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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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
– 4
201
5
6
7.0
SC
OPE
AN
D S
EQU
ENC
E
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
Mathematics Syllabus Forms 1 - 4
4
7. 2
Sets
Mat
hem
atics
Syl
labu
s For
m 1
– 4
201
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
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ING
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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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
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ronm
ent
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raille
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eria
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nd
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pmen
t
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ing
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ftwar
e
Mathematics Syllabus Forms 1 - 4
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
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ant t
exts
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tool
s
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ronm
ent
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raille
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eria
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ftwar
e
Mathematics Syllabus Forms 1 - 4
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
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pmen
t
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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
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ronm
ent
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raille
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eria
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pmen
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ftwar
e
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
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ant t
exts
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tool
s
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ronm
ent
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raille
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eria
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nd
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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
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ant t
exts
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tool
s
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ronm
ent
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raille
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eria
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pmen
t
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ing
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ftwar
e
Mathematics Syllabus Forms 1 - 4
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
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ant t
exts
ICT
tool
s
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ronm
ent
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raille
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eria
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pmen
t
Talk
ing
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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
Mathematics Syllabus Forms 1 - 4
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
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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
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ronm
ent
B
raille
mat
eria
ls a
nd
equi
pmen
t
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
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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
Mathematics Syllabus Forms 1 - 4
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
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ING
OB
JEC
TIVE
S
Lear
ners
sho
uld
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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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
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pmen
t
Talk
ing
book
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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
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raille
mat
eria
ls a
nd
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pmen
t
Talk
ing
book
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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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 4
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
Mathematics Syllabus Forms 1 - 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
1 per term 2 per term 1 per term
4,5%
Form 3 Topic tasks Written tests End of term tests
1 per term 2 per term 1 per term
4,5%
Form 4 Topic tasks Written tests End of term tests
1 per term 2 per term 1 per term
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
Mathematics Syllabus Forms 1 - 4
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%