pure mathematics syllabus - globtorch mathematics forms 3 - 4.pdf · pure mathematics syllabus...
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ZIMBABWE
MINISTRY OF PRIMARY AND SECONDARY EDUCATION
PURE MATHEMATICS SYLLABUS
FORMS 3 - 4
2015 - 2022
Curriculum Development and Technical ServicesP.O. Box MP 133Mount Pleasant
Harare© All Rights Reserved
2015
Pure Mathematics Syllabus Forms 3 - 4
ACKNOWLEDGEMENTSThe Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued contribution in the development of this syllabus:
• Panellists for Form 3-4 Pure Mathematics• Representatives of the following organizations:
- Zimbabwe School Examinations Council (ZIMSEC) - Uunited Nations Children’s Fund (UNICEF ) - United Nations Cultural, Scientific and Cultural Organisation (UNESCO)
i
Pure Mathematics Syllabus Forms 3 - 4
ii
CONTENTSACKNOWLEDGEMENTS.....................................................................................................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 ...........................................................................................................2
6.0 TOPICS ..........................................................................................................................2
7.0 SCOPE AND SEQUENCE .............................................................................................3
8.0 COMPTETNCY MATRIX ................................................................................................7
8.2 FORM 4 COMPETENCY MATRIX .................................................................................13
9.0 ASSESSMENT ...............................................................................................................20
1
Pure Mathematics Syllabus Forms 3 - 4
1.0 PREAMBLE
1.1 Introduction
In developing the Form 3 - 4 Pure Mathematics syllabus attention was paid to the need to provide continuity of mathematical concepts from Form 1through to Form 4 and lay foundations for further studies, focusing on learners who have the ability and interest. It is assumed that learners who take this syllabus will take it concurrently with the Form 1 - 4 Mathematics syllabus. The syllabus is intended to produce a citizen who is a critical thinker and problem solver in life.The two year learning phase will provide learners with opportunities to apply Mathematical concepts in other subject areas and enhance Mathematical literacy and numeracy. It also desires to produce a learner with the ability to communi-cate effectively.In learning Pure Mathematics, learners should be helped to acquire a variety of skills, knowledge and processes, and develop positive attitude towards the subject and in life. This will enable them to investigate and interpret nu-merical and spatial relationships as well as patterns that exist in the world. The syllabus also caters for learners with diverse needs to experience Pure Mathematics as relevant and worthwhile.
1.2 Rationale
Zimbabwe is undergoing a socio-economic transforma-tion where Pure Mathematics is key to development, therefore it is imperative that learners acquire necessary mathematical knowledge and skills to enable as many learners as possible to proceed to Form 5-6 Mathematics and beyond. The knowledge of Pure Mathematics enables learners to develop mathematical skills such as dealing with the abstract, presenting mathematical arguments, interpreting mathematical information and solving problems essential in life and for sustainable development. The importance of Ppure Mmathematics can be underpinned in inclusivity, human dignity and enterprise as it plays a pivotal role in careers such as reserach, actuarial science, materology and engineering
1.3 Summary of Content (Knowledge, Skills and Attitudes)
The syllabus will cover the theoretical and practical aspects of Pure Mathematics. This two year learning area will cover: algebra, coordinate geometry and
calculus.
1.4 Assumption
The syllabus assumes that the learner has: 1.4.1 mastered concepts and skills involving number,
algebra and geometry at Form 1 and 2 level 1.4.2 shown interest in pursuing Pure Mathematics1.4.3 the ability to operate some ICT tools
1.5 Cross Cutting Themes
The following are some of the cross cutting themes in Pure Mathematics:-
1.5.1 Financial literacy1.5.2 Disaster risk management1.5.3 Collaboration 1.5.4 Environmentalissues1.5.5 Enterprise skills1.5.6 Sexuality, HIV & AIDS Education
2.0 PRESENTATION OF SYLLABUS
The Pure Mathematics syllabus is presented as singled-ocument covering Form 3 - 4.It contains the preamble, aims, syllabus objectives, syllabus topics, scope and sequence and competency matrix. The syllabus also suggests a list of resources that could be used during learning and teaching process.
3.0 AIMS
This syllabus is intended to provide a guideline for Form 3 - 4 learners which will enable them to:
3.1 acquire a firm foundation for further studies and future careers
3.2 use ICT tools for learning and solving mathe-matical problems
3.3 develop an ability to apply Pure Mathematics in life and other subjects, particularly Science and Technology
3.4 develop a further understanding of mathe-matical concepts and processes in a way that
2
Pure Mathematics Syllabus Forms 3 - 4
encourages confidence, enjoyment, interest and lifelong learning
3.5 appreciate Pure Mathematics as a basis for applying the learning area in a variety of life situations
3.6 develop the ability to solve problems, reason clearly and logically as well as communicate mathematical ideas successfully
3.7 acquire enterprise skills in an indigenised and globalised economy through research and project-based learning
4.0 SYLLABUS OBJECTIVES
By the end of the two year learning period, the learners
should be able to:
4.1 use relevant mathematical symbols, terms and definitions in problem solving
4.2 use formulae and generalisations to solve a variety of problems in Pure Mathematics and other related learning areas
4.3 formulate problems into mathematical terms and apply appropriate techniques for solutions
4.4 use ICT tools for learning through problem solving
4.5 apply Pure Mathematics concepts and princi-ples in life
4.6 demonstrate an appreciation of mathematical concepts and processes
4.7 demonstrate an ability to solve problems sys-tematically, applying mathematical reasoning
4.8 communicate mathematical concepts and principles clearly
4.9 explore ways of solving routine and non-rou-tine problems in Pure Mathematics using ap-propriate formulae, algorithms and strategies
4.10 model mathematical information from one form to another e.g. verbal/words to symbolic form
4.11 conduct research projects including those related to enterprise
5.0 METHODOLOGY
It is recommended that teachers use methods and techniques in which Pure Mathematics is seen as a process which arouses an interest and confidence in tackling problems both in familiar and unfamiliar
contexts. The teaching and learning of Pure Mathematics must be learner centred and ICT driven. The following are suggested methods of the teaching and learning of Pure Mathematics
• Guided discovery • Group work• Interactive e-learning• Games and puzzles • Quiz• Problem solving• Simulation and modelling• Experimentation
5.1 Time Allocation
Six periods of 40 minutes each per week should be allocated for the adequate coverage of the syllabus
6.0 TOPICS
The following topics will be covered from Form 3 - 4
6.1 Indices and irrational numbers 6.2 Polynomials6.3 Identities, equations and inequalities 6.4 Graphs and coordinate geometry 6.5 Vectors 6.6 Functions 6.7 Sequences 6.8 Binomial expansions 6.9 Trigonometry 6.10 Logarithmic and exponential functions 6.11 Differentiation 6.12 Integration 6.13 Numerical methods
3
Pure Mathematics Syllabus Forms 3 - 47.
