1 · Web view1 week 3. Understand and use the concept of maximum and minimum values to solve problems. Use graphing calculators or dynamic geometry software to explore the concept

Form 4

CURRICULUM SPECIFICATION

ADDITIONAL MATHEMATICS

FORM FOUR

2010

A1. LEARNING AREA: FUNCTIONS

NO. OF WEEKS

LEARNING OBJECTIVES

SUGGESTED TEACHING AND

LEARNING ACTIVITIES

LEARNING OUTCOMES POINTS TO NOTE MORAL VALUES

/ GENERICS

CCTS VOCABULARY

Students will be taught to:

Students will be able to:

8

Form 4NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY

1. Understand

the concept of

relations.

Use pictures, role-play

and computer software

to introduce the concept

of relations.

1.1 Represent relations using

a) arrow diagrams

b) ordered pairs

c) graphs

1.2 Identify domain, codomain, object,

image and range of a relation.

1.3 Classify a relation shown on a mapped

diagram as: one to one, many to one,

one to many or many to many relation.

Discuss the idea of set and introduce

set notation.

Cooperation

Orderly

Contextual

Rationality

Comparison and distinguish

Differentiating

function

relation

object

image

range

domain

codomain

map

ordered pair

arrow diagram

2. Understand

the concept of

functions.

2.1 Recognize functions as a special

relation.

Represent functions using arrow

diagrams, ordered pairs or graphs. Respect

Reasoning

Collating & Categorizing

A1. LEARNING AREA: FUNCTIONSNO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY

Students will be Students will be able to:

9

Form 4NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY

taught to:

Use graphing

calculators and

computer software to

explore the image of

functions.

2.2 Express functions using function

notation.

2.3 Determine domain, object, image and

range of a function.

2.4 Determine the image of a function given

the object and vice versa.

.

e.g. f : x 2x

f (x) = 2x

"f : x 2x" is read as "function f maps x

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

absolute value.

Define and sketch absolute value

functions.

Orderly

Constructivism

Self-Reliance

Mastery Learning

Courage

Rationality

Conceptualise

Identifying Characteristics

Conceptualise

notation

10

Form 4A1. LEARNING AREA: FUNCTIONS

NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



3. Understand

the concept of

composite

functions.

Use arrow diagrams or

algebraic method to

determine composite

functions.

3.1 Determine composition of two functions.

3.2 Determine the image of composite

functions given the object and vice

versa.

3.3 Determine one of the functions in a

given composite function given the other

related function.

Involve algebraic functions only.

Images of composite functions include a range of values. (Limit to linear composite functions).

Diligence

Constructivism

Mastery Learning

Diligence

Self-Reliance

conceptualize

relational

Making Analogies

composite function

inverse

mapping

4. Understand

the concept of

inverse

functions.

4.1 Find the object by inverse mapping

given its image and function.

Limit to algebraic functions.

Exclude inverse of composite functions.

Diligence

Accuracy

Constructivism

Mastery Learning

conceptualize

relational

11

Form 4 A1. LEARNING AREA: FUNCTIONSNO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



Use sketches of graphs to show the relationship between a function and its inverse.

4.2 Determine inverse functions using

algebra.

4.3 Determine and state the condition for existence of an inverse function.

Emphasise that inverse of a function is not necessarily a function.

Diligence

Mastery learning,Self-access learning

Decision-making

Illustrationcomposite function

inverse

mapping

12

Form 4 A2. LEARNING AREA: QUADRATIC EQUATIONS NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Understand

the concept

of quadratic

equation and

its roots.

Use graphing

calculators or computer

software such as the

Geometer’s Sketchpad

and spreadsheet to

explore the concept of

quadratic equations.

1.1 Recognize a quadratic equation and

express it in general form.

1.2 Determine whether a given value is the

root of a quadratic equation by

a) substitution;

b) inspection.

1.3 Determine roots of quadratic equations

by trial and improvement method.

.

Questions for 1.2(b) are given in the

form of (x + a)(x + b) = 0; a and b are

numerical values.

