Loci

Introduction to Loci

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

In groups, learners are guided to:
-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

KLB Secondary Mathematics Form 4, Pages 73-75

Loci

Basic Locus Concepts and Laws

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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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
Locus of Points at Fixed Distance from a Line

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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

Advanced Constant Angle Constructions

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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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
Distance Inequality Loci

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

In groups, learners are guided to:
-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
-Compass

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Combined Inequality Loci

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

In groups, learners are guided to:
-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

KLB Secondary Mathematics Form 4, Pages 89-92

Loci

Advanced Inequality Applications

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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

Loci

Integration of All Loci Types

By the end of the lesson, the learner should be able to:
-Combine different types of loci in single problems
-Solve comprehensive loci challenges
-Apply multiple loci concepts simultaneously
-Use loci in geometric investigations

In groups, learners are guided to:
-Solve multi-step loci problems
-Combine circle, line, and angle loci
-Apply to real-world complex scenarios
-Practice systematic problem-solving

Exercise books
-Manila paper
-Compass
-Ruler

KLB Secondary Mathematics Form 4, Pages 73-94

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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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
Objective Functions

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

In groups, learners are guided to:
-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
-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

In groups, learners are guided to:
-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

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

In groups, learners are guided to:
-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

KLB Secondary Mathematics Form 4, Pages 166-172

Linear Programming

Plotting Multiple Constraints

By the end of the lesson, the learner should be able to:
-Plot multiple inequalities on same graph
-Find intersection of constraint lines
-Identify feasible region bounded by multiple constraints
-Handle cases with no feasible solution

In groups, learners are guided to:
-Plot system of 3-4 constraints simultaneously
-Find intersection points of constraint lines
-Identify and shade final feasible region
-Discuss unbounded and empty feasible regions

Exercise books
-Manila paper
-Rulers
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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
Differentiation

Business Applications - Production Planning
Introduction to Rate of Change

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

In groups, learners are guided to:
-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
-Real-world examples
-Graph examples

KLB Secondary Mathematics Form 4, Pages 172-176

Differentiation

Average Rate of Change

By the end of the lesson, the learner should be able to:
-Calculate average rate of change between two points
-Use formula: average rate = Δy/Δx
-Apply to distance-time and other practical graphs
-Understand limitations of average rate calculations

In groups, learners are guided to:
-Calculate average speed between two time points
-Find average rate of population change
-Use coordinate points to find average rates
-Compare average rates over different intervals

Exercise books
-Manila paper
-Calculators
-Graph paper

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Instantaneous Rate of Change

By the end of the lesson, the learner should be able to:
-Understand concept of instantaneous rate
-Recognize instantaneous rate as limit of average rates
-Connect to tangent line gradients
-Apply to real-world motion problems

In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer
-Show limiting process using smaller intervals
-Connect to tangent line slopes on curves
-Practice with motion and growth examples

Exercise books
-Manila paper
-Tangent demonstrations
-Motion examples

KLB Secondary Mathematics Form 4, Pages 177-182

Differentiation

Gradient of Curves at Points

By the end of the lesson, the learner should be able to:
-Find gradient of curve at specific points
-Use tangent line method for gradient estimation
-Apply limiting process to find exact gradients
-Practice with various curve types

In groups, learners are guided to:
-Draw tangent lines to curves on manila paper
-Estimate gradients using tangent slopes
-Use the limiting approach with chord sequences
-Practice with parabolas and other curves

Exercise books
-Manila paper
-Rulers
-Curve examples

KLB Secondary Mathematics Form 4, Pages 178-182

Differentiation

Introduction to Delta Notation

By the end of the lesson, the learner should be able to:
-Understand delta (Δ) notation for small changes
-Use Δx and Δy for coordinate changes
-Apply delta notation to rate calculations
-Practice reading and writing delta expressions

In groups, learners are guided to:
-Introduce delta as symbol for "change in"
-Practice writing Δx, Δy, Δt expressions
-Use delta notation in rate of change formulas
-Apply to coordinate geometry problems