0 SC
OPE
AN
D S
EQU
ENC
E
TOPI
C 1
: IN
DIC
ES A
ND
IRR
ATIO
NA
L N
UM
BER
S
TOPI
C 2
: PO
LYN
OM
IALS
TOPI
C 3
: ID
ENTI
TIES
, EQ
UAT
ION
S A
ND
INEQ
UA
LITI
ES
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
5 7.
0
SCO
PE A
ND
SEQ
UEN
CE
TO
PIC
1: I
ND
ICES
AN
D IR
RAT
ION
AL N
UM
BER
S
SUB
TO
PIC
FO
RM 3
FO
RM 4
Indi
ces
Law
s of
indi
ces
Equa
tions
invo
lvin
g in
dice
s
Irrat
iona
l num
bers
Surd
s
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
6 TO
PIC
2: P
OLY
NO
MIA
LS
SUB
TO
PIC
FO
RM 3
FO
RM 4
Po
lyno
mia
ls
C
ompo
nent
s of
pol
ynom
ials
Addi
tion
Subt
ract
ion
Parti
al fr
actio
ns
M
ultip
licat
ion
Div
isio
n
Fa
ctor
The
orem
Solv
ing
equa
tions
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
7 TO
PIC
3: I
DEN
TITI
ES, E
QU
ATIO
NS
AND
INEQ
UAL
ITIE
S
SUB
TO
PIC
FO
RM 3
FO
RM 4
Iden
titie
s an
d eq
uatio
ns
D
efin
ition
of i
dent
ity
U
nkno
wn
coef
ficie
nts
Equa
tions
C
ompl
etin
g th
e sq
uare
Sim
ulta
neou
s eq
uatio
ns
Ineq
ualit
ies
Qua
drat
ic in
equa
litie
s
C
ubic
ineq
ualit
ies
4
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
4: G
RA
PHS
AN
D C
OO
RD
INAT
E G
EOM
ETRY
TOPI
C 5
: VEC
TOR
S
TOPI
C 6
: FU
NC
TIO
NS
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
8 TO
PIC
4: G
RAP
HS
AND
CO
OR
DIN
ATE
GEO
MET
RY
SUB
TO
PIC
FO
RM 3
FO
RM 4
Gra
phs
St
raig
ht li
ne g
raph
s
Gra
dien
t of a
line
seg
men
t
Gra
phs
of𝑦𝑦
=𝑘𝑘𝑥𝑥
𝑛𝑛
Coo
rdin
ate
geom
etry
Dis
tanc
e be
twee
n tw
o po
ints
Coo
rdin
ates
of t
he m
id-p
oint
SUB
TO
PIC
FOR
M 3
FOR
M 4
Veco
rs in
thre
e di
men
sion
s•
Typ
es o
f vec
tors
• V
ecto
r ope
ratio
ns•
Uni
t vec
tors
• S
cala
r pro
duct
• V
ecto
r pro
perti
es o
f pla
ne s
hape
s•
Are
as o
f tria
ngle
s an
d pa
ralle
logr
am
SUB
TO
PIC
FOR
M 3
FOR
M 4
Func
tions
• D
efini
tion
of a
func
tion
• D
omai
n an
d ra
nge
• C
ompo
site
func
tion
• O
ne- o
ne fu
ncio
n•
Inve
rse
of a
func
tion
• G
raph
s of
func
tions
5
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
7: S
EQU
ENC
ES
TOPI
C 8
: BIN
OM
IAL
EXPA
NSI
ON
TOPI
C 9
: TR
IGO
NO
MET
RY
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
11
TOPI
C 7
: SEQ
UEN
CES
SUB
TO
PIC
FO
RM 3
FO
RM 4
Sequ
ence
s
D
efin
ition
of a
seq
uenc
e
Ex
ampl
es o
f seq
uenc
es
Ar
ithm
etic
pro
gres
sion
Geo
met
ric p
rogr
essi
on
SUB
TO
PIC
FOR
M 3
FOR
M 4
Plan
e Tr
igon
omet
ry• S
ine
and
cosi
ne ru
les
• Are
a of
a tr
riang
le• R
adia
ns• L
engt
h of
an
arc
• Are
a of
a s
ecto
r• A
rea
of a
seg
men
tTr
igon
omet
ric fu
nctio
ns• T
rigon
omet
rical
func
tions
for a
ngle
s of
any
siz
e•
Exac
t val
ues
of s
ine,
cos
ine
and
tang
ent o
f spe
cial
an
gles
• Equ
atio
ns
SUB
TO
PIC
FOR
M 3
FOR
M 4
Bino
mia
l exp
ansi
on•
Pasd
cal’s
Tria
ngle
• E
xapn
sion
of (
a+b)
n whe
re n
is a
pos
itive
inte
ger
6
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
10:
LO
GA
RIT
HM
IC A
ND
EXP
ON
ENTI
AL
FUN
CTI
ON
S
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
TOPI
C 1
2: IN
TEG
RAT
ION
TOPI
C 1
3: N
UM
ERIC
AL
MET
HO
DS
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
14
TOPI
C 1
0: L
OG
ARIT
HMIC
AN
D E
XPO
NEN
TIAL
FU
NC
TIO
NS
SUB
TO
PIC
FO
RM 3
FO
RM 4
Loga
rithm
s
La
ws
of lo
garit
hms
Loga
rithm
s an
d in
dice
s
N
atur
al lo
garit
hms
Eq
uatio
ns o
f the
form
a x
= b
Expo
nent
ial f
unct
ions
Ex
pone
ntia
l gro
wth
and
dec
ay
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
15
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
TOPI
C
FORM
3
FORM
4
Diff
eren
tiatio
n
G
radi
ent o
f a c
urve
at a
poi
nt
D
eriv
ed fu
nctio
n of
the
form
axn
D
eriv
ativ
e of
a s
um
Ap
plic
atio
n of
diff
eren
tiatio
n to
gra
dien
ts,
tang
ents
and
nor
mal
s, s
tatio
nary
poi
nts,
