Matrices and Transformation

Transformation on a Cartesian plane
Identification of transformation matrix

By the end of the lesson, the learner should be able to:
Relate image and objects under a given
transformation on the Cartesian plane
Determine the matrix of a
transformation

Drawing objects and
their images on
Cartesian plane
Practice Ex 1.1 P5
Practice exercise
KLB EX 1.2 and 1.3

Square boards
Peg boards and strings
Rubber band

- K.M, Advancing in
Math F4 Pg 1-3
- KLB Pg 1-6 

Matrices and Transformation
Matrices and Transformation
Statistics
Statistics
Statistics

Successive transformation
Single matrix of transformation for successive transformation
Relate Identity Matrix and Transformation
Inverse of a matrix area scale factor and determinant of a matrix
Area of scale factor and determinant of a matrix
Shear and stretch
Ogive
Median
Quartile

By the end of the lesson, the learner should be able to:
Perform successive transformation
Determine and identify a single matrix
for successive transformation
Relate identity matrix and
transformation
Determine the inverse of a
Establish and use the relationship between
area scale factor and determinant of a
matrix
Determine shear and stretch
Use cumulative frequency tables to
Draw the ogive
Estimate the median and quartiles by
Calculations
Ogive
Estimate median and quartiles by
ogive

Drawing objects and its
successive images
KLB Ex 1.4
Practice exercise Ex 1.4
KLB BK 4
Practice exercise Ex 1.5
KLB BK 4 pg 27
Drawing objects and
images under shear and
stretch. Ex 1.6
Drawing cumulative
frequency curve (ogive)
KLB Pg 4, Ex. 2.2
Practice exercise

Square boards
Peg boards and strings
Rubber band
Calculators
Boards and strings
Square boards
Peg boards and strings
Rubber band
Calculators
Graph papers

- K.M, Advancing in
Math F4 Pg 15-17
- KLB Pg 16-24 
- K.M, Advancing in
Math F4 Pg 10-13
- KLB Pg 28-34 

Statistics
Loci

Range- inter quartile range
Quartile deviation
Variance
Standard deviation
Common types of Loci
Perpendicular bisector Loci
Loci of a point at a given distance from a fixed point and fixed line
Angle bisector Loci

By the end of the lesson, the learner should be able to:
Define and calculate measure of
dispersion-range, quartiles and
inter-quartile range
Define and calculate measures of
dispersion ? quartile deviation
Dispersion, variance interpret measure
of dispersion
- Define and calculate measures of
dispersion, standard deviation
- Interpret measures of dispersion
Define locus
Describe common types of loci

Practice exercise
KLB Pg 4, Ex. 2.2
Ex. 2.3
Exams ? CATS
Practice exercise
KLB Pg 4, Ex. 3.2

Calculators
Geometrical patterns

- K.M, Advancing in
Math F4 Pg 32-33
- KLB BK 4 
- K.M, Advancing in
Math F4 Pg 40-41
- KLB Bk4 Pg 68 

Loci
Three Dimensional Geometry

Constant angle loci
Construction:- loci of the equalities
Loci involving chords
Loci under given conditions including intersecting chords
Geometrical properties of common solids
Skew lines projection of a line onto a plane
Length of a line in 3D 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:
Describe common types of loci
Construct loci
Construct loci involving chords
Construct loci involving intersecting
Loci and under given conditions
State the geometric properties of
common solids
? Education Plus Agencies
Identify projection of a line onto a
Plane
Calculate the length between two points
in 3D geometry
Identify and calculate the angle between
a line and a line
a line and a plane
Identify and calculate the angle
between a line and a plane

Practice exercise
KLB Pg 4, Ex. 3.2
Involving inequalities
KLB Pg 4, Ex. 3.5
KLB Pg 4, Ex. 3.4
Practice exercise
Advancing BK 4,
Ex. 5.1
KLB Pg 4, Ex. 5.1
KLB Pg 4, Ex. 5.2
Ex. 5.4
Ex. 5.3 and 5.4

Geometrical patterns
Geometrical
instruments
3-D models

- K.M, Advancing in
Math F4 Pg 42-43
- KLB Bk4 Pg 72-74 
- K.M, Advancing in
Math F4 Pg 72-73
- KLB BK 4
Pg 104-106 

Three Dimensional Geometry
Longitudes and Latitudes
Longitudes and Latitudes
Longitudes and Latitudes
Longitudes and Latitudes

Angles between skew lines
Latitudes and longitudes (great and small circle)
The equator and Greenwich meridian
Longitudes and Latitudes Position of a place on the surface of the earth
Radii of small and great circles
Distance between two points along the small and great circle in nautical miles and kilometres
Distance in nautical miles and kilometers along a circle of latitude
Time and longitude
Speed in knots and kilometer per hour

By the end of the lesson, the learner should be able to:
Identify and calculate the angle
between skew lines
Define the great and small circle in
relation to a sphere (including the earth)
Define the great and small circle in
Locate a place on the earth?s surface in
terms of latitude and longitude
Establish the relationship between the
radii of small and great circles
Calculate the distance between two
points along the great circles and small
circles (longitudes and latitudes) in
nautical miles (nm) and kilometres (km)
Calculate the distance in nautical miles
and kilometers along a circle of
latitude
Calculate time in relation to kilometers
per hour
Calculate speed in knots and
kilometer per hour

