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MINISTRY OF EDUCATION MALAYSIA

Integrated Curriculum for Secondary Schools

Curriculum Specifications

MATHEMATICS

Form 2

Curriculum Development CentreMinistry of Education Malaysia

2002

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CONTENTSPage

RUKUNEGARA v

NATIONAL PHILOSOPHY OF EDUCATION vii

PREFACE ix

INTRODUCTION 1

DIRECTED NUMBERS 10

SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS 14

ALGEBRAIC EXPRESSIONS II 22

LINEAR EQUATIONS 26

RATIOS, RATES AND PROPORTIONS 30PYTHAGORAS THEOREM 34

GEOMETRICAL CONSTRUCTIONS 36

COORDINATES 38

LOCI IN TWO DIMENSIONS 42

CIRCLES 45

TRANSFORMATIONS 51

SOLID GEOMETRY II 56

STATISTICS 58

CONTRIBUTORS 61

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RUKUNEGARA

DECLARATION

OUR NATION, MALAYSIA, being dedicated

to achieving a greater unity of all her peoples;

to maintaining a democratic way of life;

to creating a just society in which the wealth of the nation shall be equitably

shared;

to ensuring a liberal approach to her rich and diverse cultural traditions;

to building a progressive society which shall be oriented to modern scienceand technology;

WE, her peoples, pledge our united efforts to attain these ends guided by

these principles:

BELIEF IN GOD

LOYALTY TO KING AND

COUNTRY UPHOLDING THE

CONSTITUTION RULE OF LAW

GOOD BEHAVIOUR AND MORALITY

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NATIONAL PHILOSOPHY OF EDUCATION

Education in Malaysia is an on-going effort towards developing the potential of individuals

in a holistic and integrated manner, so as to produce individuals who are

intellectually, spiritually, emotionally and physically balanced and harmonious based

on a firm belief in and devotion to God. Such an effort is designed to produce

Malaysian citizens who are knowledgeable and competent, who possess high moral

standards and who are responsible and capable of achieving a high level of personal

well being as well as being able to contribute to the harmony and betterment of the

family, society and the nation at large.

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PREFACE

Science and technology plays a critical role in meeting

Malaysias aspiration to achieve developed nation

status. Since mathematics is instrumental in

developing scientific and technological knowledge,

the provision of quality mathematics education from

an early age in the education process is important.

The secondary school Mathematics curriculum as

outlined in the syllabus has been designed to provide

opportunities for pupils to acquire

mathematical knowledge and skills and developthe higher order problem solving and decision

making skills that they

can apply in their everyday lives. But, more

importantly, together with the other subjects in

the

secondary school curriculum, the

mathematics curriculum seeks to inculcate noble

values and love for the nation towards the final aim

of developing the wholistic person who is capable of

contributing to the harmony and prosperity of the

nation and its people.

Beginning in 2003, science and mathematics will be

taught in English following a phased implementation

schedule which will be completed by 2008.

Mathematics education in English makes use of ICT

in its delivery. Studying mathematics in the medium

of English assisted by ICT will provide greater

opportunities for pupils to enhance their knowledge

and skills because they are able to source the

various repositories of mathematical knowledge

written in English whether in electronic or print

forms. Pupils will be able to communicate

mathematically in English not only in the immediate

environment but also with pupils

from other countries thus increasing their

overall English proficiency and mathematical

competence in the process.

The development of this Curriculum Specifications

accompanying the syllabus is the work of

many individuals expert in the field. To those

who have contributed in one way or another to this

effort, on behalf of the Ministry of Education, I would

like to express my deepest gratitude and

appreciation.

(Dr. SHARIFAH MAIMUNAH SYED

ZIN) Director

Curriculum Development Centre

Ministry of Education Malaysia

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INTRODUCTION

The vision of the country to become an industrialisednation by the end of the second decade can be

achieved through a society that is educated and

competent in the application of mathematical

knowledge. To achieve this vision, it is important that

the society must be inclined towards mathematics.

Therefore, problem solving and communicational skills

in mathematics have to be nurtured from an early age

so that effective decisions can be made later in life.

Mathematics is instrumental in the development

of science and technology. As such, the acquisition

of mathematical knowledge must be intensified so

as to create a sk il led workforce as a

requirement for a country in achieving a

developed nation status. In order to create a K-

based economy, research and development skills

in Mathematics must be instilled at school level.

Based on the National Education Policy and the 2020

Vision, the Mathematics Curriculum has been

reviewed and revised. The rationale behind this move

is the need to provide Mathematical knowledge and

skills to students from various backgrounds andlevels of ability. Therefore, it is the countrys hope

that with the knowledge and skills acquired in

Mathematics,

students will be able to explore, discover, adapt, modifyand be innovative in facing ongoing changes and

future challenges. Acquisition of these skills will help

propel them forward in their future careers thus

benefiting the individual, society and the nation.

The Mathematics Curriculum (KBSM) is a continuum

from Form 1 through Form 5. The content is

categorised into three interrelated areas. These are

Numbers, Shapes and Spaces, and

Relationships. This categorisation is based on the

fact that in any situation it is imperative that a

person has knowledge and skills related to

counting, be able to recognise

shapes and measurements as well as recognise

relationships between numbers and shapes.

AIM

The Mathematics Curriculum for secondary

school aims to develop individuals who are able

to think mathematically and who can apply

mathematicalknowledge effectively and responsibly in

solving problems and making decision. This will

enable the individual to face challenges in everyday

life that arise due to the advancement of science

and technology.

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OBJECTIVES

The mathematics curriculum for the secondary

school enables students to:

1. understand definitions, concepts, laws,

principles and theorems related to Numbers,

Shape and Space, and Relationships;

2. widen applications of basic fundamental

skills such as addition, subtraction,

multiplication and division related to Numbers,

Shape and Space, and Relationships;

3. acquire basic mathematical skills such as: making estimation and rounding;

measuring and constructing;

collecting and handling data;

representing and interpreting data;

recognising and representing

relationship mathematically;

using algorithm and relationship;

solving problem; and

making decision.

4. communicate mathematically;

5. apply knowledge and the skills of

mathematics in solving problems and making

decisions;

6. relate mathematics with other areas of

knowledge;

7. use suitable technologies in concept

building, acquiring skills, solving problems

and exploring the field of mathematics;

8. cultivate mathematical knowledge and

skills effectively and responsibly;

9. inculcate positive attitudes towards

mathematics; and

10. appreciate the importance and the beauty

of mathematics.

CONTENT ORGANISATION

The Mathematics Curriculum at the secondary

level encompasses three main areas, namely

Numbers, Shape and Space, and Relationship.

The topics for each area have been been

arranged according to hierarchy . The basics haveto be taught before abstract concepts can be

introduced to students.

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The Learning Area outlines the scope of knowledge

and skills which have to be mastered in the

learning duration of the subject. They are developedaccording to the appropriate learning objectives and

represented in five columns, as follows:

Column 1 : Learning Objectives

Column 2 : Suggested Teaching and

Learning Activities

Column 3 : Learning Outcomes

Column 4 : Points To Note; and

Column 5 : Vocabulary.

The Learning Objectives define clearly what shouldbe taught. They cover all aspects of the Mathematics

curriculum programme and are presented in a

developmental sequence designed to

support students understanding of the concepts

and skill of mathematics.

The Suggested Teaching and Learning Activities

l is ts some examples of teaching and

learning activities including methods, techniques,

strategies and resources pertaining to the specific

concepts or skills. These are, however, not the

only intended approaches to be used in the

classrooms. Teachers

are encouraged to look for other examples,

determine teaching and learning strategies most

suitable for their students and provide appropriate

teaching and learning materials. Teachers shouldalso make cross-references to other resources

such as the textbooks and the Internet.

