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KEMENTERIAN PELAJARAN MALAYSIA

RANCANGAN PELAJARAN TAHUNANMATHEMATICS

Form 3

TAHUN 2012

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Integrated Curriculum for Secondary Schools

Curriculum Specifications

MATHEMATICSFORM 3

Curriculum DevelopmentCentre

Ministry of Education Malaysia

2003

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Copyright 2003 Curriculum Development CentreMinistry of Education MalaysiaPersiaran Duta50604 Kuala Lumpur

First published 2003

Copyright reserved. Except for use in a review, the reproductionor utilization of this work in any form or by any electronic,mechanical, or other means, now known or hereafter invented,

including photocopying, and recording is forbidden without priorwritten permission from the Director of the CurriculumDevelopment Centre, Ministry of Education Malaysia.

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CONTENTSPage

RUKUNEGARA v

NATIONAL PHILOSOPHY OF EDUCATION vii

PREFACE ix

INTRODUCTION 1

LINES AND ANGLES II 10

POLYGONS II 12

CIRCLES II 15

STATISTICS II 19

INDICES 21ALGEBRAIC EXPRESSIONS III 27

ALGEBRAIC FORMULAE 32

SOLID GEOMETRY III 34

SCALE DRAWINGS 40

TRANSFORMATIONS II 42

LINEAR EQUATIONS II 45

LINEAR INEQUALITIES 47

GRAPHS OF FUNCTIONS 53

RATIO, RATE AND PROPORTION II 55

TRIGONOMETRY 58

CONTRIBUTORS 62

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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 andcompetent, whopossess highmoral standards andwhoareresponsible

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.

vii

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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 develop the higher orderproblem 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 CentreMinistry of Education Malaysia

ix

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CONTENTSPage

RUKUNEGARA v

NATIONAL PHILOSOPHY OF EDUCATION vii

PREFACE ix

INTRODUCTION 1

LINES AND ANGLES II 10

POLYGONS II 12

CIRCLES II 15

STATISTICS II 19

INDICES 21

ALGEBRAIC EXPRESSIONS III 27

ALGEBRAIC FORMULAE 32

SOLID GEOMETRY III 34

SCALE DRAWINGS 40

TRANSFORMATIONS II 42

LINEAR EQUATIONS II 45

LINEAR INEQUALITIES 47

GRAPHS OF FUNCTIONS 53

RATIO, RATE AND PROPORTION II 55

TRIGONOMETRY 58

CONTRIBUTORS 62

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RUKUNEGARADECLARATION

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 aprogressive society which shall beoriented to modern science and technology;

WE, her peoples, pledge our united efforts to attain these endsguided by these principles:

BELIEF IN GOD

LOYALTY TO KING AND COUNTRY

UPHOLDING THE CONSTITUTION

RULE OF LAW

GOOD BEHAVIOUR AND MORALITY

v

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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 andcompetent, whopossess highmoral standards andwhoareresponsible

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.

vii

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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 develop the 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)

DirectorCurriculum Development CentreMinistry of Education Malaysia

ix

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1LEARNING AREA:LLIINNEESSAANNDDAANNGGLLEESS IIII Form 3

LEARNING

OBJECTIVESSUGGESTED TEACHING AND

LEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABULARY

Students will be taught to:

Explore the properties of anglesassociated with transversal usingdynamic geometry software,geometry sets, acetate overlaysor tracing paper.

Discuss when alternate andcorresponding angles are notequal.

Discuss when all anglesassociated with transversals areequal and the implication on itsconverse.

Students will be able to:

The interior angles onthe same side of thetransversal aresupplementary.

parallel lines

transversal

alternate angle

interior angle

associated

correspondingangle

intersectinglines

supplementaryangle

acetate overlay

1.1 Understand anduse properties ofangles associatedwith transversaland parallel lines.(Tarikh : 4/1/2012

13/1/2012)

i. Identify:

a) transversals

b) corresponding angles

c) alternate angles

d) interior angles.

ii. Determine that for parallel

lines:

a) corresponding anglesare equal

b) alternate angles are

equal

c) sum of interior angles is

180.

iii. Find the values of:

a) corresponding angles

b) alternate angles

c) interior angles

associated with parallel lines.

