Form 4
CURRICULUM SPECIFICATION
ADDITIONAL MATHEMATICS
FORM FOUR
2010
8
Form 4
A1. LEARNING AREA: FUNCTIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use pictures, role-play
1.1
Represent relations using
the concept of
and computer software
a) arrow diagrams
relations.
to introduce the concept
b) ordered pairs
of relations.
c) graphs
Discuss the idea of set and introduce set
Cooperation
notation.
Orderly
Comparison and
distinguish
function
relation
object
image
Contextual
range
1.2
Identify domain, codomain, object,
domain
image and range of a relation.
codomain
map
1.3
Differentiating
Classify a relation shown on a mapped
Rationality
diagram as: one to one, many to one,
arrow diagram
one to many or many to many relation.
2. Understand
the concept of
2.1
ordered pair
Recognize functions as a special
Represent functions using arrow
relation.
diagrams, ordered pairs or graphs.
Respect
Reasoning
functions.
9
Collating &
Categorizing
Form 4
A1. LEARNING AREA: FUNCTIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
2.2
e.g.
Express functions using function
Orderly
f : x  2x
Conceptualise
f (x) = 2x
notation.
"f : x  2x" is read as "function f maps x
Constructivism
to 2x".
f (x) = 2x is read as
“2x is the image of
x under the function f ”.
Include examples of functions that are
not mathematically based.
Examples of functions include algebraic
(linear and quadratic), trigonometric and
2.3
Determine domain, object, image and
absolute value.
range of a function.
Self-Reliance
Mastery Learning
Identifying
Characteristics
Define and sketch absolute value
functions.
Use graphing
2.4
calculators and
computer software to
Courage
Determine the image of a function given
Rationality
the object and vice versa.
Conceptualise
.
explore the image of
functions.
10
notation
Form 4
A1. LEARNING AREA: FUNCTIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
conceptualize
composite function
/ GENERICS
Students will be able to:
3. Understand
Use arrow diagrams or
the concept of
algebraic method to
composite
determine composite
functions.
functions.
3.1
Determine composition of two functions.
Involve algebraic functions only.
Diligence
relational
mapping
Constructivism
3.2
Images of composite functions include a
range of values. (Limit to linear
composite functions).
Determine the image of composite
functions given the object and vice
Mastery Learning
versa.
3.3
Determine one of the functions in a
Diligence
Self-Reliance
given composite function given the other
Making
Analogies
related function.
4. Understand
the concept of
inverse
4.1
Find the object by inverse mapping given
its image and function.
Limit to algebraic functions.
Diligence
conceptualize
Accuracy
relational
Exclude inverse of composite functions.
inverse
Constructivism
functions.
Mastery Learning
11
Form 4
A1. LEARNING AREA: FUNCTIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
Use sketches of graphs
to show the relationship
between a function and
its inverse.
4.2
Determine
inverse
functions
algebra.
4.3
Diligence
Decision-making
Mastery learning,
Self-access
learning
Illustration
using
Determine and state the condition for
existence of an inverse function.
Emphasise that inverse of a function is
not necessarily a function.
12
composite function
inverse
mapping
Form 4
A2. LEARNING AREA: QUADRATIC EQUATIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
1. Understand
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
Use graphing
the concept
calculators or computer
of quadratic
software such as the
equation and
Geometer’s Sketchpad
its roots.
and spreadsheet to
1.1
Rationality
.
Recognize a quadratic equation and
Pattern
Identification
Mastery Learning
express it in general form.
general form
Criticize
1.2
Self confident
Determine whether a given value is the
explore the concept of
a)
substitution;
quadratic equations.
b)
inspection.
form of (x + a)(x + b) = 0;
inspection
Decision Making
Questions for 1.2(b) are given in the
root
substitution
Exploratory
root of a quadratic equation by
quadratic equation
a and b are
trial and
improvement
method
numerical values.
1.3
Determine roots of quadratic equations
by trial and improvement method.
2. Understand
2.1
Determine the roots of a quadratic
Discuss when
the concept of
equation by
(x p)(x q) = 0, hence x – p = 0 or
quadratic
a)
factorization;
x – q = 0. Include case when p = q.
equations.
b)
completing the square
c)
using the formula.