Rationality

Mastery Learning

Self confident

Exploratory

RationalPatience

Constructivism

Pattern Identification

Criticize

Decision Making

Logical

Reasoning

quadratic equation

general form

root

substitution

inspection

trial and improvement method

2. Understand

the concept of

quadratic

equations.

2.1 Determine the roots of a quadratic

equation by

a) factorization;

b) completing the square

c) using the formula.

Discuss when

(x p)(x q) = 0, hence x – p = 0 or

x – q = 0. Include case when p = q.

Derivation of formula for 2.1c is not

required.

ConsiderationResponsibleOpen & logical mind Self-confidence

Appreciation to ICT

Logical Reasoning factorization

completing the square

13

Form 4A2. LEARNING AREA: QUADRATIC EQUATIONS

NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



2.2 Form a quadratic equation from given

roots.If x=p and x=q are the roots, then

the quadratic equation is (xp)

(xq)=0, that is

x2(pq)xpq=0.

Involve the use of: + = and

= , where and are roots of

the quadratic equation ax2 + bx + c = 0

ConsiderationResponsibleReasoning Self-confidence

Cooperative learning

Mastery learning

Exploratory

Logical Reasoning

Comparison

factorization


3. Understand and

use the conditions for

quadratic equations

to

have

a) two different

roots;

b) two equal

roots;

c) no roots.

3.1 Determine types of roots of quadratic

equations from the value of b2 4ac

3.2 Solve problems involving

b2 4ac in quadratic equations to:

a) find an unknown value;

b) derive a relation.

b2 4ac > 0

b2 4ac = 0

b2 4ac < 0

Explain that "no roots" means "no real

roots".

RationalHardworkingAccuracyConfidence

Mastery learning

Compare and Contrast

Problem solving

discriminant

real roots

14

Form 4A3. LEARNING AREA: QUADRATIC FUNCTIONS

NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Understand

the concept of

quadratic

functions and

their graphs.

Use graphing

calculators or computer

software such as


to explore the graphs

of quadratic functions.

Use examples of

everyday situations to

introduce graphs of

quadratic functions.

1.1 Recognize quadratic functions.

1.2 Plot quadratic function graphs

a) based on given tabulated values;

b) by tabulating values based on

given functions.

1.3 Recognize shapes of graphs of

quadratic functions.

1.4 Relate the position of quadratic function

graphs with types of roots for f (x) 0.

Discuss cases where

a > 0 and a < 0 for

f(x) = a x2 + bx + c = 0

Cooperation

ConstructivismContextualDrawingTabulating

Generating Ideas

Identifying characteristics

quadratic function

tabulated values

axis of symmetry

parabola

maximum point

minimum point


axis of symmetry

2. Find the

maximum and

minimum values

of quadratic

functions.

Use graphing

calculators or dynamic

geometry software such

as the Geometer’s

Sketchpad to explore

the graphs of quadratic

functions.

2.1 Determine the maximum or minimum

value of a quadratic function by

completing the square.

DiligenceRationality

Reasoning

Relating to something

15

Form 4A3. LEARNING AREA: QUADRATIC FUNCTIONS

NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



3. Sketch graphs

of quadratic

functions.

Use graphing



as the Geometer’s

Sketchpad to reinforce

the understanding of

graphs of quadratic

functions.

3.1 Sketch quadratic function graphs by

determining the maximum or minimum

point and two other points.

Emphasize the marking of maximum or

minimum point and two other points on

the graphs drawn or by finding the axis

of symmetry and the intersection with

the y-axis.

Determine other points by finding the

intersection with the x-axis (if it exists).

Diligence

ConstructivismMaking connections


Sketch

Intersection

Vertical line

Quadratic inequality

Range

Number line

4. Understand

and use the

concept of

quadratic

inequalities.

Use graphing



as the Geometer’s


the concept of quadratic

inequalities.

4.1 Determine the ranges of values of x that

satisfies quadratic inequalities.

Emphasize on sketching graphs and

use of number lines when necessary.Rationality

The use of technology

Making inferences

16

Form 4

A4. LEARNING AREA: SIMULTANEOUS EQUATIONS NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Solve

simultaneous

equations in two

unknowns: one

linear equation

and one non-

linear equation.