ra
tes
of c
hang
e, v
eloc
ity a
nd a
ccel
erat
ion
SUB
TOPI
CFO
RM
3FO
RM
4In
tegr
atio
n•
Inde
finite
inte
grat
ion
as th
e re
vers
e pr
oces
s of
diff
eren
tiatio
n •
Inte
grat
ion
of fu
nctio
ns o
f the
form
axn
• In
tegr
atio
n of
a p
olyn
omia
l
•
Area
•
Vol
ume
SUB
TOPI
CFO
RM
3FO
RM
4
SUB
TOPI
CFO
RM
3FO
RM
4N
umer
ical
met
hods
•
Sim
ple
itera
tive
proc
edur
es•
N
ewto
n R
eaph
son
met
hod
•
Trap
eziu
m R
ule
7
Pure Mathematics Syllabus Forms 3 - 4
TOPI
C 1
: IN
DIC
ES A
ND
IRR
ATIO
NA
L N
UM
BER
S
8.1
FOR
M 3
CO
MPT
ETN
CY
MAT
RIX
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
18
FORM
TH
REE
(3) S
YLLA
BU
S
8.0
CO
MPE
TEN
CY
MAT
RIX
: FO
RM
3 S
YLLA
BUS
TOPI
C 1
: IN
DIC
ES A
ND
IRR
ATIO
NAL
NU
MB
ERS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Indi
ces
stat
e th
e la
ws
of in
dice
s
us
e la
ws
of in
dice
s to
sim
plify
al
gebr
aic
expr
essi
ons
solv
e eq
uatio
ns in
volv
ing
indi
ces
La
ws
of in
dice
s
Eq
uatio
ns in
volv
ing
indi
ces
D
eriv
ing
the
law
s of
indi
ces
Sim
plify
ing
alge
brai
c ex
pres
sion
s
Ap
plyi
ng la
ws
of in
dice
s to
sol
ve
prob
lem
s
IC
T to
ols
Rel
evan
t tex
ts
Irrat
iona
l num
bers
defin
e irr
atio
nal n
umbe
rs
re
duce
a s
urd
to it
s si
mpl
est f
orm
carr
y ou
t the
four
ope
ratio
ns o
n su
rds
ra
tiona
lise
deno
min
ator
s
Su
rds
D
istin
guis
hing
bet
wee
n ra
tiona
l and
irr
atio
nal n
umbe
rs
D
eriv
ing
and
find
ing
way
s of
si
mpl
ifyin
g su
rds
Ex
pres
sing
sur
ds in
sim
ple
form
Car
ryin
g ou
t the
four
ope
ratio
ns o
n su
rds
Rat
iona
lisin
g de
nom
inat
ors
IC
T to
ols
Rel
evan
t tex
ts
8.0
CO
MPT
ETN
CY
MAT
RIX
8
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
2: P
OLY
NO
MIA
LS
TOPI
C 3
: ID
ENTI
TIES
, EQ
UAT
ION
S A
ND
INEQ
UA
LITI
ES
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
19
TOPI
C 2
: PO
LYN
OM
IALS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Poly
nom
ials
defin
e po
lyno
mia
ls
id
entif
y pr
oper
and
impr
oper
fra
ctio
ns
ca
rry
out o
pera
tions
of a
dditi
on a
nd
subt
ract
ion
of p
olyn
omia
ls
ex
pres
s a
func
tion
as a
sum
of
sim
pler
frac
tions
C
ompo
nent
s of
po
lyno
mia
ls
Ad
ditio
n
Su
btra
ctio
n
Parti
al fr
actio
ns
D
iscu
ssin
g po
lyno
mia
ls
D
istin
guis
hing
bet
wee
n pr
oper
and
im
prop
er fr
actio
ns
Ad
ding
and
sub
tract
ing
poly
nom
ials
Dec
ompo
sing
func
tions
into
frac
tions
w
ith li
near
den
omin
ator
s
IC
T to
ols
Rel
evan
t tex
ts
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
20
TOPI
C 3
: ID
ENTI
TIES
, EQ
UAT
ION
S AN
D IN
EQU
ALIT
IES
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: (S
kills
, K
now
ledg
e, A
ttitu
des)
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Iden
titie
s an
d eq
uatio
ns
di
stin
guis
h be
twee
n an
iden
tity
and
an e
quat
ion
use
iden
titie
s to
det
erm
ine
unkn
own
coef
ficie
nts
in
poly
nom
ials
solv
e cu
bic
equa
tions
usi
ng F
acto
r Th
eore
m
D
efin
ition
of i
dent
ity
U
nkno
wn
coef
ficie
nts
Eq
uatio
ns
D
iscu
ssin
g th
e di
ffere
nce
betw
een
an
iden
tity
anda
n eq
uatio
n
Fi
ndin
g un
know
n co
effic
ient
s us
ing
iden
titie
s
U
sing
the
Fact
or T
heor
em to
sol
ve
cubi
c eq
uatio
ns
IC
T to
ols
Rel
evan
t tex
ts
Ineq
ualit
ies
fact
oris
e qu
adra
tic e
xpre
ssio
ns
so
lve
quad
ratic
ineq
ualit
ies
solv
e cu
bic
ineq
ualit
ies
with
the
use
of F
acto
r The
orem
Q
uadr
atic
ineq
ualit
ies
Cub
ic in
equa
litie
s
Fact
oris
ing
quad
ratic
exp
ress
ions
Find
ing
solu
tions
of q
uadr
atic
in
equa
litie
s
Ex
plor
ing
way
s of
sol
ving
cub
ic
ineq
ualit
ies
Usi
ng th
e Fa
ctor
The
orem
to s
olve
cu
bic
ineq
ualit
ies
R
elev
ant t
exts
ICT
tool
s
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
12
TOPI