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2LEARNING AREA:PPOOLLYYGGOONNSS IIII Form 3

LEARNING




Use models of polygons andsurroundings to identify regularpolygons.

Explore properties of polygonsusing rulers, compasses,protractors, grid papers, templates,geo-boards, flash cards anddynamic geometry software.

Include examples of non-regularpolygons developed throughactivities such as folding papers inthe shape of polygons.

Relate to applications inarchitecture.


Limit to polygons witha maximum of 10sides.

Construct usingstraightedges andcompasses.

Emphasise on theaccuracy of drawings.

polygon

regularpolygon

convex

polygon

axes ofsymmetry

straightedges

angle

equilateraltriangle

square

regular

hexagon

2.1 Understand theconcepts of regularpolygons.

(Tarikh : 16/1/201220/1/2012)

Cuti Tahun Baru Cina21/129/1/2012

i. Determine if a given polygonis a regular polygon.

ii. Find:

a) the axes of symmetry

b) the number of axes of

symmetry

of a polygon.

iii. Sketch regular polygons.

iv. Draw regular polygons bydividing equally the angle atthe centre.

v. Construct equilateraltriangles, squares and

regular hexagons.

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LEARNING




Explore angles of differentpolygons through activities such asdrawing, cutting and pasting,measuring angles and usingdynamic geometry software.

Investigate the number of trianglesformed by dividing a polygon intoseveral triangles by joining onechosen vertex of the polygon to theother vertices.


interior angle

exterior angle

complementaryangle

sum

2.2 Understand anduse theknowledge ofexterior andinterior angles ofpolygons.

i. Identify the interior angles andexterior angles of a polygon.

ii. Find the size of an exteriorangle when the interior angleof a polygon is given and viceversa.

iii. Determine the sum of theinterior angles of polygons.

iv. Determine the sum of theexterior angles of polygons.

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LEARNING




Include examples from everydaysituations.


v. Find:

a) the size of an interiorangle of a regularpolygon given thenumber of sides.

b) the size of an exteriorangle of a regularpolygon given thenumber of sides.

c) the number of sides of aregular polygon given thesize of the interior orexterior angle.

vi. Solve problems involvingangles and sides ofpolygons.

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3LEARNING AREA:CCIIRRCCLLEESS IIII Form 3

LEARNING




Explore through activities such astracing, folding, drawing andmeasuring using compasses,rulers, threads, protractor, filterpapers and dynamic geometrysoftware.


diameter

axis ofsymmetry

chord

perpendicularbisector

intersect

equidistant

arc

symmetry

centre

radius

perpendicular

3.1 Understand anduse properties ofcircles involvingsymmetry, chordsand arcs.

(Tarikh : 30/1/201211/2/2012)

i. Identify a diameter of a circleas an axis of symmetry.

ii. Determine that:

a) a radius that isperpendicular to a chorddivides the chord into twoequal parts and viceversa.

b) perpendicular bisectors

of two chords intersect atthe centre.

c) two chords that are equalin length are equidistantfrom the centre and viceversa.

d) chords of the samelength cut arcs of thesame length.

iii. Solve problems involvingsymmetry, chords and arcs ofcircles.

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LEARNING




Explore properties of cyclicquadrilaterals by drawing, cuttingand pasting and using dynamicgeometry software.


cyclicquadrilateral

interior

opposite

angle

exterior angle

vi. Solve problems involvingangles subtended at thecentre and angles at thecircumference of circles.

3.3 Understand anduse the conceptsof cyclicquadrilaterals.

i. Identify cyclic quadrilaterals.

ii. Identify interior oppositeangles of cyclicquadrilaterals.

iii. Determine the relationshipbetween interior oppositeangles of cyclicquadrilaterals.

iv. Identify exterior angles andthe corresponding interioropposite angles of cyclicquadrilaterals.

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LEARNING



Students will be taught to: Students will be able to:

v. Determine the relationshipbetween exterior angles andthe corresponding interioropposite angles of cyclicquadrilaterals.

vi. Solve problems involvingangles of cyclic quadrilaterals.

vii. Solve problems involvingcircles.

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4LEARNING AREA:SSTTAATTIISSTTIICCSS IIII Form 3

LEARNING




Use sets of data from everydaysituations to evaluate and toforecast.

Discuss appropriatemeasurement in differentsituations.

