mathematics syllabus forms 1 - 4 · mathematics syllabus forms 1 - 4 ii ... 7.3 financial...

MINISTRY OF PRIMARY AND SECONDARY EDUCATION

ZIMBABWE

MATHEMATICS SYLLABUS

FORMS 1 - 4

2015 - 2022

Curriculum Development and Technical ServicesP. O. Box MP 133 Mount Pleasant

Harare

©All Rights Reserved2015

Mathematics Syllabus Forms 1 - 4

ACKNOWLEDGEMENTThe Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued con-tribution in the production of this syllabus:

• National panellists for Form 1 to 4 Mathematics• Representatives from Higher and Tertiary Institutions• Representatives from the following organisations:

- Zimbabwe School Examinations Council (ZIMSEC)- United Nations International Children’s Emergency Fund (UNICEF)- UnitedNationsEducational,ScientificandCulturalOrganisation(UNESCO)

i


ii

CONTENTSACKNOWLEDGEMENT.......................................................................................................................... i

CONTENTS............................................................................................................................................. ii

1.0 PREAMBLE....................................................................................................................................... 1

2.0 PRESENTATION OF SYLLABUS..................................................................................................... 1

3.0 AIMS.................................................................................................................................................. 1

4.0 SYLLABUS OBJECTIVES................................................................................................................ 2

5.0 METHODOLOGY AND TIME ALLOCATION.................................................................................... 2

6.0 TOPICS.............................................................................................................................................. 2

7.0 SCOPE AND SEQUENCE................................................................................................................. 3

FORM ONE (1)........................................................................................................................................ 13

8.2 FORM (2).......................................................................................................................................... 23

8.3 FORM THREE (3).............................................................................................................................. 39

8.4 FORM FOUR (4)................................................................................................................................ 56

9.0 ASSESSMENT.................................................................................................................................. 70

ASSESSMENT MODEL.......................................................................................................................... 72


1

1.0 PREAMBLE

1.1 Introduction

In developing the Mathematics syllabus attention was paid to the need to provide continuity of mathematical concepts from primary school level to form 4 and lay foundations for further studies and career development. It is intended to produce a citizen who is a critical think-er and problem solver in everyday life. The four year learning area will provide learners with opportunities to apply mathematical concepts to other learning areas and enhance mathematical literacy and numeracy. It also de-sires to produce a learner with the ability to communicate effectively, with proper qualities of team work. In learning mathematics, learners should understand and master a variety of skills, knowledge, concepts and processes in order to investigate and interpret numerical and spatial relationships and patterns that exist in the world. It also caters for learners with diverse needs to experience mathematics as relevant and worthwhile.

1.2 Rationale

Zimbabwe is undergoing a socio-economic transforma-tion where mathematics is key to development, therefore, it is imperative that learners acquire necessary mathe-matical knowledge, skills and develop a positive attitude towards the learning area. This will enable learners to be creative thinkers, problem solvers and communicators with values of unhu/vumunhu/Ubuntu such as discipline, integrity and honesty . The knowledge of mathematics enables learners to develop mathematical skills such as accuracy, research, logical and analytical competencies essential for sustainable development and in life. The im-portance of mathematics can be underpinned in inclusiv-ity and human dignity and is a universal language that cutsacrossallboundariesandunifiesdiversecultures.Mathematics plays a pivotal role in careers such as en-treprise, education, medicine, agriculture, meteorology, engineering and others.

1.3 Summary of Content

The syllabus covers the theoretical and practical broad mathematical concepts. The syllabus covers operations with real numbers, manipulation of algebraic symbols and techniques, formulating and solving equations, draw-ing and interpreting graphs and making inferences from statistical data and representation.

1.4 Assumptions

In developing the syllabus it is assumed that the learner has :

• completedprimaryeducation• basicknowledgeofprimarymathematicssyllabus

concepts such as: - number- operations- measures- relationships

• abilitytouseICTtools

1.5 Cross Cutting themes

The following are some of the cross cutting themes in Mathematics:

• Businessandfinancialliteracy• Disasterandriskmanagement• Communicationandteambuilding• Environmentalissues• Gender• Enterpriseskills• HIV&AIDS• ICT• Unhu/Ubuntu/Vumunhu

2.0 PRESENTATION OF SYLLABUS

The mathematics syllabus is a single document covering Forms 1 to 4 . It contains the preamble, aims, assess-ment objectives, syllabus topics, scope and sequence and competency matrix. The syllabus also suggests a list of resources to be used in the learning and teaching process.

3.0 AIMSThe syllabus will enable learners to:

• developanunderstandingofmathematicalconceptsandprocessesinawaythatencouragesconfidence,enjoyment and interest

• furtheracquireappropriatemathematicalskillsandknowledge

• developtheabilitytothinkclearly,workcarefullyandcommunicate mathematical ideas successfully• applymathematicsinotherlearningareasandin

life


2

• developanappreciationoftheroleofmathematicsin personal, community and national development

• engage,persevere,collaborateandshowintellec-tual honesty in performing tasks in mathematics, inthespiritofUnhu/Ubuntu/Vumunhu

• useI.C.Ttoolstosolvemathematicalproblems

4.0 SYLLABUS OBJECTIVESThe learners should be able to:

• usemathematicalsymbols,termsanddefinitionsin problem solving

• constructappropriatemathematicalmodelsthatcan be applied in solving problems in life

• drawinferencesthroughmanipulationofmathe-matical data

• communicatemathematicalideasandinformationclearly and effectively in various contexts

• solveawiderangeofproblemsinvolvingalgebraicand geometric concepts

• applymathematicalconceptsinotherlearningareas

• useI.C.Ttoolsinproblemsolving• conductresearchprojectsincludingthoserelated

to enterprise

5.0 METHODOLOGY AND TIME ALLOCATIONIt is recommended that teachers use teaching tech-niques in which mathematics is seen as a process which arouseaninterestandconfidenceinsolvingproblemsin both familiar and unfamiliar contexts. The teaching and learning of mathematics must be learner centred. Multi-sensory principles should also be applied during teaching and learning of mathematics. The following are some of the suggested methods of the teaching and learning of mathematics

• Guideddiscovery• Discussion• Interactivee-learning• Exposition• Demonstrationandillustration• Problemsolving• Individualisation• Simulation• Visualtactile• Educationaltours• Expertguestpresentation

5.1 Time Allocation

Six periods of 40 minutes each per week should be allo-cated for the adequate coverage of the syllabus.

6.0 TOPICSThe following topics will be covered from Form 1 to 4

6.1 Real Numbers6.2 Sets6.3 Financial Mathematics6.4 Measures and Mensuration6.5 Graphs6.6 Variation6.7 Algebra6.8 Geometry6.9 Statistics6.10 Trigonometry6.11 Vectors6.12 Matrices6.13 Transformation6.14 Probability


3

7.0

SCO

PE A

ND

SEQ

UEN

CE

7. 1

REA

L N

UM

BER

S

Mat

hem

atics

Syl

labu

s For

m 1

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5

6

7.0

SC

OPE

AN

D S

EQU

ENC

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7.1

Rea

l num

bers

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Num

ber C

once

pts

and

Ope

ratio

ns

N

umbe

r typ

es

Fa

ctor

s an

d m

ultip

les

D

irect

ed n

umbe

rs

Fr

actio

ns a

nd p

erce

ntag

es

O

rder

of o

pera

tions

Fa

ctor

s an

d m

ultip

les

Sq

uare

s an

d sq

uare

root

s

Cub

es a

nd c

ube

root

s

O

rder

of o

pera

tions

Irrat

iona

l num

bers

Num

ber p

atte

rns

Appr

oxim

atio

ns a

nd

estim

atio

ns

R

ound

off

num

bers

Dec

imal

pla

ces

Si

gnifi

cant

figu

res

Es

timat

ions

Sign

ifica

nt fi

gure

s

Estim

atio

ns

Li

mits

of a

ccur

acy

Rat

ios,

rate

s an

d pr

opor

tions

Rat

ios

Rat

ios

Pr

opor

tions

Rat

ios

R

ates

Prop

ortio

ns

Ord

inar

y an

d st

anda

rd fo

rm

La

rge

and

smal

l num

bers

Num

bers

in s

tand

ard

form

Ope

ratio

ns in

sta

ndar

d fo

rm

Num

ber b

ases

Num

ber b

ases

in e

very

day

life

Pl

ace

valu

es

C

onve

rting

num

bers

from

on

e ba

se to

ano

ther

(B

ases

2, 5

and

10)

O

pera

tions

in n

umbe

r ba

ses

from

bas

e 2

to b

ase

10

Scal

es a

nd s

impl

e m

ap

prob

lem

s

Scal

e m

easu

rem

ent

Sc

ale

draw

ing

Sc

ale

fact

or

Ar

ea fa

ctor


4

7. 2

Sets

Mat

hem

atics

Syl

labu

s For

m 1

– 4

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5

7

7.2

Set

s

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Sets

Sets

and

Set

not

atio

n

Type

s of

set

s

Ty

pes

of s

ets

Ve

nn d

iagr

am w

ith tw

o su

bset

s

Se

t Bui

lder

Not

atio

n

Venn

dia

gram

s w

ith th

ree

subs

ets

7.3

Fin

anci

al M

athe

mat

ics

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

8

7.3

Fin

anci

al M

athe

mat

ics

TOPI

C

FORM

1

FORM

2

FORM

3

FORM

4

Con

sum

er a

rithm

etic

Hou

seho

ld b

ills

Pr

ofit

and

loss

Dis

coun

t

Hou

seho

ld b

udge

ts

C

orpo

rate

bills

Prof

it an

d lo

ss

Si

mpl

e in

tere

st

H

ire p

urch

ase

Sm

all s

cale

ent

erpr

ise

budg

ets

Ba

nk s

tate

men

ts

C

ompo

und

inte

rest

Com

mis

sion

Hire

pur

chas

e

Fo

reig

n ex

chan

ge

Sa

les

and

inco

me

tax

rate

s (P

ay a

s yo

u ea

rn

(PAY

E))

Va

lue

adde

d ta

x (V

AT)

C

usto

ms

and

Exci

se D

uty

7.4

Mea

sure

s an

d M

ensu

ratio

n

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

9

7.4

Mea

sure

s an

d M

ensu

ratio

n

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Mea

sure

s

U

nits

of :

-

Tim

e -

Mas

s -

Leng

th

- Te

mpe

ratu

re

- C

apac

ity

U

nits

of:

- Ar

ea

- Vo

lum

e -

Cap

acity

-

Den

sity

Men

sura

tion

Perim

eter

of p

lane

sh

apes

Area

of p

lane

sha

pes

Pe

rimet

er o

f pla

ne

shap

es

Ar

ea o

f pla

ne s

hape

s

Volu

me

of c

uboi

ds

D

ensi

ty o

f cub

oids

Pe

rimet

er o

f com

bine

d sh

apes

Area

of c

ombi

ned

shap

es

Vo

lum

e of

cyl

inde

rs

Ar

ea a

nd v

olum

es o

f so

lid s

hape

s

Surfa

ce a

rea

D

ensi

ty


5

7.5

Gra

phs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

10

7.5

Gra

phs

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Func

tiona

l Gra

phs

C

arte

sian

pla

ne

Sc

ale

C

o-or

dina

tes

C

arte

sian

pla

ne

Ta

ble

of v

alue

s

Line

ar g

raph

s

Scal

e

Fu

nctio

nal N

otat

ion

Line

ar g

raph

s

Qua

drat

ic g

raph

s

C

ubic

gra

phs

In

vers

e gr

aphs

Trav

el G

raph

s

Dis

tanc

e tim

e gr

aphs

Dis

tanc

e tim

e gr

aphs

Dis

tanc

e tim

e gr

aphs

Spee

d-tim

e gr

aphs

Dis

plac

emen

t tim

e gr

aphs

Velo

city

-tim

e gr

aphs

7.6

Var

iatio

n

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

11

7.6

Var

iatio

n

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Varia

tion

Dire

ct v

aria

tion

Dire

ct v

aria

tion

In

vers

e va

riatio

n

Join

t var

iatio

n

Parti

al v

aria

tion


6

7.7

A

lgeb

ra

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

12

7.7

A

lgeb

ra

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Alge

brai

c M

anip

ulat

ion

Ba

sic

arith

met

ic

proc

esse

s in

lette

r sy

mbo

ls

Su

bstit

utio

n of

val

ues

Al

gebr

aic

expr

essi

ons

Su

bstit

utio

n of

val

ues

Al

gebr

aic

expr

essi

ons

Al

gebr

aic

fract

ions

Qua

drat

ic e

xpre

ssio

ns

Fa

ctor

isat

ion

Al

gebr

aic

fract

ions

Hig

hest

Com

mon

Fac

tor

(HC

F) a

nd L

owes

t C

omm

on M

ultip

le (L

CM

) of

alg

ebra

ic e

xpre

ssio

ns

Q

uadr

atic

exp

ress

ions

Fact

oris

atio

n

Al

gebr

aic

fract

ions

Qua

drat

ic e

xpre

ssio

ns

Fa

ctor

isat

ion

Com

plet

ing

the

squa

re

Equa

tions

Line

ar e

quat

ions

Equa

tions

with

bra

cket

s

Equa

tions

with

frac

tions

Cha

nge

of s

ubje

ct o

f fo

rmul

ae

Si

mul

tane

ous

linea

r eq

uatio

ns

Q

uadr

atic

equ

atio

ns

Si

mul

tane

ous

equa

tions

Qua

drat

ic e

quat

ions

Cha

nge

of s

ubje

ct o

f fo

rmul

ae

Su

bstit

utio

n of

val

ues

C

ompl

etin

g th

e sq

uare

Qua

drat

ic fo

rmul

ae

Ineq

ualit

ies

Ineq

ualit

y si

gns

Li

near

ineq

ualit

ies

Num

ber l

ine

Li

near

ineq

ualit

ies

N

umbe

r lin

e

Car

tesi

an p

lane

Si

mul

tane

ous

ineq

ualit

ies

G

raph

s of

ineq

ualit

ies

Li

near

pro

gram

min

g

Indi

ces

and

Log

arith

ms

Inde

x fo

rm

La

ws

of in

dice

s

In

dice

s

Lo

garit

hms

Theo

ry o

f log

arith

ms

Eq

uatio

ns in

volv

ing

indi

ces

and

loga

rithm

s


7

7. 8

G

eom

etry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

13

7. 8

G

eom

etry

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Poin

ts, l

ines

and

ang

les

Po

ints

Line

s

An

gles

An

gles

Par

alle

l and

Tra

nsve

rsal

lin

es

An

gles

of e

leva

tion

and

depr

essi

on

Bea

ring

Car

dina

l poi

nts

Th

ree

figur

e be

arin

g

Com

pass

bea

ring

Th

ree

figur

e be

arin

g

Com

pass

bea

ring

Poly

gons

and

circ

les

Po

lygo

ns

C

ircle

s

Pr

oper

ties

of p

olyg

ons

(tria

ngle

s an

d qu

adril

ater

als)

