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

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

Inverse of a Transformation
Properties of Inverse Transformations
Area Scale Factor and Determinant

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

-Define inverse transformation conceptually
-Find inverse matrices using algebraic methods
-Apply inverse transformations to return objects to original position
-Verify inverse relationships using matrix multiplication

-Demonstrate inverse transformations geometrically
-Practice finding inverse matrices algebraically
-Verify that A × A⁻¹ = I
-Apply inverse transformations to solve problems

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

KLB Secondary Mathematics Form 4, Pages 24-26

Matrices and Transformation

Shear Transformations
Stretch Transformations

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

-Define shear transformation and its properties
-Identify invariant lines in shear transformations
-Construct matrices for shear transformations
-Apply shear transformations to geometric objects

-Demonstrate shear using cardboard models
-Identify x-axis and y-axis invariant shears
-Practice constructing shear matrices
-Apply shears to triangles and rectangles

Exercise books
-Cardboard pieces
-Manila paper
-Ruler
-Rubber bands

KLB Secondary Mathematics Form 4, Pages 28-34

Matrices and Transformation
Statistics II

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

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

-Apply shear and stretch transformations in combination
-Solve complex transformation problems
-Identify transformation types from matrices
-Calculate areas under shear and stretch transformations

-Work through complex transformation sequences
-Practice identifying transformation types
-Calculate area changes under different transformations
-Solve real-world applications

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

KLB Secondary Mathematics Form 4, Pages 28-34

Statistics II

Working Mean Concept
Mean Using Working Mean - Simple Data

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

-Define working mean (assumed mean)
-Explain why working mean simplifies calculations
-Identify appropriate working mean values
-Apply working mean to reduce calculation errors

-Demonstrate calculation difficulties with large numbers
-Show how working mean simplifies arithmetic
-Practice selecting suitable working means
-Compare results with and without working mean

Exercise books
-Manila paper
-Sample datasets
-Chalk/markers
-Student data

KLB Secondary Mathematics Form 4, Pages 39-42

Statistics II

Mean Using Working Mean - Frequency Tables
Mean for Grouped Data Using Working Mean
Advanced Working Mean Techniques

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

-Calculate mean using working mean for frequency data
-Apply working mean to discrete frequency distributions
-Use the formula with frequencies correctly
-Solve real-world problems with frequency data

-Demonstrate with family size data from local community
-Practice calculating fx and fd systematically
-Work through examples step-by-step
-Students practice with their own collected data

Exercise books
-Manila paper
-Community data
-Chalk/markers
-Real datasets
-Economic data

KLB Secondary Mathematics Form 4, Pages 42-48

Statistics II

Introduction to Quartiles, Deciles, Percentiles
Calculating Quartiles for Ungrouped Data

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

-Define quartiles, deciles, and percentiles
-Understand how they divide data into parts
-Explain the relationship between these measures
-Identify their importance in data analysis

-Use physical demonstration with student heights
-Arrange 20 students by height to show quartiles
-Explain percentile ranks in exam results
-Discuss applications in grading systems

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

KLB Secondary Mathematics Form 4, Pages 49-52

Statistics II

Quartiles for Grouped Data
Deciles and Percentiles Calculations

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

-Calculate quartiles using interpolation formula
-Identify quartile classes correctly
-Apply the formula: Q = L + [(n/4 - CF)/f] × h
-Solve problems with continuous grouped data

-Work through detailed examples on chalkboard
-Practice identifying quartile positions
-Use cumulative frequency systematically
-Apply to real examination grade data

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

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

KLB Secondary Mathematics Form 4, Pages 60-65

Statistics II

Introduction to Variance
Variance Using Alternative Formula
Standard Deviation Calculations

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

KLB Secondary Mathematics Form 4, Pages 65-70

Statistics II

Standard Deviation for Grouped Data
Advanced Standard Deviation Techniques

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

-Calculate standard deviation for frequency distributions
-Use working mean with grouped data for SD
-Apply coding techniques to simplify calculations
-Solve complex grouped data problems