C 2
: PO
LYN
OM
IALS
TOPI
C 3
:IDEN
TITI
ES, E
QU
ATIO
NS
AND
INEQ
UAL
ITIE
S
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: (S
kills
, K
now
ledg
e, A
ttitu
des)
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Iden
titie
s an
d eq
uatio
ns
di
stin
guis
h be
twee
n an
iden
tity
and
an e
quat
ion
use
iden
titie
s to
det
erm
ine
unkn
own
coef
ficie
nts
in
poly
nom
ials
solv
e cu
bic
equa
tions
usi
ng F
acto
r Th
eore
m
D
efin
ition
of i
dent
ity
U
nkno
wn
coef
ficie
nts
Eq
uatio
ns
D
iscu
ssin
g th
e di
ffere
nce
betw
een
an
iden
tity
and
an e
quat
ion
Find
ing
unkn
own
coef
ficie
nts
usin
g id
entit
ies
Usi
ng th
e Fa
ctor
The
orem
to s
olve
cu
bic
equa
tions
IC
T to
ols
Rel
evan
t tex
ts
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e,
Attit
udes
}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Poly
nom
ials
defin
e po
lyno
mia
ls
id
entif
y pr
oper
and
impr
oper
fra
ctio
ns
ca
rry o
ut o
pera
tions
of
addi
tion
and
subt
ract
ion
of
poly
nom
ials
expr
ess
a fu
nctio
n as
a s
um o
f si
mpl
er fr
actio
ns
C
ompo
nent
s of
po
lyno
mia
ls
Ad
ditio
n
Su
btra
ctio
n
Parti
al fr
actio
ns
D
iscu
ssin
g po
lyno
mia
ls
D
istin
guis
hing
bet
wee
n pr
oper
an
d im
prop
er fr
actio
ns
Ad
ding
and
sub
tract
ing
poly
nom
ials
Dec
ompo
sing
func
tions
into
fra
ctio
ns w
ith li
near
de
nom
inat
ors
IC
T to
ols
Rel
evan
t tex
ts
9
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
4: G
RA
PHS
AN
D C
OO
RD
INAT
E G
EOM
ETRY
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
21
TOPI
C 4
:GR
APH
S AN
D C
OO
RD
INAT
E G
EOM
ETR
Y
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Gra
phs
sket
ch s
traig
ht li
nes
find
the
grad
ient
of a
line
seg
men
t
find
the
equa
tion
of a
stra
ight
line
iden
tify
para
llel a
nd p
erpe
ndic
ular
lin
es
so
lve
prob
lem
s in
volv
ing
stra
ight
line
gr
aphs
St
raig
ht li
ne g
raph
s
Gra
dien
t of a
line
se
gmen
t
Sk
etch
ing
stra
ight
line
s gi
ven
suffi
cien
t inf
orm
atio
n
Ex
plor
ing
how
to fi
nd e
quat
ion
of a
st
raig
ht li
ne g
iven
two
poin
ts o
r the
gr
adie
nt a
nd a
poi
nt
D
istin
guis
hing
bet
wee
n pa
ralle
l and
pe
rpen
dicu
lar l
ines
Solv
ing
prob
lem
s in
volv
ing
stra
ight
lin
e gr
aphs
Iden
tifyi
ng e
xam
ples
in li
fe w
here
lin
ear r
elat
ions
hips
occ
ur
C
arry
ing
out e
xper
imen
ts in
volv
ing
linea
r rel
atio
nshi
ps
G
eo-b
oard
ICT
tool
s
En
viro
nmen
t
Coo
rdin
ate
geom
etry
calc
ulat
e th
e di
stan
ce b
etw
een
two
poin
ts g
iven
in c
oord
inat
e fo
rm
so
lve
prac
tical
pro
blem
s in
volv
ing
dist
ance
bet
wee
n tw
o po
ints
find
the
coor
dina
tes
of th
e m
id-p
oint
of
a s
traig
ht li
ne
D
ista
nce
betw
een
two
poin
ts
C
oord
inat
es o
f the
mid
-po
int
Ex
plor
ing
way
s to
find
dis
tanc
e be
twee
n tw
o po
ints
Cal
cula
ting
coor
dina
tes
of th
e m
id-
poin
t of a
stra
ight
line
Con
duct
ing
field
wor
k to
sol
ve
prob
lem
s in
volv
ing
dist
ance
bet
wee
n tw
o po
ints
G
eo-b
oard
ICT
tool
s
En
viro
nmen
t
10
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
5: V
ECTO
RS
TOPI
C 6
: FU
NC
TIO
NS
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
22
TOPI
C 5
: VEC
TOR
S
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Vect
ors
in th
ree
dim
ensi
ons
us
e st
anda
rd n
otat
ion
of v
ecto
rs (𝑥𝑥 𝑦𝑦 𝑧𝑧)
,
xi+y
j+zk
, 𝐴𝐴𝐴𝐴→ , a
dete
rmin
epos
ition
and
free
vec
tors
iden
tify
para
llel v
ecto
rs a
nd c
o-lin
ear
poin
ts
ca
lcul
ate
the
mod
ulus
of a
vec
tor
ad
d an
d su
btra
ct v
ecto
rs
m
ultip
ly a
vec
tor b
y a
scal
ar
Ty
pes
of v
ecto
rs
Ve
ctor
ope
ratio
ns
U
sing
sta
ndar
d no
tatio
n of
vec
tors
(𝑥𝑥 𝑦𝑦 𝑧𝑧), x
i+yj
+zk,
𝐴𝐴𝐴𝐴→ , a
D
istin
guis
hing
bet
wee
n po
sitio
nand
fre
e ve
ctor
s