Use calculators to calculate themean for large sets of data.

Discuss appropriate use of mode,median and mean in certainsituations.


Involve data withmore than one mode.

Limit to cases withdiscrete data only.

Emphasise that moderefers to the categoryor score and not tothe frequency.

Include change in the

number and value ofdata.

data

mode

discrete

frequency

median

arrange

odd

evenmiddle

frequencytable

mean

4.2 Understand anduse the conceptsof mode, medianand mean to solveproblems.

i. Determine the mode of:

a) sets of data.

b) data given in frequencytables.

ii. Determine the mode and therespective frequency frompictographs, bar charts, linegraphs and pie charts.

iii. Determine the median for

sets of data.

iv. Determine the median ofdata in frequency tables.

v. Calculate the mean of:

a) sets of data

b) data in frequency tables

vi. Solve problems involvingmode, median and mean.

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5LEARNING AREA:IINNDDIICCEESS Form 3

LEARNING




Explore indices using calculatorsand spreadsheets.


Begin with squaresand cubes.

a is a real number.

Include algebraicterms.

Emphasise base andindex.

a x a x a= an

n factorsa is the base, n is theindex.

Involve fractions anddecimals.

Limit n to positiveintegers.

indices

base

index

power of

index notation

index form

express

value

real numbers

repeatedmultiplication

factor

5.1 Understand theconcepts ofindices.

(Tarikh : 27/2/20129/3/2012)

Ujian Bulanan 15/38/3/2012

Cuti PertengahanPenggal 1

10/318/3/2012

i. Express repeated

multiplication as an and viceversa.

ii. Find the value of an.

iii. Express numbers in indexnotation.

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LEARNING



Students will be taug ht to:

Explore laws of indices usingrepeated multiplication andcalculators.


Limit algebraic termsto one unknown.

Emphasise a0 = 1.

multiplication

simplify

base

algebraic term

verify

index notation

indices

law of indices

unknown

5.2 Performcomputationsinvolvingmultiplication ofnumbers in indexnotation.

i. Verify am x an = am+ n

ii. Simplify multiplication of:

a) numbers

b) algebraic terms

expressed in index notationwith the same base.

iii. Simplify multiplication of:

a) numbers

b) algebraic terms

expressed in index notationwith different bases.

5.3 Performcomputationinvolving divisionof numbers inindex notation.

i. Verify am am = am n

ii. Simplify division of:

a) numbers

b) algebraic termsexpressed in index notationwith the same base.

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LEARNING



Students will be taug ht to: Students will be able to:

( am)n = amn

m and n are positiveintegers.

Limit algebraic termsto one unknown.

Emphasise:

(am x bn)p = amp x bnp

p

am amp

=

raised to apower

base

5.4 Performcomputationsinvolving raisingnumbers andalgebraic terms inindex notation toa power.

i. Derive (am)n = amn .

ii. Simplify:

a) numbers

b) algebraic terms

expressed in index notationraised to a power.

iii. Simplify multiplication and

division of:

a) numbers

b) algebraic terms

expressed in index notationwith different bases raised toa power.

iv. Perform combinedoperations involvingmultiplication, division, andraised to a power on:

a) numbers

b) algebraic terms.


bn bnp

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LEARNING




Limit to positiveintegral roots.

1

iii. Find the value of a n .

m

iv. State a n as:

1 1

a) (a m ) n or (a n ) m

b)n

am or ( n a )m

v. Perform combined

operations of multiplication,division and raising to apower involving fractionalindices on:

a) numbers

b) algebraic terms.

m

vi. Find the value of a n .

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LEARNING




5.7 Performcomputationinvolving laws ofindices.

i. Perform multiplication,division, raised to a power orcombination of theseoperations on severalnumbers expressed in indexnotation.

ii. Perform combined operationsof multiplication, division andraised to a power involving

positive, negative andfractional indices.

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6LEARNING AREA:AALLGGEEBBRRAAIICC EEXXPPRREESSSSIIOONNSS IIIIII Form 3

LEARNING


LEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOT E VOCABULARY


Relate to concrete examples.

Explore using computer software.


Begin with linearalgebraic terms.

Limit to linearexpressions.