-Work with agricultural yield data from local farms
-Use coding method to simplify calculations
-Calculate SD step by step for grouped data
-Compare variability in different crops

Exercise books
-Manila paper
-Agricultural data
-Chalk/markers
-Transformation examples

KLB Secondary Mathematics Form 4, Pages 65-70

Loci

Introduction to Loci
Basic Locus Concepts and Laws
Perpendicular Bisector Locus

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

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:

-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
-String

KLB Secondary Mathematics Form 4, Pages 75-82

Loci

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 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

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:

-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

Introduction to Intersecting Loci
Intersecting Circles and Lines

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

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

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

Loci

Chord-Based Constructions
Advanced Chord Problems
Integration of All Loci Types

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

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
Additional Trigonometric Identities

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
-Identity reference sheet
-Calculators

KLB Secondary Mathematics Form 4, Pages 99-103

Trigonometry III

Introduction to Waves
Sine and Cosine Waves
Transformations of Sine 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)
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Period Changes in Trigonometric Functions
Combined Amplitude and Period Transformations

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
-Transformation examples

KLB Secondary Mathematics Form 4, Pages 103-109

Trigonometry III

Phase Angles and Wave Shifts
General Trigonometric Functions
Cosine Wave Transformations

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

-Understand concept of phase angle
-Plot graphs of y = sin(x + θ) functions
-Identify horizontal shifts in wave patterns
-Apply phase differences to wave analysis

-Plot y = sin(x + 45°), y = sin(x - 30°)
-Demonstrate horizontal shifting of waves
-Compare leading and lagging waves
-Apply to electrical circuits or sound waves

Exercise books
-Manila paper
-Colored pencils
-Phase shift examples
-Rulers
-Complex function examples
-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
Equations Involving Multiple Angles

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
-Multiple angle examples
-Real applications

KLB Secondary Mathematics Form 4, Pages 109-112

Trigonometry III
Three Dimensional Geometry

Using Graphs to Solve Trigonometric Equations
Trigonometric Equations with Identities
Introduction to 3D Concepts

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
-Cardboard boxes
-Real 3D objects

KLB Secondary Mathematics Form 4, Pages 109-112

Three Dimensional Geometry

Properties of Common Solids
Understanding Planes in 3D Space

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

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

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

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

KLB Secondary Mathematics Form 4, Pages 113-115

Three Dimensional Geometry

Lines in 3D Space
Introduction to Projections
Angle Between Line and Plane - Concept

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

-Understand different types of lines in 3D
-Identify parallel, intersecting, and skew lines
-Recognize that skew lines don't intersect and aren't parallel
-Find examples of different line relationships

-Use rulers/sticks to demonstrate line relationships
-Show parallel lines using parallel rulers
-Demonstrate skew lines using classroom edges
-Practice identifying line relationships in models

Exercise books
-Rulers/sticks
-3D models
-Manila paper
-Light source
-Protractor

KLB Secondary Mathematics Form 4, Pages 113-115

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
Finding Angles Between Planes

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
-Protractor
-Building examples

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Complex Plane-Plane Angle Problems
Practical Applications of Plane Angles
Understanding Skew Lines

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

KLB Secondary Mathematics Form 4, Pages 123-128

Three Dimensional Geometry

Angle Between Skew Lines
Advanced Skew Line Problems

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
-Engineering examples
-Structure diagrams

KLB Secondary Mathematics Form 4, Pages 128-135

Three Dimensional Geometry

Distance Calculations in 3D
Volume and Surface Area Applications
Coordinate Geometry 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
-Volume formulas
-Real containers
-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
Understanding Latitude

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

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Properties of Latitude Lines
Understanding Longitude
Properties of Longitude 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
-String
-World map