In
terp
retin
g op
erat
ions
in g
eom
etric
al
term
s
C
ompu
ting
the
mag
nitu
de o
f vec
tors
in
thre
e di
men
sion
s
Ad
ding
and
sub
tract
ing
vect
ors
Fi
ndin
g a
prod
uct o
f a v
ecto
r by
a sc
alar
Solv
ing
prob
lem
s in
volv
ing
vect
or
oper
atio
ns
IC
T to
ols
Mat
hem
atic
al
mod
els
Envi
ronm
ent
G
eo-b
oard
Rel
evan
t tex
ts
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
23
TOPI
C 6
:FU
NC
TIO
NS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Func
tions
defin
e a
func
tion
de
fine
dom
ain
and
rang
e of
a
func
tion
use
func
tiona
l not
atio
n
sim
plify
a c
ompo
site
func
tion
D
efin
ition
of a
func
tion
D
omai
n an
d ra
nge
Com
posi
te fu
nctio
n
Id
entif
ying
and
def
inin
g fu
nctio
ns
D
iscu
ssin
g th
e do
mai
n an
d th
e ra
nge
U
sing
func
tiona
l not
atio
ns
Si
mpl
ifyin
g co
mpo
site
func
tions
IC
T to
ols
Rel
evan
t tex
ts
11
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
7: S
EQU
ENC
ES
TOPI
C 8
: BIN
OM
IAL
EXPA
NSI
ON
TOPI
C 9
: TR
IGO
NO
MET
RY
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
25
TOPI
C 8
:BIN
OM
IAL
EXPA
NSI
ON
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Bino
mia
l exp
ansi
on
To
be
cove
red
in fo
rm 4
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
26
TOPI
C 9
: TR
IGO
NO
MET
RY
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Plan
e Tr
igon
omet
ry
us
e si
ne a
nd c
osin
e ru
les
to s
olve
pr
oble
ms
use
the
form
ula 𝐴𝐴
=1 2
𝑎𝑎𝑎𝑎s
in𝐶𝐶
to
find
the
area
of a
tria
ngle
Si
ne a
nd c
osin
e ru
les
Ar
ea o
f a tr
iang
le
D
eriv
ing
form
ulae
for t
he s
ine
and
cosi
ne ru
les
So
lvin
g pr
oble
ms
usin
g th
e si
ne a
nd
cosi
ne ru
les
D
eriv
ing
the
form
ula
for f
indi
ng a
rea
of a
tria
ngle
Solv
ing
prob
lem
s in
volv
ing
area
of a
tri
angl
e
IC
T to
ols
Rel
evan
t tex
ts
Trig
onom
etric
al
func
tions
find
the
trigo
nom
etric
al ra
tios
of
angl
es o
f any
siz
e
use
the
exac
t val
ues
of th
e tri
gono
met
rical
ratio
s of
spe
cial
an
gles
in a
var
iety
of s
ituat
ions
Tr
igon
omet
rical
fu
nctio
ns fo
r ang
les
of
any
size
Exac
t val
ues
of s
ine,
co
sine
and
tang
ent o
f sp
ecia
l ang
les
C
ompu
ting
the
trigo
nom
etric
al ra
tios
of a
ngle
s of
any
siz
e
Cal
cula
ting
the
exac
t val
ues
of th
e si
ne, c
osin
e an
d ta
ngen
t of 0
°, 30
°, 45
° ,60
°, 90
° in
a va
riety
of s
ituat
ions
IC
T to
ols
Rel
evan
t tex
ts
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
15
TOPI
C 6
:FU
NC
TIO
NS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e,
Attit
udes
}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Func
tions
defin
e a
func
tion
de
fine
dom
ain
and
rang
e of
a
func
tion
use
func
tiona
l not
atio
n
sim
plify
a c
ompo
site
func
tion
D
efin
ition
of a
fu
nctio
n
Dom
ain
and
rang
e
C
ompo
site
func
tion
Id
entif
ying
and
def
inin
g fu
nctio
ns
D
iscu
ssin
g th
e do
mai
n an
d th
e ra
nge
U
sing
func
tiona
l not
atio
ns
Si
mpl
ifyin
g co
mpo
site
fu
nctio
ns
IC
T to
ols
Rel
evan
t tex
ts
TOPI
C 7
: SEQ
UEN
CES
SU
B T
OPI
C
OB
JEC
TIVE
S
Lear
ners
sho
uld
be a
ble
to:
CO
NTE
NT:
{Ski
lls,
Kno
wle
dge,
Atti
tude
s}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Sequ
ence
s
de
fine
a se
quen
ce
lis
t the
ele
men
ts o
f a s
eque
nce
Def
initi
on o
f a
sequ
ence
Exam
ples
of
sequ
ence
s
D
iscu
ssin
g se
quen
ces
Out
linin
g el
emen
ts o
f seq
uenc
es
IC
T to
ols
Rel
evan
t tex
ts
TOPI
C 8
:BIN
OM
IAL
EXPA
NSI
ON
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e,
Attit
udes
}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Bino
mia
l ex
pans
ion
To b
e co
vere
d in
form
4
12
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
10:
LO
GA
RIT
HM
IC A
ND
EXP
ON
ENTI
AL
FUN
CTI
ON
S
