Trigonometry

Deriving the relation Sin2 0 + Cos2 0 = 1

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


Derive trigonometric identity
Sin2 0 + Cos2 0 = 1

Practice exercise
Advancing BK 4, Ex. 4.1
Ex 4.2, Ex 4.3

Charts illustrating the
unit circle and right

- K.M, Advancing in
Math F4 Pg 59-64 

Trigonometry

Trigonometric ratios of the form y = sin x y = tan x y = cos x

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


Draw graphs of trigonometric ratios of
the form y = sin x
y = tan x
y = cos x

Practice exercise
KLB Pg 4, Ex. 4.3
Advancing BK 4,
Ex. 4.4 and 4.5
Patel BK 4, Ex. 4.2

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 59-64
- KLB Bk4 Pg 96-99 

Trigonometry

Trigonometric ratios of the form y = sin x y = tan x y = cos x
Graphs of Trigonometric relations y = a sin x y = a cos x y = a tan x

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


Draw graphs of trigonometric ratios of
the form y = sin x
y = tan x
y = cos x


Draw graphs of trigonometric relations
y = sin x
y = cos x
y = tan x

Practice exercise
KLB Pg 4, Ex. 4.3
Advancing BK 4,
Ex. 4.4 and 4.5
Patel BK 4, Ex. 4.2

Drawing graphs
KLB Pg 4, Ex. 4.3
Advancing BK 4,
Ex. 4.4
Patel BK 4, Ex. 4.3

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 59-64
- KLB Bk4 Pg 96-99 
- K.M, Advancing in
Math F4 Pg 59-63
- KLB Bk4 Pg 96-99 

Trigonometry

Simple trigonometric equations, amplitudes, period, wavelength and phase angle of trigonometric function

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


Deduce from the graphs
y = sin x
y = tan x
y = cos x
The amplitude, wavelength and phase
angle

Practice exercise

Trigonometric relations
Graphs

- K.M, Advancing in
Math F4 Pg 59-63 

Trigonometry

Simple trigonometric equations, amplitudes, period, wavelength and phase angle of trigonometric function

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


Deduce from the graphs
y = sin x
y = tan x
y = cos x
The amplitude, wavelength and phase
angle

Practice exercise

Trigonometric relations
Graphs

- K.M, Advancing in
Math F4 Pg 59-63 

Trigonometry

Trigonometry y = a sin (bx + 0)

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


Draw graphs of trigonometric ratios of
the form y = a sin (bx + 0)

Drawing graphs

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 60 

Trigonometry

Trigonometry y = a cos (bx + 0) y = a tan (bx + 0)

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


Draw graphs of trigonometric ratios of
the form y = a cos (bx + 0)
y = a tan (bx + 0)

Drawing graphs

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 59-64

Trigonometry

Amplitude, period, wavelength and phase Phase angles of trigonometric function

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


Deduce the graphs y = a sin (bx + 0)
y = a cos (bx + 0)
y = a tan (bx + 0)

Practice exercise

Trigonometric relations
Graphs

- K.M, Advancing in
Math F4 Pg 59-64 

Trigonometry

Solution to simple Trigonometric equations

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


Solve simple trigonometric equations
analytically and graphically

Practice exercise
KLB Pg 4, Ex. 4.3
Advancing BK 4,
Ex. 4.6
Patel BK 4, Ex. 4.4

Trigonometric relations
Graphs

- K.M, Advancing in
Math F4 Pg 65-67
- KLB BK 4
Pg 100-102 

Three Dimensional Geometry

Geometrical properties of common solids

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


State the geometric properties of
common solids
? Education Plus Agencies

Practice exercise
Advancing BK 4,
Ex. 5.1
KLB Pg 4, Ex. 5.1

3-D models

- K.M, Advancing in
Math F4 Pg 72-73
- KLB BK 4
Pg 104-106 

Three Dimensional Geometry

Skew lines projection of a line onto a plane

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


Identify projection of a line onto a
Plane

Practice exercise
Advancing BK 4,
Ex. 5.1
KLB Pg 4, Ex. 5.2

3-D models

- K.M, Advancing in
Math F4 Pg 73
- KLB BK 4
Pg 118-119 

Three Dimensional Geometry

Length of a line in 3D geometry

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


Calculate the length between two points
in 3D geometry

Practice exercise
Advancing BK 4,
Ex. 5.4

3-D models

- K.M, Advancing in
Math F4 Pg 78-80 

Three Dimensional Geometry

Angle between a line and a line
A line and a plane
A plane and a plane

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


Identify and calculate the angle between
a line and a line


Identify and calculate the angle
between a line and a plane

Practice exercise
Advancing BK 4,
Ex. 5.4

Practice exercise
Advancing BK 4,
Ex. 5.4
KLB Pg 4, Ex. 5.2

3-D models

3-D models

- K.M, Advancing in
Math F4 Pg 77-80
- K.M, Advancing in
Math F4 Pg 78-80
- KLB BK 4
Pg 113-118 

