Trigonometry 

Pythagoras Theorem
Solutions of problems Using Pythagoras Theorem

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

Deriving Pythagoras Theorem

Chalkboard Charts Illustrating derived theorem
Charts illustrating Pythagoras theorem

KLB BK2 Pg 120   Discovering secondary pg 67

Trigonometry 

Application to real life Situation
Trigonometry Tangent, sine and cosines

By the end of the lesson, the learner should be able to:
Use the formula A = ?s(s-a)(s-b)(s-c) to solve problems in real life

Solving problems in real life using the formula A = ?s(s-a)(s-b)(s-c)

Mathematical table
Charts illustrating tangent, sine and cosine

KLB BK2 Pg 159    Discovering secondary pg 67

Trigonometry 

Trigonometric Table
Angles and sides of a right angled triangle

By the end of the lesson, the learner should be able to:
Use trigonometric tables to find the sine, cosine and tangent

Reading trigonometric tables of sines, cosines and tangent

Mathematical table
Mathematical table Charts Chalkboard

KLB BK2 Pg 127, 138, 139   Discovering secondary pg 71

Trigonometry 

Establishing Relationship of sine and cosine of complimentary angles
Sines and cosines of Complimentary angles

By the end of the lesson, the learner should be able to:
Establish the relationship of sine and cosine of complimentary angles

Using established relationship to solve problems

Chalkboards
Chalkboard Charts illustrating the relationship of sines and cosines of complimentary angles

KLB BK2 Pg 145

Trigonometry 

Relationship between tangent, sine and cosine
Trigonometric ratios of special angles 30, 45, 60 and 90

By the end of the lesson, the learner should be able to:
Relate the three trigonometric ratios, the sine, cosine and tangent

Relating the three trigonometric ratios

Charts showing the three related trigonometric ratio
Charts showing isosceles right angled triangle Charts illustrating Equilateral triangle

KLB BK2 Pg 145

Trigonometry 

Application of Trigonometric ratios in solving problems
Logarithms of Sines

By the end of the lesson, the learner should be able to:
Solve trigonometric problems without using tables

Solving trigonometric problems of special angles

Chalkboard
Chalkboard Mathematical tables

KLB BK2 Pg 148

Trigonometry 

Logarithms of cosines And tangents
Reading tables of logarithms of sines, cosines and tangents

By the end of the lesson, the learner should be able to:
Read the logarithm of cosines and tangents from mathematical tables

Reading logarithms of cosine and tangent from mathematical table

Chalkboard Mathematical table

KLB BK2 Pg 150-152

Trigonometry 

Application of trigonometry to real life situations
Area of a triangle Area of a triangle given the base and height (A = ? bh)

By the end of the lesson, the learner should be able to:
Solve problems in real life using trigonometry

Solving problems using trigonometry in real life

Mathematical table
Chart illustrating worked problem Chalkboard

KLB BK2 Pg 153-154

Trigonometry 

Area of a triangle using the formula (A = ? absin?)
Area of a triangle using the formula A = ?s(s-a)(s-b)(s-c)

By the end of the lesson, the learner should be able to:
- Derive the formula ? absinc - Using the formula derived in calculating the area of a triangle given two sides and an included angle

Deriving the formula ? absinc Using the formula to calculate the area of a triangle given two sides and an included angle

Charts illustrating a triangle with two sides and an included angle Charts showing derived formula
Charts illustrating a triangle with three sides Charts illustrating a worked example i.e. mathematical table

KLB BK2 Pg 156

Trigonometry 

Area of Quadrilateral and Polygons Area of a square, rectangle, rhombus, parallelogram and trapezium

By the end of the lesson, the learner should be able to:
Calculate the are of a triangle, square, rectangle, rhombus, parallelogram and trapezium

Calculating the area of a triangle, square, rectangle, rhombus, parallelogram and trapezium