Pr

oper

ties

of p

olyg

ons

An

gles

of p

olyg

ons

N

umbe

rs o

f sid

es o

f po

lygo

ns

C

ircle

theo

rem

s

Sim

ilarit

y an

d C

ongr

uenc

y

Si

mila

r and

con

grue

nt

figur

es

C

ases

of c

ongr

uenc

y

Sc

ale

fact

or

Ar

eas

of s

imila

r fig

ures

Volu

me

and

mas

s of

si

mila

r sol

ids

Con

stru

ctio

ns a

nd L

oci

C

onst

ruct

ion

of li

nes

and

angl

es

C

onst

ruct

ion

of a

ngle

s

Bise

ctin

g lin

es a

nd

angl

es

C

onst

ruct

ion

of tr

iang

les

and

quad

rilat

eral

s

C

onst

ruct

ion

of

diag

ram

s to

a g

iven

sc

ale

Lo

ci

Sym

met

ry

Line

sym

met

ry in

two

dim

ensi

ons

Rot

atio

nal s

ymm

etry

in

two

dim

ensi

ons


8

7.9

Sta

tistic

s

SUB

TO

PIC

FOR

M 1

FOR

M 2

FOR

M 3

FOR

M 4

Dat

a co

llect

ion,

cla

ssifi

catio

n an

d re

pres

enta

tion

•Datacollection

•Dataclassification

•Datacollection

•Classificationofungrouped

data

•Representingdatausing

frequ

ency

tabl

es, b

ar c

hare

ts

and

pie

char

ts

•Collectionandclassification

of g

roup

ed d

ata

•Frequencytable

•Piechart

•Histogram

•Frequencypolygon

•Ba

rchart

•Frequencytable

•Frequencypolygon

•Cum

ulativefrequency

tabl

e•

Cum

ulativefrequency

curv

e

Mea

sure

s of

cen

tral

tend

ency

•Mean

•Classmode

•Median

•Assumedmean

•Mean,medianandmodal

clas

s of

gro

uped

dat

a•

Assumedmean

•Medianfromcum

ulative

frequ

ency

cur

ve

Mea

sure

s of

Dis

pers

ion

•Quartiles

•Interquartilerange

•Se

mi-interquartilerange


9

7.10

Trig

onom

etry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

15

7.10

Trig

onom

etry

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Pyth

agor

as th

eore

m

P

ytha

gora

s th

eore

m

Py

thag

oria

n tri

pple

S

Trig

onom

etric

al ra

tios

Tr

igon

omet

rical

ratio

s of

ac

ute

angl

es:

- si

ne

- co

sine

-

tang

ent

Tr

igon

omet

rical

ratio

s of

ob

tuse

ang

les:

-

sine

-

cosi

ne

- ta

ngen

t

C

osin

e ru

le

Si

ne ru

le

Ar

ea o

f tri

angl

eS

7.11

Ve

ctor

s

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

16

7.11

Ve

ctor

s

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Def

initi

on a

nd N

otat

ion

Def

initi

on o

f vec

torS

Vect

or n

otat

ion

Type

s of

Vec

tors

Tr

ansl

atio

n ve

ctor

s

Neg

ativ

e ve

ctor

s

Equa

l vec

tors

Para

llel v

ecto

rs

Tr

ansl

atio

n ve

ctor

s

Neg

ativ

e ve

ctor

s

Equa

l vec

tors

Para

llel v

ecto

rs

Po

sitio

n ve

ctor

s

Ope

ratio

ns

Addi

tion

of v

ecto

rs

Su

btra

ctio

n of

vec

tors

Addi

tion

of v

ecto

rs

Su

btra

ctio

n of

vec

tors

scal

ar m

ultip

licat

ion

M

agni

tude

of v

ecto

rs

C

ombi

ned

vect

or

oper

atio

ns

Ve

ctor

pro

perti

es o

f pl

ane

shap

es


10

7.12

Mat

rices

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

17

7.12

Mat

rices

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Ord

er

Ord

er o

f mat

rices

Ty

pes

of m

atric

es

Ope

ratio

ns

Ad

ditio

n an

d su

btra

ctio

n of

mat

rices

Sc

alar

mul

tiplic

atio

n of

m

atric

es

M

ultip

licat

ion

of m

atric

es

Det

erm

inan

ts

D

eter

min

ants

of

mat

rices

Si

ngul

ar a

nd n

on-s

ingu

lar

mat

rices

Inve

rse

mat

rix

In

vers

e of

a m

atrix

Si

mul

tane

ous

linea

r eq

uatio

ns in

2 v

aria

bles


11

7.13

Tr

ansf

orm

atio

n

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

18

7.13

Tr

ansf

orm

atio

n

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Tran

slat

ion

Tr

ansl

atio

n of

pla

ne fi

gure

s

Tran

slat

ion

vect

or t

o m

ove

a po

int

tra

nsla

tion

vect

or to

m

ove

a pl

ane

figur

e on

a

Car

tesi

an p

lane

Ref

lect

ion

R

efle

ctio

n of

pla

ne

figur

es

R

efle

ctio

n of

pla

ne

figur

es o

n a

carte

sian

pl

ane

in th

e x-

axis

, y-

axis

, and

line

s of

the

form

y=a

and

x=b

R

efle

ctio

n of

pla

ne fi

gure

s in

any

line

and

usi

ng

mat

rices

Rot

atio

n

R

otat

ion

of p

lane

figu

res

on a

Car

tesi

an p

lane

by

geom

etric

met

hods

R

otat

ion

of p

lane

figu

res

by d

raw

ing

and

use

of

mat

rices

Enla

rgem

ent

En

larg

emen

t abo

ut th

e or

igin

usi

ng a

ratio

nal

scal

e by

geo

met

ric

met

hods

En

larg

emen

t usi

ng

mat

rices

and

abo

ut a

ny

poin

t usi

ng a

ratio

nal

scal

e

Stre

tch

O

ne-w

ay a

nd tw

o-w

ay

stre

tch

usin

g m

atric

es a

nd

geom

etric

al m

etho

ds

Shea

r

Sh

ear u

sing

mat

rices

and

ge

omet

rical

met

hods


12

7. 1

4 P

roba

bilit

y

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

19

7. 1

4 P

roba

bilit

y

SUB

TO

PIC

FO

RM 1

FO

RM 2

FO

RM 3

FO

RM 4

Prob

abili

ty

Def

initi

on o

f pro

babi

lity

term

s

Expe

rimen

tal p

roba

bilit

y

Ex

perim

enta

l pro

babi

lity

Th

eore

tical

pro

babi

lity

Si

ngle

eve

nts

C

ombi

ned

even

ts

O

utco

me

tabl

es

Tr

ee d

iagr

ams

Prob

abilit

y ru

les

Ap

plic

atio

n of

pro

babi

lity


13

FOR

M O

NE

(1)

8.0

CO

MPE

TEN

CY

MAT

RIX

8.1

Rea

l num

bers

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

20

FORM

ON

E (1

)

8.0

CO

MPE

TEN

CY

MAT

RIX

8.

1

R

eal n

umbe

rs

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Num

ber C

once

pts

and

oper

atio

ns

id

entif

y ty

pes

of n

umbe

rs

fin

d fa

ctor

s an

d m

ultip

les

of n

umbe

rs

fin

d H

.C.F

. and

L.C

.M

op

erat

e w

ith d

irect

ed

num

bers

appl

y di

rect

ed n

umbe

rs

to p

ract

ical

situ

atio

ns in

lif

e

oper

ate

with

frac

tions

conv

ert f

ract

ions

to

deci

mal

s

conv

ert f

ract

ions

to

perc

enta

ges

and

vice

ve

rsa

ca

rry

out c

alcu

latio

ns

invo

lvin

g pe

rcen

tage

s

carr

yout

mix

ed

oper

atio

ns u

sing

the

rule

of

pre

cede

nce

N

umbe

r typ

es

Fa

ctor

s an

d m

ultip

les

D

irect

ed n

umbe

rs

Fr

actio

ns a

nd

perc

enta

ges

O

rder

of O

pera

tions

Id

entif

ying

and

list

ing

type

s of

num

bers

List

ing

fact

ors

and

mul

tiple

s of

num

bers

Find

ing

H.C

.F a

nd L

.C.M

Usi

ng a

num

ber l

ine

on

the

oper

atio

n of

dire

cted

nu

mbe

rs

Pe

rform

ing

oper

atio

ns

invo

lvin

g fra

ctio

ns

C

onve

rting

frac

tions

to

deci

mal

s

Con

verti

ng fr

actio

ns to

pe

rcen

tage

s

Cal

cula

tions

invo

lvin

g de

cim

als

and

perc

enta

ges

C

alcu

latio

ns in

volv

ing

mix

ed o

pera

tions

usi

ng

rule

s of

pre

cede

nce

R

elev

ent T

exts

ICT

Tool

s

Brai

lle m

ater

ial a

nd

Equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Appr

oxim

atio

n an

d es

timat

ion

ro

und

off n

umbe

rs to

the

give

n pl

ace

valu

e

Who

le n

umbe

rs

D

ecim

al n

umbe

rs

R

ound

ing

off n

umbe

rs

R

elev

ant t

exts

ICT

tool

s


14

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

21

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

ro

und

off n

umbe

rs to

the

give

n de

cim

al p

lace

s

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Rat

ios,

rate

s an

d pr

opor

tions

sim

plify

ratio

s

solv

e pr

oble

ms

invo

lvin

g ra

tios

R

atio

Ex

pres

sing

ratio

s in

thei

r si

mpl

est f

orm

s

Dis

cuss

ing

the

use

of

ratio

s in

life

Solv

ing

prob

lem

s in

volv

ing

ratio

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Ord

inar

y an

d st

anda

rd fo

rm

ex

pres

s sm

all a

nd la

rge

num

bers

in d

igits

and

w

ords

La

rge

and

smal

l nu

mbe

rs

ex

pres

sing

sm

all a

nd

larg

e nu

mbe

rs in

dig

its

and

wor

ds

R

elev

ant t

exts

ICT

tool

s

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Num

ber b

ases

iden

tify

Num

ber b

ases

in

ever

yday

life

pla

ce

fin

d pl

ace

valu

es fo

r co

mm

on b

ases

N

umbe

r bas

es in

ev

eryd

ay li

fe p

lace

Plac

e va

lues

Id

entif

y nu

mbe

r bas

es in

ev

eryd

ay li

fe p

lace

findi

ng p

lavc

e va

lues

for

com

mon

bas

es

R

elev

ant t

exts

ICT

tool

s

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Scal

es a

nd s

impl

e m

ap

prob

lem

s

iden

tify

type

s of

sca

les

fin

d sc

ales

from

giv

en

info

rmat

ion

m

easu

re le

ngth

s us

ing

a gi

ven

scal

e

R

epre

sent

ativ

e Fr

actio

n

Rat

io s

cale

Id

entif

ying

type

s of

sc

ales

Mea

surin

g le

ngth

s us

ing

give

n sc

ales

R

elev

ant t

exts

ICT

tool

s

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


15

8.1.

2

Se

ts M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

2

3

8.1

. 2

Se

ts

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Sets

and

Set

not

atio

n

de

fine

a se

t by

listin

g th

e el

emen

ts

d

escr

ibe

give

n se

ts u

sing

se

t not

atio

n

Se

ts a

nd s

et n

otat

ion

Li

stin

g el

emen

ts o

f va

rious

set

s

Dis

cuss

ing

exam

ples

of

sets

in li

fe

Ex

plai

ning

the

mea

ning

s of

set

not

atio

n an

d th

eir

uses

Usi

ng s

et n

otat

ion

to

desc

ribe

sets

R

elev

ant t

exts

ICT

tool

s

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Type

s of

Set

s

desc

ribe

the

type

s of

set

s

illust

rate

the

type

s of

set

s by

mea

ns o

f dia

gram

s

form

sub

sets

from

un

iver

sal s

ets

di

scus

s un

ion

and

inte

rsec

tion

of s

ets

U

nive

rsal

set

Fini

te s

et

In

finite

set

Nul

l or e

mpt

y se

t

Equa

l set

s

Subs

et

U

nion

of a

set

Inte

rsec

tion

of a

set

D

iscu

ssin

g th

e ty

pes

of

sets

Dis

tingu

ishi

ng th

e ty

pes

of s

ets

Fo

rmin

g su

bset

s fro

m

univ

ersa

l set

Dis

cuss

ing

unio

n an

d in

ters

ectio

n of

set

s

R

elev

ant t

exts

ICT

tool

s

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


16

8.1.

3

Fina

ncia

l Mat

hem

atic

s M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

2

4

8.1.

3

Fina

ncia

l Mat

hem

atic

s

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Con

sum

er a

rithm

etic

in

terp

ret b

ills

ex

tract

dat

a fro

m

hous

ehol

d bi

lls fo

r ca

lcul

atio

ns

ca

lcul

ate

prof

it an

d lo

ss

ca

lcul

ate

disc

ount

prep

are

hous

ehol

d bu

dget

s

H

ouse

hold

bills

Prof

it an

d lo

ss

D

isco

unt

H

ouse

hold

bud

gets

In

terp

retin

g ho

useh

old

bills

Solv

ing

prob

lem

s in

volv

ing

hous

ehol

d bi

lls

C

alcu

latin

g pr

ofit

and

loss

Cal

cula

ting

disc

ount

Prep

arin

g an

d di

scus

sing

ho

useh

old

budg

ets

R

elev

ant t

exts

ICT

En

viro

nmen

t

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


17

8.1.

4

Mea

sure

s an

d m

ensu

ratio

n M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

2

5

8

.1. 4

M

easu

res

and

men

sura

tion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Mea

sure

s

us

e th

e un

its o

f m

easu

rem

ent i

n lif

e

mak

e ca

lcul

atio

ns u

sing

th

e un

its o

f mea

sum

ent

co

nver

t uni

ts o

f m

easu

rem

ent f

rom

one

fo

rm to

ano

ther

solv

e pr

oble

ms

usin

g th

e un

its o

f m

easu

rem

ent

un

its o

f: -

Tim

e -

Mas

s -

Leng

th

- Te

mpe

ratu

re

- C

apac

ity

U

sing

the

units

of

mea

sure

men

t in

life

M

akin

g ca

lcul

atio

ns u

sing

th

e un

its o

f mea

sum

ent

C

onve

rting

uni

ts o

f m

easu

rem

ent f

rom

one

fo

rm to

ano

ther

Solv

ing

prob

lem

s us

ing

the

units

of m

esur

emen

t

R

elev

ant t

exts

ICT

tool

s

En

viro

nmen

t

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Men

sura

tion

find

perim

eter

of p

lane

sh

apes

calc

ulat

e ar

ea o

f pla

ne

shap

es

so

lve

prob

lem

s in

volv

ing

plan

e sh

apes

pe

rimet

er o

f pla

ne

shap

es

A

rea

of p

lane

shap

es

Fi

ndin

g th

e pe

rimet

er o

f pl

ane

shap

es

C

alcu

latin

g ar

ea o

f pla

ne

shap

es

U

sing

the

area

and

pe

rimet

er o

f pla

ne s

hape

s to

sol

ve p

robl

ems

in li

fe

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


18

8.1.

5

Gra

phs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

26

8.1.