Use graphing



as the Geometer’s


the concept of

simultaneous equations.

Use examples in real-

life situations such as

area, perimeter and

others.

1.1 Solve simultaneous equations using the

substitution method.

1.2 Solve simultaneous equations involving

real-life situations.

Limit non-linear equations up to second

degree only.

CooperationCourageCareful

Problem solvingMaking inferenceMaking analogy

Creating

Creating Mental Pictures

Relating to Something

Making Analogies

Drawing Conclusions

simultaneous equations

intersection

substitution method

17

Form 4A5. LEARNING AREA: INDICES AND LOGARITHMS

NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Understand

and use the

concept of

indices and laws

of indices to

solve problems.

Use examples of real-

life situations to

introduce the concept

of indices.

Use computer software

such as the

spreadsheet to

enhance the

understanding of

indices.

1.1 Find the value of numbers given in the

form of:

a) integer indices.

b) fractional indices.

1.2 Use laws of indices to find the value of

numbers in index form that are

multiplied, divided or raised to a power.

1.3 Use laws of indices to simplify algebraic

expressions.

Discuss zero index and negative

indices.

AwarenessHardworkingSelf reliance

Respect

Contextual learning

Generating ideas


Identifying characteristics

base

integer indices

fractional indices

index form

raised to a power

law of indices

2. Understand

and use the

concept of

logarithms and

laws of

logarithms to

solve problem

Use scientific

calculators to enhance

the understanding of

the concept of

logarithm.

2.1 Express equation in index form to

logarithm form and vice versa.

Explain definition of logarithm.N = ax ; loga N = x with a > 0, a ≠ 1.

Emphasize that:loga 1 = 0; loga a = 1.

Self reliance

Contextual learning

Predicting

Making hypotheses

index form

logarithm form

logarithm

undefined

18


NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



2.2 Find logarithm of a number. Emphasize that:

a) logarithm of negative numbers is

undefined;

b) logarithm of zero is undefined.

Discuss cases where the given number

is in

a) index form

b) numerical form.

Respect

Identify the relation

Multiple intelligence

Pattern identification

index form

logarithm form

logarithm

undefined

2.3 Find logarithm of numbers by using

laws of logarithms.

2.4 Simplify logarithmic expressions to the

simplest form.

Discuss laws of logarithms

3. Understand

and use the

change of base

of logarithms to

solve problems.

3.1 Find the logarithm of a number by

changing the base of the logarithm to a

suitable base.

3.2 Solve problems involving the change of

base and laws of logarithms.

Discuss:

loga b = Respect

Identify the relation

Cooperative learning


Problem solving

19


NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



4. Solve equations involving indices and logarithms.

4.1 Solve equations involving indices.

4.2 Solve equations involving logarithms.

Equations that involve indices and

logarithms are limited to equations with

single solution only.

Solve equations involving indices by:

a) comparison of indices and

bases;

b) using logarithms.

Diligence

Problem solving

Mastery learning

Problem solving

20

Form 4 G1. LEARNING AREA: COORDINATE GEOMETRY

NO. OF WEEKS

LEARNING OBJECTIVES


LEARNING ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Find

distance

between two

points.

Use examples of real-

life situations to find

the distance between

two points.

1.1 Find the distance between two points

using formula.

Use the Pythagoras’ Theorem to find

the formula for distance between two

points.

Systematic

Accuracy

Translation

Mastery learning

Create Mental Pictures

distance

midpoint

coordinate

ratio

2. Understand

the concept

of division of

a line

segment.

2.1 Find the midpoint of two given points.

2.2 Find the coordinates of a point that

divides a line according to a given ratio

m : n.

Limit to cases where m and n are

positive.

Derivation of the formula

is not

required.

Determine relation

Rational

Comparing

Differentiating

Mastery learning



21

Form 4G1. LEARNING AREA: COORDINATE GEOMETRY

NO. OF WEEKS

LEARNING OBJECTIVES

SUGGESTED TEACHING AND LEARNING

ACTIVITIES


/ GENERICS

CCTS VOCABULARY



3. Find areas of

polygons.

Use dynamic geometry


Geometer’s Sketchpad to


area of polygons.