Exercise books
-Manila paper
-Delta notation examples
-Symbol practice

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

The Limiting Process

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

In groups, learners are guided to:
-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

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

Introduction to Derivatives

By the end of the lesson, the learner should be able to:
-Define derivative as limit of rate of change
-Use dy/dx notation for derivatives
-Understand derivative as gradient function
-Connect derivatives to tangent line slopes

In groups, learners are guided to:
-Introduce derivative notation dy/dx
-Show derivative as gradient of tangent
-Practice derivative concept with simple functions
-Connect to previous gradient work

Exercise books
-Manila paper
-Derivative notation
-Function examples

KLB Secondary Mathematics Form 4, Pages 182-184

Differentiation

Derivative of Linear Functions

By the end of the lesson, the learner should be able to:
-Find derivatives of linear functions y = mx + c
-Understand that derivative of linear function is constant
-Apply to straight line gradient problems
-Verify using limiting process

In groups, learners are guided to:
-Find derivative of y = 3x + 2 using definition
-Show that derivative equals the gradient
-Practice with various linear functions
-Verify results using first principles

Exercise books
-Manila paper
-Linear function examples
-Verification methods

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of y = x^n (Basic Powers)

By the end of the lesson, the learner should be able to:
-Find derivatives of power functions
-Apply the rule d/dx(x^n) = nx^(n-1)
-Practice with x², x³, x⁴, etc.
-Verify using first principles for simple cases

In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles
-Apply power rule to various functions
-Practice with x³, x⁴, x⁵ examples
-Verify selected results using definition

Exercise books
-Manila paper
-Power rule examples
-First principles verification

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Constant Functions
Derivative of Coefficient Functions

By the end of the lesson, the learner should be able to:
-Understand that derivative of constant is zero
-Apply to functions like y = 5, y = -3
-Explain geometric meaning of zero derivative
-Combine with other differentiation rules

In groups, learners are guided to:
-Show that horizontal lines have zero gradient
-Find derivatives of constant functions
-Explain why rate of change of constant is zero
-Apply to mixed functions with constants

Exercise books
-Manila paper
-Constant function graphs
-Geometric explanations
-Coefficient examples
-Rule combinations

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Derivative of Polynomial Functions

By the end of the lesson, the learner should be able to:
-Find derivatives of polynomial functions
-Apply term-by-term differentiation
-Practice with various polynomial degrees
-Verify results using first principles

In groups, learners are guided to:
-Differentiate y = x³ + 2x² - 5x + 7
-Apply rule to each term separately
-Practice with various polynomial types
-Check results using definition for simple cases

Exercise books
-Manila paper
-Polynomial examples
-Term-by-term method

KLB Secondary Mathematics Form 4, Pages 184-188

Differentiation

Applications to Tangent Lines

By the end of the lesson, the learner should be able to:
-Find equations of tangent lines to curves
-Use derivatives to find tangent gradients
-Apply point-slope form for tangent equations
-Solve problems involving tangent lines

In groups, learners are guided to:
-Find tangent to y = x² at point (2, 4)
-Use derivative to get gradient at specific point
-Apply y - y₁ = m(x - x₁) formula
-Practice with various curves and points

Exercise books
-Manila paper
-Tangent line examples
-Point-slope applications

KLB Secondary Mathematics Form 4, Pages 187-189

Differentiation

Applications to Normal Lines

By the end of the lesson, the learner should be able to:
-Find equations of normal lines to curves
-Use negative reciprocal of tangent gradient
-Apply to perpendicular line problems
-Practice with normal line calculations

In groups, learners are guided to:
-Find normal to y = x² at point (2, 4)
-Use negative reciprocal relationship
-Apply perpendicular line concepts
-Practice normal line equation finding

Exercise books
-Manila paper
-Normal line examples
-Perpendicular concepts

KLB Secondary Mathematics Form 4, Pages 187-189

Differentiation

Introduction to Stationary Points

By the end of the lesson, the learner should be able to:
-Define stationary points as points where dy/dx = 0
-Identify different types of stationary points
-Understand geometric meaning of zero gradient
-Find stationary points by solving dy/dx = 0