The Learning Outcomes define specifically

what students should be able to do. They

prescribe the knowledge, skills or mathematical

processes and values that should be inculcated

and developed at the appropriate level. These

behavioural objectives are measureable in all

aspects.

In the Points To Note column, attention is drawn to

the more significant aspects of

mathematical concepts and skills. These

emphases are to be taken into account so as to

ensure that the concepts and skills are taught and

learnt effectively as intended.

The Vocabulary consists of standard mathematical

terms, instructional words or phrases which are

relevant in structuring activities, in asking questions

or sett ing tasks. I t is important to pay

careful attention to the use of correct terminology

and these need to be systematically introduced to

students in various contexts so as to enable them

to understand their meaning and learn to use them

appropriately.

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EMPHASES IN TEACHING AND LEARNING

This Mathematics Curriculum is arranged in such away so as to give flexibility to teachers to

implement an enjoyable, meaningful, useful and

challenging teaching and learning environment. At

the same time,

it is important to ensure that students show

progression in acquring the mathematical concepts

and skills.

In determining the change to another learning area or

topic, the following have to be taken into

consideration:

The skills or concepts to be acquired in thelearning area or in certain topics;

Ensuring the hierarchy or relationshipbetween learning areas or topics has been

followed accordingly; and

Ensuring the basic learning areas have

been acquired fully before progressing tomore abstract areas.

The teaching and learning processes emphasise

concept building and skill acqusition as well as the

inculcation of good and positive values.Besides these, there are other elements that have

to be taken into account and infused in the teaching

and learning processes in the classroom. The

main elements focused in the teaching and

learning of mathematics are as follows:

1. Problem Solving in Mathematics

Problem solving is the main focus in the teachingand learning of mathematics. Therefore the

teaching and learning process must include

problem solving skills

which are comprehensive and cover the

whole curriculum. The development of problem

solving skills need to be emphasised so that

students are able to solve various problems

effectively. The skills involved are:

Understanding the problem;

Devising a plan;

Carrying out the plan; and Looking back at the solutions.

Various strategies and steps are used to solve

problems and these are expanded so as to be

applicable in other learning areas. Through these

act iv it ies, students can app ly the ir

conceptua l understanding of mathematics and be

confident when facing new or complex situations.

Among the problem solving strategies that could be

introduced are:

Trying a simple case;

Trial and improvement;

Drawing diagrams;

Identifying patterns;

Making a table, chart or systematic list;

Simulation;

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Using analogies;

Working backwards;

Logical reasoning; and

Using algebra.

2. Communication in Mathematics

Communication is an essential means of sharing

ideas and clarifying the understanding of

Mathematics.

Through communica ti on ,

mathematical ideas become the object of reflection,

discussion and modification. The process ofanalytical and systematic reasoning helps students

to reinforce and strengthen their knowledge

and understanding of mathematics to a deeper

level.

Through effective communication students will

become efficient in problem solving and be able to

explain their conceptual understanding and

mathematical skills to their peers and teachers.

Students who have developed the skills to

communicate mathematically will become more

inquisitive and, in the process, gain confidence.Communicational skil ls in mathematics

include reading and understanding problems,

interpreting diagrams and graphs, using correct

and concise mathematical terms during oral

presentations and in

writing. The skill should be expanded to include

listening.

Communication in mathematics through the

listening process occurs when individuals

respond to what they hear and this encourages

individuals to think

using their mathematical knowledge in making

decisions.

Communication in mathematics through the reading

process takes place when an individual

collects information and data and rearranges the

relationship between ideas and concepts.

Communication in mathematics through thevisualisation process takes place when

an individual makes an observation, analyses,

interprets and synthesises data, and presents

them in the form of geometric board, pictures and

diagrams, tables and graphs.

An effective communication environment

can be created by taking into consideration the

following methods:

Identifying relevant contexts associated with

environment and everyday life experience

of students; Identifying students interests;

Identifying suitable teaching materials;

Ensuring active learning;

Stimulating meta-cognitive skills;

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Inculcating positive attitudes; and

Setting up conducive learning environment.Effective communication can be developed through

the following methods.

Oral communication is an interactive processthat

involves psychomotor activities like listening,

touching, observing, tasting and smelling. It is a

two- way interaction that takes place between

teacher and student, student and student, and

student and object. Some of the more effective

and meaningful oral

communication techniques in the learning ofmathematics are as follows:

Story-telling, question and answer sessions

using ones own words;

Asking and answering questions;

Structured and unstructured interviews;

Discussions during forums, seminars,

debates and brainstorming sessions; and

Presentation of findings of assignments.

Wri tten communication is the process

whereby mathematical ideas and information are

disseminated through writing. The written work isusually the result of discussion, input from people

and brainstorming activities when working on

assignments. Through writing, students will be

encouraged to think in

depth about the mathematics content and observe

the relationships between concepts. Examples ofwritten communication activities that can be

developed through assignments are:

Doing exercises;

Keeping journal;

Keeping scrap books;

Keeping folio;

Keeping Portfolios;

Undertaking projects; and

Doing written tests.

Representation is a process of analysing a

mathematical problem and interpreting it from one

mode to another. Mathematical representation

enables students to f ind relat ionships

between mathematical ideas that are informal,

intuitive and abstract using everyday language.

For example 6xy can be interpreted as a

rectangular area with sides

2x and 3y. This will make students realise that

some methods of representation are more

effective and useful if they know how to usethe elements of mathematical representation.

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3. Reasoning in Mathematics

Logical Reasoning or thinking is the basis forunderstanding and solving mathematical problems.

The development of mathematical reasoning is

closely related to the intellectual and communicative

development of s tudents. Emphasis on

logical thinking, during mathematical activities

opens up students minds to accept mathematics

as a powerful tool in the world today.

Students are encouraged to estimate, predict and

make intelligent guesses in the process of seeking

solutions. Students at all levels have to be trained

to investigate their predictions or guesses byusing

concrete material, calculators, computers,

mathematical representation and others.

Logical reasoning has to be absorbed in the

teaching of mathemati cs so t hat students can

recognise , construct and evaluate predictions and

mathematical arguments.

4. Mathematical Connections

In the mathematics curriculum, opportunitiesfor making connections must be created so that

students can link conceptual to procedural

knowledge and relate topics within mathematics

and other learning

areas in general.

The mathematics curriculum consists of severalareas such as arithmetic, geometry, algebra,

measures and problem solving. Withoutconnections between these areas, students will

have to learn and memorise too many concepts and

skills separately. By making connections,

students are able to see mathematics as an

integrated whole rather

than a jumble of unconnected ideas. When

mathematical ideas and the curriculum are

connected to real life within or outside the

classroom, students will become more consciousof the importance and significance of mathematics.

They will also be able to use mathematics

contextually in different learning areas and in real

life situations.

5. Application of Technology

The teaching and learning of mathematics should

employ the latest technology to help students

understand mathematical concepts in depth,

meaningfully and precisely and enable them

to explore mathematical ideas. The use ofcalculators, computers, educational software,

websites in the Internet and relevant learning

packages can help to upgrade the pedagogical

approach and thus promote the understanding of

mathematical concepts.

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The use of these teaching resources will also

help students absorb abstract ideas, be creative,feel confident and be able to work independently

or in groups. Most of these resources are

designed for self-access learning. Through self-

access learning students will be able to access

knowledge or skills and informations independently

according to their own pace. This will serve to

stimulate students interest and develope a sense

of responsibility towards their learning and

understanding of mathematics.

Technology however does not replace the need for

all students to learn and master the basicmathematical skills.

Students must be able

to efficiently add, subtract, multiply and divide

without the use of calculators or other electronic

tools. The use of technology must therefore

emphasise the acquisition of mathematical

concepts and knowledge rather than merely doing

calculation.

APPROACHES IN TEACHING AND LEARNING

Various changes occur that influence the content andpedagogy in the teaching of mathematics in

secondary schools. These changes demand

various ways of teaching mathematics in schools.