Derivation of formula for 2.1c is not
required.
13
Rational
Patience
Logical
Constructivism
Reasoning
Consideration
Responsible
Open & logical
mind
Self-confidence
Logical
Reasoning
Appreciation to
ICT
factorization
completing the
square
Form 4
A2. LEARNING AREA: QUADRATIC EQUATIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
Students will be
taught to:
SUGGESTED
TEACHING AND
LEARNING
ACTIVITIES
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
2.2
Form a quadratic equation from given
If x=p and x=q are the roots, then the
roots.
quadratic equation is (xp)(xq)=0,
that is x (pq)xpq=0.
2
Involve the use of: + =
=
c
a
b
a
Consideration
Responsible
Reasoning
Self-confidence
Logical
Reasoning
factorization
completing the
square
and
Cooperative
learning
, where and  are roots of the
Mastery learning
2
quadratic equation ax + bx + c = 0
Exploratory
Comparison
Compare and
Contrast
b2  4ac < 0
Rational
Hardworking
Accuracy
Confidence
quadratic equations to
Explain that "no roots" means "no real
Mastery learning
have
roots".
b2  4ac > 0
3. Understand and
3.1 Determine types of roots of quadratic
equations from the value of b2  4ac
use the conditions for
a) two different
roots;
b) two equal
roots;
b  4ac = 0
2
3.2
real roots
Solve problems involving
b2  4ac in quadratic equations to:
a)
find an unknown value;
b)
derive a relation.
Problem solving
c) no roots.
14
discriminant
Form 4
A3. LEARNING AREA: QUADRATIC FUNCTIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use graphing
1.1
the concept of
calculators or computer
quadratic
software such as
functions and
Geometer’s Sketchpad
a)
based on given tabulated values;
their graphs.
to explore the graphs of
b)
by tabulating values based on
1.2
quadratic functions.
Cooperation
Recognize quadratic functions.
Generating
Ideas
quadratic function
tabulated values
axis of symmetry
Plot quadratic function graphs
parabola
Constructivism
Contextual
Drawing
Tabulating
given functions.
maximum point
minimum point
completing the square
1.3
Use examples of
Recognize shapes of graphs of
Discuss cases where
quadratic functions.
a > 0 and a < 0 for
everyday situations to
Identifying
characteristics
f(x) = a x2 + bx + c = 0
introduce graphs of
quadratic functions.
1.4
Relate the position of quadratic function
graphs with types of roots for f (x)  0.
2. Find the
Use graphing calculators
2.1
maximum and
or dynamic geometry
value of a quadratic function by
minimum values
software such as the
completing the square.
of quadratic
Geometer’s Sketchpad
functions.
to explore the graphs of
Diligence
Rationality
Determine the maximum or minimum
Reasoning
quadratic functions.
15
Relating to
something
axis of symmetry
Form 4
A3. LEARNING AREA: QUADRATIC FUNCTIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
3. Sketch graphs
of quadratic
functions.
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
Use graphing calculators
or
dynamic
3.1
geometry
software such as the
Geometer’s
to
Sketchpad
reinforce
Sketch quadratic function graphs by
Emphasize the marking of maximum or
Diligence
determining the maximum or minimum
minimum point and two other points on
point and two other points.
the graphs drawn or by finding the axis
Constructivism
Making
connections
of symmetry and the intersection with
the
Relating to
something
Quadratic inequality
the y-axis.
Range
Determine other points by finding the
Number line
intersection with the x-axis (if it exists).
4. Understand
Use graphing calculators
and use the
or dynamic geometry
concept of
software such as the
quadratic
Geometer’s Sketchpad
inequalities.
to explore the concept of
4.1
Emphasize on sketching graphs and use
Determine the ranges of values of x that
Rationality
of number lines when necessary.
satisfies quadratic inequalities.
The use of
technology
quadratic inequalities.
16
Intersection
Vertical line
understanding of graphs
of quadratic functions.