Emphasise:

(a b)(a b)

= (a b)2

Include:

(a + b)(a + b)

(ab)(ab)

(a + b)(ab)

(ab)(a + b)

linear algebraicterms

like terms

unlike terms

expansion

expand

single brackets

two brackets

multiply

6.1 Understand anduse the concept ofexpandingbrackets.

(Tarikh : 19/3/201230/3/2012)

i. Expand single brackets.

ii. Expand two brackets.

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LEARNING




Explore using concrete materialsand computer software.


Emphasise therelationship betweenexpansion andfactorisation.

Note that 1is a factor for allalgebraic terms.

The difference of twosquares means:

a2 b2

= (a b)(am b).

Limit to four algebraicterms.

abac = a(bc)

e2f 2 = (e +f ) (ef)

x2 + 2xy +y2 = (x +y) 2

limit answers to

(ax + by) 2

ab + ac + bd + cd

=(b + c)(a + d)

factorisation

square

common factor

term

highest

(HCF)

difference oftwo squares

6.2 Understand anduse the conceptof factorisation ofalgebraicexpressions tosolve problems.

i. State factors of an algebraicterm.

ii. State common factors and theHCF for several algebraicterms.

iii. Factorise algebraicexpressions:

a) using common factor

b) the difference of twosquares.

.


common factor

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LEARNING






Begin with one-termexpressions for thenumerator anddenominator.

Limit to factorisationinvolving commonfactors and differenceof two squares.

numerator

denominator

algebraicfraction

factorisation

iv. Factorise and simplifyalgebraic fractions.

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LEARNING





Relate to real-life situations.


The concept of LCMmay be used.

Limit denominators toone algebraic term.

common factor

lowestcommonmultiple (LCM)

multiple

denominator

6.3 Perform additionand subtraction onalgebraic fractions.

i. Add or subtract two algebraicfractions with the samedenominator.

ii. Add or subtract two algebraicfractions with onedenominator as a multiple ofthe other denominator.

iii. Add or subtract two algebraicfractions with denominators:

a) without any commonfactor

b) with a common factor.

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LEARNING

OBJECTIVESSUGGESTED T EACHING AND





Begin multiplicationand division withoutsimplification followedby multiplication anddivision withsimplification.

simplification6.4 Performmultiplication anddivision onalgebraic fractions.

i. Multiply two algebraicfractions involvingdenominator with:

a) one term

b) two terms.

ii. Divide two algebraic fractionsinvolving denominator with:

a) one term

b) two terms

iii. Perform multiplication anddivision of two algebraicfractions using factorisationinvolving common factors andthe different of two squares.

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7LEARNING AREA:AALLGGEEBBRRAAIICC FFOORRMMUULLAAEE Form 3

LEARNING


LEARNING ACTIVITIESLEARNI NG OUTCOMES POINTS TO NOTE VOCABULARY


Use examples of everydaysituations to explain variables andconstants.


Variables include

integers, fractions anddecimals.

quantity

variable

constant

possible value

formula

value

letter symbol

formulae

7.1 Understand theconcepts ofvariables andconstants.

(Tarikh : 2/4/20126/4/2012)

i. Determine if a quantity in agiven situation is a variableor a constant.

ii. Determine the variable in agiven situation and representit with a letter symbol.

iii. Determine the possible

values of a variable in agiven situation.

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7LEARNING AREA:AALLGGEEBBRRAAIICC FFOORRMMUULLAAEE Form 3

LEARNING




Symbols representinga quantity in a formulamust be clearlystated.

Involve scientificformulae.

subject of aformula

statement

power

roots

formulae

7.2 Understand theconcepts offormulae to solveproblems.

i. Write a formula based on agiven:

a) statement

b) situation.

ii. Identify the subject of a givenformula.

iii. Express a specified variableas the subject of a formulainvolving:

a) one of the basicoperations: +, , x,

b) powers or roots

c) combination of the basicoperations and powers orroots.

iv. Find the value of a variablewhen it is:

a) the subject of the formula

b) not the subject of theformula.

v. Solve problems involvingformulae.

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8LEARNING AREA: Form 3SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII

LEARNING




Use concrete models to derivethe formulae.

Relate the volume of right prismsto right circular cylinders.


Prisms and cylindersrefer to right prismsand right circularcylinders respectively.