KLB Secondary Mathematics Form 4, Pages 136-139

Longitudes and Latitudes

Position of Places on Earth
Latitude and Longitude Differences

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

KLB Secondary Mathematics Form 4, Pages 139-143

Longitudes and Latitudes

Introduction to Distance Calculations
Distance Along Great Circles

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

-Understand relationship between angles and distances
-Learn that 1° on great circle = 60 nautical miles
-Define nautical mile and its relationship to kilometers
-Apply basic distance formulas for great circles

-Demonstrate angle-distance relationship using globe
-Show that 1' (minute) = 1 nautical mile
-Convert between nautical miles and kilometers
-Practice basic distance calculations

Exercise books
-Globe
-Calculator
-Conversion charts
-Manila paper
-Real examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Distance Along Small Circles (Parallels)
Shortest Distance Problems
Advanced Distance Calculations

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
-Flight path examples
-Surveying examples

KLB Secondary Mathematics Form 4, Pages 143-156

Longitudes and Latitudes

Introduction to Time and Longitude
Local Time Calculations

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
-Manila paper
-World time examples
-Calculator

KLB Secondary Mathematics Form 4, Pages 156-161

Longitudes and Latitudes

Greenwich Mean Time (GMT)
Complex Time Problems
Speed Calculations

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
-Calculator
-Navigation examples

KLB Secondary Mathematics Form 4, Pages 156-161

Matrices and Transformations

Transformation on a Cartesian plane
Basic Transformation Matrices
Identification of transformation matrix
Two Successive Transformations
Complex Successive Transformations

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

-Define transformation in mathematics
-Identify different types of transformations
-Plot objects and their images on Cartesian plane
-Relate transformation to movement of objects

-Q/A on coordinate geometry review
-Drawing objects and their images on Cartesian plane
-Practical demonstration of moving objects (reflection, rotation)
-Practice identifying transformations from diagrams
-Class discussion on real-life transformations

Square boards
-Peg boards
-Graph papers
-Mirrors
-Rulers
-Protractors
-Calculators
Graph papers
-Exercise books
-Matrix examples
-Colored pencils

KLB Secondary Mathematics Form 4, Pages 1-6

Matrices and Transformations

Single matrix of transformation for successive transformations
Matrix Multiplication Properties
Identity Matrix and Transformation
Inverse of a matrix

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

-Find single matrix equivalent to successive transformations
-Use matrix multiplication to combine transformations
-Apply single matrix to find final image directly
-Verify results using both methods

-Introduction to 2×2 matrix multiplication
-Working examples combining two transformation matrices
-Verification: successive vs single matrix application
-Practice with matrix multiplication calculations
-Discussion on computational efficiency

Calculators
-Graph papers
-Matrix multiplication charts
-Exercise books
-Matrix worksheets
-Formula sheets
-Matrix examples

KLB Secondary Mathematics Form 4, Pages 15-17, 21

Matrices and Transformations

Determinant and Area Scale Factor
Area scale factor and determinant relationship

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

-Calculate determinant of 2×2 matrix
-Understand relationship between determinant and area scaling
-Apply formula: area scale factor =

det(matrix)

-Solve problems involving area changes under transformations
Calculators
-Graph papers
-Formula sheets
-Area calculation tools

-Determinant calculation practice
-Demonstration using shapes with known areas
-Establishing that area scale factor =

Matrices and Transformations

Shear Transformation
Stretch Transformation and Review

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

-Define shear transformation and its properties
-Find matrices for shear parallel to x-axis and y-axis
-Calculate images under shear transformations
-Understand that shear preserves area but changes shape

-Physical demonstration using flexible materials
-Derivation of shear transformation matrices
-Drawing effects of shear on rectangles and parallelograms
-Verification that area is preserved under shear
-Practice exercises Ex 1.6

Square boards
-Flexible materials
-Graph papers
-Rulers
-Calculators
Graph papers
-Elastic materials
-Comparison charts
-Review materials

KLB Secondary Mathematics Form 4, Pages 10-13, 28-34