5

Gra

phs

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Func

tiona

l gra

phs

dr

aw th

e C

arte

sian

pla

ne

usin

g a

give

n sc

ale

id

entif

y po

ints

on

the

Car

tesi

an p

lane

stat

e po

ints

in c

o-or

dina

te

form

plot

poi

nts

on th

e C

arte

sian

pla

ne

C

arte

sian

pla

ne

Sc

ale

C

o-or

dina

tes

D

raw

ing

Car

tesi

an p

lane

us

ing

give

n sc

ale

Id

entif

ying

poi

nts

on th

e C

arte

sian

pla

ne a

nd

stat

ing

them

in c

o-or

dina

te fo

rm

Pl

ottin

g po

ints

on

the

Car

tesi

an p

lane

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Geo

-boa

rd

M

athe

mat

ical

inst

rum

ents

Trav

el g

raph

s

inte

rpre

t dis

tanc

e tim

e gr

aphs

D

ista

nce

time

grap

hs

D

iscu

ssin

g di

stan

ce ti

me

grap

hs

So

lvin

g pr

oble

ms

invo

lvin

g di

stan

ce ti

me

grap

hs

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Geo

-boa

rd

M

athe

mat

ical

inst

rum

ents


19

8.1.

6 A

lgeb

ra M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

2

7

8

.1.6

Alg

ebra

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Alge

brai

c M

anip

ulat

ion

si

mpl

ify a

lgeb

raic

ex

pres

sion

s us

ing

the

rule

s of

bas

ic o

pera

tions

subs

titut

e va

lues

in

alge

brai

c te

rms

fin

d H

.C.F

of l

inea

r al

gebr

aic

expr

essi

ons

so

lve

prob

lem

s in

volv

ing

alge

brai

c ex

pres

sion

s

Ba

sic

alge

brai

c pr

oces

ses

Su

bstit

utio

n of

val

ues

Al

gebr

aic

expr

essi

ons

si

mpl

ifyin

g a

lgeb

raic

ex

pres

sion

s us

ing

the

rule

s of

bas

ic o

pera

tions

subs

titut

ing

valu

es in

al

gebr

aic

expr

essi

ons

fin

d H

.C.F

of l

inea

r al

gebr

aic

expr

essi

ons

so

lvin

g pr

oble

ms

invo

lvin

g al

gebr

aic

expr

essi

ons

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Equa

tions

solv

e lin

ear e

quat

ions

w

here

the

unkn

own

appe

ars

on o

ne s

ide

so

lve

line

ar e

quat

ions

w

here

the

unkn

own

appe

ars

on b

oth

side

s of

th

e eq

uatio

n

form

ulat

e lin

ear e

quat

ions

fro

m g

iven

info

rmat

ion

Li

near

equ

atio

ns

So

lvin

g li

near

equ

atio

ns

whe

re th

e un

know

n ap

pear

s on

one

sid

e in

clud

ing

wor

d pr

oble

ms

So

lvin

g li

near

equ

atio

ns

whe

re th

e un

know

n ap

pear

on

both

sid

es

incl

udin

g w

ord

prob

lem

s

Form

ulat

ing

linea

r eq

uatio

ns fr

om g

iven

in

form

atio

n

R

elev

ant t

exts

ICT

tool

s

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Ineq

ualit

ies

expl

ain

the

mea

ning

of

ineq

ualit

y si

gns

re

pres

ent l

inea

r in

equa

litie

s on

a n

umbe

r lin

e

form

ulat

e lin

ear

ineq

ualit

ies

so

lve

linea

r ine

qual

ities

In

equa

lity

sign

s

Line

ar in

equa

litie

s

Num

ber l

ine

D

iscu

ssin

g th

e m

eani

ng

and

use

of in

equa

lity

sign

s

Rep

rese

ntin

g lin

ear

ineq

ualit

ies

on a

num

ber

line

Fo

rmul

atin

g lin

ear

ineq

ualit

ies

So

lvin

g lin

ear i

nequ

aliti

es

R

elev

ant t

exts

ICT

tool

s

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


20

8.1.

6 A

lgeb

ra C

ontd

.. M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

2

8 SU

B T

OPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Indi

ces

and

loga

rithm

s

ex

pres

s nu

mbe

rs fr

om

ordi

nary

to

inde

x fo

rm a

nd

vice

ver

sa

In

dex

form

Ex

pres

sing

num

bers

from

or

dina

ry to

inde

x fo

rm

and

vice

ver

sa

R

elev

ant t

exts

ICT

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


21

8.1

.7 G

eom

etry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

29

8.7

. Geo

met

ry

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Poin

ts, l

ines

and

ang

les

D

efin

e a

poin

t

Iden

tify

type

s of

line

s

iden

tify

type

s of

ang

les

m

easu

re a

ngle

s

calc

ulat

e an

gles

on

a st

raig

ht li

ne a

nd a

roun

d a

poin

t

solv

e pr

oble

ms

invo

lvin

g an

gles

on

a st

raig

ht li

ne

and

arou

nd a

poi

nt

Po

ints

Line

s

Angl

es

D

iscu

ssin

g a

poin

t

Dis

cuss

ing

type

s of

lin

es a

nd a

ngle

s

Mea

surin

g an

gles

Cal

cula

ting

angl

es o

n a

stra

ight

line

and

aro

und

a po

int

So

lvin

g pr

oble

ms

invo

lvin

g an

gles

on

a st

raig

ht li

ne a

nd a

roun

d a

poin

t

G

eom

etric

al In

stru

men

ts

R

elev

ant t

exts

ICT

tool

s

En

viro

nmen

t

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Poly

gons

and

circ

les

de

fine

a po

lygo

n

stat

e th

e na

mes

of n

-si

ded

poly

gons

(up

to

n=10

)

nam

e pa

rts, l

ines

and

re

gion

s in

a c

ircle

Po

lygo

ns

C

ircle

s

Dis

cuss

ing

poly

gons

w

ith u

p to

ten

side

s

Dra

win

g an

d na

min

g pa

rts o

f a c

ircle

R

elev

ant t

exts

ICT

tool

s

En

viro

nmen

t

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Con

stru

ctio

n an

d lo

ci

co

nstru

ct li

nes

and

angl

es

C

onst

ruct

ion

of li

nes

and

angl

es

C

onst

ruct

ing

lines

and

an

gles

G

eom

etric

al in

stru

men

ts

IC

T to

ols

R

elev

ant t

exts

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


22

8.1.

8

Stat

istic

s

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

30

8

.1. 8

St

atis

tics

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Dat

a co

llect

ion

and

clas

sific

atio

n an

d re

pres

enta

tion

co

llect

sta

tistic

al d

ata

cl

assi

fy s

tatis

tical

dat

a

desc

ribe

the

use

of c

ase

stud

ies/

que

stio

nnai

re to

co

llect

dat

a

D

ata

colle

ctio

n

Dat

a cl

assi

ficat

ion

C

olle

ctin

g st

atis

tical

da

ta

C

lass

ifyin

g st

atis

tical

da

ta

D

iscu

ssin

g th

e us

e of

ca

se s

tudi

es/

ques

tionn

aire

to c

olle

ct

data

R

elev

ant t

exts

Envi

ronm

ent

IC

T to

ols

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

8.1.

9

Tra

nsfo

rmat

ion

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

31

8.1

. 9

Tra

nsfo

rmat

ion

SUB

TO

PIC

Le

arni

ng O

BJE

CTI

VES

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Tran

slat

ion

defin

e tra

nsfo

rmat

ion

de

fine

trans

latio

n

trans

late

pla

ne fi

gure

s

Tr

ansl

atio

n of

pla

ne

figur

es

D

efin

ing

trans

form

atio

n an

d tra

nsla

tion

Tr

ansl

atin

g pl

ane

figur

es

R

elev

ant t

exts

Geo

-boa

rd

IC

T to

ols

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


23

8.2

FO

RM

(2)

8.2

1

R

eal N

umbe

rs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

32

8.2

FOR

M (2

)

8

.2 1

R

eal N

umbe

rs

SUB

TO

PIC

O

BJE

CTI

VES

lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Num

ber c

once

pts

and

oper

atio

ns

fin

d H

.C.F

. and

L.C

.M.

ca

lcul

ate

squa

res

and

squa

re ro

ots

ca

lcul

ate

cube

s an

d cu

be ro

ots

Fa

ctor

s an

d m

ultip

les

Sq

uare

s an

d sq

uare

root

s

Cub

es a

nd c

ube

root

s

Fi

ndin

g H

.C.F

and

L.C

.M.

C

ompu

ting

squa

res

and

squa

re ro

ots

C

alcu

latin

g cu

bes

and

cube

root

s

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Appr

oxim

atio

n an

d es

timat

ion

ro

und

off n

umbe

rs t

o gi

ven

sign

ifica

nt fi

gure

s

solv

e pr

oble

ms

invo

lvin

g ap

prox

imat

ion

and

estim

atio

n

Si

gnifi

cant

figu

res

Es

timat

ions

Rou

ndin

g of

f num

bers

to

requ

ired

sign

ifica

nt

figur

es

U

sing

app

roxi

mat

ion

and

estim

atio

n to

sol

ve

prob

lem

s

R

elev

ant T

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Rat

ios

rate

s an

d pr

opor

tions

sim

plify

ratio

s

sol

ve p

robl

ems

usin

g th

e co

ncep

t of r

atio

dist

ingu

ish

betw

een

dire

ct a

nd in

vers

e pr

opot

ion

s

olve

pro

blem

s th

at

invo

lve

dire

ct a

nd

inve

rse

prop

ortio

n

R

atio

s

Prop

ortio

ns

D

iscu

ssin

g th

e us

e of

ra

tios

in li

fe s

ituat

ions

Dis

cuss

ing

exam

ples

of

dire

ct a

nd in

vers

e pr

opor

tion

D

istin

guis

hing

bet

wee

n di

rect

and

inve

rse

prop

otio

n

Solv

ing

prob

lem

s th

at

invo

lve

ratio

s an

d pr

opor

tion

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


24

8.2

1

R

eal N

umbe

rs C

ontd

.. M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

3

3

Ord

inar

y an

d st

anda

rd fo

rm

ex

pres

s nu

mbe

rs in

or

dina

ry fo

rm to

st

anda

rd fo

rm a

nd v

ise

vers

a

N

umbe

rs in

sta

ndar

d fo

rm

D

iscu

ss im

porta

nce

of

stan

dard

form

in li

fe

Ex

pres

sing

num

bers

in

stan

dard

form

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Num

ber b

ases

conv

ert a

num

ber i

n an

y ba

se to

bas

e te

n

co

nver

t a n

umbe

r in

base

ten

to a

ny b

ase

so

lve

prob

lem

s in

life

us

ing

num

ber b

ases

co

nver

ting

num

bers

from

on

e ba

se to

ano

ther

C

onve

rting

num

ber

base

s

Iden

tifyi

ng n

umbe

rs in

th

eir r

espe

ctiv

e ba

ses

So

lve

prob

lem

s in

life

us

ing

num

ber b

ases

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Scal

es a

nd s

impl

e m

ap

prob

lem

s

disc

uss

type

s of

sca

les

fin

d sc

ales

from

giv

en

info

rmat

ion

m

ake

mea

sure

men

ts

usin

g a

give

n sc

ale

dr

aw li

nes

or d

iagr

ams

to a

giv

en s

cale

calc

ulat

e di

stan

ces

usin

g a

give

n sc

ale

Sc

ale

draw

ings

Id

entif

ying

type

s of

sc

ales

Mea

surin

g le

ngth

s us

ing

give

n sc

ales

Mak

ing

scal

e dr

awin

gs

usin

g ap

prop

riate

/giv

en

scal

e

Cal

cula

ting

dist

ance

s

Solv

e pr

oble

ms

in

fam

iliar a

nd le

ss fa

milia

r co

ntex

t usi

ng th

e co

ncep

t of

sca

les

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


25

8.2.

2

Sets

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

34

8.2.

.2

Set

s

SUB

TO

PIC

Le

arni

ng O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Sets

find

unio

n an

d in

ters

ectio

n of

set

s

repr

esen

t set

s on

Ven

n di

agra

ms

co

nver

t wor

d pr

oble

ms

into

set

not

atio

n

solv

e lif

e pr

oble

ms

usin

g a

Venn

dia

gram

with

no

mor

e th

an 2

sub

sets

Ty

pes

of s

ets

Ve

nn d

iagr

am w

ith tw

o su

bset

s

Set n

otat

ion

Fi

ndin

g un

ion

and

inte

rsec

tion

of s

ets

D

iscu

ssin

g w

ord

prob

lem

s in

rela

tion

to s

et

nota

tion

R

epre

sent

ing

give

n in

form

atio

n on

Ven

n di

agra

m

So

lve

prob

lem

s us

ing

Venn

dia

gram

s

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


26

8.2.

3

Fin

anci

al M

athe

mat

ics

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

35

8

.2.3

Fina

ncia

l Mat

hem

atic

s

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Con

sum

er a

rithm

etic

inte

rpre

t bills

mak

e ca

lcul

atio

ns b

ased

on

dat

a fro

m c

orpo

rate

bi

lls

ca

lcul

ate

prof

it an

d lo

ss

fin

d si

mpl

e in

tere

st

pr

epar

e an

ent

erpr

ise

budg

et fo

r a s

mal

l bu

sine

ss

so

lve

prob

lem

s in

volv

ing

hire

pur

chas

e

C

orpo

rate

bills

Prof

it an

d lo

ss

Si

mpl

e in

tere

st

H

ire p

urch

ase

Sm

all s

cale

ent

erpr

ise

budg

ets

D

iscu

ssin

g co

rpor

ate

bills

Mak

ing

calc

ulat

ions

bas

ed

on d

ata

extra

cted

from

co

rpor

ate

bills

Cal

cula

ting

prof

it an

d lo

ss

Fi

ndin

g si

mpl

e in

tere

st

Pr

epar

ing

an e

nter

pris

e bu

dget

for a

sm

all

busi

ness

Solv

ing

prob

lem

s in

volv

ing

hire

pur

chas

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


27

8.2.

4 M

easu

res

and

Men

sura

tion

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

36

8.2

..4

Mea

sure

s an

d M

ensu

ratio

n

SUB

TO

PIC

Le

arni

ng O

BJE

CTI

VES

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Mea

sure

s

use

the

units

of

mea

sure

men

ts in

life

so

lve

prob

lem

s us

ing

the

diffe

rent

uni

ts o

f

mea

sure

men

ts

U

nits

of:

- Ar

ea

- Vo

lum

e -

Cap

acity

-

Den

sity

D

iscu

ssin

g th

e im

porta

nce

of u

nits

of

mea

sure

men

ts in

life

Solv

ing

prob

lem

s us

ing

the

diffe

rent

uni

ts o

f m

easu

rem

ents

R

elev

ant t

exts

Envi

ronm

ent

IC

T to

ols

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Men

sura

tion

calc

ulat

e pe

rimet

er o

f pl

ane

shap

es

ca

lcul

ate

area

of p

lane

sh

apes

calc

ulat

e vo

lum

es o

f cu

boid

s

solv

e pr

oble

ms

invo

lvin

g ar

ea a

nd v

olum

es

so

lve

sim

ple

dens

ity

prob

lem

s

Pe

rimet

er o

f pla

ne s

hape

s

Area

of p

lane

sha

pes

Vo

lum

e of

cub

oids

Den

sity

of c

uboi

ds

C

alcu

latin

g pe

rimet

er

and

area

of p

lane

sha

pes

C

alcu

latin

g vo

lum

e of

cu

boid

s

Solv

ing

pro

blem

s in

volv

ing

area

and

vo

lum

e in

life

Solv

ing

sim

ple

dens

ity

prob

lem

s

R

elev

ant t

exts

Envi

ronm

ent

IC

T to

ols

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


28

8.2.