In groups, learners are guided to:
-Show horizontal tangents at stationary points
-Find stationary points of y = x² - 4x + 3
-Identify maximum, minimum, and inflection points
-Practice finding where dy/dx = 0

Exercise books
-Manila paper
-Curve sketches
-Stationary point examples

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Types of Stationary Points

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

In groups, learners are guided to:
-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

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Finding and Classifying Stationary Points

By the end of the lesson, the learner should be able to:
-Solve dy/dx = 0 to find stationary points
-Apply systematic classification method
-Use organized approach for point analysis
-Practice with polynomial functions

In groups, learners are guided to:
-Work through complete stationary point analysis
-Use systematic gradient sign testing
-Create organized solution format
-Practice with cubic and quartic functions

Exercise books
-Manila paper
-Systematic templates
-Complete examples

KLB Secondary Mathematics Form 4, Pages 189-195

Differentiation

Curve Sketching Using Derivatives

By the end of the lesson, the learner should be able to:
-Use derivatives to sketch accurate curves
-Identify key features: intercepts, stationary points
-Apply systematic curve sketching method
-Combine algebraic and graphical analysis

In groups, learners are guided to:
-Sketch y = x³ - 3x² + 2 using derivatives
-Find intercepts, stationary points, and behavior
-Use systematic curve sketching approach
-Verify sketches using derivative information

Exercise books
-Manila paper
-Curve sketching templates
-Systematic method

KLB Secondary Mathematics Form 4, Pages 195-197

Differentiation

Introduction to Kinematics Applications
Acceleration as Second Derivative

By the end of the lesson, the learner should be able to:
-Apply derivatives to displacement-time relationships
-Understand velocity as first derivative of displacement
-Find velocity functions from displacement functions
-Apply to motion problems

In groups, learners are guided to:
-Find velocity from s = t³ - 2t² + 5t
-Apply v = ds/dt to motion problems
-Practice with various displacement functions
-Connect to real-world motion scenarios

Exercise books
-Manila paper
-Motion examples
-Kinematics applications
-Second derivative examples
-Motion analysis

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Motion Problems and Applications

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

In groups, learners are guided to:
-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

KLB Secondary Mathematics Form 4, Pages 197-201

Differentiation

Introduction to Optimization

By the end of the lesson, the learner should be able to:
-Apply derivatives to find maximum and minimum values
-Understand optimization in real-world contexts
-Use calculus for practical optimization problems
-Connect to business and engineering applications

In groups, learners are guided to:
-Find maximum area of rectangle with fixed perimeter
-Apply calculus to profit maximization
-Use derivatives for cost minimization
-Practice with geometric optimization

Exercise books
-Manila paper
-Optimization examples
-Real applications

KLB Secondary Mathematics Form 4, Pages 201-204

Differentiation

Geometric Optimization Problems

By the end of the lesson, the learner should be able to:
-Apply calculus to geometric optimization
-Find maximum areas and minimum perimeters
-Use derivatives for shape optimization
-Apply to construction and design problems

In groups, learners are guided to:
-Find dimensions for maximum area enclosure
-Optimize container volumes and surface areas
-Apply to architectural design problems
-Practice with various geometric constraints

Exercise books
-Manila paper
-Geometric examples
-Design applications

KLB Secondary Mathematics Form 4, Pages 201-204

Differentiation

Business and Economic Applications

By the end of the lesson, the learner should be able to:
-Apply derivatives to profit and cost functions
-Find marginal cost and marginal revenue
-Use calculus for business optimization
-Apply to Kenyan business scenarios

In groups, learners are guided to:
-Find maximum profit using calculus
-Calculate marginal cost and revenue
-Apply to agricultural and manufacturing examples
-Use derivatives for business decision-making