Use

for substitution of

coordinates into the

formula.

3.1 Find the area of a triangle based on

the area of specific geometrical

shapes.

3.2 Find the area of a triangle by using

formula.

3.3 Find the area of a quadrilateral using

formula.

Limit to numerical values.

Emphasize the relationship between the

sign of the value for area obtained with

the order of the vertices used.

Derivation of the formula:

(x1y2 + x2y3 + x3y1 – x2y1 – x3y2 – x1y3)

is not required.

Emphasize that when the area of

polygon is zero, the given points are

collinear.

Rational

Building diagram

Classification

Determine the patterns

Mastery learning

Collating and Categorizing

Sequencing

Making Analogies

area

polygon

geometrical shape

quadrilateral

vertex

vertices

clockwise

anticlockwise

modulus

collinear

22

1321

132121

yyyyxxxx

Form 4G1. LEARNING AREA: COORDINATE GEOMETRY

NO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



4. Understand

and use the

concept of

equation of a

straight line.





equation of a straight line.

4.5 Determine the x-intercept and the y-

intercept of a line.

4.2 Find the gradient of a straight line

that passes through two points.

4.3 Find the gradient of a straight line

using the x-intercept and y-intercept.

Cooperation

Interpretation

Mastery learning

Accuracy

Summarize

Mastery learning




x-intercept

y-intercept

gradient

4.4 Find the equation of a straight line

given:

a) gradient and one point;

b) two points;

c) x-intercept and y-intercept.

Answers for learning outcomes 4.4(a)

and 4.4(b) must be stated in the

simplest form.

Involve changing the equation into gradient and intercept form.

Making Inferences

straight line

general form

intersection

gradient form

intercept form

23

Form 4

G1. LEARNING AREA: COORDINATE GEOMETRYNO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



5.1 Find the gradient and the intercepts of

a straight line given the equation.

4.6 Change the equation of a straight line

to the general form.

5.2 Find the point of intersection of two

lines.

Cooperation

Tolerance

Accuracy

Categorize

Constructivism

Differentiating


Analyzing

5. Understand

and use the

concept of

parallel and

perpendicular -

lines.

Use examples of real-life

situations to explore

parallel and

perpendicular lines.

5.3 Determine whether two straight lines

are parallel when the gradients of both

lines are known and vice versa.

5.2 Find the equation of a straight line

that passes through a fixed point and

parallel to a given line.

Emphasize that for parallel lines:

m1 = m 2.

Emphasizes that for perpendicular lines

m 1 m 2 = –1.

Derivation of m 1 m 2 = –1 is not required.

Connection

Rational

Comparison

Evaluating


parallel

perpendicular

24

Form 4

G1. LEARNING AREA: COORDINATE GEOMETRYNO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



Use graphic calculator and

dynamic geometry

software such as


to explore the concept of

parallel and perpendicu-

lar lines.

5.3 Determine whether two straight lines

are perpendicular when the gradients

of both lines are known and vice

versa

5.4 Determine the equation of a straight

line that passes through a fixed point

and perpendicular to a given line.

5.4 Solve problems involving equations of

straight lines.

Cooperation

Tolerance

Accuracy

Categorize

Constructivism


Evaluating

Solve ProblemsMake Decisions

equation of locus

moving point

loci

6. Understand

and use the

concept of

equation of locus

involving

distance

between two

points



equation of locus

involving distance

between two points.

6.1 Find the equation of locus that

satisfies the condition if:

a) the distance of a moving point

from a fixed point is constant;

b) the ratio of the distances of a

moving point from two fixed

points is constant.

6.2 Solve problems involving loci.

Hardworking

Comparison

Cooperative

AnalysingEvaluating

Solve problems

25

Form 4NO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY

26

Form 4S1. LEARNING AREA: STATISTICS

NO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



Understand and use the concept of measures of central tendency to solve problems.

Use scientific calculators,

graphing calculators and

spreadsheets to explore

measures of central

tendency.

Students collect data from

real-life situations to

investigate measures of

central tendency.