Sketch
Making
inferences
Form 4
A4. LEARNING AREA: SIMULTANEOUS EQUATIONS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
1. Solve
Use graphing calculators
simultaneous
or dynamic geometry
equations in two
software such as the
unknowns: one
Geometer’s Sketchpad
linear equation
to explore the concept of
and one non-
simultaneous equations.
1.1
Solve simultaneous equations using the
Limit non-linear equations up to second
substitution method.
degree only.
Cooperation
Courage
Careful
Creating
simultaneous
equations
Creating Mental
Pictures
intersection
substitution method
Problem solving
Making inference
Making analogy
linear equation.
Use examples in real-life
situations such as area,
perimeter and others.
1.2
Relating to
Something
Solve simultaneous equations involving
real-life situations.
Making
Analogies
Drawing
Conclusions
17
Form 4
A5.
NO. OF
WEEKS
LEARNING AREA: INDICES AND LOGARITHMS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use examples of real-
and use the
life situations to
form of:
concept of
introduce the concept
a)
integer indices.
indices and laws
1.1
Find the value of numbers given in the
of indices.
b)
fractional indices.
Discuss zero index and negative indices.
Awareness
Hardworking
Self reliance
Use computer software
1.2
numbers in index form that are
spreadsheet to
multiplied, divided or raised to a power.
Relating to
something
Identifying
characteristics
Use laws of indices to find the value of
such as the
Generating ideas
base
integer indices
fractional indices
index form
of indices to
solve problems.
CCTS
raised to a power
law of indices
enhance the
understanding of
indices.
1.3
Use laws of indices to simplify algebraic
Respect
expressions.
2. Understand
and use the
concept of
logarithms and
laws of
Use scientific
calculators to enhance
2.1
Contextual
learning
Express equation in index form to
Explain definition of logarithm.
N = ax ; loga N = x with a > 0, a ≠ 1.
logarithm form and vice versa.
the understanding of
Emphasize that:
loga 1 = 0; loga a = 1.
the concept of
logarithm.
logarithms to
solve problem
18
Self reliance
Contextual
learning
Predicting
Making
hypotheses
index form
logarithm form
logarithm
undefined
Form 4
A5.
NO. OF
WEEKS
LEARNING AREA: INDICES AND LOGARITHMS
LEARNING
OBJECTIVES
Students will be
taught to:
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
/ GENERICS
Students will be able to:
2.2
Find logarithm of a number.
Emphasize that:
Respect
a)
Identify the
relation
logarithm of negative numbers is
undefined;
b)
Pattern
identification
2.3
Find logarithm of numbers by using laws
index form
b)
numerical form.
Discuss laws of logarithms
of logarithms.
2.4
Simplify logarithmic expressions to the
simplest form.
3.1
Find the logarithm of a number by
and use the
changing the base of the logarithm to a
change of base
suitable base.
of logarithms to
solve problems.
3.2
Relating to
something
Discuss:
loga b =
1
logb a
Respect
Identify the
relation
Solve problems involving the change of
Problem solving
base and laws of logarithms.
Cooperative
learning
19
logarithm form
undefined
Multiple
intelligence
is in
a)
index form
logarithm
logarithm of zero is undefined.
Discuss cases where the given number
3. Understand
VOCABULARY
Form 4
A5. LEARNING AREA: INDICES AND LOGARITHMS
NO. OF
WEEKS
LEARNING
OBJECTIVES
Students will be
taught to:
4. Solve
equations
involving indices
and logarithms.
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
/ GENERICS
Students will be able to:
4.1
Solve equations involving indices.
Equations that involve indices and
Diligence
logarithms are limited to equations with
single solution only.
Solve equations involving indices by:
4.2
Solve equations involving logarithms.
20
a)
comparison of indices and bases;
b)
using logarithms.
Problem solving
Mastery learning
Problem solving
VOCABULARY
Form 4
G1. LEARNING AREA: COORDINATE GEOMETRY
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED
TEACHING AND
LEARNING ACTIVITIES
Students will be
taught to:
1. Find distance
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
/ GENERICS
Students will be able to:
Use examples of real-
between two
life situations to find the
points.
distance between two
1.1
Find the distance between two points
Use the Pythagoras’ Theorem to find the
Systematic
using formula.
formula for distance between two points.