Limit the bases toshapes of trianglesand quadrilaterals.

derive

prism

cylinder

right circularcylinder

circular

base

radiusvolume

area

cubic units

square

rectangle

triangle

dimension

height

8.1 Understand anduse the conceptsof volumes ofright prisms andright circularcylinders to solveproblems.

(Tarikh : 9/4/201214/4/2012)

i. Derive the formula forvolume of:

a) prisms

b) cylinders.

ii. Calculate the volume of aright prism in cubic unitsgiven the height and:

a) the area of the base

b) dimensions of the base.

iii. Calculate the height of aprism given the volume andthe area of the base.

iv. Calculate the area of thebase of a prism given thevolume and the height.

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8LEARNING AREA:SSOOLLIIDD GGEEOOMMEETTRRYY IIIIII Form 3

LEARNING




cubic metre

cubiccentimetre

cubicmillimetre

millilitre

litre

convert

metric unit

v. Calculate the volume of acylinder in cubic units given:

a) area of the base and theheight.

b) radius of the base andthe height

of the cylinder.

vi. Calculate the height of a

cylinder, given the volumeand the radius of the base.

vii. Calculate the radius of thebase of a cylinder given thevolume and the height.

viii. Convert volume in one metricunit to another:

a) mm3, cm3 and m3

b) cm3, ml and l .

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LEARNING


LEARNING ACTIVITIESLEARNING OUTCOMES POINTS TO NOTE VOCABUL ARY


Limit the shape ofcontainers to rightcircular cylinders andright prisms.

liquid

containerix. Calculate volume of liquid in acontainer.

x. Solve problems involvingvolumes of prisms andcylinders.

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LEARNING




Use concrete models to derivethe formula.

Relate volumes of pyramids toprisms and volumes of cones tocylinders.


Include bases ofdifferent types ofpolygons.

pyramid

cone

volume

base

height

dimension

8.2 Understand anduse the conceptof volumes ofright pyramidsand right circularcones to solveproblems.

i. Derive the formula for thevolume of:

a) pyramids

b) cones.

ii. Calculate the volume of

pyramids in mm3, cm3 and

m3, given the height and:

a) area of the base

b) dimensions of base.

iii. Calculate the height of apyramid given the volume andthe dimension of the base.

iv. Calculate the area of the baseof a pyramid given the volumeand the height.

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LEARNING




height

dimension

v. Calculate the volume of a

cone in mm3, cm3 and m3,given the height and radiusof the base.

vi. Calculate the height of acone, given the volume andthe radius of the base.

vii. Calculate the radius of thebase of a cone given thevolume and the height.

viii. Solve problems involvingvolumes of pyramids andcones.

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9LEARNING AREA:

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9LEARNING AREA:SSCCAALLEE DDRRAAWWIINNGGSS IIIIII Form 3

LEARNING




Explore scale drawings usingdynamic geometry software, gridpapers, geo-boards or graphpapers.


Limit objects to two-dimensionalgeometric shapes.

Emphasise on theaccuracy of thedrawings.

Include grids ofdifferent sizes.

sketch

draw

objects

grid paper

geo-boards

software

scale

geometrical

shapes

compositeshapes

smaller

larger

accurate

size

9.1 Understand theconcepts of scaledrawings.

(Tarikh : 16/4/201220/4/2012)

i. Sketch shapes:

a) of the same size as theobject

b) smaller than the object

c) larger than the object

using grid papers.

ii. Draw geometric shapes

according to scale 1 : n,where n = 1, 2, 3, 4, 5 ,1 , 1 .2 10

iii. Draw composite shapes,according to a given scaleusing:

a) grid papers

b) blank papers.

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9LEARNING AREA:SSCCAALLEE DDRRAAWWIINNGGSS IIIIII Form 3

LEARNING




Relate to maps, graphics andarchitectural drawings.


Emphasise that gridsshould be drawn onthe original shapes.

redrawiv. Redraw shapes on grids ofdifferent sizes.

v. Solve problems involvingscale drawings.

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10LEARNING AREA:TTRRAANNSSFFOORRMMAATTIIOONNSS IIII Form 3

LEARNING




Involve examples from everydaysituations.

Explore the concepts ofenlargement using grid papers,

concrete materials, drawings,geo-boards and dynamicgeometry software.

Relate enlargement to similarityof shapes.