1.1 Calculate the mean of ungrouped data.

1.2 Determine the mode of ungrouped data.

1.3 Determine the median of ungrouped data.

1.4 Determine the modal class of grouped

data from frequency distribution tables.

1.5 Find the mode from histograms.

1.6 Calculate the mean of grouped data.

1.7 Calculate the median of grouped data from

cumulative frequency distribution tables.

1.8 Estimate the median of grouped data from

an ogive.

1.9 Determine the effects on mode, median

and mean for a set of data when:

a) each data is changed uniformly;

b) extreme values exist;

c) certain data is added or removed.

1.10 Determine the most suitable measure of

central tendency for given data.

Discuss grouped data and

ungrouped data.

Involve uniform class intervals only.

Derivation of the median formula is not required.

Ogive is also known as cumulative frequency curve.

Involve grouped and ungrouped data

Cooperation

Neat

In order

Rule & Regulation

Moderate

Rule & Regulation

Precise

Rational

Contextual

Courteous conduct and speed

Open and logical mind

Contextual

Gather & Classify

Interpret

Interpret

Interpret

To infer

Make generalization

measure of central tendency

mean

mode

median

ungrouped data

frequency distribution table

modal class

uniform class interval

histogram

27

Form 4S1. LEARNING AREA: STATISTICSNO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



2. Understand and use the concept of measures of dispersion to solve problems.

2.1 Find the range of ungrouped data.

2.2 Find the interquartile range of ungrouped

data.

2.3 Find the range of grouped data.

2.4 Find the interquartile range of grouped

data from the cumulative frequency table.

2.5 Determine the interquartile range of

grouped data from an ogive.

2.6 Determine the variance of

a) ungrouped data;

b) grouped data.

2.7 Determine the standard deviation of:

a) ungrouped data

b) grouped data.

Determine upper and lower

quartiles by using the first

principle.

Independent

Confident

Neat

Constructivism

Courage

Contextual

To compare & differentiate

Evaluate , to compare & differentiate

standard deviation

class interval

upper quartile

lower quartile

variance

28

Form 4S1. LEARNING AREA: STATISTICSNO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



2.8 Determine the effects on range,

interquartile range, variance and standard

deviation for a set of data when:

a) each data is changed uniformly;

b) extreme values exist;

c) certain data is added or removed.

2.9 Compare measures of central tendency

and dispersion between two sets of data.

Emphasize that comparison between two sets of data using only measures of central tendency is not sufficient.

Rules & regulation

Rational

Mastery learning

Make analogy

To identify

Make generalization

29

Form 4T1. LEARNING AREA: CIRCULAR MEASURESNO. OF WEEKS

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Understand

the concept of

radian.





circular measure.

1.1 Convert measurements in radians to

degrees and vice versa.

Discuss the definition of one

radian.

“rad” is the abbreviation of radian.

Include measurements in radians expressed in terms of .

CooperationAccuracy Drawing

DiagramInterpretationContextual

radian

degree

2. Understand

and use the

concept of

length of arc of a

circle to solve

problems.



circular measure.

2.1 Determine:

a) length of arc;

b) radius; and

c) angle subtended at the centre of

a circle

based on given information.

2.2 Find perimeter of segments of circles.

2.3 Solve problems involving lengths of arcs.

Courage

Diligence

Rational

Honesty

Independence

Self confident

Reasoning

Self Access

Mastery Learning

Visualize

Generate ideas

Constructivism

length of arc

angle subtended

circle

perimeter

segment

30

Form 4T1. LEARNING AREA: CIRCULAR MEASURESNO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



3. Understand

and use the

concept of area

of sector of a

circle to solve

problems.

3.1 Determine the:

a) area of sector;

b) radius; and

c) angle subtended at the centre of

a circle

based on given information.

3.2 Find the area of segments of circles.

3.3 Solve problems involving areas of sectors.

Diligence

CourageRational

Open logical mind

ComparisonFormulateMaster Learning

ReasoningAnalyst

Generate ideaDrawing diagram

area

sector

31

Form 4 C1. LEARNING AREA: DIFFERENTIATION

NO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1 week

1. Understand

and use the

concept of

gradients of

curve and

differentiation.