Accuracy
Create Mental
Pictures
Translation
2.1
Determine relation
Limit to cases where m and n are
Find the midpoint of two given points.
the concept
Rational
positive.
Identifying
Characteristics
Comparing
of division of
segment.
midpoint
ratio
Mastery learning
a line
distance
coordinate
points.
2. Understand
VOCABULARY
Derivation of the
2.2
Find the coordinates of a point that
 nx1  mx2 ny1  my 2 
formula 
,

mn 
 mn
divides a line according to a given ratio
m : n.
not required.
21
Differentiating
is
Mastery learning
Relating to
Something
Form 4
G1. LEARNING AREA: COORDINATE GEOMETRY
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
3. Find areas of
Use dynamic geometry
3.1
Find the area of a triangle based on
polygons.
software such as the
the area of specific geometrical
Geometer’s Sketchpad to
shapes.
Limit to numerical values.
Rational
Building diagram
Collating and
Categorizing
sign of the value for area obtained with
Classification
geometrical shape
quadrilateral
the order of the vertices used.
area of polygons.
vertex
3.2
Derivation of the formula:
Find the area of a triangle by using
1
(x1y2 + x2y3 + x3y1 – x2y1 – x3y2 – x1y3)
2
formula.
x1 x2
y1 y 2
polygon
Emphasize the relationship between the
explore the concept of
1
Use
2
area
x3
x1
y3
y1
Determine the
patterns
Sequencing
clockwise
anticlockwise
is not required.
for substitution of
Emphasize that when the area of
coordinates into the
polygon is zero, the given points are
formula.
collinear.
3.3
Find the area of a quadrilateral using
modulus
Mastery learning
collinear
Making
Analogies
formula.
22
vertices
Form 4
G1. LEARNING AREA: COORDINATE GEOMETRY
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
4. Understand
Use dynamic geometry
and use the
software such as the
concept of
Geometer’s Sketchpad to
equation of a
explore the concept of
straight line.
equation of a straight line.
Cooperation
4.5 Determine the x-intercept and the y-
Interpretation
intercept of a line.
Identifying
Characteristics
x-intercept
y-intercept
gradient
Mastery learning
4.2
Find the gradient of a straight line that
passes through two points.
Accuracy
Identifying
Characteristics
Summarize
4.3
Find the gradient of a straight line
Mastery learning
using the x-intercept and y-intercept.
Relating to
Something
straight line
4.4
Find the equation of a straight line
Answers for learning outcomes 4.4(a)
given:
and 4.4(b) must be stated in the simplest
a)
gradient and one point;
form.
b)
two points;
c)
x-intercept and y-intercept.
Involve changing the equation into
gradient and intercept form.
Making
Inferences
general form
intersection
gradient form
intercept form
23
Form 4
G1. LEARNING AREA: COORDINATE GEOMETRY
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
5.1 Find the gradient and the intercepts of a
Cooperation
straight line given the equation.
Differentiating
Tolerance
4.6
5.2
Change the equation of a straight line
Accuracy
to the general form.
Categorize
Relating to
Something
Find the point of intersection of two
Constructivism
Analyzing
Connection
Evaluating
lines.
5. Understand
Use examples of real-life
and use the
situations to explore
concept of
parallel and
5.3 Determine whether two straight lines
Emphasize that for parallel lines:
m1 = m 2.
are parallel when the gradients of both
parallel and perpendicular
lines are known and vice versa.
lines.
5.2
perpendicular
Comparison
perpendicular lines.
Rational
Find the equation of a straight line
Emphasizes that for perpendicular lines
m 1 m 2 = –1.
that passes through a fixed point and
parallel to a given line.
Derivation of
required.
24
m 1 m 2 = –1 is not
parallel
Relating to
Something
Form 4
G1. LEARNING AREA: COORDINATE GEOMETRY
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
Use
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
/ GENERICS
Students will be able to:
graphic
calculator
dynamic
software
Geometer’s
and
5.3
geometry
such
as
Sketchpad
5.4
to explore the concept of
parallel and perpendicu-
Determine whether two straight lines
Relating to
Something
are perpendicular when the gradients
Cooperation
of both lines are known and vice versa
Tolerance
moving point
Determine the equation of a straight
Accuracy
loci
line that passes through a fixed point
Categorize
and perpendicular to a given line.