Emphasise that for atriangle, if thecorresponding anglesare equal, then thecorresponding sidesare proportional.

Emphasise the caseof reduction.

Emphasise the casewhenscale factor = 1

Emphasise that thecentre of enlargementis an invariant point.

shape

similar

side

angle

proportion

centre ofenlargement

transformation

enlargementscale factor

object

image

invariant

reduction

size

orientation

similarity

10.1 Understand anduse the conceptsof similarity.

(Tarikh : 23/4/201227/4/2012)

i. Identify if given shapes aresimilar.

ii. Calculate the lengths ofunknown sides of two similarshapes.

10.2 Understand anduse the concepts

of enlargement.

i. Identify an enlargement.

ii. Find the scale factor, giventhe object and its image of anenlargement when:

a) scale factor 0

b) scale factor 0.

iii. Determine the centre ofenlargement, given theobject and its image.

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10 TTRRAANNSSFFOORRMMAATTIIOONNSS IIII Form 3LEARNING




Emphasise themethod ofconstruction.

propertiesiv. Determine the image of anobject given the centre ofenlargement and the scalefactor.

v. Determine the properties ofenlargement.

vi. Calculate the:

a) scale factorb) the lengths of sides of the

image

c) the lengths of sides of theobject

of an enlargement.

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10 TTRRAANNSSFFOORRMMAATTIIOONNSS IIII Form 3LEARNING




Use grid papers and dynamicgeometry software to explore therelationship between the area ofthe image and its object.


Include negative scalefactors.

areavii. Determine the relationshipbetween the area of theimage and its object.

viii. Calculate the:

a) area of image

b) area of object

c) scale factor

of an enlargement.

ix. Solve problems involvingenlargement.

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11LEARNING AREA:

F 3

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11 LLIINNEEAARR EEQQUUAATTIIOONNSS IIII Form 3LEARNING




Use trial and improvementmethod.

Use examples from real-lifesituations.


Include letter symbolsother thanx andy torepresent variables.

linear equation

variable

simultaneouslinearequation

solution

substitution

elimination

11.2 Understand anduse the conceptsof twosimultaneouslinear equationsin two variablesto solveproblems.

i. Determine if two givenequations are simultaneouslinear equations.

ii. Solve two simultaneouslinear equations in twovariables by

a) substitution

b) elimination

iii. Solve problems involving twosimultaneous linearequations in two variables.

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12LEARNING AREA:LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS Form 3

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12 LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS Form 3LEARNING




Use everyday situations to illustratethe symbols and the use of > , b

is equivalent to b < a.

> read as greaterthan.

< read as lessthan.

read as greaterthan or equal to.

read as lessthan or equal to.

inequality

greater

less

greater than

less than

equal to

include

equivalent

solution

12.1 Understand anduse the conceptsof inequalities.

(Tarikh : 11/6/201215/6/2012)

i. Identify the relationship:

a) greater than

b) less than

based on given situations.

ii. Write the relationshipbetween two given numbersusing the symbol >or

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h is a constant,x is aninteger.

relationship

linear

unknown

number line

12.2 Understand anduse theconcepts oflinearinequalities inone unknown.

i. Determine if a givenrelationship is a linearinequality.

ii. Determine the possiblesolutions for a given linearinequality in one unknown:

a) x > h;

b) x < h;

c) x h;

d) x h.

iii. Represent a linear inequality:

a) x > h;

b) x < h;

c) x h;

d) x h.

on a number line and viceversa.

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Involve examples from everydaysituations.


Emphasise that thecondition of inequalityis unchanged.

Emphasise that whenwe multiply or divideboth sides of aninequality by the samenegative number, theinequality is reversed.

iv. Construct linear inequalitiesusing symbols:

a) > or

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Information given fromreal-life situations.

Include also

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LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS Form 3\LEARNING




Explore using dynamic geometrysoftware and graphic calculators.


Emphasise that for asolution, the variableis written on the leftside of theinequalities.

add

subtract

multiply

divide

12.4 Performcomputations tosolve inequalitiesin one variable.

i. Solve a linear inequality by:

a) adding a number

b) subtracting a number

on both sides of the

inequality.

ii. Solve a linear inequality by

a) multiplying a number

b) dividing a numberon both sides of theinequality.

iii. Solve linear inequalities inone variable using acombination of operations.