The use of teaching resources is vital in forming

mathematical concepts. Teachers should use

real or concrete

materials to help students gain experience, construct

abstract ideas, make inventions, build selfconfidence, encourage independence and inculcate

the spirit of cooperation.

The teaching and learning materials used

should contain self diagnostic elements so that

pupils know how far they have understood the

concepts and acquire the skills.

In order to assist students in having positive

attitudes and personalities, the intrinsic

mathematical values of accuracy, confidence and

thinking systematically have to be infused into

the teaching and learning process. Good moralvalues can be cultivated through suitable contexts.

Learning in groups for example can help students

develop social skills, encourage cooperation and

build self confidence. The element of patriotism

should also be inculcated through the teaching and

learning process in the classroom using certain

topics.

Brief historical anecdotes related to aspects of

ma th ema ti cs a nd f am ou s m at he ma ti ci an s

associated with the learning areas are also

incorporated into the curriculum. It shouldbe presented at appropriate points where it

provides students with a better understanding and

appreciation of mathematics.

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Various teaching strategies and approaches such as

direct instruction, discovery learning, investigation,

guided discovery or other methods must

be

incorporated. Amongst the approaches that can be

given consideration include the following:

Student-centered learning that is interesting;

Different learning abilities and styles of

students;

Usage of relevant, suitable and effective

teaching materials; and

Formative evaluation to determine the

effectiveness of teaching and learning.

The choice of an approach that is suitable will stimulate

the teaching and learning environment inside or outside

the classroom. Approaches that are considered

suitable include the following:

Cooperative learning;

Contextual learning;

Mastery learning;

Constructivism;

Enquiry-discovery; and

Future Studies.

EVALUATION

Evaluation or assessment is part of the teaching and

learning process to ascertain the strengths

and weaknesses of students. It has to be

planned and carried out as part of the classroom

activities. Different methods of assessment can be

conducted. These maybe in the form of

assignments, oral questioning and answering,

observations and interviews. Based on the

r es po ns e, t ea che rs c an re ct if y st ud en ts

misconceptions and weaknesses and also

improve their own teaching skills. Teachers can

then take subsequent effective measures in

conducting remedial

and enrichment activities in upgrading students

performance.

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1. LEARNING AREA: DIRECTED NUMBERSForm 2

LEARNINGOBJECTIVES

SUGGESTED TEACHING ANDLEARNING AC TIVITIES

LEARNING OUTCOMES POINTS TO NO TE VOCABULARY

Students w ill be taught to: Students w ill be abl e to:

1.1 Perf ormcomputat ions

involving

mu ltip licatio nanddivision of integersto solve problems.

Use concrete materials such ascoloured chips and multiplication

tables to de monstratemu ltip licatio n and d ivisionof integers.

Co mp lete mu ltip lication tab leby recognising patterns.

Solve proble ms relate d to real-life situations.

i. Mu ltip ly integers.

ii. Solve proble msinvolving

mu ltip licatio n ofintegers.

iii. Divid e integ ers.

iv. Solve proble msinvolving

division of integers.

Begin mu ltiplicat ioninvolving tw o integersonly.

Re late divisio nof integers to

mu ltip licatio n.

Divisio n by zero

is undef ined.

directednumbers

mu ltip ly

divide

integer

positive

negativeproduct

quotient

like sign

unlike sign

undef ined

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LEARNINGOBJECTIVES





involving co mbined

operations ofadditio n,subtraction,

mu ltip licatio n anddivision of integers

to solve proble ms.

e.g.

( 2) 3 + ( 4)

4 x ( 3) ( 6)

Students use calculators tocompare and verif y answers.

Solve proble ms relate d to real-life situations such as money and

temp erature.

i. Perf orm co mputat ionsinvolving co mbine d

operations of addition,subtraction, mu ltip licatio nanddivision of integers.

ii. Solve proble ms involving

combin ed operations ofadditio n, subtraction,

mu ltip licatio n and d ivisionofintegers includin g the use of

brackets.

Emphasise the orderof operations.

Co mb ined operations also know nas mixed operations.

integer

plus

minus

mu ltip ly

divide

positive

negative

bracket

mixed

operations

order of

operations

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1. LEARNING AREA: DIRECTED NUMBERS

Form 2

LEARNING

OBJECTIVES

SUGGESTED TEACHING AND

LEARNING AC TIVITIES



1.3 Extend th econcept

of integers to

f ractions to solveproble ms.

1.4 Extend th econcept

of integers to

decima ls to solveproble ms.

Co mpare f ractionsusing:

a) number lin es

b) scientif iccalculators.

Co mpare d ecimalsusing:

a) number lin es

b) scientif iccalculators.

i. Co mpare a nd order fractions.

ii. Perf orm ad dition,subtraction,

mu ltip licatio n or division onfractions.

i. Co mpare a nd orderdecimals.

ii. Perf orm ad dition,subtraction,

mu ltip licatio n or division ondecima ls.

Begin w ith two f ractions.

Begin w ith two decima ls.

f raction

compare

order

greater than

less than

positive

negative

decima l

add

minus

mu ltip ly

divide

product

quotient

sum

dif f erence

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LEARNINGOBJECTIVES





involving directed

numbers (integers,f ractions and

decima ls).

Explore addit ion, subtraction,mu ltip licatio n and d ivisionusing

standard algorith m and estimat ion.

Perf orm op erations on integers. e.g.

2 + ( 3) x 4

Perf orm op erations on fractions. e.g.

i. Perf orm ad dition,subtraction,

mu ltip licatio n or divisioninvolving tw o directed

numbers.

ii. Perf orm co mputat ions

involving co mbinat ion of tw

oor more operat ions on

directed nu mbers including

the use of brackets.

Emphasise the orderof operations.

plus

minus

mu ltip ly

divide

positive

negative

1 3 1 x 4 5 2

Perf orm op erations on decimals. e.g.

2.5 1.2 x ( 0.3)

Perf orm op erations on in

tegers,f ractions and decima ls.

e.g.

iii. Pose and solve proble msinvolving directed nu mbers.

1.25

2 x ( 4)

5

Solve proble ms relate d to real-life situations.


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2. LEARNING AREA: SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTSForm 2

LEARNINGOBJECTIVES




2.1 Understand anduse the concept

of squares of

numbers.

Recognise squares ofnumbers as the areas of theassociated squares.

i. State a nu mb er multiplied byitself as a number to the power

of tw o and vice-versa.

152

read as: f ifteen to the pow er oftw of if teen squared, or

the square of f ifteen.

Emphasise that a2

is

a notation f ora x a.

square

product

pow er

expand

expanded f orm

12

22 3

2

Use pencil-and-pap er method,ment al and speed calculationstoevaluate squares of numbers

Include integers,

f ractions anddecima ls.

e.g.

( 8)2

= ( 8) x ( 8)

2

3 3 3w here appropriate. = x5 5 5

0.62 = 0.6 x 0.6


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2. LEARNING AREA: SQUARES , SQUARE ROOTS , CUBES AND CUBEROOTS

Form 2

LEARNING

OBJECTIVES





ii. Deter mine the squaresof

numbers w ithout using

calculators.

Emphasise that thesquare of any numberis greater than orequal to zero.

reasonable

estimat e

approximat ion

Use estimat ion to check whether answ ers are reasonable.

e.g.

27 is betw een 20 and 30.

272

is betw een 400 and 900.

Explore square numbers usingcalculators.

iii. Estimate the squares of

numbers.

iv. Deter mine the squares ofnumbers using calculators.

Emphasise thereasonableness ofansw ers.

Discuss that readings

f rom calculatorsmay beapproximations.

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a


LEARNINGOBJECTIVES




Explore perf ect squares. v. List perf ect squares.

vi. Deter mine if a nu mber is aperf ect square.

vii. Pose and solve proble ms

involving squares of numbers.