5

Gra

phs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

37

8

.2. 5

G

raph

s

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Func

tiona

l gra

phs

dr

aw th

e C

arte

sian

pl

ane,

usi

ng a

giv

en

scal

e

plot

poi

nts

on th

e C

arte

sian

pla

ne

co

nstru

ct a

tabl

e of

va

lues

for a

giv

en li

near

fu

nctio

n

dr

aw s

traig

ht li

ne g

raph

s

C

arte

sian

pla

ne

Ta

ble

of v

alue

s

Line

ar g

raph

s

Scal

e

D

raw

ing

the

Car

tesi

an

plan

e, u

sing

a g

iven

sc

ale

Pl

ottin

g po

ints

on

the

Car

tesi

an p

lane

Con

stru

ctin

g ta

ble

of

valu

es

D

raw

ing

stra

ight

line

gr

aphs

on

the

Car

tesi

an

plan

e

R

elev

ant t

exts

Geo

-boa

rd

M

athe

mat

ical

inst

rum

ents

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

IC

T to

ols

Trav

el g

raph

s

inte

rpre

t dis

tanc

e - t

ime

grap

hs

dr

aw d

ista

nce

- tim

e gr

aphs

use

dist

ance

-tim

e gr

aphs

to

sol

ve p

robl

ems

D

ista

nce

time

grap

hs

In

terp

retin

g di

stan

ce ti

me

grap

hs

D

raw

ing

dist

ance

tim

e gr

aphs

Usi

ng d

ista

nce-

time

grap

hs to

sol

ve p

robl

ems

R

elev

ant t

exts

Geo

-boa

rd

M

athe

mat

ical

inst

rum

ents

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

IC

T To

ols


29

8.2.

6 V

aria

tion

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

38

8

.2.6

Va

riatio

n

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Varia

tion

ex

pres

s di

rect

var

iatio

n in

alg

ebra

ic te

rms

so

lve

prob

lem

s in

volv

ing

dire

ct v

aria

tion

D

irect

var

iatio

n

D

iscu

ssin

g th

e co

ncep

t of

dire

ct v

aria

tion

Ex

pres

sing

dire

ct v

aria

tion

in a

lgeb

raic

term

s

Dis

cuss

ing

rela

tions

hips

be

twee

n va

riabl

es

So

lvin

g pr

oble

ms

invo

lvin

g di

rect

var

iatio

n

R

elev

ant t

exts

Envi

ronm

ent

IC

T to

ols

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


30

8.2.

7

Alg

ebra

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

39

8.2.

7

Alg

ebra

SUB

TO

PIC

O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Alge

brai

c M

anip

ulat

ion

s

ubst

itute

val

ues

in

alge

brai

c te

rms

fa

ctor

ise

linea

r alg

ebra

ic

expr

essi

ons

fa

ctor

ise

quad

ratic

al

gebr

aic

expr

essi

ons

si

mpl

ify a

lgeb

raic

fra

ctio

ns

ex

pand

alg

ebra

ic

expr

essi

ons

with

bra

cket

solv

e pr

oble

ms

invo

lvin

g al

gebr

aic

man

ipul

atio

ns

Su

bstit

utio

n of

val

ues

Al

gebr

aic

expr

essi

ons

Al

gebr

aic

fract

ions

Qua

drat

ic e

xpre

ssio

ns

Fa

ctor

isat

ion

Su

bstit

utin

g va

lus

in

alge

brai

c te

rms

Fa

ctor

isin

g lin

ear a

nd

quad

ratic

alg

ebra

ic

expr

essi

ons

S

impl

ifyin

g al

gebr

aic

fract

ions

Expa

ndin

g al

gebr

aic

expr

essi

ons

with

bra

cket

s

Solv

ing

prob

lem

s in

volv

ing

alge

brai

c m

anip

ulat

ions

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Equa

tions

sim

plify

equ

atio

ns w

ith

brac

kets

carr

y ou

t cal

cula

tions

in

volv

ing

chan

ge o

f su

bjec

t of f

orm

ulae

solv

e eq

uatio

ns w

ith

alge

brai

c fra

ctio

ns

so

lve

sim

ulta

neou

s lin

ear

equa

tions

solv

e q

uadr

atic

equ

atio

n w

here

the

coef

ficie

nt o

f x2 i

s on

e

Eq

uatio

ns w

ith b

rack

ets

Eq

uatio

ns w

ith fr

actio

ns

C

hang

e of

sub

ject

of

form

ulae

Sim

ulta

neou

s lin

ear

equa

tions

Qua

drat

ic e

quat

ions

Ex

pand

ing

and

solv

ing

equa

tions

with

bra

cket

s

Car

ryin

g ou

t cal

cula

tions

in

volv

ing

chan

ge o

f su

bjec

ts o

f for

mul

ae

So

lvin

g eq

uatio

ns

invo

lvin

g al

gebr

aic

fract

ions

Solv

ing

sim

ulta

neou

s lin

ear e

quat

ions

Solv

ing

quad

ratic

eq

uatio

ns w

here

the

coef

ficie

nt o

f 𝑥𝑥2

is o

ne

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


31

8.2.

7

Alg

ebra

Con

td..

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

40

Ineq

ualit

ies

repr

esen

t lin

ear

ineq

ualit

ies

on a

num

ber

line

fo

rmul

ate

linea

r in

equa

litie

s

repr

esen

t ine

qual

ities

on

a C

arte

sian

pla

ne

so

lve

line

ar in

equa

litie

s

lin

ear i

nequ

aliti

es

N

umbe

r lin

e

Car

tesi

an p

lane

R

epre

sent

ing

linea

r in

equa

litie

s on

a n

umbe

r lin

e

Form

ulat

ing

linea

r in

equa

litie

s

Iden

tifyi

ng in

equa

litie

s re

pres

ente

d on

a

Car

tesi

an p

lane

Solv

ing

linea

r ine

qual

ities

R

elev

ant t

exts

ICT

tool

s

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Indi

ces

and

loga

rithm

s

Car

ry o

ut c

alcu

latio

ns

invo

lvin

g la

ws

of in

dice

s (x

a x x

b ; x

a ÷ x

b ; x

o and

x –a

)

solv

e pr

oble

ms

invo

lvin

g

indi

ces

usin

g th

e la

ws

of

indi

ces

La

ws

of in

dice

s

Fi

ndin

g sq

uare

s an

d sq

uare

root

s of

giv

en

num

bers

in in

dex

form

Appl

ying

the

law

s of

in

dice

s to

alg

ebra

ic

expr

essi

ons

Solv

ing

prob

lem

s in

volv

ing

in

dice

s us

ing

the

law

s of

in

dice

s

R

elev

ant t

exts

ICT

tool

s

Brai

lle m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


32

8.2.

8

Geo

met

ry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

41

8.2

.8

G

eom

etry

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Poin

ts,li

nes

and

angl

es

id

entif

y th

e ty

pes

of a

ngle

s

form

ed o

n pa

ralle

l and

trans

vers

al li

nes

ca

lcul

ate

unkn

own

angl

es

on p

aral

lel a

nd tr

ansv

ersa

l

line

usin

g ge

omet

rical

fact

s

An

gles

Par

alle

l and

Tra

nsve

rsal

lin

es

D

iscu

ssin

g an

gles

fo

rmed

on

para

llel a

nd

trans

vers

al li

nes

C

alcu

late

ang

les

on

para

llel a

nd tr

anve

rsal

lin

es

R

elev

ant t

exts

ICT

tool

s

Geo

-boa

rd

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Bea

ring

iden

tify

card

inal

poi

nts

gi

ve d

irect

ions

usi

ng

card

inal

poi

nts

fin

d co

mpa

ss b

earin

g of

po

ints

calc

ulat

e th

ree-

figur

e be

arin

g of

poi

nts

so

lve

prob

lem

s in

life

in

volv

ing

bear

ing

C

ardi

nal p

oint

s

Thre

e-fig

ure

bear

ings

Com

pass

bea

ring

D

iscu

ssin

g c

ardi

nal

poin

ts

D

iscu

ssin

g im

porta

nce

of

com

pass

in li

fe

Fi

ndin

g co

mpa

ss

bear

ings

Cal

cula

ting

thre

e-fig

ure

bear

ings

Solv

ing

prob

lem

s in

life

in

volv

ing

bear

ing

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


33

8.2.

8

Geo

met

ry C

ontd

.. M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

4

2 Po

lygo

ns a

nd C

ircle

s

st

ate

the

nam

es o

f n-s

ided

po

lygo

ns (u

p to

n=1

0)

de

scrib

e th

e pr

oper

ties

of

trian

gles

and

qu

adril

ater

als

Pr

oper

ties

of p

olyg

ons

(tria

ngle

s an

d qu

adril

ater

al)

N

amin

g po

lygo

ns w

ith u

p to

ten

side

s

Stat

ing

prop

ertie

s of

tri

angl

es a

nd

quad

rilat

eral

s

R

elev

ant t

exts

Envi

ronm

ent

IC

T to

ols

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Sim

ilarit

y an

d co

ngru

ency

iden

tify

sim

ilar a

nd

cong

ruen

t fig

ures

stat

e ca

ses

of c

ongr

uenc

y

solv

e pr

oble

ms

invo

lvin

g si

mila

r and

con

grue

nt

figur

es

Si

mila

r and

con

grue

nt

figur

es

C

ases

of c

ongr

uenc

y

Id

entif

ying

sim

ilar a

nd

cong

ruen

t fig

ures

Dis

cuss

ing

case

s of

co

ngru

ency

Solv

ing

prob

lem

s in

volv

ing

sim

ilar a

nd

cong

ruen

t fig

ures

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Con

stru

ctio

n an

d lo

ci

co

nstru

ct li

nes

and

angl

es

bi

sect

line

s an

d an

gles

Con

stru

ctio

n of

line

s an

d an

gles

Bise

ctin

g lin

es a

nd

angl

es

C

onst

ruct

ing

lines

and

an

gles

Bise

ctin

g lin

es a

nd

angl

es

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

s in

volv

ing

cons

truct

ion

and

expl

orin

g th

eir

appl

icat

ion

in li

fe

G

eom

etric

al in

stru

men

ts

IC

T to

ol

R

elev

ant t

exts

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Sym

met

ry

id

entif

y lin

es o

f sym

met

ry

of re

gula

r pol

ygon

s

dr

aw li

nes

of s

ymm

etry

on

plan

e sh

apes

lin

e sy

mm

etry

in tw

o di

men

sion

s

St

atin

g nu

mbe

r of l

ines

of

sym

met

ry

D

raw

ing

shap

es a

nd

show

ing

lines

of

sym

met

ry

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


34

8.2.

9

Sta

tistic

s M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

4

4 8.

2. 9

S

tatis

tics

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Dat

a co

llect

ion,

cl

assi

ficat

ion

and

repr

esen

tatio

n

co

llect

dat

a

gr

oup

stat

istic

al d

ata

re

pres

ent d

ata

usin

g fre

quen

cy ta

ble,

bar

ch

art a

nd p

ie c

hart

D

ata

colle

ctio

n

Cla

ssifi

catio

n of

un

grou

ped

data

Rep

rese

ntin

g da

ta u

sing

fre

quen

cy ta

ble,

bar

cha

rt an

d pi

e ch

art

D

iscu

ssin

g c

olle

cted

da

ta

G

roup

ing

stat

istic

al d

ata

R

epre

sent

ing

data

usi

ng

frequ

ency

tabl

e, b

ar

char

t and

pie

cha

rt

Con

duct

ing

educ

atio

nal

tour

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Mea

sure

s of

cen

tral

te

nden

cy

de

fine

mea

sure

s of

ce

ntra

l ten

denc

y

stat

e th

e m

ode

in a

gi

ven

dist

ribut

ion

ca

lcul

ate

the

mea

n an

d m

edia

n

ca

lcul

ate

mea

n us

ing

assu

med

mea

ns

M

ean

M

ode

M

edia

n

Assu

med

mea

n

D

iscu

ssin

g th

e m

eani

ngs

of th

e m

easu

res

of c

entra

l te

nden

cy

D

eter

min

ing

the

mod

e in

a

give

n di

strib

utio

n

Cal

cula

ting

the

mea

n an

d m

edia

n

C

alcu

latin

g m

ean

usin

g as

sum

ed m

ean

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

s in

volv

ing

the

mea

sure

s of

cen

tral t

ende

ncy

and

expl

orin

g th

eir

appl

icat

ions

in li

fe

R

elev

ant t

exts

ICT

tool

s

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


35

8.2.

10

Vec

tors

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

45

8.2.

10

Vec

tors

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Def

initi

on a

nd n

otat

ion

de

fine

vect

or

in

terp

ret v

ecto

r not

atio

n

D

efin

ition

of v

ecto

rs

Ve

ctor

not

atio

n

D

iscu

ssin

g ve

ctor

s

Expr

essi

ng v

ecto

rs in

co

lum

n fo

rm

R

epre

sent

ing

vect

ors

usin

g ve

ctor

not

atio

n

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Type

s of

vec

tors

iden

tify

vario

us ty

pes

of

vect

ors

re

pres

ent t

rans

latio

n ve

ctor

in c

olum

n fo

rm

dr

aw tr

ansl

atio

n ve

ctor

on

a C

arte

sian

pla

ne

so

lve

prob

lem

s us

ing

the

conc

ept o

f vec

tors

Tr

ansl

atio

n ve

ctor

s

N

egat

ive

vect

ors

Eq

ual v

ecto

rs

Pa

ralle

l vec

tors

D

iscu

ssin

g th

e va

rious

ty

pes

of v

ecto

rs

R

epre

sent

ing

a tra

nsla

tion

by c

olum

n ve

ctor

s

Dra

win

g tra

nsla

tion

vect

or o

n a

Car

tesi

an

plan

e

Iden

tifyi

ng v

ario

us ty

pes

of v

ecto

rs fr

om th

e C

arte

sian

pla

ne

So

lvin

g pr

oble

ms

usin

g th

e co

ncep

t of v

ecto

rs

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Ope

ratio

ns

ad

d ve

ctor

s

subt

ract

vec

tors

solv

e pr

oble

ms

invo

lvin

g ad

ditio

n an

d su

btra

ctio

n of

vec

tors

Ad

ditio

n of

vec

tors

Subt

ract

ion

of v

ecto

rs

Ad

ding

and

sub

tract

ing

vect

ors

So

lvin

g pr

oble

ms

invo

lvin

g ad

ditio

n an

d su

btra

ctio

n of

vec

tors

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


36

8.2.