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LLIINNEEAARR IINNEEQQUUAALLIITTIIEESS Form 3LEARNING




Emphasise themeaning ofinequalities such as:

i. a x b

ii. a x b

iii. a x b

iv. a x b

Emphasise that formssuch as:

i. a x b

ii. a x b

iii. a xb

are not accepted.

determine

common value

simultaneous

combining

linearinequality

number line

equivalent

12.5 Understand theconcepts ofsimultaneouslinearinequalities inone variable.

i. Represent the commonvalues of two simultaneouslinear inequalities on anumber line.

ii. Determine the equivalentinequalities for two givenlinear inequalities.

iii. Solve two simultaneous linear

inequalities.

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13LEARNING AREA:GGRRAAPPHHSS OOFF FFUUNNCCTTIIOONNSS Form 3

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GGRRAAPPHHSS OOFF FFUUNNCCTTIIOONNSS Form 3LEARNING



Students will be taug ht to:

Explore using functionmachines.


Involve functions suchas:

i. y = 2x + 3

ii. p = 3q2 + 4q5

iii. A = B3

1iv. W =

Z

function

relationship

variable

dependentvariable

independentvariable

ordered pairs

13.1 Understand anduse the conceptsof functions.

(Tarikh : 18/6/201222/6/2012)

i. State the relationship betweentwo variables based on giveninformation.

ii. Identify the dependent andindependent variables in agiven relationship involvingtwo variables.

iii. Calculate the value of thedependent variable, given thevalue of the independentvariable.

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13LEARNING AREA:GGRRAAPPHHSS OOFF FFUUNNCCTTIIOONNSS Form 3

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GGRRAAPPHHSS OOFF FFUUNNCCTTIIOONNSS Form 3LEARNING




Limit to linear,quadratic and cubicfunctions.

Include cases whenscales are not given.

coordinateplane

table of values

origin

graph

x-coordinate

y-coordinate

x-axis

y-axisscale

13.2 Draw and usegraphs offunctions.

i. Construct tables of values forgiven functions.

ii. Draw graphs of functionsusing given scale.

iii. Determine from a graph the

value ofy, given the value ofx and vice versa.

iv. Solve problems involvinggraphs of functions.

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14LEARNING AREA:RRAATTIIOO,, RRAATTEEAANNDD PPRROOPPOORRTTIIOONN IIII Form 3

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,, Form 3LEARNING




Use examples from everydaysituations.


Moral values relatedto traffic rules shouldbe incorporated.

Include the use ofgraphs.

speeddistance

time

uniform

non-uniform

differentiate

14.2 Understand anduse the conceptof speed.

i. Identify the two quantitiesinvolved in speed.

ii. Calculate and interpret speed.

iii. Calculate:

a) the distance, given thespeed and the time

b) the time, given the speedand the distance.

iv. Convert speed from one unitof measurement to another.

v. Differentiate between uniformspeed and non-uniformspeed.

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14LEARNING AREA:RRAATTIIOO,, RRAATTEEAANNDD PPRROOPPOORRTTIIOONN IIII Form 3

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, Form 3LEARNING




Use examples from dailysituations.

Discuss the difference betweenaverage speed and mean speed.


Include cases ofretardation.

Retardation is alsoknown deceleration.

average speeddistance

time

acceleration

retardation

14.3 Understand anduse the conceptsof average speed.

i. Calculate the average speedin various situations.

ii. Calculate:

a) the distance, given theaverage speed and thetime.

b) the time, given theaverage speed and thedistance.

iii. Solve problems involvingspeed and average speed.

14.4 Understand anduse the conceptsof acceleration.

i. Identify the two quantitiesinvolved in acceleration.

ii. Calculate and interpretacceleration.

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15LEARNING AREA:TTRRIIGGOONNOOMMEETTRRYY Form 3

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Form 3LEARNING




Use right-angled triangles withreal measurements and developthrough activities.

Discuss the ratio of the oppositeside to the adjacent side whenthe angle approaches 90o.

Explore tangent of a given anglewhen:

a) The size of the triangle variesproportionally.

b) The size of angle varies.


Use only right-angledtriangle.

Tangent can bewritten as tan .

Emphasise thattangent is a ratio.

