Matrices and Transformation

Matrices of Transformation
Identifying Common Transformation Matrices

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

KLB Secondary Mathematics Form 4, Pages 1-5

Matrices and Transformation

Finding the Matrix of a Transformation
Using the Unit Square Method
Successive Transformations
Matrix Multiplication for Combined Transformations
Single Matrix for Successive Transformations
Inverse of a Transformation

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

-Determine the matrix representing a given transformation
-Use coordinate geometry to find transformation matrices
-Apply algebraic methods to find matrix elements
-Verify transformation matrices using test points

-Work through algebraic method of finding matrices
-Use simultaneous equations to solve for matrix elements
-Practice with different types of transformations
-Verify results by applying matrix to test objects

Exercise books
-Manila paper
-Ruler
-Chalk/markers
-String
-Coloured pencils

KLB Secondary Mathematics Form 4, Pages 6-16

Matrices and Transformation

Properties of Inverse Transformations
Area Scale Factor and Determinant
Shear Transformations

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

-Calculate determinants of 2×2 matrices
-Use determinant formula for matrix inverses
-Identify when inverse matrices exist
-Apply inverse matrix formula efficiently

-Practice determinant calculations on chalkboard
-Use formula: A⁻¹ = (1/det A) × adj A
-Identify singular matrices (det = 0)
-Solve systems using inverse matrices

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

KLB Secondary Mathematics Form 4, Pages 24-26

Matrices and Transformation

Stretch Transformations
Combined Shear and Stretch Problems

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

KLB Secondary Mathematics Form 4, Pages 28-34

Matrices and Transformation
Statistics II
Statistics II

Isometric and Non-isometric Transformations
Introduction to Advanced Statistics
Working Mean Concept

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

-Distinguish between isometric and non-isometric transformations
-Classify transformations based on shape and size preservation
-Identify isometric transformations from matrices
-Apply classification to solve problems

-Compare congruent and non-congruent images using cutouts
-Classify transformations systematically
-Practice identification from matrices
-Discuss real-world applications of each type

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

KLB Secondary Mathematics Form 4, Pages 35-38

Statistics II

Mean Using Working Mean - Simple Data
Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean

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

KLB Secondary Mathematics Form 4, Pages 42-48

Statistics II

Advanced Working Mean Techniques
Introduction to Quartiles, Deciles, Percentiles

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

-Apply coding techniques with working mean
-Divide by class width to simplify further
-Use transformation methods efficiently
-Solve complex grouped data problems

-Demonstrate coding method on chalkboard
-Show how dividing by class width helps
-Practice reverse calculations to get original mean
-Work with economic data from Kenya

Exercise books
-Manila paper
-Economic data
-Chalk/markers
-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

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

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Introduction to Cumulative Frequency
Drawing Cumulative Frequency Curves (Ogives)
Reading Values from Ogives

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

-Construct cumulative frequency tables
-Understand "less than" cumulative frequencies
-Plot cumulative frequency against class boundaries
-Identify the characteristic S-shape of ogives

-Create cumulative frequency table with class data
-Plot points on manila paper grid
-Join points to form smooth curve
-Discuss properties of ogive curves

Exercise books
-Manila paper
-Ruler
-Class data
-Pencils
-Completed ogives

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II

Applications of Ogives
Introduction to Measures of Dispersion

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

-Use ogives to solve real-world problems
-Find number of values above/below certain points
-Calculate percentage of data in given ranges
-Compare different datasets using ogives

-Solve problems about pass rates in examinations
-Find how many students scored above average
-Calculate percentages for different grade ranges
-Use agricultural production data for analysis

Exercise books
-Manila paper
-Real problem datasets
-Ruler
-Comparative datasets
-Chalk/markers

KLB Secondary Mathematics Form 4, Pages 52-60

Statistics II

Range and Interquartile Range
Mean Absolute Deviation
Introduction to Variance

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

-Calculate range for different datasets
-Find interquartile range (Q3 - Q1)
-Calculate quartile deviation (semi-interquartile range)
-Compare advantages and limitations of each measure

-Calculate range for student heights in class
-Find IQR for the same data
-Discuss effect of outliers on range
-Compare IQR stability with range

Exercise books
-Manila paper
-Student data
-Measuring tape
-Test score data
-Chalk/markers
-Simple datasets

KLB Secondary Mathematics Form 4, Pages 60-65

Statistics II

Variance Using Alternative Formula
Standard Deviation Calculations
Standard Deviation for Grouped Data

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

-Apply the formula: σ² = (Σx²/n) - x̄²
-Use alternative variance formula efficiently
-Compare computational methods
-Solve variance problems for frequency data

-Demonstrate both variance formulas
-Show computational advantages of alternative formula
-Practice with frequency tables
-Students choose efficient method

Exercise books
-Manila paper
-Frequency data
-Chalk/markers
-Exam score data
-Agricultural data

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II
Loci

Advanced Standard Deviation Techniques
Introduction to Loci

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

-Apply transformation properties of standard deviation
-Use coding with class width division
-Solve problems with multiple transformations
-Verify results using different methods

-Demonstrate coding transformations
-Show how SD changes with data transformations
-Practice reverse calculations
-Verify using alternative methods

Exercise books
-Manila paper
-Transformation examples
-Chalk/markers
-String

KLB Secondary Mathematics Form 4, Pages 65-70

Loci

Basic Locus Concepts and Laws
Perpendicular Bisector Locus
Properties and Applications of Perpendicular Bisector

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

-Understand that loci follow specific laws or conditions
-Identify the laws governing different types of movement
-Distinguish between 2D and 3D loci
-Apply locus concepts to simple problems

-Physical demonstrations with moving objects
-Students track movement of classroom door
-Identify laws governing pendulum movement
-Practice stating locus laws clearly

Exercise books
-Manila paper
-String
-Real objects
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 73-75

Loci

Locus of Points at Fixed Distance from a Point
Locus of Points at Fixed Distance from a Line
Angle Bisector Locus

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
-Ruler
-Set square
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Properties and Applications of Angle Bisector
Constant Angle Locus

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
-Protractor

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

Advanced Constant Angle Constructions
Introduction to Intersecting Loci
Intersecting Circles and Lines

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

-Construct constant angle loci for various angles
-Find centers of constant angle arcs
-Solve complex constant angle problems
-Apply to geometric theorem proving

-Find centers for 60°, 90°, 120° angle loci
-Construct major and minor arcs
-Solve problems involving multiple angle constraints
-Verify constructions using measurement

Exercise books
-Manila paper
-Compass
-Protractor
-Ruler

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

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:

-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
-Real-world scenarios
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 83-89

Loci

Distance Inequality Loci
Combined 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
-Ruler

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Advanced Inequality Applications
Introduction to Loci Involving Chords
Chord-Based Constructions
Advanced Chord Problems
Integration of All Loci Types

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

-Apply inequality loci to linear programming introduction
-Solve real-world optimization problems
-Find maximum and minimum values in regions
-Use graphical methods for decision making

-Solve simple linear programming problems
-Find optimal points in feasible regions
-Apply to business and farming scenarios
-Practice identifying corner points

Exercise books
-Manila paper
-Ruler
-Real problem data
-Compass

KLB Secondary Mathematics Form 4, Pages 89-92