Use graphing calculators

or dynamic geometry

software such as



differentiation.

1.1 Determine the value of a function when its

variable approaches a certain value.

1.2 Find the gradient of a chord joining two

points on a curve.

1.3 Find the first derivative of a function y = f(x),

as the gradient of tangent to its graph.

1.4 Find the first derivative of polynomials

using the first principles.

1.5 Deduce the formula for first derivative of

the function y = f(x) by induction.

Idea of limit to a function can be

illustrated using graphs.

The concept of first derivative of a

function is explained as a tangent

to a curve can be illustrated using

graphs.

Limit to

y = axn;

a, n are constants, n = 1, 2, 3.

Notation of f '(x) is equivalent to

when y = f(x),

f’ ‘ (x) read as “f prime x”.

Confidence

Accuracy

Patience

Rational

Constructivism

Conscientious

Confidence

Cooperative

Evaluating

Generate ideas

Finding relation

Interpreting

Making conclusion

limit

tangent

first derivative

gradient

induction

curve

fixed point

32

Form 4C1. LEARNING AREA: DIFFERENTIATION

NO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1 week

2. Understand

and use the

concept of first

derivative of

polynomial

functions to

solve problems.

2.1 Determine the first derivative of the

function y = axn using formula.

2.2 Determine value of the first derivative of

the function y = axn for a given value of

x.

2.3 Determine first derivative of a function

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.

2.6 Determine the first derivative of composite

function using chain rule.

Effort

Rational

Careful

Confidence

Conscientious

Mastery learning

Generate ideas

Evaluating

Applications

Identify relation

Identify relation

Problem solving

33


NO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



2.7 Determine the gradient of tangent at a

point on a curve.

2.8 Determine the equation of tangent at a

point on a curve.

2.9 Determine the equation of normal at a

point on a curve.

Limit cases in learning outcomes 2.7 - 2.9 to rules introduced in 2.4 - 2.6.

Contextual

Evaluating

Application

Problem solving

product

quotient

composite function

chain rule

normal

1 week

3. Understand

and use the

concept of

maximum and

minimum values

to solve

problems.


or dynamic geometry

software to explore the

concept of maximum and

minimum values

3.1 Determine coordinates of turning points of

a curve.

3.2 Determine whether a turning point is a

maximum or a minimum point.

3.3 Solve problems involving maximum or

minimum values.

Emphasize the use of first

derivative to determine the turning

points.

Exclude points of inflexion.

Limit problems to two variables only.

Reasoning

Prudence

Determination

Cooperative

Making inference

Evaluating

Solving

problems

turning point

minimum point

maximum point

34


NO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



4. Understand

and use the

concept of rates

of change to

solve problems.


with computer base

ranger to explore the

concept of rates of

change.

4.1 Determine rates of change for related

quantities.

Limit problems to 3 variables only. Cooperation

Diligence

Mastery Learning

Generate ideasFinding relations

rates of change

1 week5. Understand

and use the

concept of small

changes and

approximations

to solve

problems.

5.1 Determine small changes in quantities.

5.2 Determine approximate values using

differentiation.

Exclude cases involving

percentage change.

Confidence

Self access Learning

Analysing data

Making inference

approximation

6. Understand

and use the

concept of

second

derivative to

solve problems.

6.1 Determine the second derivative of

function y = f (x).

6.2 Determine whether a turning point is

maximum or minimum point of a curve

using the second derivative.

Introduce as

or

f ”(x) = .

Rational

Self access learning

Cooperation

Self access learning

Finding relations

Making inference

Problem solving

second derivative

35

Form 4AST1. LEARNING AREA: SOLUTION OF TRIANGLESNO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Understand

and use the

concept of sine

rule to solve

problems.




explore the sine rule.


situations to explore the

sine rule.

1.1 Verify sine rule.

1.2 Use sine rule to find unknown sides or

angles of a triangle.

1.3 Find the unknown sides and angles of a

triangle involving ambiguous case.

1.4 Solve problems involving the sine rule.

Include obtuse-angled triangles.

