Recognize examples of great and small circles on Earth

-Demonstrate great circles using globe and string
-Show that great circles pass through center
-Compare radii of great and small circles
-Identify equator as the largest circle

Exercise books
-Globe
-String
-Manila paper
-Tape/string
-Protractor
-Calculator
-World map

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Position of Places on Earth
Latitude and Longitude Differences
Introduction to Distance Calculations
Distance Along Great Circles
Distance Along Small Circles (Parallels)

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
-Manila paper
-Calculator
-Navigation examples
-Conversion charts
-Real examples
-African city examples

KLB Secondary Mathematics Form 4, Pages 139-143

Longitudes and Latitudes

Shortest Distance Problems
Advanced Distance Calculations
Introduction to Time and Longitude
Local Time Calculations
Greenwich Mean Time (GMT)

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
-Globe
-Light source
-Time zone examples
-World time examples
-World map
-Time zone charts

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes
Linear Programming
Linear Programming
Linear Programming

Complex Time Problems
Speed Calculations
Introduction to Linear Programming
Forming Linear Inequalities from Word Problems
Types of Constraints

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

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

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

Exercise books
-Manila paper
-International examples
-Travel scenarios
-Calculator
-Navigation examples
-Real-life examples
-Chalk/markers
-Local business examples
-Agricultural scenarios
-Industry examples
-School scenarios

KLB Secondary Mathematics Form 4, Pages 156-161

Linear Programming

Objective Functions
Complete Problem Formulation
Introduction to Graphical Solution Method
Plotting Multiple Constraints
Properties of Feasible Regions

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
-Complete examples
-Systematic templates
-Rulers
-Colored pencils
-Different colored pencils
-Calculators
-Algebraic methods

KLB Secondary Mathematics Form 4, Pages 165-167

Linear Programming

Introduction to Optimization
The Corner Point Method
The Iso-Profit/Iso-Cost Line Method
Comparing Solution Methods
Business Applications - Production Planning

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
-Evaluation templates
-Systematic approach
-Rulers
-Sliding technique
-Method comparison
-Verification examples
-Manufacturing examples
-Kenyan industry data

KLB Secondary Mathematics Form 4, Pages 172-176

Differentiation

Introduction to Rate of Change
Average Rate of Change
Instantaneous Rate of Change
Gradient of Curves at Points
Introduction to Delta Notation

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
-Calculators
-Graph paper
-Tangent demonstrations
-Motion examples
-Rulers
-Curve examples
-Delta notation examples
-Symbol practice

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

The Limiting Process
Introduction to Derivatives
Derivative of Linear Functions
Derivative of y = x^n (Basic Powers)
Derivative of Constant Functions

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

-Understand concept of limit in differentiation
-Apply "as Δx approaches zero" reasoning
-Use limiting process to find exact derivatives
-Practice systematic limiting calculations

-Demonstrate limiting process with numerical examples
-Show chord approaching tangent as Δx → 0
-Calculate limits using table of values
-Practice systematic limit evaluation

Exercise books
-Manila paper
-Limit tables
-Systematic examples
-Derivative notation
-Function examples
-Linear function examples
-Verification methods
-Power rule examples
-First principles verification
-Constant function graphs
-Geometric explanations

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

Derivative of Coefficient Functions
Derivative of Polynomial Functions
Applications to Tangent Lines
Applications to Normal Lines
Introduction to Stationary Points

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

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

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

Exercise books
-Manila paper
-Coefficient examples
-Rule combinations
-Polynomial examples
-Term-by-term method
-Tangent line examples
-Point-slope applications
-Normal line examples
-Perpendicular concepts
-Curve sketches
-Stationary point examples

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Types of Stationary Points
Finding and Classifying Stationary Points
Curve Sketching Using Derivatives
Introduction to Kinematics Applications
Acceleration as Second Derivative

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
-Systematic templates
-Complete examples
-Curve sketching templates
-Systematic method
-Motion examples
-Kinematics applications
-Second derivative examples
-Motion analysis

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation
Matrices and Transformations

Motion Problems and Applications
Introduction to Optimization
Geometric Optimization Problems
Business and Economic Applications
Advanced Optimization Problems
Transformation on a Cartesian plane

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

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

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

Exercise books
-Manila paper
-Complete motion examples
-Real scenarios
-Optimization examples
-Real applications
-Geometric examples
-Design applications
-Business examples
-Economic applications
-Complex examples
-Engineering applications
Square boards
-Peg boards
-Graph papers
-Mirrors
-Rulers

KLB Secondary Mathematics Form 4, Pages 197-201

Matrices and Transformations

Basic Transformation Matrices
Identification of transformation matrix
Two Successive Transformations
Complex Successive Transformations
Single matrix of transformation for successive transformations
Matrix Multiplication Properties
Identity Matrix and Transformation
Inverse of a matrix
Determinant and Area Scale Factor

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

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

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

Square boards
-Peg boards
-Graph papers
-Protractors
-Calculators
Graph papers
-Exercise books
-Matrix examples
-Colored pencils
-Rulers
Calculators
-Matrix multiplication charts
-Matrix worksheets
-Formula sheets
-Solve problems involving area changes under transformations

KLB Secondary Mathematics Form 4, Pages 1-16

Matrices and Transformations
Integration
Integration
Integration
Integration
Integration
Integration
Integration
Integration
Integration

Area scale factor and determinant relationship
Shear Transformation
Stretch Transformation and Review
Introduction to Reverse Differentiation
Basic Integration Rules - Power Functions
Integration of Polynomial Functions
Finding Particular Solutions
Introduction to Definite Integrals
Evaluating Definite Integrals
Area Under Curves - Single Functions
Areas Below X-axis and Mixed Regions
Area Between Two Curves

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

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

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

Calculators
-Graph papers
-Formula sheets
-Area calculation tools
Square boards
-Flexible materials
-Rulers
-Calculators
Graph papers
-Elastic materials
-Comparison charts
-Review materials
-Differentiation charts
-Exercise books
-Function examples
-Power rule charts
-Algebraic worksheets
-Polynomial examples
-Curve examples
-Geometric models
-Integration notation charts
-Step-by-step worksheets
-Evaluation charts
-Curve sketching tools
-Colored pencils
-Area grids
-Colored materials
-Equation solving aids

KLB Secondary Mathematics Form 4, Pages 26-27