Perf ect squaresare w hole numbers.

The perf ect squaresare 1, 4, 9, 16, 25,

Emphasise that

decima ls and fractions are not perf

ectsquares.

square

perf ect square

square root

f raction

decima l

deno minator

numerator

2.2 Understand anduse the conceptof square roots of

positive numbers.

Explore the concept of squareroots using areas of squares.

i. State the square root of apositive nu mber as thenumber mult iplied by itself

equals to the g iven number.

ii. Deter mine the square roots of

perf ect squares w ithoutusing

calculator.

is a symbol f

or square root.

5 read as:square root of five.

2= a

Find ing the squareroot is the inverse ofsquaring.

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LEARNINGOBJECTIVES




iii. Deter mine the squareroots

of numbers w ithout using

calculators.

.30Limit to :

a) f ractions thatcan be reducedsuch

that the nu meratorsand deno minatorsare perf ectsquares

b) decima ls thatcan be w ritten inthef orm of the square

of anotherdecima ls.

Investigate multiplications involving squareroots of :

a) the same nu mber

b) dif f erent

numbers.

iv. Mu ltip ly tw o square roots. Emphasise that:

a x a = a2

=a

a x b = ab


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LEARNINGOBJECTIVES




Use estimat ion to check whether answ ers are reasonable.

e.g.

7 is betw een 4 and 9


Use calculators to explore therelationship b etw een squaresand square roots.

v. Estimate square roots ofnumbers.

vi. Find the square roots of

numbers using calculators.

vii. Pose and solve proble ms

involving squares and squareroots.


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LEARNINGOBJECTIVES




2.3 Un derstand anduse the concept ofcube of numbers.

Recognise cube of a nu mberas the volu me of the associatedcube.

13

23

33

i. State a nu mb er multipliedby

itself tw ice as a number to

the pow er of three andvice-

versa.

ii. Deter mine cubes of numbers

43

read as:f our to the pow er of

three or f our cubedor the cube of f our.

Include integers,f ractions anddecima ls.

Emphasise that a3

is a

notation f or a x a x a.3

cube

pow er

negativenumber

2 2 2 2w ithout usingcalculators.

i. = x x

Use pencil-and-pap er method,speed and mental calculations toevaluate cubes of numbers.

5 5 5 5

ii. 0.23

= 0.2 x 0.2 x 0.2

Discuss that cubesof negative nu mbersare negative.


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LEARNINGOBJECTIVES




Explore estimation of cubes ofnumbers.e.g.

0.48 is betw een 0.4 and 0.5

0.483

is betw een 0.064 and 0.125

Explore cubes of numbers usingcalculators.

iii. Estimate cubes of numbers.

iv. Deter mine cubes ofnumbers

using calculators.

v. Pose and solve proble ms

involving cubes of numbers.


2.4 Un derstand and

use the concept ofcube roots of

numbers.

Use calculators to explore therelationship b etw een cubesand cube roots.

i. State the cube root of anumber as the nu mbermu ltip lied by itself tw iceequals to the g iven number.

ii. Deter mine the cube roots of

integers w ithout usingcalculators.

3 is the symbol f or

cube root of a number.

38 read as:

cube root of eight.

Limit to nu mbersw hose cube roots areintegers, f or example:

1 , 8 , 27 ,

cube root

equal f actors

integer

20


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2. LEARNING AREA: S QUARES, S QUARE ROOTS, CUBES AND CUBEROOTS

Form 2

LEARNING

OBJECTIVES





iii. Deter mine the cube rootsof

numbers w ithout using

calculators.

Explore estimation of cube roots

Limit to :a) Fractions that can

be reduced suchthat thenumerators and

of numbers.e.g.


3 20 is betw een 2 and 3.

Explore the relat ionship between cubes and cube roots usingcalculators.

iv. Estimate cube roots of

numbers.

v. Deter mine cube roots of

numbers using calculators.

vi. Pose and solve proble ms

involving cubes and cuberoots.

vii. Perf orm co mputat ionsinvolving add ition,

subtraction,mu ltip licatio n, division andmixed operations on squares,square roots, cubes and cube

roots.

deno minators arecubes of integers.

b) Decima ls thatcan be w ritten inthef orm of cube of

another decimal.


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3. LEARNING AREA: ALGEBRAIC EXPRESS IONSII

Form 2

LEARNING

OBJECTIVES





3.1 Understand theconcept of

algebraic ter msin

tw o or more

Students ident if y unknow nsin given algebraic ter ms.

e.g.

i. Ident if y unknow ns inalgebraic

terms in tw o or moreunknow ns.

a2

= a x a

y3

=yx yx

y

n

algebraic ter m

algebraic

expression

unknow ns.3ab : a & b are unknow ns.

ii. Ident if y algebraic terms in two

In ge neraly

is ncoeff icient

3d2

: d is an un know n.

Use exa mples of everydaysituations to explain alge braicterms in tw o or more unknowns.

or more un know ns as theproduct of the unknow ns w

itha nu mber.

iii. Ident if y coeff icients ingiven

algebraic ter ms in tw o ormore un know ns.

iv. Ident if y like and unlikealgebraic ter ms in tw o or

more un know ns.

v. State like ter ms f or a givenalgebraic ter m.

times y mu ltip lied by

itself .

2pqr me ans

2 p q r

a2b means

1 a2

x b

= 1 a a b

rs3

means

1 x rx s3

= 1 x rx s x s x s

Coef f icients inthe term 4pq:

Coef f icient ofpq is4. Coef f icient of q is4p. Coef f icient ofpis 4q.

unknow n

like ter ms

unlike ter ms


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3. LEARNING AREA: ALGEBRAIC EXP RESSIONS IIForm 2

LEARNINGOBJECTIVES





involvingmu ltip licatio nanddivision of tw oor

more ter ms.

Explore mult iplication anddivision of algebraic terms usingconcrete mater ials or pictorialrepresentations.

e.g.

Find the area of a w all coveredby10 pieces of tiles each measuring

xcm by ycm.

e.g.

a) 4rs x 3r= 12r2

s

i. Find the product of tw oalgebraic ter ms.

ii. Find the quot ient of tw oalgebraic ter ms.

iii. Perf orm mu ltiplicat ionand

division involvin g algebraicterms.

product

unknow n

quotient

b) 2p2

6pq2 p p p

6 p q 3q

Perf orm mu ltiplicat ion anddivision such as:

6pq2

x 3p 2qr

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LEARNINGOBJECTIVES





algebraicexpressions.

Use situatio ns to de monstratethe concept of algebraicexpression.

e.g.

a) Add 7 to a number: n + 7.

b) A number mult iplied by 2and then 5 added: (n x 2) + 5or

2n + 5.

Investigate th e dif f erencebetw een expressions such as2n and n + 2 ; 3(c+ 5) and 3c+ 5;

n2

and 2n; 2n2

and (2n)2.

i. Write algebra ic expressionsf or given situations using

letter symbols.

ii. Recognise a lgebraicexpressions in tw o or more

unknow ns.

iii. Deter mine the nu mber ofterms in g iven algebra icexpressions in tw o or more

unknow ns.

iv. Simp lif y algebraic

expressions by collecting like

terms.

2xyis an expressionw ith 1 term.

5 + 3ab is anexpression w ith 2terms.

algebraicexpression

letter symbols

simp lif y

substitute

evaluate

like ter ms

v. Evaluate express ions by

substituting nu mbers f

orletters.

24


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a) 8 (3x 2)

b) (4x 6) 2 or


LEARNINGOBJECTIVES




3.4 Perf ormcomputations

involving


Use situatio ns to explaincomputat ions involving algebraic

expressions.

i. Mu ltip ly and divide algebraic

expressions by a number.

ii. Perf orm:

mu ltip ly

divide

add

subtract

4x 6

2

Investigate w hy 8(3x 2)

= 24x 16.

a) addition

b) subtraction

involving tw o


simp lif y

like ter ms

Add and subtract algebraicexpressions by removing bracketand collecting like ter ms.