Charts illustrating formula used in calculating the areas of the quadrilateral

KLB BK2 Pg 161-163

Trigonometry 

Area of a kite
Area of other polygons (regular polygon) e.g. Pentagon

By the end of the lesson, the learner should be able to:
Find the area of a kite

Calculating the area of a Kite

Model of a kite
Mathematical table Charts illustrating Polygons

KLB BK2 Pg 163

Trigonometry 

Area of irregular Polygon
Area of part of a circle Area of a sector (minor sector and a major sector)

By the end of the lesson, the learner should be able to:
Find the area of irregular polygons

Finding the area of irregular polygons

Charts illustrating various irregular polygons Polygonal shapes
Charts illustrating sectors

KLB BK2 Pg 166

Trigonometry 

Defining a segment of a circle Finding the area of a segment of a circle
Area of a common region between two circles given the angles and the radii

By the end of the lesson, the learner should be able to:
- Define what a segment of a circle is - Find the area of a segment of a circle

Finding the area of a segment by first finding the area of a sector less the area of a smaller sector given R and r and angle ?

Chart illustrating a Segment
Charts illustrating common region between the circles Use of a mathematical table during calculation

KLB BK2 Pg 169-170

Trigonometry 

Area of a common region between two circles given only the radii of the two circles and a common chord
Surface area of solids Surface area of prisms Cylinder (ii) Triangular prism (iii) Hexagonal prism

By the end of the lesson, the learner should be able to:
Calculate the area of common region between two circle given the radii of the two intersecting circles and the length of a common chord of the two circles

Finding the area of a common region between two intersecting

Charts illustrating common region between two intersecting circles
Models of cylinder, triangular and hexagonal prisms

KLB BK 2 Pg 176

Trigonometry 

Area of a square based Pyramid
Surface area of a Rectangular based Pyramid

By the end of the lesson, the learner should be able to:
Find the total surface area of a square based pyramid

Finding the surface area of a square based pyramid

Models of a square based pyramid
Models of a Rectangular based pyramid

KLB BK 2 Pg 178

Trigonometry 

Surface area of a cone using the formula A = ?r2 + ?rl
Surface area of a frustrum of a cone and a pyramid

By the end of the lesson, the learner should be able to:
Find the total surface area of the cone by first finding the area of the circular base and then the area of the curved surface

Finding the area of the circular part Finding the area of the curved part Getting the total surface Area

Models of a cone
Models of frustrum of a cone and a pyramid

KLB BK 2 Pg 181

Trigonometry 

Finding the surface area of a sphere
Surface area of a Hemispheres

By the end of the lesson, the learner should be able to:
Find the surface area of a sphere given the radius of a sphere

Finding the surface area of a sphere

Models of a sphere Charts illustrating formula for finding the surface area of a sphere
Models of a hemisphere

KLB BK 2 Pg 183

Trigonometry 

Volume of Solids Volume of prism (triangular based prism)
Volume of prism (hexagonal based prism) given the sides and angle

By the end of the lesson, the learner should be able to:
Find the volume of a triangular based prism

Finding the volume of a triangular based prism

Models of a triangular based prism
Models of hexagonal based prism

KLB BK 2 Pg 186

Trigonometry 

Volume of a pyramid (square based and rectangular based)
Volume of a cone

By the end of the lesson, the learner should be able to:
Find the volume of a square based pyramid and rectangular based pyramid

Finding the surface area of the base Applying the formula V=?x base area x height to get the volume of the pyramids (square and rectangular based)

Models of square and Rectangular based Pyramids
Model of a cone

KLB BK 2 Pg 189-190

Trigonometry 

Volume of a frustrum of a cone
Volume of a frustrum of a pyramid

By the end of the lesson, the learner should be able to:
Find the volume of a frustrum of a cone

Finding the volume of a full cone before its cutoff Finding the volume of a cut cone then subtracting

Models of a frustrum of a cone
Models of frustrum of a pyramid

KLB BK 2 Pg 192

Trigonometry 

Volume of a sphere (v = 4/3?r3)

By the end of the lesson, the learner should be able to:
Find the volume of sphere given the radius of the sphere