11

Mat

rices

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

47

8

.2.1

1

Mat

rices

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Ord

er

st

ate

the

orde

r of a

giv

en

mat

rix

id

entif

y th

e di

ffere

nt ty

pes

of m

atric

es

di

scus

s th

e us

es o

f m

atric

es

O

rder

of m

atric

es

Ty

pes

of m

atric

es

C

ompu

ting

info

rmat

ion

in

mat

rix fo

rm

Li

stin

g ty

pes

of m

atric

es

D

iscu

ssin

g th

e or

der o

f m

atric

es

Lo

cate

ele

men

ts in

a

give

n m

atrix

Dis

cuss

ing

the

impo

rtanc

e of

mat

rices

in

life

Mod

ellin

g lif

e si

tuat

ion

invo

lvin

g m

atric

es to

so

lve

prob

lem

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


37

8.2.

12

Tra

nsfo

rmat

ion

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

48

8

.2.1

2

Tran

sfor

mat

ion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

RES

OU

RC

ES

Tran

slat

ion

defin

e tra

nsfo

rmat

ion

de

scrib

e tra

nsla

tion

tra

nsla

te p

lane

figu

res

and

poin

ts

Tr

ansl

atio

n ve

ctor

to m

ove

a po

int a

nd p

alne

figu

res

D

iscu

ss e

xam

ples

of

trans

form

atio

n

Dis

cuss

ing

the

use

of

trans

latio

n ve

ctor

in

trans

latin

g fig

ures

Tran

slat

ing

plan

e fig

ures

an

d po

ints

def

inin

g a

refle

ctio

n

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Ref

lect

ion

defin

e re

flect

ion

re

flect

a p

oint

or a

pla

ne

figur

e in

a g

iven

mirr

or

line

R

efle

ctio

n of

pla

ne fi

gure

s

Ref

lect

ing

a po

int o

r ob

ject

in a

giv

en m

irror

lin

e

Rep

rese

ntin

g lif

e ph

enom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g re

flect

ion

trans

form

atio

n an

d ex

plor

ing

thei

r ap

plic

atio

ns in

life

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


38

8.2.

13 P

roba

bilit

y

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

49

8.2

.13

Prob

abili

ty

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(atti

tude

s, s

kills

an

d kn

owle

dge)

SU

GG

ESTE

D N

OTE

S AN

D

ACTI

VITI

ES

SUG

GES

TED

R

ESO

UR

CES

Def

initi

on o

f pro

babi

lity

de

fine

prob

abilit

y an

d pr

obab

ility

term

s

ca

lcul

ate

prob

abilit

y of

si

ngle

eve

nts

de

scrib

e ex

perim

enta

l pr

obab

ility

so

lve

prob

lem

s in

volv

ing

prob

abilit

y in

life

D

efin

ition

of p

roba

bilit

y te

rms

Ex

perim

enta

l pro

babi

lity

St

atin

g ex

ampl

es o

f eac

h pr

obab

ility

term

Cal

cula

ting

prob

abilit

y of

si

ngle

eve

nts

Car

ryin

g ou

t pro

babi

lity

expe

rimen

ts

So

lvin

g pr

oble

ms

invo

lvin

g th

e co

ncep

t of p

roba

bilit

y in

lif

e

Rep

rese

ntin

g lif

e ph

enom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g th

e co

ncep

t of

prob

abilit

y an

d ex

plor

ing

thei

r app

licat

ions

in li

fe

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


39

8.3

FOR

M T

HR

EE (3

)

8.3.

1 R

eal N

umbe

rs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

50

8.3

FOR

M T

HR

EE (3

)

8.

3.1

Rea

l Num

bers

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Num

ber c

once

pts

and

oper

atio

ns

pe

rform

arit

hmet

ic

oper

atio

ns u

sing

ord

er o

f op

erat

ions

iden

tify

ratio

nal a

nd

irrat

iona

l num

bers

dist

ingu

ish

betw

een

ratio

nal a

nd ir

ratio

nal

num

bers

perfo

rm o

pera

tions

iden

tify

num

ber p

atte

rns

in a

seq

uenc

e

solv

e pr

oble

ms

invo

lvin

g irr

atio

nal n

umbe

rs

O

rder

of o

pera

tions

Irrat

iona

l num

bers

Num

ber p

atte

rns

Ap

plyi

ng th

e ru

les

of

prec

eden

ce in

real

nu

mbe

rs

Pe

rform

ing

oper

atio

ns

D

iffer

entia

ting

betw

een

ratio

nal a

nd ir

ratio

nal

num

bers

Expl

orin

g an

d di

scov

erin

g nu

mbe

r pa

ttern

s

So

lvin

g pr

oble

ms

invo

lvin

g irr

atio

nal

num

bers

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Rat

ios,

rate

s an

d

prop

ortio

ns

si

mpl

ify ra

tios

perfo

rm c

alcu

latio

ns

invo

lvin

g ra

tio,ra

tes

and

prop

ortio

n

appl

y di

rect

and

inve

rse

prop

ortio

n to

sol

ve

prob

lem

s

R

atio

Rat

es

Pr

opor

tions

R

educ

ing

ratio

s to

si

mpl

est f

orm

and

sh

arin

g qu

antit

ies

usin

g ra

tio

C

alcu

latin

g a

nd s

olvi

ng

prob

lem

s in

volv

ing

ratio

,rate

and

pro

porti

on

So

lvin

g pr

oble

ms

invo

lvin

g di

rect

and

in

vers

e pr

opor

tion

focu

ssin

g on

life

si

tuat

ions

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


40

8.3.

1 R

eal N

umbe

rs C

ontd

.. M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

5

1

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

s in

volv

ing

the

conc

ept o

f ra

tios,

rate

s an

d pr

opor

tion

and

expl

orin

g th

eir a

pplic

atio

ns in

life

Ord

inar

y an

d st

anda

rd fo

rm

pe

rform

ope

ratio

ns in

st

anda

rd fo

rm

O

pera

tions

in s

tand

ard

form

Addi

ng a

nd s

ubtra

ctin

g nu

mbe

rs in

sta

ndar

d fo

rm

D

ivid

ing

and

mul

tiply

ing

num

bers

in

stan

dard

fo

rm

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Num

ber b

ases

perfo

rm o

pera

tions

in

volv

ing

num

ber b

ases

Ope

ratio

ns in

num

ber

base

s

Ad

ding

and

sub

tract

ing

in

num

ber b

ases

Solv

ing

equa

tions

in

volv

ing

num

ber b

ases

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Scal

es a

nd s

impl

e m

ap

prob

lem

s

us

e gi

ven

scal

es to

ca

lcul

ate

dist

ance

and

ar

ea

so

lve

prob

lem

invo

lvin

g di

stan

ce a

nd a

rea

usin

g sc

ale

Sc

ale

fact

or

Ar

ea fa

ctor

C

alcu

latin

g di

stan

ce a

nd

area

usi

ng g

iven

sca

les

Fi

ndin

g ar

ea fa

ctor

giv

en

the

scal

e fa

ctor

Find

ing

scal

e fa

ctor

giv

en

the

area

fact

or

Ap

plyi

ng s

cale

s in

sol

ving

pr

oble

ms

in li

fe s

ituat

ions

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

en

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


41

8.3.

2

Sets

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

52

8.3.

2

Sets

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Sets

de

scrib

e se

ts u

sing

a s

et

build

er n

otat

ion

draw

Ven

n di

agra

ms

to

show

rela

tions

hips

in

diffe

rent

sub

sets

solv

e pr

oble

ms

usin

g Ve

nn d

iagr

ams

Se

t bui

lder

not

atio

n

Venn

dia

gram

s up

to

thre

e su

bset

s

Li

stin

g el

emen

ts o

f set

s

U

sing

sym

bols

of s

ets

to d

escr

ibe

sets

Des

crib

ing

sets

usi

ng s

et b

uild

er

nota

tion

D

emon

stra

ting

rela

tions

hips

of

diffe

rent

sub

sets

Dis

cuss

ing

Venn

dia

gram

s w

ith u

p to

thre

e su

bset

s

So

lvin

g pr

oble

ms

invo

lvin

g Ve

nn

diag

ram

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls

and

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


42

8.3.

3

Fin

anci

al M

athe

mat

ics

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

53

8.3.

3

Fin

anci

al M

athe

mat

ics

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Con

sum

er a

rithm

etic

inte

rpre

t ban

k st

atem

ents

calc

ulat

e co

mpo

und

inte

rest

calc

ulat

e co

mm

issi

on

so

lve

prob

lem

s on

hire

pu

rcha

se

Ba

nk s

tate

men

ts

C

ompo

und

inte

rest

Com

mis

sion

Hire

pur

chas

e

D

iscu

ssin

g th

e co

nten

ts o

f th

e ba

nk s

tate

men

ts

Ex

tract

ing

data

from

ban

k st

atem

ents

to u

se it

for

calc

ulat

ions

Dis

cuss

ing

com

poun

d in

tere

st, c

omm

issi

on a

nd

hire

pur

chas

e

C

ompu

ting

com

poun

d in

tere

st, c

omm

issi

on a

nd

hire

pur

chas

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


43

8.3.

4

M

easu

res

And

Men

sura

tion

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

54

8.3.

4

M

easu

res

And

Men

sura

tion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Men

sura

tion

calc

ulat

e pe

rimet

er o

f co

mbi

ned

shap

es

ca

lcul

ate

area

of

com

bine

d sh

apes

calc

ulat

e vo

lum

e of

cy

linde

rs

Pe

rimet

er o

f com

bine

d sh

apes

Area

of c

ombi

ned

shap

es

Vo

lum

e of

cyl

inde

rs

C

alcu

latin

g pe

rimet

er

and

area

of c

ombi

ned

shap

es

C

alcu

latin

g vo

lum

e of

cy

linde

rs

C

arry

ing

out a

n ex

perim

ent t

o sh

ow th

e re

latio

nshi

p be

twee

n m

ass

and

volu

me

Solv

ing

prob

lem

s in

volv

ing

mas

s an

d vo

lum

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


44

8.3.

5

Gra

phs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

55

8.3.

5

Gra

phs

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Func

tiona

l gra

phs

us

e th

e fu

nctio

nal

nota

tion 𝑓𝑓(𝑥𝑥)

in:

- ev

alua

ting

func

tions

-

solv

ing

linea

r and

qu

adra

tic

equa

tions

draw

gra

phs

of li

near

and

qu

adra

tic fu

nctio

ns

usin

g:

- ta

ble

of v

alue

s

- ax

es in

terc

epts

sket

ch:

- st

raig

ht li

ne

- qu

adra

tic g

raph

s

usin

g ax

es in

terc

epts

use

grap

hs to

find

un

know

n va

lues

in li

near

an

d qu

adra

tic e

quat

ions

Fu

nctio

nal n

otat

ion

Li

near

gra

phs

Qua

drat

ic g

raph

s

D

iscu

ssin

g us

e of

fu

nctio

nal n

otat

ion

usin

g fa

milia

r fun

ctio

ns

D

raw

ing

linea

r an

d qu

adra

tic g

raph

s

Sk

etch

ing

stra

ight

line

an

d qu

adra

tic g

raph

s

Fi

ndin

g un

know

n va

lues

in

line

ar a

nd q

uadr

atic

eq

uatio

ns u

sing

the

grap

h

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Trav

el g

raph

s

draw

dis

tanc

e-tim

e gr

aphs

draw

spe

ed-ti

me

grap

hs

so

lve

prob

lem

s in

volv

ing

trave

l gra

phs

D

ista

nce-

time

grap

hs

Sp

eed-

time

grap

hs

D

iscu

ssin

g re

latio

nshi

p in

volv

ing

dist

ance

, spe

ed

and

time

in e

very

day

life

Dra

win

g di

stan

ce -

time

an

d sp

eed

- tim

e gr

aphs

Solv

ing

prob

lem

s in

life

in

volv

ing

trave

l gra

phs

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


45

8.3.

6

Var

iatio

n M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

5

6 8.

3.6

V

aria

tion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Varia

tion

ex

pres

s in

vers

e va

riatio

n in

alg

ebra

ic te

rms

dist

ingu

ish

betw

een

dire

ct

and

inve

rse

varia

tion

Illus

trate

dire

ct a

nd

inve

rse

varia

tion

usin

g sk

etch

gra

phs

so

lve

prob

lem

s in

volv

ing

varia

tion

D

irect

var

iatio

n

In

vers

e va

riatio

n

D

iscu

ssin

g re

latio

nshi

ps

show

ing

dire

ct o

r inv

erse

va

riatio

n

Dis

cuss

ing

exam

ples

of

dire

ct a

nd in

vers

e va

riatio

ns

Sk

etch

ing

grap

hs o

f di

rect

and

inve

rse

func

tions

Solv

ing

prob

lem

s in

volv

ing

varia

tion

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


46

8.3

.7

Alg

ebra

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

59

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Alge

brai

c M

anip

ulat

ion

fin

d H

CF

and

LCM

of

alge

brai

c ex

pres

sion

s

si

mpl

ify a

lgeb

raic

fra

ctio

ns

fa

ctor

ise

quad

ratic

ex

pres

sion

s of

the

form

w

here

fa

ctor

ise

alge

brai

c ex

pres

sion

s

Al

gebr

aic

fract

ions

LCM

and

HC

F of

al

gebr

aic

expr

essi

ons

Qua

drat

ic e

xpre

ssio

ns

Fa

ctor

isat

ion

Fi

ndin

g LC

M a

nd H

CF

of a

lgeb

raic

ex

pres

sion

s

Si

mpl

ifyin

g al

gebr

aic

fract

ions

Fact

oris

ing

quad

ratic

ex

pres

sion

s

fact

oris

e al

gebr

aic

expr

essi

ons

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Equa

tions

solv

e lin

ear s

imul

tane

ous

equa

tions

usi

ng:

- el

imin

atio

n -

subs

titut

ion

-

grap

hica

l met

hod

so

lve

quad

ratic

equ

atio

ns

usin

g:

- fa

ctor

isat

ion

-

grap

hica

l met

hods

chan

ge th

e su

bjec

t of

form

ulae

subs

titut

e va

lues

in a

gi

ven

form

ulae

Si

mul

tane

ous

equa

tions

Qua

drat

ic e

quat

ions

Cha

nge

of s

ubje

ct o

0f

fdor

mul

ae

Su

bstit

utio

n of

val

ues

so

lvin

g si

mul

tane

ous

linea

r equ

atio

ns u

sing

: -

elim

inat

ion

- su

bstit

utio

n

- gr

aphi

cal m

etho

d -

solv

ing

quad

ratic

eq

uatio

ns u

sing

:

- fa

ctor

isat

ion

-

grap

hica

l met

hods

solv

ing

prob

lem

s fro

m

life

situ

atio

ns u

sing

eq

uatio

ns

ch

angi

ng th

e su

bjec

t of

form

ulae

subs

titut

ing

valu

es in

gi

ven

form

ulae

Dis

cuss

ing

chan

ge o

f su

bjec

t and

its

appl

icat

ions

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


47

8.3

.7

Alg

ebra

Con

td..