Simp lif y algebraicexpressions such as:

a) 3x (7x 5x)

b) 5(x+ 2y) 3(2x 2y)

iii. Simp lif y algebraicexpressions.

c)1

(a + 7b c) +1

(4 b 2c)2

d) 8(3x 2) +

3

4x 6

2

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4. LEARNING AREA: LINEAR EQUATIONSForm 2

LEARNINGOBJECTIVES




4.1 Understand anduse the concept

of equality.

Use concrete examples to

illustrate = and .

Discuss cases such as:a) Ifa = b then b = a.

e.g.

2+3 = 4 +1 then 4 +1 = 2+3b) Ifa = b and b = c, then a =c.

e.g.

4+5 = 2+7, then 2 +7=3+6, then 4+5 = 3+6

i. State the relat ionshipbetw een tw o quantities by

using the symbo ls = or

.

= read as:is equal to.

read as:is not equal to.

Re late to the balancemeth od f orequations.

equality

equals to

linear a lgebraic

terms

algebraic

expression

4.2 Understand anduse the conceptof linear

equations in oneunknow n.

Discuss w hy given algebraicterms and expressions are linear.

Given a list of terms, studentsidentif y linear ter ms.

e.g. 3x,xy,x2

3x is a lin ear term.

Select linear expressions given a

list of algebraic expressions.e.g. 2x+ 3,x 2y, xy + 2,x2

1

2x+ 3,x 2y are linearexpressions.

i. Recognise linear alg ebraicterms.

ii. Recognise linear a lgebraicexpressions.

26


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LEARNINGOBJECTIVES




Select linear equat ions given alist of equations.

e.g.

x+ 3 = 5,x 2y= 7,xy= 10

x+ 3 = 5, x 2y= 7 are linearequations.

x+ 3 = 5 is linear equat ion

in one unknow n. Include examples f rom

everyday situations.

iii. Deter mine if a given equat ionis:a) a linear equa tion

b) a linear equa tion in oneunkn ow n.

iv. Write linear equations in oneunknow n f or given s tatements

and vice versa.

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4.3 Understand the Use concrete examples to explain i. Deter mine if a nu merical valu The solut ions ofconcept of solutions of linear equat ion in one is a solution of a given linear equations are also

solutions of linear unknow n. equation in one u nknow n. know n as the roots of


LEARNINGOBJECTIVES





solution

root of

equationequations in oneunknow n.

e.g.

Re latex+ 2 = 5 to + 2 = 5.

Solve and ver if y linear equationsin one un know n by inspection

and systematic trial, using w holenumbers, w ith and w ithout theuse of calculators.

ii. Deter mine the solut ion of alinear equat ion in one

unknow n by trial andimproveme nt method.

iii. Solve equat ions in the f orm of:

a) x+ a = bb) x a = bc) ax= b

x

the equatio ns.

Trial and improvementmeth od should bedone systematically.

Emphasise theappropriate use of

equals sign.

numericalvalue

d) = ba

w here a, b , care integers andxis an unknow n.

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LEARNINGOBJECTIVES




iv. Solve equat ions in the f ormofax+ b = c, w here a, b , c

are integers and x is an

unknow n.

v. Solve linear equat ions in one

unknow n.

Involve exa mples f romeveryday situations.

vi. Pose and solve proble msinvolving linear equat ions inone unknow n.

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5. LEARNING AREA: RATIOS, RATES AND P ROPORTIONSForm 2

LEARNINGOBJECTIVES




5.1 Un derstand theconcept of ratio of

tw o quantities.

Use everyday examples tointroduce the concept of ratio.

Use concrete examples toexplore:

i. Co mpare tw o quantities in the

f orm a : b ora

.b

Include quantities ofdif f erent units.

The ratio 3 : 5 means3 parts to 5 parts andread as: three to f ive.

ratio

quantity

equivalent

sum

a) equivalent ratios

b) related ratios .

ii. Deter mine w hether givenratios are equivalent ratios.

iii. Simp lif y ratios to the lowest

terms.

iv. State ratios related t o agiven

ratio.

Include :Given x: y, find:

a) y:x

b) x:x y

c) x:x+ y

dif f erence

low est terms

compare

part

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LEARNINGOBJECTIVES





proportion to

solve problems.

Use everyday examples tointroduce the concept ofproportion.

Verif y the method of crossmu ltip licatio n and use it t o f ind

the missing ter ms of aproportion.

i. State w hether tw o pairs ofquantities is a proportion.

ii. Deter mine if a quantity is

proportional to a notherquantity given tw o values of

each quantity.

iii. Find the value of a quantity

given the ratio of the tw o

quantities and the value ofanother quantity.

a=

c

b d

read as: a to b as cto d.

Begin w ithunitary meth od.

Emphasise that

proportion

ratio

sum

dif f erence

proportional

cross-mu ltip licatio n

iv. Find the value of a quant itygiven the ratio an d the su mof

Ifa

=c

b d

the tw o quantities.

v. Find the su m of tw oquantities

given the ratio of thequantities and the dif f erencebetw een the quantities.

vi. Pose and solve proble ms

involving ratios andproportions.

then ad= bc

(b 0, d 0)


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LEARNINGOBJECTIVES




5.3 Un derstand anduse the concept of

ratio of three

quantities to solveproble ms.

Use everyday examples tointroduce the concept of ratio ofthree quantit ies.

Use concrete examples toexplore equivalent rat ios.

i. Co mpare three quantit ies inthe f orm a : b : c.

ii. Deter mine w hether given

ratios are equivalent ratios.

iii. Simp lif y ratio of three

quantities to the low est terms.

iv. State the ratio of any tw oquantities given ratio of three

quantities.

v. Find the ratio ofa : b : cgiventhe ratio ofa : b and b : c.

Include quantities ofdif f erent units.

a : b =p : qb : c= m : nw hen a) q = m

b) q m

Begin w ithunitary meth od.

simp lif y

equivalent

low est terms

value

sum

dif f erence

vi. Find the value of the otherquantities, given the ratio ofthree quantit ies and the value

of one of the quantities.

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LEARNINGOBJECTIVES




vii. Find the value of each of thethree quantit ies

given:

a) the ratio and th e sum of

three quantities

b) the ratio and th e dif f erence

betw een tw o of the three

quantities.

viii. Find the su m ofthree

quantities given the ratio a ndthe dif f erence betw een tw o of

the three quantities.

ix. Pose and solve proble msinvolving ratio of three

quantities.


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6. LEARNING AREA: P YTHAGORAS THEOREM

Form 2

LEARNING

OBJECTIVES





6.1 Understand therelationship

betw een thesides of a right-angled triangle.

Students ident if y thehypotenuse of right-angledtriangles draw n in diff erentorientations.

Use dyna mic geo metry sof tware, grid papers or geo-boards to

i. Ident if y the hypotenuse ofright-angled tria ngles.

ii. Deter mine the relationship

betw een the lengths of the

sides of a right-angled

C

ab

A c B

Pythagorastheorem

hypotenuse

right-angledtriangle

side

explore and investigate the

Pythagoras the orem.

triangle.

iii. Find the len gth of themissing

side of a right-angled triangleusing the Pythagoras

theorem.

iv. Find the len gth of sides of

geo metric shapes using

Pythagoras the orem.

Emphasise that

a2

= b2

+ c2

is thePythagoras theorem.

Begin w ith thePythagorean Triples. e.g. (3, 4, 5)

(5, 12, 13)

Include comb inedgeo metricshapes.

missing sidePythagorean

Triples

combin edgeo metric

shape

v. Solve proble ms using th e

Pythagoras theorem.


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6. LEARNING AREA: P YTHAGORAS THEOREM

Form 2

LEARNING

OBJECTIVES





6.2. Understand anduse the converse

of thePythagorastheorem.