Three Dimensional Geometry

Angles between skew lines

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


Identify and calculate the angle
between skew lines

Practice exercise
Advancing BK 4,
Ex. 5.4
KLB Pg 4, Ex. 5.2

3-D models

- K.M, Advancing in
Math F4 Pg 78-80
- KLB BK 4
Pg 118-119 

Longitudes and Latitudes

Latitudes and longitudes (great and small circle)

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


Define the great and small circle in
relation to a sphere (including the earth)

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1

Globe
Ball

- K.M, Advancing in
Math F4 Pg 81-83
- KLB BK 4
Pg 125-126 

Longitudes and Latitudes

Latitudes and longitudes (great and small circle)

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


Define the great and small circle in
relation to a sphere (including the earth)

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1

Globe
Ball

- K.M, Advancing in
Math F4 Pg 81-83
- KLB BK 4
Pg 125-126 

Longitudes and Latitudes

The equator and Greenwich meridian

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


Define the great and small circle in
relation to a sphere (including the earth)

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1

Globe
Ball

- K.M, Advancing in
Math F4 Pg 83
- KLB BK 4
Pg 126-127 

Longitudes and Latitudes

The equator and Greenwich meridian
Longitudes and Latitudes Position of a place on the surface of the earth

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


Define the great and small circle in
relation to a sphere (including the earth)


Locate a place on the earth?s surface in
terms of latitude and longitude

Practice exercise
Advancing BK 4,
Ex. 6.2
KLB Pg 4, Ex. 6.1

Globe
Ball

- K.M, Advancing in
Math F4 Pg 83
- KLB BK 4
Pg 126-127 
- K.M, Advancing in
Math F4 Pg 86
- KLB BK 4
Pg 128-129 

Longitudes and Latitudes

Radii of small and great circles

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


Establish the relationship between the
radii of small and great circles

Practice exercise
Advancing BK 4,
Ex. 6.4
KLB Pg 4, Ex. 6.2

Globe
Ball

- K.M, Advancing in
Math F4 Pg 89
- KLB BK 4
Pg 133-134 

Longitudes and Latitudes

Distance between two points along the small and great circle in nautical miles and kilometres

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


Calculate the distance between two
points along the great circles and small
circles (longitudes and latitudes) in
nautical miles (nm) and kilometres (km)

Practice exercise
Advancing BK 4,
Ex. 6.4
KLB Pg 4, Ex. 6.2

Globe
Ball

- K.M, Advancing in
Math F4 Pg 87-90
- KLB BK 4
Pg 130-139 

Longitudes and Latitudes

Distance in nautical miles and kilometers along a circle of latitude

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


Calculate the distance in nautical miles
and kilometers along a circle of
latitude

Practice exercise
Advancing BK 4,
Ex. 6.5
KLB Pg 4, Ex. 6.3

Globe
Ball
Calculators

- K.M, Advancing in
Math F4 Pg 87-98
- KLB BK 4
Pg 130-133 

Longitudes and Latitudes

Distance in nautical miles and kilometers along a circle of latitude

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


Calculate the distance in nautical miles
and kilometers along a circle of
latitude

Practice exercise
Advancing BK 4,
Ex. 6.5
KLB Pg 4, Ex. 6.3

Globe
Ball
Calculators

- K.M, Advancing in
Math F4 Pg 87-98
- KLB BK 4
Pg 130-133 

Longitudes and Latitudes

Time and longitude
Speed in knots and kilometer per hour

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


Calculate time in relation to kilometers
per hour


Calculate speed in knots and
kilometer per hour

Practice exercise
Advancing BK 4,
Ex. 6.5
KLB Pg 4, Ex. 6.3

Practice exercise
Advancing BK 4,
Ex. 6.6
KLB Pg 4, Ex. 6.3

Globe
Ball
Calculators

Real life situation

- K.M, Advancing in
Math F4 Pg 91-92
- KLB Bk4Pg141-142 
- K.M, Advancing in
Math F4 Pg 96-98
- KLB BK 4 Pg 150 

Linear Programming

Formation of linear Inequalities

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


Form linear inequalities based on real
life situations

Practice exercise
Advancing BK 4,
Ex. 7.3
KLB BK 4, Ex. 7.1

Inequalities

- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Formation of linear Inequalities

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


Form linear inequalities based on real
life situations

Practice exercise
Advancing BK 4,
Ex. 7.3
KLB BK 4, Ex. 7.1

Inequalities

- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Formation of linear Inequalities

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


Form linear inequalities based on real
life situations

Practice exercise
Advancing BK 4,
Ex. 7.3
KLB BK 4, Ex. 7.1

Inequalities

- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Analytical solutions of linear inequalities

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


Analyze solutions of linear inequalities

Practice exercise
Advancing BK 4,
Ex. 7.1
KLB BK 4, Ex. 7.2

Square boards
Graph papers

- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155 

Linear Programming

Analytical solutions of linear inequalities
Solutions of linear inequalities by graph