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

60

Ineq

ualit

ies

solv

e si

mul

tane

ous

linea

r in

equa

litie

s in

one

va

riabl

e

re

pres

ent s

olut

ion

set o

n a

line

grap

h

solv

e si

mul

tane

ous

linea

r in

equa

litie

s gr

aphi

cally

Si

mul

tane

ous

ineq

ualit

ies

Gra

phs

of in

equa

litie

s

So

lvin

g si

mul

tane

ous

linea

r ine

qual

ities

in

one

varia

ble

Rep

rese

ntin

g so

lutio

n se

t on

a lin

e gr

aph

Rep

rese

ntin

g lin

ear

ineq

ualit

ies

in tw

o va

riabl

es o

n th

e C

arte

sian

pla

ne b

y sh

adin

g th

e un

wan

ted

regi

ons

R

epre

sent

ing

the

solu

tion

set o

f si

mul

tane

ous

line

ar

ineq

ualit

ies

in a

C

arte

sian

pla

ne

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Indi

ces

and

loga

rithm

s

sim

plify

alg

ebra

ic

expr

essi

ons

invo

lvin

g in

dice

s

de

fine

loga

rithm

s

eval

uate

loga

thm

s

ap

ply

the

law

s of

lo

garit

hms

to e

valu

ate

loga

rithm

s

sim

plify

exp

ress

ions

us

ing

law

s of

loga

rithm

s

so

lve

equa

tions

invo

lvin

g in

dice

s an

d lo

garit

hms

In

dice

s

Loga

rithm

s

Theo

ry o

f log

arith

ms

Eq

uatio

ns in

volv

ing

indi

ces

and

loga

rithm

s

Si

mpl

ifyin

g al

gebr

aic

expr

essi

ons

invo

lvin

g in

dice

s

D

iscu

ssin

g lo

garit

hms

Eval

uatin

g lo

garit

hms

Ex

plor

ing

law

s of

lo

garit

hms

Sim

plify

ing

expr

essi

ons

usin

g la

ws

of

loga

rithm

s

So

lvin

g eq

uatio

ns

invo

lvin

g In

dice

s an

d lo

garit

hms

Rel

evan

t tex

ts

IC

T to

ols

En

viro

nmen

t

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are


48

8.3.

8

Geo

met

ry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

61

8.3.

8

Geo

met

ry

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Poin

ts, l

ines

and

ang

les

co

nstru

ct a

ngle

s of

el

evat

ion

and

depr

essi

on

so

lve

prob

lem

s on

ang

les

of e

leva

tion

and

depr

essi

on

An

gles

of e

leva

tion

and

depr

essi

on

C

onst

ruct

ing

angl

es o

f el

evat

ion

and

depr

essi

on

So

lvin

g pr

oble

ms

on

angl

es o

f ele

vatio

n an

d de

pres

sion

usi

ng s

cale

dr

awin

g

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Bea

ring

illu

stra

te b

earin

g on

di

agra

ms

so

lve

prob

lem

s in

volv

ing

thre

e fig

ure

bear

ing

and

com

pass

bea

ring

Th

ree

- fig

ure

bear

ing

C

ompa

ss b

earin

g

C

onst

ruct

ing

diag

ram

s to

sh

ow b

earin

g

So

lvin

g pr

oble

ms

invo

lvin

g th

ree

figur

e be

arin

g an

d co

mpa

ss

bear

ing

Loca

ting

the

posi

tion

of a

n ob

ject

usi

ng th

ree

figur

e be

arin

g an

d co

mpa

ss

bear

ing

Rel

evan

t tex

ts

IC

T to

ols

En

viro

nmen

t

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

softw

are

Poly

gons

desc

ribe

prop

ertie

s of

po

lygo

ns

so

lve

prob

lem

s in

volv

ing

n-si

ded

poly

gon

Ap

ply

the

prop

ertie

s of

n-

side

d po

lygo

ns

Pr

oper

ties

of p

olyg

ons

Angl

es o

f pol

ygon

s

Num

ber o

f sid

es o

f po

lygo

ns

D

iscu

ssin

g pr

oper

ties

of

n-si

ded

poly

gons

Solv

ing

prob

lem

s in

volv

ing

n-si

ded

poly

gons

Appl

ying

the

prop

ertie

s of

n-

side

d po

lygo

ns

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Sim

ilarit

y an

d C

ongr

uenc

y

find

the

scal

e fa

ctor

from

tw

o gi

ven

sim

ilar s

hape

s

ca

lcul

ate

the

leng

th o

f si

des

of s

imila

r fig

ures

Sc

ale

fact

or

Ar

eas

of s

imila

r fig

ures

Volu

me

and

mas

s of

si

mila

r sol

ids

D

iscu

ssin

g sc

ale

fact

or,

area

fact

or a

nd v

olum

e fa

ctor

Com

putin

g le

ngth

s in

si

mila

r sha

pes

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t


49

8.3.

8

Geo

met

ry c

ontd

.. M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

6

2 SU

B T

OPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

ca

lcul

ate

the

area

of

sim

ilar f

igur

es

ca

lcul

ate

the

volu

me

and

mas

s of

sim

ilar s

olid

s

C

ompu

ting

area

s of

si

mila

r sha

pes

Solv

ing

prob

lem

s on

vo

lum

es a

nd m

asse

s of

si

mila

r sol

ids

Ta

lkin

g bo

oks/

softw

are

Con

stru

ctio

ns a

nd lo

ci

co

nstru

ct tr

iang

les

cons

truct

qua

drila

tera

ls

so

lve

life

prob

lem

s us

ing

cons

truct

ion

of tr

iang

les

and

quad

rilat

eral

s

Tr

iang

les

Qua

drila

tera

ls

C

onst

ruct

ing

trian

gles

an

d qu

adril

ater

als

Solv

ing

prob

lem

s us

ing

cons

truct

ion

of tr

iang

les

and

quad

rilat

eral

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e

Sym

met

ry

id

entif

y ro

tatio

nal

sym

met

ry in

two

dim

ensi

ons

st

ate

the

orde

r of

rota

tiona

l/poi

nt s

ymm

etry

in

pla

ne s

hape

s

so

lve

prob

lem

s in

volv

ing

rota

tiona

l sym

met

ry

R

otat

iona

l sym

met

ry in

tw

o di

men

sion

s

Id

entif

ying

rota

tiona

l sy

mm

etry

in tw

o di

men

sion

s

Dis

cuss

ing

rota

tiona

l/poi

nt

sym

met

ry

St

atin

g th

e or

der o

f ro

tatio

nal s

ymm

etry

of

plan

e sh

apes

Solv

ing

prob

lem

s in

volv

ing

rota

tiona

l sy

mm

etry

in li

fe

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/so

ftwar

e


50

8.3.

9

Sta

tistic

s

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

63

8.3.

9

Sta

tistic

s

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Dat

a C

olle

ctio

n,

Cla

ssifi

catio

n an

d R

epre

sent

atio

n

co

llect

sta

tistic

al d

ata

grou

p ra

w d

ata

into

cl

asse

s

stat

e th

e cl

ass

wid

ths

for

the

grou

ped

data

cons

truct

freq

uenc

y ta

bles

draw

bar

cha

rt, p

ie

char

t,his

togr

am a

nd

frequ

ency

pol

ygon

anal

yse

info

rmat

ion

on th

e gr

aphs

D

ata

colle

ctio

n an

d C

lass

ifica

tion

of

grou

ped

data

Dat

a re

pres

enta

tion

- Fr

eque

ncy

tabl

e -

Bar g

raph

-

Pie

char

t -

His

togr

am

- Fr

eque

ncy

poly

gon

C

olle

ctin

g of

sta

tistic

al

data

Con

duct

ing

expe

rimen

ts

to c

olle

ct d

ata

Cla

ssify

ing

the

colle

cted

da

ta

Fi

ndin

g th

e cl

ass

wid

th o

f gr

oupe

d da

ta

C

onst

ruct

ing

frequ

ency

ta

bles

Con

stru

ctin

g gr

aphs

Inte

rpre

ting

the

grap

h

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Mea

sure

s of

Cen

tral

Te

nden

cy

co

mpu

te th

e m

ean

of

grou

ped

data

find

the

mod

e an

d m

edia

n

ca

lcul

ate

the

mea

n us

ing

the

assu

med

mea

n

M

ean,

med

ian

and

mod

el c

lass

Assu

med

mea

n

C

alcu

latin

g th

e m

ean

of

grou

ped

data

Com

putin

g th

e m

ean

usin

g th

e as

sum

ed m

ean

Fi

ndin

g th

e m

ode

and

the

med

ian

Expl

aini

ng th

e si

gnifi

canc

e of

mea

sure

s of

cen

tral t

ende

ncy

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


51

8.3.

10

T

rigon

omet

ry M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

6

4

8.

3. 1

0

Trig

onom

etry

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Pyth

agor

as

theo

rem

deriv

e th

e Py

thag

oras

theo

rem

solv

e rig

ht a

ngle

d tri

angl

es b

y ap

plyi

ng th

e P

ytha

gora

s th

eore

m

sh

ow w

heth

er th

e gi

ven

tripp

les

are

Pyt

hago

rean

Py

thag

oras

theo

rem

Pyth

agor

ean

tripp

les

U

sing

the

met

hod

of c

ount

ing

squa

res

to d

eriv

e th

e Py

thag

oras

theo

rem

Find

ing

the

mis

sing

sid

e in

righ

t an

gled

tria

ngle

s us

ing

Pyth

agor

as th

eore

m

So

lvin

g pr

oble

ms

in e

very

day

life

usin

g th

e Py

thag

oras

th

eore

m

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

in

volv

ing

Pyt

hago

ras

The

orem

an

d ex

plor

ing

its a

pplic

atio

n in

lif

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls

and

equi

pmen

t

Talk

ing

book

s/

softw

are

Trig

onom

etric

al

ratio

s

find

sine

, cos

ine,

tang

ent o

f acu

te

angl

es

fi

nd s

ine,

cos

ine,

tang

ent o

f ob

tuse

ang

les

solv

e pr

oble

ms

invo

lvin

g rig

ht

angl

ed tr

iang

les

in tw

o di

men

sion

s

Tr

igon

omet

rical

ratio

s of

ac

ute

and

obtu

se a

ngle

s

- Si

ne

- C

osin

e

- Ta

ngen

t

D

emos

ntra

ting

whe

ther

the

givc

en tr

iple

s ar

e py

htha

gora

n

Cal

cula

ting

sine

, cos

ine

and

tang

ent o

f acu

te a

nd o

btus

e an

gles

Solv

ing

prob

lem

s in

volv

ing

right

ang

led

trian

gles

in tw

o di

men

sion

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls

and

equi

pmen

t

Talk

ing

book

s/

softw

are


52

8.3.

11

V

ecto

rs

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

65

8.3.

11

V

ecto

rs

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Type

s of

vec

tors

desc

ribe

type

s of

vec

tors

repr

esen

t typ

es o

f vec

tors

on

Car

tesi

an p

lane

iden

tify

vario

us ty

pes

of

vect

ors

on th

e C

arte

sian

pl

ane

Tr

ansl

atio

n ve

ctor

s

N

egat

ive

vect

ors

Eq

ual v

ecto

rs

Pa

ralle

l vec

tors

Posi

tion

vect

ors

D

iscu

ssin

g va

rious

ty

pes

of v

ecto

rs

D

raw

ing

diffe

rent

type

s of

vec

tors

on

the

Car

tesi

an p

lane

Iden

tifyi

ng d

iffer

ent

type

s of

vec

tors

on

the

Car

tesi

an p

lane

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

l equ

ipm

ent

Ta

lkin

g bo

oks/

sof

twar

e

Ope

ratio

ns

Ad

d ve

ctor

s

sub

tract

vec

tors

mul

tiply

a v

ecto

r by

a sc

alar

calc

ulat

e th

e m

agni

tude

of

a ve

ctor

solv

e pr

oble

ms

invo

lvin

g ve

ctor

ope

ratio

ns

Ad

ditio

n of

vec

tors

Subt

ract

ion

of v

ecto

rs

Sc

alar

mul

tiplic

atio

n

Mag

nitu

de o

f vec

tors

Com

bine

d ve

ctor

op

erat

ions

M

anip

ulat

ing

vect

ors

by

addi

ng a

nd s

ubtra

ctin

g

M

ultip

licat

ion

of a

vec

tor

by a

sca

lar

C

ompu

ting

the

mag

nitu

de o

f a v

ecto

r

Solv

ing

prob

lem

s in

volv

ing

vect

ors

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


53

8.3.

12

Mat

rices

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

66

8.3.

12

Mat

rices

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Ope

ratio

ns

ad

d m

atric

es

su

btra

ct m

atric

es

m

ultip

ly a

mat

rix b

y a

scal

ar

m

ultip

ly m

atric

es

Ad

ditio

n an

d su

btra

ctio

n of

m

atric

es

Sc

alar

mul

tiplic

atio

n of

m

atric

es

M

ultip

licat

ion

of m

atric

es

C

arry

ing

out o

pera

tions

in

volv

ing

mat

rices

Usi

ng s

cala

r qua

ntiti

es

to m

ultip

ly m

atric

es

So

lvin

g pr

oble

ms

invo

lvin

g m

atric

es

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

in

volv

ing

mat

rices

and

ex

plor

ing

its a

pplic

atio

n in

life

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Det

erm

inan

ts

fin

d th

e de

term

inan

t of a

2 𝑋𝑋

2 m

atrix

dist

ingu

ish

betw

een

sing

ular

and

non

-sin

gula

r m

atric

es

us

e th

e fa

ct th

at th

e de

term

inan

t of a

sin

gula

r m

atrix

is z

ero

to fi

nd th

e un

know

n in

a 2

𝑋𝑋 2

mat

rix

so

lve

prob

lem

s th

at

invo

lve

sing

ular

and

non

-si

ngul

ar m

atric

es

D

eter

min

ants

of m

atric

es

Si

ngul

ar a

nd n

on-s

ingu

lar

mat

rices

C

alcu

latin

g th

e de

term

inan

t of

2 𝑋𝑋 2

mat

rices

Usi

ng th

e fa

ct th

at th

e de

term

inan

t of a

si

ngul

ar m

atrix

is z

ero

to fi

nd th

e un

know

n in

a

2x 2

mat

rix

so

lvin

g pr

oble

ms

that

in

volv

e si

ngul

ar a

nd

non-

sing

ular

mat

rices

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Inve

rse

mat

rix

fin

d th

e in

vers

e of

a 2

𝑋𝑋 2

non

-sin

gula

r mat

rix

In

vers

e of

a m

atrix

Sim

ulta

neou

s lin

ear

equa

tions

in 2

var

iabl

es

C

alcu

latin

g th

e in

vers

e of

a 2

𝑋𝑋 2

non

-sin

gula

r m

atrix

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

67

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

so

lve

sim

ulta

neou

s eq

uatio

ns u

sing

the

mat

rix m

etho

d

So

lvin

g si

mul

tane

ous

equa

tions

usi

ng th

e m

atrix

met

hod

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


54

8.3.

13 T

rans

form

atio

n M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

6

8 8.