Explore and investigate the converse of thePythagoras theorem through activities.

i. Deter mine w hether atriangle

is a right-angled triangle.

ii. Solve proble ms involvingthe

converse Pythagoras

theorem.

Note th at:

Ifa2

> b2

+ c2, then

A

is an obtuse angle.

If a2

< b2

+ c2

, thenAis an acute angle.

obtuse angle

acute angle

converse


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7. LEARNING AREA: GEOM ETRICAL CONS TRUCTIONSForm 2

LEARNINGOBJECTIVES





7.1 Perf orm Re late constructions to properties i. Construct a line seg me nt of Emphasise on constructconstructions of rhombus and isosceles given length. accuracy of draw ing. ruler

using straightedge (ruler andset square) andcompass.

triangle.

ii. Construct a triangle given thelength of the sides.

iii. Construct:

a) perpendicular bisector of

a given line seg mentb) perpendicular to a line

passing through a pointon the line

c) perpendicular to a lin epassing through a pointnot on the line.

Include equilateral,

isosceles and scalenetriangles.

Emphasise theconstructions inLearning Outcome (iii)

are used to constructan angle of 90 .

straight edge

set square

protractor

point

line seg ments

compass

sideperpendicular

perpendicular

bisector

triangle

right-angledtriangle

equilat eraltriangle

isosceles

triangle

scalene

triangle

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7. LEARNING AREA: GEOM ETRICAL CONS TRUCTIONSForm 2

LEARNINGOBJECTIVES




Re late the construction to theproperties of equilateral trian gle.

Explore situation w hen two dif f erent triangles can beconstructed.

iv. Construct:

a) angle of 60 and 1

20

b) bisector of an angle.

v. Construct triangles given:

a) one side and tw o angles

b) tw o sides and oneangle.

Emphasise the use ofthe bisector of anangle to construct

angles of 30 , 45and15 and etc.

Measure ang lesusing protractors.

protractor

angle

equilat eral

bisector

compass

set square

parallel lines

parallelogra m

vi. Construct:

a) paralle llines

b) paralle logra m given its

sides and an angle.

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8. LEARNING AREA: COORDINATESForm 2

LEARNINGOBJECTIVES




8.1 Understand and Introduce the concept of i. Ident if y thex-axis, y-axis and Coordinates of origin Cartesianuse the concept coordinates using everyday the origin o n a Cartesian is (0, 0). plane

of coordinates. examples.e.g.

State the location of :a) a seat in the classroom

b) a point on square grids.

Introduce Cartesiancoordinates as a systematic way of marking the location of apoint.

plane.

ii. Plot po ints and state the

coordinates of the pointsgiven distances f rom they-axis andx-axis.

iii. Plot po ints and state thedistances of the points fromthe y-axis andx-axis given

coordinates of the points.

iv. State the coordinates of

points on Cartesian plane.

For LearningOutco mes ii iii, involve the first quadrantonly.

Involve all the four quadrants.

origin

x-axis

y-axis

coordinate

distance

positionsquare grid

plot

points

quadrant

horizontal

vertical

x-coordinate

y-coordinate

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8.2 Understand and Use dyna mic geo metry sof tw i. Mark the values on both axes Emphasise that the scaleuse the concept to explore and investigate t he by extending the sequence of scales used on the mark


LEARNINGOBJECTIVES




of scales f orthecoordinate axes.

concept scales.

Explore the ef f ects of shapes ofobjects by using dif f erentscales.

Explore positions of places ontopography maps.

Pose and solve proble msinvolving coordinates of verticesof shapes such as:

Na me the shape f ormed byA(1, 5), B(2, 5), C(4, 3) andD(3, 3).

Three of the f our vertices ofa square are ( 1, 1), (2, 5)

and (6, 2). State thecoordinates of the f ourthvertex.

given values on the axes.

ii. State the scales used in givencoordinate axes w here:

a) scales f or axes are the

same

b) scales f or axes are

dif f erent.

iii. Mark the values on both axes,w ith ref erence to the scales

given.

iv. State the coordinates of agiven point w ith ref erence to

the scales given.

v. Plot po ints, given thecoordinates, w ith ref erence

tothe scales given.

axes must be uniform.

Scales should be

w ritten in the f orm:a) 2 unit represents

3 units.b) 1 : 5.

extend

sequence

axes

coordinate

plot

unif orm

vertex

vi. Pose and solve proble msinvolving coordinates.

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8.3 Understand and Discuss diff erent methods of i. Find the distance betw een Emphasise that the distanceuse the concept of f inding distance betw een tw o tw o points w ith: line join ing the points point

22


LEARNINGOBJECTIVES




distance betw eentw o points on aCartesian p lane.

points such as:

a) inspection

b) moving one po int to th eother

c) comput ing the d if f erencebetw een thex-coordinates ory-coordinates.

a) common y-coordinates

b) commonx-coordinates.

ii. Find the distance betw eentw o points using

Pythagorastheorem.

are parallel to thex-axis or parallel to they-axis.

Include positive andnegative coordinates.

The f ormu la f ordistance betw een tw

o points (x1 ,y1) and(x2 , y2) is

common

positive

negative

parallel

y-coordinate

x-coordinate

Pythagoras

theorem.

(x

2

x1) (y

2

y1)

Students draw the appropriateright-angled tria ngle usin g the

distance betw een the tw opoints as the hypotenuse.

need not beintroduced.

iii. Pose and solve proble ms

involving distance betw eentw o

points.


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LEARNINGOBJECTIVES




8.4 Understand anduse the concept of

midpoints.

Introduce the concept ofmidpoints through activities suchas f olding, constructing, drawing and counting.

Use dyna mic geo metry sof tware to explore and investigate the concept of midpoints.

i. Ident if y the midpoint of astraight line join ing tw opoints.

ii. Find the coordinates of themidpoint of a straight line

join ing tw o points w ith:

a) commony-coordinates

b) commonx-coordinates.

The f ormu la of

midpoint f or (x1 ,y1)

and (x2 , y2) is

midpoint

x-coordinate

y-coordinate

straight line

(

x1

x2

,

y1

2

y2

)2

iii. Find the coordinates of the

midpoint of the line joining tw opoints.

iv. Pose and solve proble msinvolving midpoints.

need not beintroduced.

Involve shapes.

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9. LEARNING AREA: LOCI IN TWO DIM ENSIONS

Form 2

LEARNINGOBJECTIVES




9.1 Un derstand theconcept of tw o-

dimensiona lloci.

Use everyday examples such asf amiliar routes and simplepaths

to introduce the concept of loci.

Discuss the locus of a point in agiven diagra m.

e.g. Describe a locus of a point

equidistant f romA and C.A D

i. Describe and sketch the locusof a moving ob ject.

ii. Deter mine the locus of pointsthat are of :

a) constant distance f rom af ixed point

b) equid istant f rom tw o

f ixed pointsc) constant distance f rom a

straight line

d) equid istant f rom tw o

Emphasise theaccuracy of drawings.

Re late to propertiesof isosceles triangle.

Emphasise locus as:a) path of a moving

pointb) a point or set ofpoints

that satisf ies given

conditions.

accuracy

route

locus

loci

moving object

equidistant

pointsf ixed point

straight line

B C intersecting lines. perpendicular

distance

constant

intersectinglines

parallel lines

condition

set of points

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9. LEARNING AREA: LOCI IN TWO DIM ENSIONSForm 2

LEARNINGOBJECTIVES



Students w ill be taught to: Students w ill be abl e to:iii. Construct the locus of a set of

all po ints that satisf ies the

condition:

a) the point is at a constantdistance f rom a f ixed point

b) the point is at equid istant

f rom tw o f ixed points

c) the point is at a constantdistance f rom a straight

line

d) the point is at equid istantf rom tw o intersecting

lines.