Evaluating
lar lines.
Constructivism
5.4 Solve problems involving equations of
straight lines.
Solve Problems
Make Decisions
6.
Understand
Use examples of real-life
and use the
situations to explore
concept of
equation of locus
equation of locus
involving distance
involving
between two points.
6.1
Find the equation of locus that
Hardworking
satisfies the condition if:
Analysing
Evaluating
Comparison
a)
the distance of a moving point
from a fixed point is constant;
b)
distance
Cooperative
the ratio of the distances of a
moving point from two fixed
between two
points
VOCABULARY
points is constant.
6.2
Solve problems
Solve problems involving loci.
25
equation of locus
Form 4
S1. LEARNING AREA: STATISTICS
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
Understand and
use the concept
of measures of
central tendency
to solve
problems.
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
Neat
Determine the median of ungrouped data.
In order
Interpret
Determine the modal class of grouped data
Rule & Regulation
1.1
Calculate the mean of ungrouped data.
Discuss grouped data and
graphing calculators and
1.2
Determine the mode of ungrouped data.
ungrouped data.
spreadsheets to explore
1.3
measures of central
1.4
tendency.
Students collect data from
1.5
Find the mode from histograms.
1.6
Calculate the mean of grouped data.
1.7
Calculate the median of grouped data from
investigate measures of
cumulative frequency distribution tables.
1.8
central tendency.
Estimate the median of grouped data from
an ogive.
1.9
ungrouped data
frequency
distribution table
Precise
modal class
Interpret
Contextual
uniform class
interval
histogram
Determine the effects on mode, median
To infer
Courteous conduct
and speed
and mean for a set of data when:
1.10
Interpret
Rule & Regulation
Rational
Ogive is also known as cumulative
frequency curve.
mean
median
Moderate
Derivation of the median formula is
not required.
measure of central
tendency
mode
Involve uniform class intervals only.
from frequency distribution tables.
real-life situations to
Cooperation
Gather &
Classify
Use scientific calculators,
a)
each data is changed uniformly;
b)
extreme values exist;
c)
certain data is added or removed.
Determine the most suitable measure of
central tendency for given data.
26
Involve grouped and ungrouped
data
Open and logical
mind
Contextual
Make
generalization
Form 4
S1. LEARNING AREA: STATISTICS
NO. OF
WEEKS
LEARNING
OBJECTIVES
Students will be
taught to:
2. Understand
and use the
concept of
measures of
dispersion to
solve
problems.
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
2.1
Find the range of ungrouped data.
Determine upper and lower
Independent
quartiles by using the first
2.2
Find the interquartile range of ungrouped
principle.
To compare &
differentiate
Confident
standard deviation
class interval
upper quartile
lower quartile
data.

2.3
Find the range of grouped data.
2.4
Find the interquartile range of grouped data
Neat
from the cumulative frequency table.
2.5
Determine the interquartile range of
Constructivism
grouped data from an ogive.
2.6
2.7
Determine the variance of
a)
ungrouped data;
b)
grouped data.
Courage
Contextual
Evaluate , to
compare &
differentiate
Determine the standard deviation of:
a)
ungrouped data
b)
grouped data.
variance
27
Form 4
S1. LEARNING AREA: STATISTICS
NO. OF
WEEKS
LEARNING
OBJECTIVES
Students will be
taught to:
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
/ GENERICS
Students will be able to:
2.8
Determine the effects on range,
Rules & regulation
Make analogy
interquartile range, variance and standard
deviation for a set of data when:
Rational
a)
each data is changed uniformly;
b)
extreme values exist;
c)
certain data is added or removed.
Make
generalization
Mastery learning
2.9
Compare measures of central tendency
and dispersion between two sets of data.
28
To identify
Emphasize that comparison
between two sets of data using only
measures of central tendency is not
sufficient.