Exercise books
-Manila paper
-Business examples
-Economic applications

KLB Secondary Mathematics Form 4, Pages 201-204

Differentiation
Area Approximation

Advanced Optimization Problems
Area Approximation - Introduction to area approximation

By the end of the lesson, the learner should be able to:
-Solve complex optimization with multiple constraints
-Apply systematic optimization methodology
-Use calculus for engineering applications
-Practice with advanced real-world problems

In groups, learners are guided to:
-Solve complex geometric optimization problems
-Apply to engineering design scenarios
-Use systematic optimization approach
-Practice with multi-variable situations

Exercise books
-Manila paper
-Complex examples
-Engineering applications
Wall map of Kenya, traced outlines, real leaves, chalkboard

KLB Secondary Mathematics Form 4, Pages 201-204

Area Approximation

Area Approximation - Tracing and overlaying on a square grid
Area Approximation - Counting full and partial squares

By the end of the lesson, the learner should be able to:
- trace an irregular outline onto tracing paper
- overlay the tracing onto a 1 cm square grid
- distinguish between fully and partially enclosed squares

- Practical activity: learners trace an irregular shape onto tracing paper and overlay on graph paper
- Teacher demonstrates correct alignment
- Learners shade full and partial squares in different colours

Tracing paper, graph paper, pencils, coloured pencils, rulers
Traced outlines, graph paper, calculators, manila paper

KLB Sec. Maths Form 4, pg. 206

Area Approximation

Area Approximation - Applying scale to find actual area
Area Approximation - Subdividing irregular regions into known shapes

By the end of the lesson, the learner should be able to:
- interpret a given map scale (e.g. 1:50 000)
- apply the rule (linear scale)² = area scale
- solve problems involving counting technique with scales

- Worked example on actual area calculation from a 1:50 000 scale map
- Learners solve textbook problems in pairs
- Discussion on common errors when squaring the scale factor

Topographical map sample, graph paper, calculators, chalkboard
Manila paper outlines, rulers, set squares, calculators

KLB Sec. Maths Form 4, pg. 208

Area Approximation

Area Approximation - Deriving the trapezium rule
Area Approximation - Applying the trapezium rule to irregular shapes

By the end of the lesson, the learner should be able to:
- recall the formula for area of a trapezium
- derive the trapezium rule A = (h/2)[y₀ + yₙ + 2(y₁ + … + yₙ₋₁)]
- identify ordinates and the strip width h

In groups, learners are guided to:
- Review of trapezium area formula
- Step-by-step derivation by dividing a region into strips and summing areas
- Guided drawing of strips under a sample curve

Graph paper, manila paper, rulers, chalkboard
Graph paper, rulers, calculators, worksheets

KLB Sec. Maths Form 4, pg. 210

Area Approximation

Area Approximation - Estimating area under a curve using the trapezium rule
Area Approximation - Deriving and applying the mid-ordinate rule

By the end of the lesson, the learner should be able to:
- construct a table of values for a given function y = f(x)
- apply the trapezium rule to estimate area between a curve and the x-axis
- discuss how the number of strips affects accuracy

- Worked example: area under y = x² + 1 from x = 0 to x = 4 using 4 then 8 strips
- Learners construct tables of values and compute areas
- Discussion linking the rule to definite integration

Graph paper, calculators, worksheets, chalkboard

KLB Sec. Maths Form 4, pg. 215

Area Approximation
Integration

Area Approximation - Comparison of methods and consolidation
Introduction to Reverse Differentiation

By the end of the lesson, the learner should be able to:
- apply all three approximation methods to the same region
- identify sources of error and compare accuracy
- solve mixed-method problems including real-life applications

In groups, learners are guided to:
- Whole-class problem-solving using all three methods on one region
- Group work to tabulate and compare estimates
- End-of-topic short test (10 minutes) covering all three methods

Graph paper, calculators, comparison tables, test handout
Graph papers
-Differentiation charts
-Exercise books
-Function examples

KLB Sec. Maths Form 4, pg. 219

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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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

In groups, learners are guided to:
-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