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9. LEARNING AREA: LOCI IN TWO DIM ENSIONSForm 2

LEARNINGOBJECTIVES




intersection of

tw o loci.of tw o loci.

Mark the po ints that satisf ythe conditions:

a) Eq uid istant f romA and

C. b) 3 cm f rom A.

D C

and locating t he points thatsatisfy the conditions of thetw o loci.

Objective 9.1.satisfy

intersection

A B

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10. LEARNING AREA : CIRCLESForm 2

LEARNINGOBJECTIVES



Students w ill be taught to: Students w ill be abl e to:10.1 Recognise and

draw parts ofacircle.

Introduce the concept of circle asa locus.

Use dyna mic geo metry sof tware to explore parts of a circle.

i. Ident if y circle as a set ofpoints equid istant f rom a fixed

point.

ii. Ident if y parts of a circle:

a) center

b) c ircumf erence

c) radius

d) dia meter

e) chord

f ) arc

g) sector

h) segment

iii. Draw :

a) a circle given the radius

and centre

b) a circle given thedia meter

c) a dia met er passingthrough a specif ic pointin a circle given the

centre.

circle

centre

circumf erence

radius

dia meter

chord

sector

arc

segment

equidistant

point

f ixed point

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LEARNINGOBJECTIVES



Students w ill be taught to: Students w ill be abl e to:d) a chord of a given length

passing through a point

on the circumf erence

e) sector given the size ofthe angle at the centre

and radius of the circle.

dia meter

circumf erence

sector

radius

centre

iv. Deter minethe:

a) centerb) radius

of a given circle by

construction.

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LEARNINGOBJECTIVES



Students w ill be taught to: Students w ill be abl e to:10.2 Understand and

use the concept

of circumference

to solveproble ms.

Measure dia meter andcircumf erence of circularobjects.

Explore the history of .

Explore the value of usingdynamic geo metry sof tware.

i. Estimate the value of .

ii. Derive the f ormu la of thecircumf erence of a circle.

iii. Find the circumf erence ofa

circle, given its:

a) dia meter

b) radius.

iv . Fin d the:

Develope dthrough activities.

The ratio of thecircumf erence to thedia meter is kn ow n

as and read aspi.

Emphasise

22

radius

f ormula

ratio

constant

pi

approximat e

estimat e

derive

a) dia meter

b) radius

given the circumf erence ofacircle.

| 3.142 or .7 circular object

v. Solve proble ms involvingcircumf erence of circles.

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LEARNINGOBJECTIVES




use the concept

of arc of acircle

to solveproble ms.

Explore the relat ionship between the length of arc and angle atthe centre of a circle usingdynamic geo metry sof tw are.

i. Derive the f ormu la of thelength of an arc.

ii. Find the len gth of arc given

the angle at the centre andthe radius.

iii. Find the ang le at the centregiven the leng th of the arcand the radius of a circle.

iv. Find the len gth of radius of a

circle given the length of thearc and the angle at th e

centre.

v. Solve proble ms involvingarcs

of a circle.

The length of arc isproportional to t heangle at the centre ofa circle.

Include combined shapes.

arc

angle at the

centre

proportional

radius

circumf erence

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LEARNINGOBJECTIVES




use the concept of

area of a circle to

solve problems.

Explore the relat ionship between the radius and the area of acircle:

a) using dynamic geo

metry sof tw are

b) through activities such ascutting the circle into e qualsectors and rearranging the minto rectangular f orm.

i. Derive the f ormu la of thearea

of a circle.

ii. Find the area of a circle giventhe:

a) radius

b) dia meter .

Include f inding thearea of the annulus.

area

annulus

radius

iii.Find:

a) radius

b) diameter

given the area of a circle.

iv. Find the area of a circle giventhe circumf erence and vice

versa.

v. Solve proble ms involving area

of circles.


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LEARNINGOBJECTIVES




use the concept

of area of sector

of a circle to solveproble ms.

Explore the relat ionship betw eenthe area of a sector and the angleat the centre of the circle usingdynamic geo metry sof tw are.

i. Derive the f ormu la of thearea

of a sector.

ii. Find the area of a sectorgiven the radius and ang le at

the centre.

iii. Find the ang le at the centre

given the radius and area of asector.

area

sector

angle at the

centre

radius

circle

arc

iv. Find the radius given the areaof a sector and the angle atthe centre.

v. Solve proble ms involvingarea

of sectors and area of circles.

Include comb inedshapes

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11.1 Understand the i. Ident if y a transf ormation as a A one-to-oneconcept of transf ormationa l geo metry using one-to-one correspondence correspondence

transf ormations. concrete materials, draw ings, betw een points in a plane. betw een points of a

11. LEARNING AREA : TRANS FORMATIONS

Form 2

LEARNINGOBJECTIVES




geo-boards and dynamicgeo metry sof tw are.

ii. Ident if y the object andits

image in a given

transf ormation.

plane is a lso calleda map ping.

Includetransf ormations inarts and nature.

The ob ject ismapped onto theimage.

transf ormation

plane

object

image

map

one-to-onecorrespondence

translation

11.2 Understand and

use the concept Explore translations given in the

a

i. Ident if y atranslation.

Grid papers may beused.

orientation

parallel

of translations. direction

f orm b

.

ii. Deter mine the image ofan

object under a given

a

distance

translation.

iii. Descr ibe a translation:

a) by stating thedirection

and distance of themove ment

a

b

a is the move mentparallel to thex-axisand b is themove ment paralle lto the y-axis.

move ment

b) in the form

b .


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11. LEARNING AREA : TRANS FORMATIONS

Form 2

LEARNINGOBJECTIVES




11.3 Understand and

use the conceptof ref lections.

Investigate th e shapes andsizes, lengths and angles of theimages and the o bjects.

Explore the ima ge of anobject under a ref lection bydraw ing, using tracing paper,or paperf olding.

iv. Deter mine the properties oftranslation.

v. Deter mine the coordinat es of:

a) the image, given thecoordinates of the object

b) the object, given th e

coordinates of the image

under a translation .

vi. Solve proble ms involvingtranslations.

i. Ident if y a ref lection.

ii. Deter mine the image of an

object under a ref lection on agiven line .

Emphasise that undera translation, theshapes, sizes, andorientations of theobject and itsimage are thesame.

The line is know n

as line of ref lectionor axis of ref lection.

properties

image

shape

size

length

angle

coordinateref lection

axis ofref lection

tracing paper

laterally

inverted

line

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11. LEARNING AREA : TRANS FORMATIONSForm 2

LEARNINGOBJECTIVES




Investigate th e shapes andsizes, lengths and angles of theimages and ob jects.

iii. Deter mine the properties ofref lections.

iv. Deter mine:

a) the image of an ob ject,given the axis of

ref lection

b) the axis of ref lection,given

the object and its image.

using the met hod of

construction

Emphasise that, undera ref lection

a) the shapes and

sizes of theobject and itsimage are thesame; a nd

b) the orientatio n ofhe image is laterallyinverted ascompared to tha t ofthe object.

v. Deter mine the coordinat esof :

a) the image , given the

coordinates of the object

b) the object, g iven thecoordinates of the image

under a ref lection.

vi. Describe a ref lection giventhe

object and image.

Emphasise that allpoints on the axis of

ref lection do notchange their positio ns.

Include x-axis

and y-axis asaxes of ref lection.

vii. Solve proble ms involvingref

lections.


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LEARNINGOBJECTIVES




11.4 Understand anduse the conceptof rotations.

Explore the ima ge of an objectunder a rotation by draw ing andusing tracing paper.

i. Ident if y a rotation.

ii. Deter mine the image of an

object under a rotation giventhe centre, the angle a nddirection of rotation.

iii. Deter mine the properties of

rotations.

iv. Deter mine:

a) image of an object, given

the centre, angle anddirection of rotation

b) the centre, angle an ddirection of rotation, giventhe object and the image.

using the met hod of

construction

v. Deter mine the coordinat esof

a) the image , given thecoordinates of the object;

b) the object, g iven the

coordinates of the image

under a rotation.