Finding the volume of a Sphere

Model of a sphere Mathematical table

KLB BK 2 Pg 195 

Trigonometry 

Volume of a Hemisphere {(v = ? (4/3?r3)}
Application of area of triangles to real life

By the end of the lesson, the learner should be able to:
Find the volume of a hemisphere

Working out the volume of a hemisphere

Models of hemisphere
Mathematical table Chart illustrating formula used

Macmillan BK 2 Pg 173

Trigonometric Ratios

Tangent of an angle

By the end of the lesson, the learner should be able to:
name the sides of a right-angled triangle as opposite, adjacent and hypotenuse. Find the tangent of an angle by calculation

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Using tangents in calculations
Application of tangents

By the end of the lesson, the learner should be able to:
calculate the size of an angle given two sides and an angle from tables

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

The sine of an angle
The cosine of an angle

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

find the sine of an angle by calculations and through tables

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Application of sine and cosine
Complementary angles

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

apply sines to work out lengths and angles. Apply cosine to work out length and angles

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Special angles
Application of Special angles

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

find the sine, cos, and tan of 300,600,450,00,900, without using tables

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Logarithms of sines, cosines and tangents
Relationship between sin, cos and tan

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

solve problems using logarithms of sines cosines and tangents

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Trigonometric Ratios

Application to real life situation
Problem solving

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

apply the knowledge of trigonometry to real life situations

Measuring lengths/angles
Dividing numbers
Drawing right angles
Reading mathematical tables

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Area of A Triangle

Area =
Solve problems involving =

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

derive the formula Area =

Discussions
Drawing triangles
Measuring lengths/angles
Calculating area

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 155-157

Area of A Triangle

A =?s(s-a) (s-b) (s-c)

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

find the area of a triangle given the three sides

Discussions
Drawing triangles
Measuring lengths/angles
Calculating area

Protractor
Ruler
Right corners
Mathematical tables

KLB Maths Bk2 Pg. 155-157

Area of A Triangle
Area of Quadrilaterals

Problem solving
Area of parallelogram

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

solve problems on area of a triangle given the three sides

Discussions
Drawing triangles
Measuring lengths/angles
Calculating area

Protractor
Ruler
Right corners
Mathematical tables
Parallelograms
Trapeziums
Polygons
Squares/rectangles

KLB Maths Bk2 Pg. 155-157

Area of Quadrilaterals

Area of Rhombus
Area of trapezium and kite

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

find the area of a regular polygon.

Drawing trapeziums/polygons
Measuring lengths/angles
Reading mathematical tables
Discussions

Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables

KLB Maths Bk2 Pg. 161

Area of Quadrilaterals

Area of regular polygons
Problem solving

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

find the area of a regular polygon by using the formula A=

Drawing trapeziums/polygons
Measuring lengths/angles
Reading mathematical tables
Discussions

Parallelograms
Trapeziums
Polygons
Squares/rectangles
Mathematical tables Chalkboard illustrations
Mathematical tables

KLB Maths Bk2 Pg. 119-122

Area of Part of a Circle

Area of a sector
Area of a segment

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

find area of a sector

Drawing circles
Measuring radii/diameters
Measuring angles
Calculating the area of a circle
Discussions

Circles
Chart illustrating the area of a sector
Chart illustrating the area of a minor segment

KLB Maths Bk2 Pg. 167-169

Area of Part of a Circle

Common region between two circles
Common region between two circles

By the end of the lesson, the learner should be able to:
find the area of the common region between two circles.