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


Analyze solutions of linear inequalities


Represent the linear inequalities on a
graph

Practice exercise
Advancing BK 4,
Ex. 7.1
KLB BK 4, Ex. 7.2

Representing inequalities
in a graph
Advancing BK 4,
Ex. 7.2
KLB BK 4, Ex. 7.2

Square boards
Graph papers


Square boards

- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155 
- K.M, Advancing in
Math F4 Pg 94-95
- KLB BK 4
Pg 151-152 

Linear Programming

Optimization (include objective)

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


Solve and interpret the optimum
solution of the linear inequalities

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3

Graph paper

- K.M, Advancing in
Math F4 Pg 95-96
- KLB BK 4
Pg 152-155

Linear Programming

Application of linear programming to real life situation

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


Solve and interpret the optimum
solution of the linear programming to
real life situations

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3

Real life situations
Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 99-100
- KLB BK 4
Pg 157-159 

Linear Programming

Application of linear programming to real life situation

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


Solve and interpret the optimum
solution of the linear programming to
real life situations

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3

Real life situations
Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 99-100
- KLB BK 4
Pg 157-159 

Linear Programming

Application of linear programming to real life situation

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


Solve and interpret the optimum
solution of the linear programming to
real life situations

Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3

Real life situations
Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 99-100
- KLB BK 4
Pg 157-159 

Differentiation

Average and instantaneous rates of change

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


Find out the average rates of change
and instantaneous rate of change

Practice exercise
Advancing BK 4,
Ex. 8.1
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg100-103
- KLB BK 4
Pg 157-159 

Differentiation

Average and instantaneous rates of change
Differentiation Gradient of a curve at a point

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


Find out the average rates of change
and instantaneous rate of change


Find the gradient of a curve at a point
using tangent

Practice exercise
Advancing BK 4,
Ex. 8.1
KLB BK 4, Ex. 8.1

Practice exercise
Advancing BK 4,
Ex. 8.2
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg100-103
- KLB BK 4
Pg 157-159 
- K.M, Advancing in
Math F4 Pg 109
- KLB BK 4
Pg 162-163 

Differentiation

Gradient of y = xn where n is a positive interger

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


Find the gradient function of the form
y = xn (n = positive interger)

Practice exercise
Advancing BK 4,
Ex. 8.2 and 8.3
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 110
- KLB BK 4
Pg 164-167 

Differentiation

Gradient of y = xn where n is a positive interger

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


Find the gradient function of the form
y = xn (n = positive interger)

Practice exercise
Advancing BK 4,
Ex. 8.2 and 8.3
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 110
- KLB BK 4
Pg 164-167 

Differentiation

Gradient of y = xn where n is a positive interger

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


Find the gradient function of the form
y = xn (n = positive interger)

Practice exercise
Advancing BK 4,
Ex. 8.2 and 8.3
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg 110
- KLB BK 4
Pg 164-167 

Differentiation

Delta notation (?)

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


- Relate the delta notation to rates of
change
- Define derivative of a function
polynomial and differentiation

Practice exercise
Advancing BK 4,
Ex. 8.2 and 8.4
KLB BK 4, Ex. 8.1

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg114-115
- KLB BK 4
Pg 167-170 

Area Approximations

Area by counting technique
Trapezium rule

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


Relate approximate area of irregular
shapes by counting technique


Find and derive trapezium rule

Practice exercise
Advancing BK 4, Ex. 9.1
KLB BK 4, Ex. 9.1

Practice exercise
Advancing BK 4, Ex. 9.3
KLB BK 4, Ex. 9.2

Irregular shapes from
Maps
Tracing papers


Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg125-127
- KLB BK 4
Pg 190-193 
- K.M, Advancing in
Math F4 Pg128-130
- KLB BK 4
Pg 194-199 

Area Approximations

Area using trapezium rule

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


Apply trapezium rule estimate area
under curves

Practice exercise
Advancing BK 4, Ex. 9.4
KLB BK 4, Ex. 9.2

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg130-132
- KLB BK 4
Pg 195-199

Area Approximations

Mid ordinate rule

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


Derive the mid ordinate rule

Practice exercise
Advancing BK 4, Ex. 9.5
KLB BK 4, Ex. 9.3

Square boards
Graph paper

- K.M, Advancing in
Math F4 Pg132-133
- KLB BK 4
Pg 202-205

Area Approximations

Area by mid ordinate rule

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


Apply mid ordinate rule to approximate
area under a curve

Practice exercise
Advancing BK 4, Ex. 9.5
KLB BK 4, Ex. 9.3

Real life situations

- K.M, Advancing in
Math F4 Pg132-133
- KLB BK 4
Pg 202-205 

Area Approximations

Area by mid ordinate rule

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


Apply mid ordinate rule to approximate
area under a curve

Practice exercise
Advancing BK 4, Ex. 9.5
KLB BK 4, Ex. 9.3

Real life situations

- K.M, Advancing in
Math F4 Pg132-133
- KLB BK 4
Pg 202-205