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
TOPI
C 1
2: IN
TEG
RAT
ION
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
28
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Diff
eren
tiatio
n
fin
d th
e gr
adie
nt o
f a c
urve
at a
poi
nt
usin
g th
e ta
ngen
t
diffe
rent
iate
line
ar a
nd q
uadr
atic
ex
pres
sion
s fro
m fi
rst p
rinci
ples
find
the
deriv
ativ
e of
func
tions
of t
he
form
axn w
here
n is
a ra
tiona
l num
ber
di
ffere
ntia
te a
pol
ynom
ial
G
radi
ent o
f a c
urve
at a
po
int
D
eriv
ed fu
nctio
n of
the
form
axn
D
eriv
ativ
e of
a s
um
C
alcu
latin
g th
e gr
adie
nt o
f a c
urve
at
a g
iven
poi
nt u
sing
tang
ents
Dis
cuss
ing
situ
atio
ns in
life
whe
re
grad
ient
s of
cur
ves
are
impo
rtant
Diff
eren
tiatin
g lin
ear a
nd q
uadr
atic
ex
pres
sion
s fro
m fi
rst p
rinci
ples
Diff
eren
tiatin
g fu
nctio
ns o
f the
form
ax
n usi
ng th
e fo
rmul
a
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
16
TOPI
C 9
: TR
IGO
NO
MET
RY
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e,
Attit
udes
}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Plan
e Tr
igon
omet
ry
us
e si
ne a
nd c
osin
e ru
les
to
solv
e pr
oble
ms
use
the
form
ula 𝐴𝐴
=1 2
𝑎𝑎𝑎𝑎s
in𝐶𝐶
to
find
the
area
of a
tria
ngle
Si
ne a
nd c
osin
e ru
les
Ar
ea o
f a tr
iang
le
D
eriv
ing
form
ulae
for t
he s
ine
and
cosi
ne ru
les
So
lvin
g pr
oble
ms
usin
g th
e si
ne a
nd c
osin
e ru
les
D
eriv
ing
the
form
ula
for f
indi
ng
area
of a
tria
ngle
Solv
ing
prob
lem
s in
volv
ing
area
of a
tria
ngle
IC
T to
ols
Rel
evan
t tex
ts
Trig
onom
etric
al
func
tions
find
the
trigo
nom
etric
al ra
tios
of a
ngle
s of
any
siz
e
use
the
exac
t val
ues
of th
e tri
gono
met
rical
ratio
s of
sp
ecia
l ang
les
in a
var
iety
of
situ
atio
ns
Tr
igon
omet
rical
fu
nctio
ns fo
r ang
les
of a
ny s
ize
Exac
t val
ues
of
sine
, cos
ine
and
tang
ent o
f spe
cial
an
gles
C
ompu
ting
the
trigo
nom
etric
al
ratio
s of
ang
les
of a
ny s
ize
C
alcu
latin
g th
e ex
act v
alue
s of
th
e si
ne, c
osin
e an
d ta
ngen
t of
0°, 3
0°, 4
5° ,6
0°, 9
0° in
a
varie
ty o
f situ
atio
ns
IC
T to
ols
Rel
evan
t tex
ts
TOPI
C 1
0: L
OG
ARIT
HM
IC A
ND
EXP
ON
ENTI
AL F
UN
CTI
ON
S SU
B T
OPI
C
OB
JEC
TIVE
S
Lear
ners
sho
uld
be a
ble
to:
CO
NTE
NT:
{Ski
lls,
Kno
wle
dge,
Atti
tude
s}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Loga
rithm
s
st
ate
the
law
s of
loga
rithm
s
use
the
law
s of
loga
rithm
s in
sol
ving
pr
oble
ms
iden
tify
the
rela
tions
hips
bet
wee
n
La
ws
of lo
garit
hms
Lo
garit
hms
and
indi
ces
Ex
plor
ing
the
law
s of
loga
rithm
s
Ap
plyi
ng la
ws
of lo
garit
hms
in s
olvi
ng
prob
lem
s
Ex
pres
sing
loga
rithm
s in
inde
x fo
rm
IC
T to
ols
Rel
evan
t tex
ts
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
17
loga
rithm
s an
d in
dice
s
and
vice
ver
sa
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Diff
eren
tiatio
n
fin
d th
e gr
adie
nt o
f a c
urve
at a
po
int u
sing
the
tang
ent
di
ffere
ntia
te li
near
and
qua
drat
ic
expr
essi
ons
from
firs
t prin
cipl
es
fin
d th
e de
rivat
ive
of fu
nctio
ns o
f th
e fo
rm a
xn whe
re n
is a
ratio
nal
num
ber
di
ffere
ntia
te a
pol
ynom
ial
G
radi
ent o
f a c
urve
at
a p
oint
Der
ived
func
tion
of
the
form
axn
D
eriv
ativ
e of
a s
um
C
alcu
latin
g th
e gr
adie
nt o
f a
curv
e at
a g
iven
poi
nt u
sing
ta
ngen
ts
D
iscu
ssin
g si
tuat
ions
in li
fe
whe
re g
radi
ents
of c
urve
s ar
e im
porta
nt
D
iffer
entia
ting
linea
r and
qu
adra
tic e
xpre
ssio
ns fr
om
first
prin
cipl
es
D
iffer
entia
ting
func
tions
of
the
form
axn u
sing
the
form
ula
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
TOPI
C 1
2: IN
TEG
RAT
ION
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Inte