VOCABULARY
Form 4
T1. LEARNING AREA: CIRCULAR MEASURES
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use dynamic geometry
the concept of
software such as the
radian.
Geometer’s Sketchpad to
1.1
Convert measurements in radians to
Discuss the definition of one radian.
degrees and vice versa.
radian
Drawing
Diagram
Interpretation
Contextual
degree
Include measurements in radians
expressed in terms of .
circular measure.
Use examples of real-life
Cooperation
Accuracy
“rad” is the abbreviation of radian.
explore the concept of
2. Understand
MORAL VALUES
2.1
Determine:
and use the
situations to explore
a)
length of arc;
concept of length
circular measure.
b)
radius; and
c)
angle subtended at the centre of a
of arc of a circle
to solve
Courage
Self Access
length of arc
Diligence
Mastery
Learning
angle subtended
circle
problems.
based on given information.
Visualize
2.2
Find perimeter of segments of circles.
Rational
Honesty
Independence
2.3
Solve problems involving lengths of arcs.
Self confident
Reasoning
29
circle
Generate ideas
Constructivism
perimeter
segment
Form 4
T1. LEARNING AREA: CIRCULAR MEASURES
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be
taught to:
Students will be able to:
3. Understand
3.1
Diligence
Determine the:
and use the
a)
area of sector;
concept of area
b)
radius; and
of sector of a
c)
angle subtended at the centre of a
circle to solve
circle
problems.
based on given information.
3.2
Find the area of segments of circles.
3.3
Solve problems involving areas of sectors.
30
Comparison
Formulate
Master
Learning
Courage
Rational
Reasoning
Analyst
Open logical mind
Generate idea
Drawing
diagram
area
sector
Form 4
C1. LEARNING AREA: DIFFERENTIATION
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
1 week
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use graphing calculators
and use the
or dynamic geometry
concept of
software such as
gradients of
Geometer’s Sketchpad to
curve and
explore the concept of
differentiation.
differentiation.
1.1
Determine the value of a function when its
Idea of limit to a function can be
variable approaches a certain value.
illustrated using graphs.
The concept of first derivative of a
1.2
Find the gradient of a chord joining two
points on a curve.
Confidence
Evaluating
limit
Accuracy
Generate ideas
tangent
Patience
first derivative
Rational
gradient
induction
function is explained as a tangent
to a curve can be illustrated using
Constructivism
Finding relation
curve
graphs.
1.3
Find the first derivative of a function y =
f(x), as the gradient of tangent to its graph.
Interpreting
Limit to
y = axn;
1.4
Find the first derivative of polynomials
a, n are constants,
n = 1, 2, 3.
using the first principles.
Notation of f '(x) is equivalent to
1.5
Deduce the formula for first derivative of
the function
y = f(x) by induction.
dy
dx
Confidence
when y = f(x),
f’ ‘ (x) read as
31
Conscientious
Cooperative
“f prime x”.
Making
conclusion
fixed point
Form 4
C1. LEARNING AREA: DIFFERENTIATION
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
LEARNING OUTCOMES
MORAL VALUES
CCTS
/ GENERICS
Students will be
taught to:
Students will be able to:
2. Understand
2.1
Effort
Determine the first derivative of the
Generate ideas
function y = axn using formula.
and use the
1 week
POINTS TO NOTE
concept of first
derivative of
2.2
Evaluating
Determine value of the first derivative of
polynomial
the function
functions to
x.
y = axn for a given value of
solve problems.
2.3
Determine first derivative of a function
Rational
Applications
Careful
Identify relation
Confidence
Identify relation
involving:
a)
addition, or
b)
subtraction
of algebraic terms.
2.4
Determine the first derivative of a product
of two polynomials.
2.5
Determine the first derivative of a quotient
of two polynomials.
Conscientious
2.6
Determine the first derivative of composite
Problem
solving
function using chain rule.
Mastery learning
32
VOCABULARY
Form 4
C1. LEARNING AREA: DIFFERENTIATION
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
/ GENERICS
Students will be able to:
2.7
Determine the gradient of tangent at a
Evaluating
Limit cases in learning outcomes
2.7 - 2.9 to rules introduced in 2.4
- 2.6.
point on a curve.