Limit to opposite andadjacent sides.

Include cases thatrequire the use of

PythagorasTheorem.

right-angledtriangle

angle

hypotenuse

opposite side

adjacent side

ratio

tangent

value

length

size

15.1 Understand anduse tangent of anacute angle in aright-angledtriangle.

(Tarikh : 9/7/201220/7/2012)

PeperiksaanPercubaan PMR

23/727/7/2012

i. Identify the:a) hypotenuseb) the opposite side and the

adjacent side with respectto one of the acuteangles.

ii. Determine the tangent of anangle.

iii. Calculate the tangent of an

angle given the lengths ofsides of the triangle.

iv. Calculate the lengths of sidesof a triangle given the value oftangent and the length ofanother side.

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LEARNING




Explore sine of a given anglewhen:


b) The size of the angle varies.

Explore cosine of a given anglewhen:


b) The size of the angle varies.


Sine can be writtenas sin.

Include cases thatrequire the use ofPythagoras Theorem.

Cosine can bewritten as cos.

Include cases thatrequire the use ofPythagorasTheorem.

ratioright-angledtriangle

length value

hypotenuse

opposite side

size

constant

increase

proportion

15.2 Understand anduse sine of anacute angle in aright-angledtriangle.

i. Determine the sine of anangle.

ii. Calculate the sine of anangle given the lengths ofsides of the triangle.

iii. Calculate the lengths of sidesof a triangle given the valueof sine and the length ofanother side.

15.3 Understand anduse cosine of anacute angle in aright-angledtriangle.

i. Determine the cosine of anangle.

ii. Calculate the cosine of anangle given the lengths ofsides of the triangle.

iii. Calculate the lengths of sidesof a triangle given the value ofcosine and the length ofanother side.

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LEARNING




angledegree

minute

tangent

sine

cosine

. v. Find the angles given thevalues of:

a) tangent

b) sine

c) cosine

using scientific calculators.

vi. Solve problems involvingtrigonometric ratios.

61

Form 3

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CONTRIBUTORS

Advisor Dr. Sharifah Maimunah Syed Zin Director

Curriculum Development Centre

Dr. Rohani Abdul Hamid Deputy Director


Editorial Ahmad Hozi H.A. Rahman Principal Assistant Director

Advisors (Science and Mathematics Department)


Rusnani Mohd Sirin Assistant Director

(Head of Mathematics Unit)Curriculum Development Centre

S. Sivagnanachelvi Assistant Director

(Head of English Language Unit)


Editor Rosita Mat Zain Assistant Director


62

Form 3

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WRITERS

Rusnani Mohd Sirin


Abdul Wahab Ibrahim


Rosita Mat Zain


Rohana IsmailCurriculum Development Centre Susilawati EhsanCurriculum Development Centre

Dr. Pumadevi a/p Sivasubramaniam

Maktab Perguruan Raja Melewar,

Seremban, Negeri Sembilan

Lau Choi FongSMK Hulu KelangHulu Kelang, Selangor

Prof. Dr. Nor Azlan ZanzaliUniversity Teknologi Malaysia

Krishen a/l GobalSMK Kg. Pasir PutehIpoh, Perak

Kumaravalu a/l RamasamyMaktab Perguruan Tengku Ampuan

Afzan, Kuala Lipis

Raja Sulaiman Raja HassanSMK Puteri, Kota BharuKelantan

Noor Aziah Abdul Rahman Safawi

SMK Perempuan PuduKuala Lumpur

Cik Bibi Kismete Kabul KhanSMK Dr. Megat KhasIpoh, Perak

Krishnan a/l MunusamyJemaah Nazir Sekolah

Ipoh, Perak

Mak Sai MooiSMK Jenjarom

Selangor

Azizan Yeop ZaharieMaktab Perguruan Persekutuan PulauPinang

Ahmad Shubki Othman

SMK DatoAbdul Rahman YaakobBota, Perak

Zaini Mahmood

SMK JabiPokok Sena, Kedah

Lee Soon KuanSMK Tanah MerahPendang, Kedah

Ahmad Zamri AzizSMK Wakaf BharuKelantan

63

Form 3

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LAYOUT AND ILLUSTRATION

Rosita Mat Zain


Mohd Razif Hashim


64

Documents

RPT MT F3 2012