grat
ion
re
cogn
ise
inde
finite
inte
grat
ion
as th
e re
vers
e pr
oces
s of
diff
eren
tiatio
n
in
tegr
ate
func
tions
of t
he fo
rm a
xn w
here
n is
ratio
nal
in
tegr
ate
poly
nom
ials
In
defin
ite in
tegr
atio
n as
the
reve
rse
proc
ess
of
diffe
rent
iatio
n
In
tegr
atio
n of
func
tions
of
the
form
axn
In
tegr
atio
n of
a p
olyn
omia
l
D
iscu
ssin
g in
defin
ite in
tegr
atio
n as
th
e re
vers
e pr
oces
s of
di
ffere
ntia
tion
Pe
rform
ing
inte
grat
ion
of fu
nctio
ns
of th
e fo
rm a
xn whe
re n
is ra
tiona
l
Com
putin
g in
defin
ite in
tegr
als
of
poly
nom
ials
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
13
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
13:
NU
MER
ICA
L M
ETH
OD
S
8.2
FO
RM
4C
OM
PETE
NC
Y M
ATR
IX
TOPI
C 1
: IN
DIC
ES A
ND
IRR
ATIO
NA
L N
UM
BER
S
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
30
TOPI
C 1
3: N
UM
ERIC
AL M
ETH
OD
S
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, Kno
wle
dge,
At
titud
es}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Itera
tive
met
hods
To b
e co
vere
d in
form
4
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
31
FORM
FO
UR
(4) S
YLLA
BU
S
8.0
CO
MPE
TEN
CY
MAT
RIX
: FO
RM
4 S
YLLA
BUS
TOPI
C 1
: IN
DIC
ES A
ND
IRR
ATIO
NAL
NU
MB
ERS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Indi
ces
Cov
ered
in fo
rm 3
Irrat
iona
l num
bers
14
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
2: P
OLY
NO
MIA
LS
TOPI
C 3
: ID
ENTI
TIES
, EQ
UAT
ION
S A
ND
INEQ
UA
LITI
ES
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
32
TOPI
C 2
: PO
LYN
OM
IALS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Poly
nom
ials
mul
tiply
pol
ynom
ials
divi
de o
ne p
olyn
omia
l by
anot
her
us
e th
e Fa
ctor
The
orem
to fa
ctor
ise
poly
nom
ials
solv
e cu
bic
equa
tions
usi
ng th
e Fa
ctor
The
orem
use
Fact
or T
heor
em to
eva
luat
e un
know
n co
effic
ient
s
M
ultip
licat
ion
Div
isio
n
Fa
ctor
The
orem
Solv
ing
equa
tions
D
eter
min
ing
the
prod
uct o
f po
lyno
mia
ls
U
sing
long
div
isio
n to
find
the
quot
ient
an
d re
mai
nder
Der
ivin
g th
e Fa
ctor
theo
rem
Usi
ng th
e Fa
ctor
The
orem
to
fact
oris
e po
lyno
mia
ls
So
lvin
g cu
bic
equa
tions
usi
ng th
e Fa
ctor
The
orem
Eval
uatin
g un
know
n co
effic
ient
s us
ing
the
Fact
or T
heor
em
IC
T to
ols
Rel
evan
t tex
ts
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
20
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e,
Attit
udes
}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Poly
nom
ials
mul
tiply
pol
ynom
ials
divi
de o
ne p
olyn
omia
l by
anot
her
us
e th
e Fa
ctor
The
orem
to
fact
oris
e po
lyno
mia
ls
so
lve
cubi
c eq
uatio
ns u
sing
th
e Fa
ctor
The
orem
use
Fact
or T
heor
em to
ev
alua
te u
nkno
wn
coef
ficie
nts
M
ultip
licat
ion
Div
isio
n
Fa
ctor
The
orem
Solv
ing
equa
tions
D
eter
min
ing
the
prod
uct o
f po
lyno
mia
ls
U
sing
long
div
isio
n to
find
the
quot
ient
and
rem
aind
er
D
eriv
ing
the
Fact
or th
eore
m
U
sing
the
Fact
or T
heor
em to
fa
ctor
ise
poly
nom
ials
Solv
ing
cubi
c eq
uatio
ns u
sing
th
e Fa
ctor
The
orem
Eval
uatin
g un
know
n co
effic
ient
s us
ing
the
Fact
or
Theo
rem
IC
T to
ols
Rel
evan
t tex
ts
TOPI
C 3
: ID
ENTI
TIES
, EQ
UAT
ION
S AN
D IN
EQU
ALIT
IES
SU
B T
OPI
C
OB
JEC
TIVE
S
Lear
ners
sho
uld
be a
ble
to:
CO
NTE
NT:
{Ski
lls,
Kno
wle
dge,
Atti
tude
s}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Iden
titie
s an
d eq
uatio
ns
ex
pres
s ax
2 + b
x +
c in
the
form
d(
x+e)
2 +f
de
rive
the
quad
ratic
form
ula
solv
e qu
adra
tic e
quat
ions
by
com
plet
ing
the
squa
re
so
lve
sim
ulta
neou
s eq
uatio
ns b
y su
bstit
utio
n
C
ompl
etin
g th
e sq
uare