3.13

Tra

nsfo

rmat

ion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Tran

slat

ion

tra

nsla

te p

lane

figu

res

on

Car

tesi

an P

lane

usi

ng

trans

latio

n ve

ctor

s

de

scrib

e fu

lly th

e tra

nsla

tions

bet

wee

n gi

ven

obje

cts

and

imag

es

Tr

ansl

atio

n ve

ctor

s to

m

ove

a pl

ane

figur

e on

a

carte

sian

pla

ne

D

raw

ing

of p

lane

sha

pes

on th

e C

arte

sian

Pla

ne

M

ovin

g pl

ane

figur

es/s

hape

s us

ing

trans

latio

n ve

ctor

s

D

escr

ibin

g fu

lly th

e tra

nsla

tions

bet

wee

n gi

ven

obje

cts

and

imag

es

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Ref

lect

ion

refle

ct p

lane

figu

res

in a

lin

e of

refle

ctio

n

fin

d th

e ax

is o

f ref

lect

ion

of

give

n ob

ject

s an

d im

ages

R

efle

ctio

n of

pla

ne

figur

es o

n a

carte

sian

pl

ane

in th

e x-

axis

, y-

axis

, lin

es o

f the

form

y=

a an

d x=

b

D

raw

ing

imag

es o

f pla

ne

figur

es u

nder

refle

ctio

n

Fi

ndin

g co

ordi

nate

s of

im

ages

of p

lane

figu

res

unde

r ref

lect

ion

Det

erm

inin

g th

e ax

is o

f re

flect

ion

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Rot

atio

n

ro

tate

poi

nts

and

plan

e fig

ures

on

a C

arte

sian

pl

ane

usin

g ge

omet

ric

met

hods

find

the

cent

re o

f rot

atio

n

de

term

ine

the

angl

e of

ro

tatio

n

R

otat

ion

of p

lane

fig

ures

on

the

Car

tesi

an

plan

e us

ing

the

geom

etric

met

hods

D

iscu

ssin

g ro

tatio

n of

pl

ane

figur

es a

nd p

oint

s on

the

Car

tesi

an p

lane

Rot

atin

g fig

ures

to fi

nd

imag

es o

n th

e C

arte

sian

pl

ane

Fi

ndin

g th

e ce

ntre

and

an

gle

of ro

tatio

n

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Enla

rgem

ent

en

larg

e pl

ane

figur

es

abou

t the

orig

in u

sing

a

ratio

nal s

cale

geo

met

rical

m

etho

ds

fin

d th

e sc

ale

fact

or

En

larg

emen

t abo

ut th

e or

igin

usi

ng a

ratio

nal

scal

e by

geo

met

ric

met

hods

D

raw

ing

imag

es o

f pla

ne

figur

es

D

eter

min

ing

the

scal

e fa

ctor

(enl

arge

men

t fa

ctor

)

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


55

8.3.

13 T

rans

form

atio

n C

ontd

.. M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

6

9 SU

B T

OPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

de

term

ine

the

cent

re o

f en

larg

emen

t

de

term

inin

g th

e ce

ntre

of

enla

rgem

ent

8.3

.14

Pr

obab

ility

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

70

8.3

.14

Pr

obab

ility

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Prob

abili

ty

de

scrib

e ex

perim

enta

l and

th

eore

tical

pro

babi

lity

dedu

ce p

roba

bilit

ies

from

re

sults

of e

xper

imen

ts

id

entif

y si

tuat

ions

whe

re

expe

rimen

tal a

nd

theo

retic

al p

roba

bilit

ies

are

appl

ied

use

prob

abilit

y ru

les

to

com

pute

pro

babi

litie

s of

si

ngle

eve

nts

solv

e pr

oble

ms

that

in

volv

e ex

perim

enta

l and

th

eore

tic p

roba

bilit

y in

life

Ex

perim

enta

l pro

babi

lity

Theo

retic

al p

roba

bilit

y

Si

ngle

eve

nts

D

iscu

ssin

g th

eore

tical

an

d ex

perim

enta

l pr

obab

ility

Car

ryin

g ou

t pr

obab

ility

expe

rimen

ts

C

ompu

ting

prob

abilit

ies

of s

ingl

e ev

ents

Solv

ing

prob

lem

s th

at

invo

lve

expe

rimen

tal a

nd

theo

retic

pro

babi

lity

in li

fe

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s so

ftwar

e


56

8.4

FOR

M F

OU

R (4

) 8

.4.1

F

inan

cial

Mat

hem

atic

s

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

71

8.4

FOR

M F

OU

R (4

)

8.4

.1

Fin

anci

al M

athe

mat

ics

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Con

sum

er a

rithm

etic

inte

rpre

t dat

a in

the

form

of

doc

umen

ts s

uch

as

rate

s, ta

xes,

cus

tom

s an

d ex

cise

dut

y

co

nver

t fro

m o

ne c

urre

ncy

to a

noth

er u

sing

rate

solv

e pr

oble

ms

rela

ted

to

sale

s ta

x, in

com

e ta

x ,

cust

oms

and

exci

se d

uty

an

d Va

lue

Adde

d Ta

x (V

AT)

Fo

reig

n ex

chan

ge

Sa

les

and

inco

me

tax

rate

s (P

ay a

s yo

u Ea

rn)

PAYE

Valu

e Ad

ded

Tax

(VAT

)

Cus

tom

s an

d Ex

cise

Dut

y

D

iscu

ssin

g fo

reig

n ex

chan

ge a

nd ty

pes

of

taxe

s

In

terp

retin

g da

ta in

the

form

of d

ocum

ents

suc

h as

rate

s, ta

xes,

cus

tom

s an

d ex

cise

dut

y

so

lve

prob

lem

s re

late

d to

sa

les

tax,

inco

me

tax

, cu

stom

s an

d ex

cise

dut

y

and

Valu

e Ad

ded

Tax

(VAT

)

cond

uctin

g ed

ucat

iona

l to

urs

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


57

8.4

.2

Mea

sure

s A

nd M

ensu

ratio

n

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

73

8.4

3

Gra

phs

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Func

tiona

l gra

phs

dr

aw c

ubic

and

inve

rse

grap

hs

so

lve

prob

lem

s in

volv

ing

cubi

c an

d in

vers

e fu

nctio

ns

C

ubic

gra

phs

Inve

rse

grap

hs

D

iscu

ssin

g cu

bic

and

inve

rse

func

tions

Dra

win

g cu

bic

grap

hs

D

raw

ing

grap

hs o

f in

vers

e fu

nctio

ns o

f the

fo

rm

𝑎𝑎𝑏𝑏𝑏𝑏

+𝑐𝑐 w

here

𝑎𝑎,𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎 𝑐𝑐 a

re in

tege

rs

So

lvin

g pr

oble

ms

invo

lvin

g cu

bic

or

inve

rse

func

tions

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Trav

el g

raph

s

expl

ain

the

rela

tions

hip

of

disp

lace

men

t, ve

loci

ty,

acce

lera

tion

and

time

draw

dis

plac

emen

t-tim

e gr

aphs

draw

vel

ocity

-tim

e gr

aphs

solv

e pr

oble

ms

invo

lvin

g di

spla

cem

ent-t

ime

and

velo

city

-tim

e gr

aphs

D

ispl

acem

ent-t

ime

grap

hs

Ve

loci

ty-ti

me

grap

hs

D

iscu

ssin

g di

spla

cem

ent

velo

city

,acc

eler

atio

n an

d tim

e

D

raw

ing

disp

lace

men

t-tim

e gr

aphs

Dra

win

g ve

loci

ty-ti

me

grap

hs

So

lvin

g pr

oble

ms

invo

lvin

g di

spla

cem

ent-

time

and

velo

city

-tim

e gr

aphs

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


58

8.4

3

Gra

phs

M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

7

3 8.

4 3

G

raph

s

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Func

tiona

l gra

phs

dr

aw c

ubic

and

inve

rse

grap

hs

so

lve

prob

lem

s in

volv

ing

cubi

c an

d in

vers

e fu

nctio

ns

C

ubic

gra

phs

Inve

rse

grap

hs

D

iscu

ssin

g cu

bic

and

inve

rse

func

tions

Dra

win

g cu

bic

grap

hs

D

raw

ing

grap

hs o

f in

vers

e fu

nctio

ns o

f the

fo

rm

𝑎𝑎𝑏𝑏𝑏𝑏

+𝑐𝑐 w

here

𝑎𝑎,𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎 𝑐𝑐 a

re in

tege

rs

So

lvin

g pr

oble

ms

invo

lvin

g cu

bic

or

inve

rse

func

tions

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Trav

el g

raph

s

expl

ain

the

rela

tions

hip

of

disp

lace

men

t, ve

loci

ty,

acce

lera

tion

and

time

draw

dis

plac

emen

t-tim

e gr

aphs

draw

vel

ocity

-tim

e gr

aphs

solv

e pr

oble

ms

invo

lvin

g di

spla

cem

ent-t

ime

and

velo

city

-tim

e gr

aphs

D

ispl

acem

ent-t

ime

grap

hs

Ve

loci

ty-ti

me

grap

hs

D

iscu

ssin

g di

spla

cem

ent

velo

city

,acc

eler

atio

n an

d tim

e

D

raw

ing

disp

lace

men

t-tim

e gr

aphs

Dra

win

g ve

loci

ty-ti

me

grap

hs

So

lvin

g pr

oble

ms

invo

lvin

g di

spla

cem

ent-

time

and

velo

city

-tim

e gr

aphs

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


59

8.4

.4

Var

iatio

n M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

7

4 8.

4.4

V

aria

tion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Varia

tion

de

term

ine

conn

ectin

g fo

rmul

ae fo

r joi

nt v

aria

tion

and

parti

al v

aria

tion

calc

ulat

e un

know

n va

riabl

es u

sing

the

appr

opria

te fo

rmul

a

cons

truct

gra

phs

to s

how

re

latio

nshi

p be

twee

n va

riabl

es

so

lve

prob

lem

s in

volv

ing

join

t and

par

tial v

aria

tion

Jo

int v

aria

tion

Parti

al v

aria

tion

D

iscu

ssin

g jo

int a

nd

parti

al v

aria

tions

Com

putin

g un

know

n va

riabl

es u

sing

the

appr

opria

te fo

rmul

a

Sket

chin

g va

riatio

n gr

aphs

Solv

ing

prob

lem

s in

life

si

tuat

ions

invo

lvin

g jo

int

and

parti

al v

aria

tion

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


60

8.4.

5

Alg

ebra

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

75

8.4.

5

Alg

ebra

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Alge

brai

c M

anip

ulat

ion

si

mpl

ify a

lgeb

raic

frac

tions

fact

oris

e qu

adra

tic

expr

essi

on

co

mpl

ete

the

squa

re

Al

gebr

aic

fract

ions

Qua

drat

ic e

xpre

ssio

ns

Fa

ctor

isat

ion

C

ompl

etin

g th

e sq

uare

Si

mpl

ifyin

g al

gebr

aic

fract

ions

usi

ng L

CM

of

deno

min

ator

s an

d fa

ctor

isat

ion

Fa

ctor

isin

g qu

adra

tic

expr

essi

ons

com

plet

ely

co

mpl

ete

the

squa

re

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Equa

tions

solv

e qu

adra

tic e

quat

ions

by

com

plet

ing

the

squa

re

de

rive

the

quad

ratic

form

ula

solv

e pr

oble

ms

by a

pply

ing

the

quad

ratic

form

ula

C

ompl

etin

g th

e sq

uare

Qua

drat

ic fo

rmul

a

Solv

ing

quad

ratic

eq

uatio

ns b

y co

mpl

etin

g th

e sq

uare

Der

ivin

g th

e qu

adra

tic

form

ula

by c

ompl

etin

g th

e sq

uare

Solv

ing

prob

lem

s us

ing

quad

ratic

form

ula.

Solv

ing

prob

lem

s fro

m

life

situ

atio

ns u

sing

the

quad

ratic

form

ula

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s / s

oftw

are

Ineq

ualit

ies

expr

ess

a gi

ven

life

situ

atio

n u

sing

ineq

ualit

y sy

mbo

ls

re

pres

ent i

nequ

aliti

es o

n th

e C

arte

sian

pla

ne

so

lve

life

prob

lem

s us

ing

ineq

ualit

ies

Li

near

pro

gram

min

g

D

iscu

ssin

g fo

rmul

atio

n of

ineq

ualit

ies

from

gi

ven

life

situ

atio

ns

D

educ

ing

ineq

ualit

ies

repr

esen

ted

on th

e C

arte

sian

pla

ne

R

epre

sent

ing

ineq

ualit

ies

on a

C

arte

sian

pla

ne

So

lvin

g pr

oble

ms

usin

g in

equa

litie

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


61

8.4.

5

Alg

ebra

Con

td..

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

76

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

in

volv

ing

ineq

ualit

ies

and

expl

orin

g its

ap

plic

atio

n in

life


62

8.4.

6

Geo

met

ry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

77

8.4.

6

Geo

met

ry

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Poly

gons

and

Circ

le

ap

ply

the

circ

le th

eore

m

asso

ciat

ed w

ith

cent

re,c

ircum

fere

nce,

diam

eter

, ta

ngen

t, cy

clic

qua

drila

tera

l, ch

ord

and

alte

rnat

e se

gmen

ts

ca

lcul

ate

angl

es u

sing

circ

le

theo

rem

s

C

ircle

theo

rem

s

Ap

plyi

ng th

e ci

rcle

theo

rem

as

soci

ated

with

ce

ntre

,circ

umfe

renc

e,di

amet

er,

tang

ent,

cycl

ic q

uadr

ilate

ral,

chor

d an

d al

tern

ate

segm

ent.

C

alcu

latin

g an

gles

usi

ng c

ircle

th

eore

m

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/

softw

are

Con

stru

ctio

ns

de

fine

locu

s

co

nstru

ct lo

cus

of p

oint

s in

a

plan

e w

hich

are

equ

idis

tant

fro

m a

fixe

d po

int,

a fix

ed

stra

ight

line

, tw

o fix

ed p

oint

s

and/

or tw

o in

ters

ectin

g lin

es

so

lve

prob

lem

s in

volv

ing

be

arin

g, s

cale

, ang

les

of

elev

atio

n an

d or

dep

ress

ion

usin

g lo

ci

co

nstru

ctio

n of

di

agra

ms

to a

giv

en

scal

e

Loci

D

iscu

ssin

g lo

cus

Con

stru

ctin

g lo

cus

of p

oint

s in

a

plan

e w

hich

are

equ

idis

tant

fro

m a

fixe

d po

int,

a fix

ed

stra

ight

line

, tw

o fix

ed p

oint

s

and

or tw

o in

ters

ectin

g lin

es

so

lvin

g pr

oble

ms

invo

lvin

g be

arin

g, s

cale

, ang

les

of

elev

atio

n an

d/or

dep

ress

ion

usin

g lo

ci

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/

softw

are


63

8.4.

7

Stat

istic

s M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

7

8 8.