Drawing circles
Measuring radii/diameters
Measuring angles
Calculating the area of a circle
Discussions

Circles
Chart illustrating the area of a minor segment

KLB Maths Bk2 Pg. 167-169

Area of Part of a Circle
Surface Area of Solids

Problem solving
Surface area of prisms

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

solve problems involving the area of part of a circle

Drawing circles
Measuring radii/diameters
Measuring angles
Calculating the area of a circle
Discussions

Circles
Chart illustrating the area of a minor segment Chalkboard illustrations
Prism Chalkboard illustrations

KLB Maths Bk2 Pg. 167-169

Surface Area of Solids

Surface area of pyramid
Surface area of a cone

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

find the surface area of a pyramid

Drawing pyramids
Measuring lengths/
angles
Opening pyramids to
form nets
Discussions
Calculating area

Pyramids with square base, rectangular base, triangular base
Cone

KLB Maths Bk2 Pg. 178

Surface Area of Solids

Surface area of frustrum with circular base
Surface area of frustrum with square base

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

find the surface area of frustrum with circular base

Drawing cones/frustums
Making cones/frustums
Measuring lengths/
angles
Discussions

Chart illustrating the surface area of a frustrum
Chart illustrating frustrum with a square base

KLB Maths Bk2 Pg. 181-283
KLBMathematics Bk2
Discovering Secondary Mathematics Bk2

Surface Area of Solids

Surface area of frustrum with rectangular base
Surface area of spheres

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

find the surface area of frustrum with rectangular base

Drawing cones/frustums
Making cones/frustums
Measuring lengths/
angles
Discussions

Chart illustrating frustrum with a rectangular base
Chalkboard illustrations

KLB Maths Bk2 Pg. 181-183

Surface Area of Solids
Volume of Solids

Problem solving
Volume of prism

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

solve problems on surface area of solids

Learners solve problems

Past paper questions
Prism

KLB Maths Bk2 Pg. 183

Volume of Solids

Volume of pyramid

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

find the volume of a pyramid

Drawing pyramids
Making pyramids
Opening pyramids to
form nets
Discussions

Pyramid

KLB Maths Bk2 Pg. 189-190

Volume of Solids

Volume of a cone
Volume of a sphere

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

find the volume of a cone

Making cones/frustums
Opening cones/frustums
to form nets

Cone
Sphere

KLB Maths Bk2 Pg. 191

Volume of Solids

Volume of frustrum
Volume of frustrum with a square base

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

find the volume of a frustrum with a circular base

Making cones/frustums
Opening cones/frustums
to form nets

Frustrum with circular base
Frustrum with square base

KLB Maths Bk2 Pg. 192-193

Volume of Solids

Volume of frustrum with a rectangular base
Application to real life situation

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

find the volume of a frustrum with a rectangular base

Making cones/frustums
Opening cones/frustums
to form nets

Frustrum with rectangular base
Models of pyramids, prism, cones and spheres

KLB Maths Bk2 Pg. 192-193

Volume of Solids
Quadratic Expressions and Equations

Problem solving
Expansion of Algebraic Expressions

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

solve problems on volume of solids

Making cones/frustums
Opening cones/frustums
to form nets

Past paper questions
Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 196

Quadratic Expressions and Equations

Quadratic identities
Application of identities

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

derive the three Algebraic identities

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 204-205

Quadratic Expressions and Equations

Factorise the Identities
Factorise other quadratic expressions

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

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions
Chart illustrating factorization of a quadratic expression

KLB Maths Bk2 Pg. 205-208

Quadratic Expressions and Equations

Factorisation of expressions of the form k2-9y2
Simplification of an expression by factorisation

By the end of the lesson, the learner should be able to:
factorise a difference of two squares

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 205-208

Quadratic Expressions and Equations

Solving quadratic equations
The formation of quadratic equations

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

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 208

Quadratic Expressions and Equations

Formation and solving of quadratic equations from word problems
Solving on quadratic equations

By the end of the lesson, the learner should be able to:
form and solve quadratic equations from word problems

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 208-210

Quadratic Expressions and Equations

Forming quadratic equations from the roots

By the end of the lesson, the learner should be able to:
form quadratic equations given the roots of the equation

Discussions
Multiplying numbers
Dividing numbers
Adding numbers
Subtracting numbers
Exercises

Real-life experiences
Worked out
expressions

KLB Maths Bk2 Pg. 210