Emphasise that underrotation; the shapes,sizes and orientationsof an object and theimage are the sa me.

Emphasise that thecentre of rotation isthe only point thatdoes not change its

position.

Include 90 a nd

180as angles of rotation.

rotation

centre of

rotation

direction ofrotation

angle of

rotation

clockw ise

anticlockw ise

properties

shape

size

object

image

coordinate

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i. Ident if y an isometry. Iso metr is a

use the concept isometry. ii. Deter mine w hether a given transf ormation t hat

11.6 Understand and i. Ident if y if tw o f igures are Em hasise thatuse the concept translations, ref lections and congruent. congruent f igures


LEARNINGOBJECTIVES




vi. Describe a rotation g iventhe

object and image.

vii. Solve proble ms involvingrotations.

isometry

congruence

congruent

congruency

of isometry.

of congruence.

11.7 Understand and

use the propertiesof quadrilaterals

using concept of

transf ormations.

rotations.

Explore the properties ofvarious quadrilatera ls bycomparing the sides, anglesand diag onals.

transf ormation is an isometry.

iii. Construct patterns usingisometry.

ii. Ident if y congruency between

tw o f igures as a property of

an iso metry.

iii. Solve proble ms involving

congruence.

i. Deter mine the properties of

quadrilatera ls usingref lections and rotations.

preserves the shapeand the size of theobject.

have the same sizeand shape regardlessof their orientation

Quadrilateralsinclude squares,rectangles,parallelogra ms,

rhombus, and kites.

size

pattern

f igure

property

orientation

quadrilatera l

square

rectangle

rhombus

parallelogra m

kite

diagona l

preserve

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12. LEARNING AREA : S OLID GEOM ETRYII

Form 2

LEARNINGOBJECTIVES




12.1 Understandgeo metricproperties of

prisms,pyramids,

cylinders, conesand spheres.

12.2 Understand theconcept of nets.

Explore and investigateproperties of geometric solidsusing concrete mode ls.

Explore the similarities anddiff erences betw een netsofprisms, pyramids, cylinders andcones using concrete models.

i. State the geo metric propertiesof prisms, pyramids,

cylinders, cones and spheres.

i. Draw nets f or prisms,pyramids, cylinders and cones.

ii. State the types of solids giventheir nets.

iii. Construct mo dels of solids

given their nets.

Net is also know nas layout.

Pris ms includ ecubes and cuboids.

prism

pyramid

cylinder

cone

sphere

net

solidcube

cuboid

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12. LEARNING AREA : SOLID GEOM ETRY IIForm 2

LEARNINGOBJECTIVES




12.3 Understand theconcept ofsurf ace area.

Explore and derive the f ormulae of the surf ace areas ofprisms, pyramids, cylinders andcones.

i. State the surf ace areas ofprisms, pyramids, cylinders

and cones.

ii. Find the surf ace area ofprisms, pyramids, cylinders

and cones.Standard f ormula for surf ace area of

2

surf ace area

dimension

standardf ormula

similarit ies

iii. Find the surf ace area ofspheres using the standard

f ormula.

iv. Find dimensio ns:

a) length of sides

b) height

c) slant height

d) radius

e) dia meter

of a solid given its surf aceareaand other relevant inf ormat ion.

v. Solve proble ms involving

surf ace areas.

sphere is 4 rr is the radius.

where

dif f erences

base

lateral sidevertex

edge

height

radius

dia meter

slant height

curve surf ace

derive

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13. LEARNING AREA: STATISTICSForm 2

LEARNINGOBJECTIVES




13.1 Understand theconcept of data.

13.2 Understand the

concept off requency.

Carry out activities to introducethe concept of data as acollection of inf ormatio n or facts.

Discuss methods of collectingdata such as counting,observations, measuring, usingquestionnaires and interview s.

Use activities to introduce theconcept of f requency.

i. Classif y data according tothose

that can be collected by:

a) counting

b) measuring.

ii. Co llect and record data

systematically.

i. Deter mine t he f requency ofdata.

ii. Deter mine the dat a w ith:

a) the highest f requency

b) the low est frequency

c) f requency of a specif ic

value.

Use tally charts torecord data.

data

count

measure

collection ofdata

questionnaire

interview s

systematic

record

tally chart

f requency

horizontal

vertical

highest

low est

f requency tableinf ormation

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13.3 Represent and Use everyday situations to i. Construct pictograms to Include horizontalinterpret data in: introduce pictogra ms, bar charts represent data. and vertical


LEARNINGOBJECTIVES




iii. Organise data by constructing:

a) tally charts

b) f requency tables.

iv. Obtain inf ormat ion f romf requency tables.

Use tw o columns ortw o row s topresent data.

data

organise

pictogram

tally chart

column

row

obtain

key

i. pic tograms

ii. bar charts

iii. line graphs

to solve

proble ms.

and lin egraphs. ii. Obtain inf ormat ion

frompictograms.

iii. Solve proble msinvolving

pictograms.

pictograms usingsymbols to representf requencies.

Include the use oftitle an d keys(legend) onpictograms, bargraphs and linegraphs.

legend

bar graph

line graph

horizontal

vertical

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LEARNINGOBJECTIVES




iv. Construct bar charts torepresent data.

v. Obtain inf ormat ion f rombar

charts.

vi. Solve proble ms involvingbar

charts.

Include bar chartsrepresenting tw o setsof data.

Use vertical andhorizontal bars.Include vertical andhorizontal barcharts using scales

such as:

a) 1 : 1

b) n, w here n is aw hole number.

vii. Represent data usin g linegraphs.

viii. Obtain inf ormat ion f romline

graphs.

ix. Solve proble ms involvingline

graphs.

Emphasise on theuse of suitable scales

f or line graphs.

Discuss on thechoice of usingvarious methods to

represent dataeff ectively.

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CONTRIBUTORS

Advis or Dr. Sharif ah Ma imunah Syed Zin Director

Curriculu m Develo p ment Centre

Dr. Rohan i Abdul Ha mid Deputy Director


Editorial Ahmad Hozi H.A. Ra h man Principal Assistant Director

Advis ors (Science and Mathe mat ics Depart ment)


Rusnani Mohd Sirin Assistant Director

(Head of Mathe mat ics Unit)

Curriculu m Develo p ment

Centre

S. Sivagnanache lvi Assistant Director

(Head of English Language Un

it) Curriculu m Develo p ment

Centre

Editor Rosita Mat Zain Assistant Director


Form 2

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WRITERS

Form 2

Rus nani Mohd Sirin


Centre

Ros ita M at Zain


Centre

Rohana Ism ail


Dr. Pum ade vi a/p Sivasubramaniam

Ma ktab Perguruan Raja Melewar, Seremban, Negeri Se mb ilan

Chong Tat Keong

SMJK Yu Hua , Kajang, Se langor

Lau Choi Fong

SMK Hulu Kelang, Hulu Ke

lang, Selangor

Lee Lui Kai

SMK Raja Mahad i, Klang, Selangor

Prof. M adya Dr. Noraini Idris

Faku lti Pend idikan Universiti Malaya

Kum aravalu a/l Ram as am y

SMK Seri Gar in g, Raw ang, Selangor

Ang Kah Che ngSMK P) Meth odist, Ipoh, Perak

Lan Foo Huat

SMK Bu kit Goh, Kuantan,Pahang

Ahm ad Shubk i Othm anSMK Dato Abdul Rah man Yaakob, Bota, Perak

Ahm ad Tek ah

Ma ktab Perguruan Batu Pahat,Johor

Haji Yus of AdamSMK Seri Tan jung, Me laka

Saniah Ahm ad

SMK Bu kit Ja

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