4.7

St

atis

tics

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Dat

a re

pres

enta

tion

co

nstru

ct f

requ

ency

ta

bles

draw

freq

uenc

y po

lygo

ns

dr

aw c

umul

ativ

e fre

quen

cy

curv

es

so

lve

prob

lem

s in

volv

ing

the

cum

ulat

ive

frequ

ency

cu

rve

fre

quen

cy ta

ble

fre

quen

cy p

olyg

on

C

umul

ativ

e fre

quen

cy

tabl

e

C

umul

ativ

e fre

quen

cy

curv

e

C

onst

ruct

ing

frequ

ency

ta

bles

Dra

win

g fre

quen

cy

poly

gons

Dra

win

g th

e cu

mul

ativ

e fre

quen

cy c

urve

s

So

lvin

g pr

oble

ms

invo

lvin

g th

e

cum

ulat

ive

frequ

ency

cu

rve

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Mea

sure

s of

cen

tral

te

nden

cy a

nd d

ispe

rsio

n

find

the

med

ian

from

cu

mul

ativ

e fre

quen

cy

curv

e

ca

lcul

ate

the

rang

e

find

the

quar

tiles

from

cu

mul

ativ

e fre

quen

cy

curv

e (o

give

)

calc

ulat

e th

e:

- in

terq

uarti

le ra

nge

-

sem

i int

er-q

uarti

le

rang

e

m

edia

n

R

ange

Qua

rtile

s

In

terq

uarti

le ra

nge

Sem

i int

er-q

uarti

le ra

nge

D

eter

min

ing

the

med

ian

from

the

cum

ulat

ive

frequ

ency

cur

ve (o

give

)

Cal

cula

ting

the

rang

e

Estim

atin

g th

e qu

artil

es

from

cum

ulat

ive

frequ

ency

cur

ve

C

ompu

ting

the

inte

r-qu

artil

e ra

nge

and

sem

i in

ter-q

uarti

le ra

nge

Dis

cuss

ing

the

impo

rtanc

e of

in

terq

uarti

le a

nd s

emi

inte

r-qua

rtile

rang

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


64

8.4.

8

Trig

onom

etry

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

79

8.4.

8

Trig

onom

etry

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Trig

onom

etric

al ra

tios

ap

ply

the

sine

rule

to s

olve

pr

oble

ms

appl

y co

sine

rule

to s

olve

pr

oble

ms

use

the

form

ula

area

= 1 2ab

Si

nC to

cal

cula

te th

e ar

ea

of a

tria

ngle

solv

e tri

angl

es u

sing

sin

e an

d co

sine

rule

Solv

e 3

dim

ensi

onal

pr

oble

ms

usin

g th

e si

ne

and

cosi

ne ru

le

C

osin

e ru

le

Si

ne ru

le

Ar

ea o

f tria

ngle

s

Ap

plyi

ng th

e si

ne a

nd

cosi

ne ru

le to

sol

ve

prob

lem

s

Usi

ng th

e fo

rmul

a a

rea=

1 2ab

Sin

C to

cal

cula

te th

e ar

ea o

f a tr

iang

le

U

sing

the

sine

rule

and

co

sine

rule

to s

olve

tri

angl

es

So

lvin

g 3

dim

ensi

onal

pr

oble

ms

usin

g th

e si

ne

and

cosi

ne ru

le

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


65

8.4.

9

Vect

ors

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

80

8.

4.9

Vec

tors

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D R

ESO

UR

CES

Ope

ratio

ns

ex

pres

s ed

ges

and

diag

onal

s of

pla

ne s

hape

s as

line

ar c

ombi

natio

n of

ve

ctor

s

find

num

eric

al v

alue

s of

sc

alar

s in

equ

al v

ecto

rs

de

term

ine

ratio

of p

aral

lel

edge

s/di

agon

als

of p

lane

sh

apes

Ve

ctor

pro

perti

es o

f pl

ane

shap

es

Sk

etch

ing

of p

lane

sh

apes

Rep

rese

ntin

g e

dges

and

di

agon

als

of p

lane

sh

apes

as

linea

r co

mbi

natio

n of

vec

tors

Cal

cula

ting

num

eric

al

valu

es o

f sca

lars

usi

ng

equa

l vec

tors

Com

putin

g ra

tio o

f pa

ralle

l edg

es/d

iago

nals

of

pla

ne s

hape

s

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


66

8.4.

10

Tran

sfor

mat

ion

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

81

8.4.

10

Tran

sfor

mat

ion

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Ref

lect

ion

refle

ct p

lane

figu

res

in a

ny

line

of th

e fo

rm 𝑦𝑦

=𝑚𝑚𝑚𝑚

+𝑐𝑐

dete

rmin

e m

atric

es fo

r the

re

flect

ion

in

𝑚𝑚 𝑎𝑎𝑎𝑎𝑎𝑎 𝑦𝑦−𝑎𝑎𝑚𝑚𝑎𝑎𝑎𝑎

: 𝑦𝑦=𝑚𝑚,𝑦𝑦

=−𝑚𝑚

R

efle

ctio

n of

pla

ne fi

gure

s in

any

line

and

us

ing

m

atric

es

D

raw

ing

imag

es o

f ob

ject

s

D

eter

min

ing

the

axes

of

refle

ctio

n

Cal

cula

ting

coor

dina

tes

of im

ages

Rep

rese

ntin

g lif

e ph

enom

ena

usin

g m

athe

mat

ical

mod

el

invo

lvin

g re

flect

ion

of

plan

e fig

ures

and

ex

plor

ing

its a

pplic

atio

n in

life

R

elev

ant t

exts

ICT

tool

s

Geo

-boa

rds

En

viro

nmen

t

Bra

ille m

ater

ials

and

eq

uipm

ent

Ta

lkin

g bo

oks/

sof

twar

e

Rot

atio

n

ro

tate

pla

ne s

hape

s by

dr

awin

g

rota

te p

lane

sha

pes

usin

g m

atric

es

fin

d m

atric

es o

f rot

atio

ns

abou

t the

orig

in th

roug

h an

gles

whi

ch a

re m

ultip

les

of 9

0°

de

scrib

e fu

lly th

e ro

tatio

n

give

n:

- a

mat

rix

- ob

ject

and

its

imag

e

R

otat

ion

of p

lane

figu

res

by d

raw

ing

and

use

of

mat

rices

C

alcu

latin

g co

ordi

nate

s of

imag

es u

sing

m

atric

es

D

raw

ing

imag

es o

f pl

ane

shap

es

D

eter

min

ing

the

mat

rices

of r

otat

ions

desc

ribin

g fu

lly th

e ro

tatio

n gi

ven

the

mat

rix, o

bjec

t and

its

imag

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Enla

rgem

ent

en

larg

e pl

ane

figur

es

usin

g m

atric

es a

bout

the

orig

in

En

larg

emen

t usi

ng

mat

rices

abo

ut th

e or

igin

Enla

rgem

ent a

bout

any

po

int u

sing

a ra

tiona

l sca

le

C

alcu

latin

g co

ordi

nate

s of

imag

es u

sing

m

atric

es

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent


67

8.4.

10

Tran

sfor

mat

ion

Con

td..

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

82

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

en

larg

e pl

ane

figur

es

abou

t any

poi

nt u

sing

a

ratio

nal s

cale

by

draw

ing

desc

ribe

fully

an

enla

rgem

ent f

or a

: -

stat

ed m

atrix

-

obje

ct a

nd it

s im

age

D

raw

ing

imag

es o

f pl

ane

figur

es o

n th

e C

arte

sian

pla

ne

de

scrib

ing

fully

the

enla

rgem

ent f

or a

giv

en:

- M

atrix

-

Obj

ect a

nd it

s im

age

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Stre

tch

Def

ine

stre

tch

Dra

w im

ages

of p

lane

sh

apes

usi

ng g

eom

etric

al

met

hods

calc

ulat

e co

ordi

nate

s of

th

e im

age

give

n th

e m

atric

es

dr

aw im

ages

of p

lane

fig

ures

giv

en m

atric

es

id

entif

y in

varia

nt li

ne/p

oint

desc

ribe

fully

a s

tretc

h gi

ven

a

- m

atrix

-

obje

ct a

nd it

s im

age

O

ne w

ay a

nd tw

o w

ay

stre

tch

usin

g ge

omet

rical

m

etho

ds a

nd m

atric

es

D

iscu

ssin

g a

stre

tch

Dra

win

g im

ages

of

plan

e sh

ape

usin

g ge

omet

rical

met

hods

Com

putin

g co

ordi

nate

s of

imag

es g

iven

the

mat

rices

Plot

ting

imag

es o

f pla

ne

figur

es g

iven

mat

rices

Iden

tifyi

ng in

varia

nt

line/

poin

t

desc

ribin

g a

stre

tch

fully

gi

ven

a m

atrix

or o

bjec

t an

d its

imag

e

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

Br

aille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are

Shea

r

defin

e sh

ear

D

raw

imag

es o

f pla

ne

shap

e us

ing

geom

etric

al

met

hods

com

pute

coo

rdin

ates

of

the

imag

es g

iven

a m

atrix

draw

imag

es o

f pla

ne

figur

es g

iven

the

mat

rix

Sh

ear u

sing

geo

met

rical

m

etho

ds a

nd m

atric

es

D

iscu

ssin

g a

shea

r

Dra

win

g im

ages

of

plan

e sh

ape

usin

g ge

omet

rical

met

hods

Cal

cula

ting

coor

dina

tes

of im

age

give

n th

e m

atrix

Plot

ting

imag

es o

f pla

ne

figur

es g

iven

mat

rices

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


68

8.4.

10

Tran

sfor

mat

ion

Con

td..

Mat

hem

atics

Syl

labu

s For

m 1

– 4

201

5

83

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

de

scrib

e co

mpl

etel

y th

e sh

ear g

iven

a

- m

atrix

-

obje

ct a

nd it

s im

age

de

scrib

ing

fully

a s

hear

gi

ven

a m

atrix

or a

n ob

ject

and

its

imag

e


69

8.4.

11

Prob

abili

ty M

athe

mat

ics S

ylla

bus F

orm

1 –

4 2

015

8

4 8.

4.11

P

roba

bilit

y

SUB

TO

PIC

LE

ARN

ING

OB

JEC

TIVE

S

Lear

ners

sho

uld

be a

ble

to:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Com

bine

d Ev

ents

defin

e co

mbi

ned

even

ts

co

nstru

ct o

utco

me

tabl

es

co

nstru

ct tr

ee d

iagr

am

ap

ply

prob

abilit

y ru

les

in

the

com

puta

tion

of

prob

abilit

ies

de

mon

stra

te th

e ap

plic

atio

n of

pro

babi

lity

in

life

C

ombi

ned

even

ts

O

utco

me

tabl

es

Tr

ee d

iagr

ams

Prob

abilit

y ru

les

Appl

icat

ion

of p

roba

bilit

y

D

iscu

ssin

g co

mbi

ned

even

ts

C

onst

ruct

ing

outc

ome

tabl

es a

nd tr

ee

diag

ram

s

C

ompu

ting

prob

abilit

ies

usin

g pr

obab

ility

rule

s

dem

onst

ratin

g th

e ap

plic

atio

n of

pro

babi

lity

in li

fe

R

epre

sent

ing

life

phen

omen

a us

ing

mat

hem

atic

al m

odel

s in

volv

ing

com

bine

d pr

obab

ility

even

ts a

nd

expl

orin

g its

app

licat

ion

in li

fe

R

elev

ant t

exts

ICT

tool

s

Envi

ronm

ent

B

raille

mat

eria

ls a

nd

equi

pmen

t

Talk

ing

book

s/ s

oftw

are


70

9.0 ASSESSMENT

9.1 Assessment Objectives

Learners will be assessed on their ability to:-

• recogniseandapplymathematicalsymbols,termsanddefinitions• carryoutcalculationsaccurately• useasuitabledegreeofaccuracyinapproximationandmeasurement• measuretoasuitabledegreeofaccuracy• drawtables,graphs,chartsanddiagramsaccurately• interprettables,graphs,chartsanddiagramsaccurately• applymathematicalreasoningandcommunicatemathematicalideasclearly• carryoutgeometricalconstructionsandmanipulationsaccurately• deduceanddrawinferencesthroughmanipulationofstatisticaldata• solveroutineandnon-routineproblemsusingappropriateformulae,algorithmsandprocedures• conductresearchprojectsincludingthoserelatedtoenterprise• makeeffectiveuseofavarietyofICTtoolsinsolvingproblems

9.2 Scheme of Assessment

Forms 1-4 Mathematics assessment will be based on 30% continuous assessment and 70% summative assessment.

The syllabus’ scheme of assessment is grounded in the principle of equalisation of opportunities hence, does not con-donedirectorindirectdiscriminationoflearners.Arrangements,accommodationsandmodificationsmustbevisiblein both continuous and summative assessments to enable candidates with special needs to access assessments and receive accurate performance measurement of their abilities. Access arrangements must neither give these candi-dates an undue advantage over others nor compromise the standards being assessed.Candidates who are unable to access the assessments of any component or part of component due to disability (tran-sitory or permanent) may be eligible to receive an award based on the assessment they would have taken.NBForfurtherdetailsonarrangements,accommodationsandmodificationsrefertotheassessmentprocedurebook-let.

9.2 (a) Continuous Assessment

Continuous assessment for Forms 1 – 4 will consists of topic tasks, written tests, end of term examinations, project andprofilingtomeasuresoftskills

• TopicTasksThese are activities that teachers use in their day to day teaching. They should include practical activities, assign-ments and group work activities.

• WrittenTests

These are tests set by the teacher to assess the concepts covered during a given period of up to a month. The tests should consists of short structured questions as well as long structured questions.

• Endoftermexaminations

These are comprehensive tests of the whole term’s or year’s work. They can be set at school, district or provincial level.

•Project

The project would be cumulative in nature and done as one project from forms 1-2 and another one from forms 3-4


71

Level Assessment task Frequency WeightingForm 1 Topic tasks

Written tests End of term tests

1 per term 2 per term 1 per term

4,5%

Form 2 Topic tasks Written tests End of term tests


4,5%



4,5%



4,5%

Project 1 covering Forms 1 - 2 and 1 covering Forms 3-4Total 30%

9.2 (b) Summative Assessment

The Summative assessment consists of two papers of equal weighting

Description of the papers Paper 1 Duration: 2 hours 30 minutes The paper consists of about 30 short structured questions marked out of 100 and is compulsory, set covering all sylla-bus topics.

Paper 2Duration: 2 hours 30 minutes The paper consists of two sections, Section A and Section B and it will be set covering all topics of the syllabus.

Section A:Consistsoffive(5)compulsoryquestionsmarkedoutof52

Section B: Consists of seven (7) long questions. The candidates are expected to answer 4 questions of their choice. Each question carries twelve (12) marks and the section is marked out of 48


72

Descriptiontable

Paper Paper type Marks Duration Weighting1 Structured – short answer

questions100 2 1/2 hours 35%

2 Structured– short and long answer questions

100 2 1/2 hours 35%

Total 70%

9.3 Specification Grid

Skill Paper 1 Paper 2Knowledge and comprehension 50% 35%Application and Analysis 40% 45%Problem solving 10% 20%TOTAL 100% 100%

ASSESSMENT MODEL

Assessment of learner performance in Mathematics100%

Continuous assessment 30% Summative assessment 70%

Profiling Topic Tasks 4,5%

Written Tests 4,5%

End of term Tests

4,5%

Project12%

Paper 1 35 %

Paper 2 35 %

Profile

Exit Profile

Continuous assessment 30% Examination Mark 70%

FINAL MARKS 100%

mathematics syllabus forms 1 - 4 · mathematics syllabus forms 1 - 4 ii ... 7.3 financial...

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