Practice exercise
Advancing BK 4,
Ex. 5.4
KLB Pg 4, Ex. 5.2
Ex. 6.2
KLB Pg 4, Ex. 6.1
Ex. 6.4
KLB Pg 4, Ex. 6.2
Practice exercise
Advancing BK 4,
Ex. 6.4
KLB Pg 4, Ex. 6.2
Ex. 6.5
KLB Pg 4, Ex. 6.3
Ex. 6.6

3-D models
Globe
Ball
Globe
Ball
Calculators
Real life situation

- K.M, Advancing in
Math F4 Pg 78-80
- KLB BK 4
Pg 118-119 
- K.M, Advancing in
Math F4 Pg 87-90
- KLB BK 4
Pg 130-139 

Linear Programming
Linear Programming
Differentiation

Formation of linear Inequalities
Analytical solutions of linear inequalities
Solutions of linear inequalities by graph
Optimization (include objective)
Application of linear programming to real life situation
Average and instantaneous rates of change

By the end of the lesson, the learner should be able to:
Form linear inequalities based on real
life situations
Analyze solutions of linear inequalities
Represent the linear inequalities on a
graph
Solve and interpret the optimum
solution of the linear inequalities
solution of the linear programming to
real life situations
Find out the average rates of change
and instantaneous rate of change

Practice exercise
Advancing BK 4,
Ex. 7.3
KLB BK 4, Ex. 7.1
Ex. 7.1
KLB BK 4, Ex. 7.2
Representing inequalities
in a graph
Ex. 7.2
Practice exercise
Advancing BK 4,
Ex. 7.5
KLB BK 4, Ex. 7.3
Ex. 8.1
KLB BK 4, Ex. 8.1

Inequalities
Square boards
Graph papers
Graph paper
Real life situations
Square boards

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

Differentiation
Differentiation
Area Approximations

Differentiation Gradient of a curve at a point
Gradient of y = xn where n is a positive interger
Delta notation (?)
Derivation of a Polynomial
Equations of tangents And normal to the Curve
Stationery point
Curve sketching
Application of differentiation to calculation of distance velocity and acceleration
Maxima and minima
Area by counting technique

By the end of the lesson, the learner should be able to:
Find the gradient of a curve at a point
using tangent
Find the gradient function of the form
y = xn (n = positive interger)
- Relate the delta notation to rates of
change
- Define derivative of a function
polynomial and differentiation
Determine the derivate of a polynomial
Find the equations of tangents and
normals to the curves
Sketch a sketch
Sketch a curve
Apply differentiation in calculating
distance, velocity and accelaration
Apply differentiation in finding maxima
and minima of a function
Relate approximate area of irregular
shapes by counting technique

Practice exercise
Advancing BK 4,
Ex. 8.2
KLB BK 4, Ex. 8.1
Ex. 8.2 and 8.3
Ex. 8.2 and 8.4
Ex. 8.1
Ex. 8.5
KLB BK 4, Ex. 8.2
Practice exercise
Advancing BK 4,
Ex. 8.6
KLB BK 4, Ex. 8.3
Ex. 8.7
KLB BK 4, Ex. 8.4
Ex. 8.8
KLB BK 4, Ex. 8.5
Ex. 8.9
KLB BK 4, Ex. 8.6
Advancing BK 4, Ex. 9.1
KLB BK 4, Ex. 9.1

Square boards
Graph paper
Polynomials
Square boards
Graph paper
Irregular shapes from
Maps
Tracing papers

- K.M, Advancing in
Math F4 Pg 109
- KLB BK 4
Pg 162-163 
- K.M, Advancing in
Math F4 Pg118-120
- KLB BK 4
Pg 174-179 

Area Approximations
Integration

Trapezium rule
Area using trapezium rule
Mid ordinate rule
Area by mid ordinate rule
Differentiation
Reverse differentiation
Integration, notation and sum of area trapezia
Indefinite and definite intergral
Integral notation
Application in Kinematics

By the end of the lesson, the learner should be able to:
Find and derive trapezium rule
Apply trapezium rule estimate area
under curves
Derive the mid ordinate rule
Apply mid ordinate rule to approximate
area under a curve
Carry out the process of differentiation
Reverse differentiation
Integrate notations and sum of areas
of trapezia
Indefine and define intergral
Intergral notation
Apply in kinematics

Practice exercise
Advancing BK 4, Ex. 9.3
KLB BK 4, Ex. 9.2
Advancing BK 4, Ex. 9.4
Advancing BK 4, Ex. 9.5
KLB BK 4, Ex. 9.3
Advancing BK 4,
Ex. 10.1
KLB BK 4, Ex. 10.1
Practice exercise
Advancing BK 4,
Ex. 10.1 and 10.2
KLB BK 4, Ex. 10.1
Ex. 10.3
Ex. 10.4
KLB BK 4, Ex. 10.2
Ex. 10.5
KLB BK 4, Ex. 10.3
Ex. 10.6
KLB BK 4, Ex. 10.4

Square boards
Graph paper
Real life situations
Real life situations
Square boards
Graph paper
Polynomials

- K.M, Advancing in
Math F4 Pg128-130
- KLB BK 4
Pg 194-199 
- K.M, Advancing in
Math F4 Pg135-138
- KLB BK4  Pg207-210