Determine the equation of tangent at a
normal
Determine the equation of normal at a
Contextual
point on a curve.
3. Understand
Use graphing calculators
and use the
or dynamic geometry
concept of
software to explore the
maximum and
concept of maximum and
minimum values
minimum values
3.1
Determine coordinates of turning points of
Emphasize the use of first
a curve.
derivative to determine the turning
Problem
solving
Making inference
Reasoning
maximum point
Prudence
Determine whether a turning point is a
maximum or a minimum point.
Evaluating
Exclude points of inflexion.
to solve
problems.
3.3
Solve problems involving maximum or
Determination
minimum values.
Limit problems to two variables only.
33
turning point
minimum point
points.
3.2
composite function
chain rule
point on a curve.
2.9
product
quotient
Application
2.8
1 week
VOCABULARY
Cooperative
Solving problems
Form 4
C1. LEARNING AREA: DIFFERENTIATION
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
4.
and
Understand
use
the
concept of rates
of
change
to
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
Use graphing calculators
4.1
with computer base ranger
Determine rates of change for related
Limit problems to 3 variables only.
quantities.
Cooperation
Generate ideas
Diligence
Finding
rates of change
relations
to explore the concept of
Mastery Learning
rates of change.
solve problems.
5. Understand
1 week
5.1
Determine small changes in quantities.
5.2
Determine approximate values using
and use the
concept of small
Confidence
Analysing data
Self access
Learning
Making
Rational
Finding relations
percentage change.
changes and
approximation
Exclude cases involving
differentiation.
inference
approximations
to solve
problems.
6. Understand
and use the
6.1
Introduce
Determine the second derivative of
function y = f (x).
concept of
f ”(x) =
derivative to
solve problems.
as
d  dy 
 
dx  dx 
Self access
learning
second derivative
or
second
6.2
d2y
dx2
Determine whether a turning point is
maximum or minimum point of a curve
d
 f x .
dx
Making inference
Cooperation
Self access
learning
using the second derivative.
34
Problem solving
Form 4
AST1. LEARNING AREA: SOLUTION OF TRIANGLES
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use dynamic geometry
and use the
software such as the
concept of sine
Geometer’s Sketchpad to
rule to solve
LEARNING OUTCOMES
explore the sine rule.
1.1
Rational
Verify sine rule.
Constructivism
1.2
problems.
Include obtuse-angled triangles.
Use sine rule to find unknown sides or
The use of
Technology
Exploratory
situations to explore the
1.3
acute-angled
triangle
ambiguous
Contextual
Use examples of real-life
sine rule
obtuse-angled
triangle
Analyze
angles of a triangle.
sine rule.
Using arithmetic,
algebra, formula
Drawing
diagrams
Find the unknown sides and angles of a
triangle involving ambiguous case.
Accuracy
1.4
Problem solving
Solve problems involving the sine rule.
Mastery Learning
2.
Understand
and
use
concept
cosine
the
of
rule
to
Use dynamic geometry
2.1
Verify cosine rule.
Include obtuse-angled triangles
explore the cosine rule.
Identifying
patterns
Analyze
software such as the
Geometer’s Sketchpad to
Rational
2.2
Use cosine rule to find unknown sides or
Cooperation
angles of a triangle.
Contextual
solve problems.
35
Drawing
diagrams
cosine rule
Form 4
AST1. LEARNING AREA: SOLUTION OF TRIANGLES
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
CCTS
VOCABULARY
/ GENERICS
Students will be able to:
Use examples of real-life
2.3
Solve problems involving cosine rule.
situations to explore the
cosine rule.
2.4
Solve problems involving sine and cosine
Self-Reliance
Problems solving
Diligence
Self-Access
Learning
Identifying patterns
rules.
3. Understand
Use dynamic geometry
and use the
software such as the
formula for areas
Geometer’s Sketchpad to
of triangles to
explore the concept of
solve problems.
areas of triangles.
3.1
Find the area of triangles using the formula
Cooperation
Identify shapes
1
ab sin C or its equivalent.