Rational

Constructivism

The use of Technology

Analyze

Contextual

Exploratory

Accuracy

Mastery Learning

Using arithmetic, algebra, formula

Drawing diagrams

Problem solving

sine rule

acute-angled triangle

obtuse-angled triangle

ambiguous

2. Understand

and use the

concept of

cosine rule to

solve problems.




explore the cosine rule.

2.1 Verify cosine rule.

2.2 Use cosine rule to find unknown sides or

angles of a triangle.

Include obtuse-angled triangles Rational

Analyze

Cooperation

Contextual

Identifying patterns

Drawing diagrams

cosine rule

36

Form 4AST1. LEARNING AREA: SOLUTION OF TRIANGLES NO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY




situations to explore the

cosine rule.

2.3 Solve problems involving cosine rule.

2.4 Solve problems involving sine and cosine

rules.

Self-Reliance

Diligence

Identifying patterns

Problems solving

Self-Access Learning

3. Understand

and use the

formula for

areas of

triangles to

solve problems.





areas of triangles.


situations to explore area

of triangles.

3.1 Find the area of triangles using the

formula ab sin C or its equivalent.

3.2 Solve problems involving three-

dimensional objects.

Cooperation

Identify shapes

Mastery learning

Future Learning

Using arithmetic, algebra, formula

Problem solving three- dimensional object

37

Form 4 ASS1. LEARNING AREA: INDEX NUMBERNO. OF WEEK

S

LEARNING OBJECTIVES


ACTIVITIES


/ GENERICS

CCTS VOCABULARY



1. Understand

and use the

concept of index

number to solve

problems.



index numbers.

1.1 Calculate index number.

1.2 Calculate price index.

1.3 Find Q0 or Q 1 given relevant information.

Explain index number.

Q 0 = Quantity at base time.

Q 1 = Quantity at specific time.

Accuracy

Cooperation

Cooperative

Predicting

Making inferences

Related to something

Making hypotheses

index number

price index

quantity at base time

quantity at specific time

2. Understand and use the concept of composite index to solve problems



composite index.

2.1 Calculate composite index.

2.2 Find index number or weightage given

relevant information.

2.3 Solve problems involving index number and

composite index.

Explain weightage and composite index.

Independence

Kindness

SynthesizingAnalysingSolve problems

composite index

weightage

38

Form 4 PROJECT WORK

LEARNING OBJECTIVES SUGGESTED TEACHING AND LEARNING ACTIVITIES

LEARNING OUTCOMES POINTS TO NOTE VOCABULARY

Students will be guided to: Students will be able to:

1. Carry out project work. 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.

Emphasize effective mathematical communication.

conjecture

systematic

critical evaluation

mathematical reasoning

justification

conclusion

generalization

mathematical communication

rubric

39

Form 4CONTRIBUTORS

Advisor Dr. Sharifah Maimunah Syed Zin Director

Curriculum Development Centre

Dr. Rohani Abdul Hamid Deputy Director


Editorial Cheah Eng Joo Acting Principal Assistant Director

Advisors (Science and Mathematics Department)


Abdul Wahab Ibrahim Assistant Director

(Head of Mathematics Unit)


S. Sivagnanachelvi Assistant Director

(Head of English Language Unit)


Editor Rosita Mat Zain Assistant Director


40

Form 4WRITERS

Abdul Wahab IbrahimCurriculum Development Centre

Rusnani Mohd Sirin Curriculum Development Centre

Rosita Mat ZainCurriculum Development Centre

Susilawati EhsanCurriculum Development Centre

Wong Sui YongCurriculum Development Centre

Dr. Pumadevi a/p SivasubramaniamMaktab Perguruan Raja Melewar

Seremban, Negeri Sembilan

Lau Choi FongSMK Hulu Kelang

Hulu Kelang, Selangor

Mak Sai MooiSMK Jenjarom

Klang, Selangor

Bibi Kismete Kabul KhanSMK Dr. Megat Khas

Ipoh, Perak

LAYOUT AND ILLUSTRATION

Rosita Mat Zain


Mohd Razif Hashim


41

Documents

1 · Web view1 week 3. Understand and use the concept of maximum and minimum values to solve problems. Use graphing calculators or dynamic geometry software to explore the concept