2
Mastery learning
Use examples of real-life
situations to explore area
3.2
Using arithmetic,
algebra, formula
Solve problems involving three-
Future Learning
dimensional objects.
of triangles.
36
Problem solving
three- dimensional
object
Form 4
ASS1. LEARNING AREA: INDEX NUMBER
NO. OF
WEEKS
LEARNING
OBJECTIVES
SUGGESTED TEACHING
AND LEARNING
ACTIVITIES
Students will be
taught to:
LEARNING OUTCOMES
POINTS TO NOTE
MORAL VALUES
VOCABULARY
/ GENERICS
Students will be able to:
1. Understand
Use examples of real-life
and use the
situations to explore index
concept of index
numbers.
1.1
1.2
Explain index number.
Calculate index number.
Calculate price index.
Q 0 = Quantity at base time.
number to solve
1.3
problems.
Find Q0 or Q 1 given relevant information.
Accuracy
Predicting
index number
Cooperation
Making
inferences
price index
Cooperative
Q 1 = Quantity at
Use examples of real-life
2.1
Explain weightage and composite
index.
composite index.
Find index number or weightage given
relevant information.
2.3
quantity at base
time
quantity at specific
time
composite index
Calculate composite index.
situations to explore
2.2
Related to
something
Making
hypotheses
specific time.
2. Understand
and use the
concept of
composite index
to solve
problems
CCTS
Solve problems involving index number
and composite index.
37
Independence
Kindness
Synthesizing
Analysing
Solve problems
weightage
Form 4
PROJECT WORK
LEARNING OBJECTIVES
SUGGESTED TEACHING AND LEARNING
ACTIVITIES
Students will be guided to:
1. Carry out project work.
LEARNING OUTCOMES
POINTS TO NOTE
VOCABULARY
Students will be able to:



Use scientific calculators, graphing
calculators or computer software to carry out
project work.
Students are allowed to carry out project
work in groups but written reports must be
done individually.
Students should be given opportunity to give
oral presentation of their project work.
1.1
Define the problem/situation to be
studied.
1.2
State relevant conjectures.
1.3
Use problem solving strategies to solve
problems.
1.4
Interpret and discuss results.
1.5
Draw conclusions and/or generalizations
based on critical evaluation of results.
1.6
Present systematic and comprehensive
written reports.
Emphasize the use of Polya’s
four-step problem solving
process.
Use at least two problem
solving strategies.
conjecture
systematic
critical evaluation
mathematical
reasoning
justification
conclusion
generalization
mathematical
communication
Emphasize effective
mathematical communication.
38
rubric
Form 4
CONTRIBUTORS
Advisor
Dr. Sharifah Maimunah Syed Zin
Director
Curriculum Development Centre
Dr. Rohani Abdul Hamid
Deputy Director
Curriculum Development Centre
Editorial
Cheah Eng Joo
Acting Principal Assistant Director
Advisors
(Science and Mathematics Department)
Curriculum Development Centre
Abdul Wahab Ibrahim
Assistant Director
(Head of Mathematics Unit)
Curriculum Development Centre
S. Sivagnanachelvi
Assistant Director
(Head of English Language Unit)
Curriculum Development Centre
Editor
Rosita Mat Zain
Assistant Director
Curriculum Development Centre
39
Form 4
WRITERS
Abdul Wahab Ibrahim
Rusnani Mohd Sirin
Rosita Mat Zain
Curriculum Development Centre
Curriculum Development Centre
Curriculum Development Centre
Susilawati Ehsan
Wong Sui Yong
Dr. Pumadevi a/p Sivasubramaniam
Curriculum Development Centre
Curriculum Development Centre
Maktab Perguruan Raja Melewar
Seremban, Negeri Sembilan
Lau Choi Fong
Mak Sai Mooi
Bibi Kismete Kabul Khan
SMK Hulu Kelang
SMK Jenjarom
SMK Dr. Megat Khas
Hulu Kelang, Selangor
Klang, Selangor
Ipoh, Perak
LAYOUT AND ILLUSTRATION
Rosita Mat Zain
Mohd Razif Hashim
Curriculum Development Centre
Curriculum Development Centre
40