Sim
ulta
neou
s eq
uatio
ns
Ex
plor
ing
way
s of
exp
ress
ing
ax2
+ bx
+ c
in th
e fo
rm d
(x+e
)2 +f
C
ompl
etin
g th
e sq
uare
to d
eriv
e th
e qu
adra
tic fo
rmul
a
Solv
ing
quad
ratic
equ
atio
ns b
y co
mpl
etin
g th
e sq
uare
Solv
ing
sim
ulta
neou
s eq
uatio
ns (o
ne
linea
r and
one
impl
icit)
by
subs
titut
ion
IC
T to
ols
Rel
evan
t tex
ts
15
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
4: G
RA
PHS
AN
D C
OO
RD
INAT
E G
EOM
ETRY
TOPI
C 5
: VEC
TOR
S
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
34
TOPI
C 4
:GR
APH
S AN
D C
OO
RD
INAT
E G
EOM
ETR
Y
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Gra
phs
sket
ch g
raph
s of
the
form
𝑦𝑦=𝑘𝑘𝑥𝑥
𝑛𝑛
expl
ain
the
geom
etric
al e
ffect
of t
he
valu
e of
k o
n th
e sh
ape
of th
e gr
aph
of 𝑦𝑦
=𝑘𝑘𝑥𝑥
𝑛𝑛
G
raph
s of
𝑦𝑦=𝑘𝑘𝑥𝑥
𝑛𝑛
Sket
chin
g th
e st
anda
rd c
urve
s w
here
n
and
k ar
e ra
tiona
l
Dis
cuss
ing
the
geom
etric
al e
ffect
of
the
valu
e of
k o
n th
e sh
ape
of th
e gr
aph
for a
giv
en v
alue
of n
IC
T to
ols
Rel
evan
t tex
ts
G
eo-b
oard
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
35
TOPI
C 5
:VEC
TOR
S
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Vect
ors
in th
ree
dim
ensi
ons
ca
lcul
ate
unit
vect
ors
defin
e th
e sc
alar
pro
duct
use
the
scal
ar p
rodu
ct to
det
erm
ine
the
angl
e be
twee
n ve
ctor
s
id
entif
y ve
ctor
pro
perti
es o
f qu
adril
ater
als
solv
e pr
oble
ms
invo
lvin
g pe
rpen
dicu
lar v
ecto
rs
ca
lcul
ate
area
s of
tria
ngle
s an
d pa
ralle
logr
ams
U
nit v
ecto
rs
Sc
alar
pro
duct
Vect
or p
rope
rties
of
plan
e sh
apes
Area
s of
tria
ngle
s an
d pa
ralle
logr
ams
C
ompu
ting
unit
vect
ors
Dis
cuss
ing
the
scal
ar p
rodu
ct
D
eter
min
ing
the
angl
e be
twee
n ve
ctor
s
Ex
plor
ing
vect
or p
rope
rties
of
quad
rilat
eral
s
So
lvin
g pr
oble
ms
invo
lvin
g pe
rpen
dicu
lar v
ecto
rs
C
ompu
ting
area
s of
tria
ngle
s an
d pa
ralle
logr
ams
IC
T to
ols
Mat
hem
atic
al
mod
els
Envi
ronm
ent
16
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
6: F
UN
CTI
ON
S
TOPI
C 7
: SEQ
UEN
CES
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
36
TOPI
C 6
: FU
NC
TIO
NS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Func
tions
defin
e a
one-
one
func
tion
re
stric
t the
dom
ain
to g
et a
one
-one
fu
nctio
n
sk
etch
the
grap
h of
a fu
nctio
n fo
r a g
iven
do
mai
n
de
fine
the
inve
rse
of a
func
tion
fin
d th
e in
vers
e of
a g
iven
func
tion
illust
rate
gra
phic
ally
the
rela
tions
hip
betw
een
a fu
nctio
n an
d its
inve
rse
O
ne-o
ne fu
nctio
n
Inve
rse
of a
func
tion
G
raph
s of
func
tions
D
iscu
ssin
g on
e-on
e fu
nctio
ns
Sk
etch
ing
grap
hs o
f fun
ctio
ns fo
r a
give
n do
mai
n
Dis
cuss
ing
the
inve
rse
of a
func
tion
Det
erm
inin
g th
e ra
nge
of fu
nctio
ns
D
eter
min
ing
the
inve
rse
of a
giv
en
func
tion
excl
udin
g in
vers
es o
f qu
adra
tic fu
nctio
ns
Ill
ustra
ting
grap
hica
lly th
e re
latio
nshi
p be
twee
n a
func
tion
and
its in
vers
e
IC
T to
ols
Rel
evan
t tex
ts
G
eo-b
oard
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
37
TOPI
C 7
: SEQ
UEN
CES
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D A
CTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Sequ
ence
s
de
rive
the
form
ulas
for t
he g
ener
al
term
s of
the
AP a
nd G
P
use
the
form
ula
for t
he n
th te
rm o
f an
AP a
nd G
P
deriv
e th
e fo
rmul
a fo
r the
sum
of t
he
first
n te
rms
of a
n AP
and
GP
and
use
it to
sol
ve p
robl
ems
dist
ingu
ish
betw
een
APs
and
GPs
Ar
ithm
etic
pro
gres
sion
Geo
met
ric p
rogr
essi
on
Ex
plor
ing
way
s of
find
ing
the
form
ula
for t
he g
ener
al te
rm o
f an
AP a
nd a
G
P
Solv
ing
prob
lem
s us
ing
the
form
ula
for t
he n
th te
rm o
f an
AP a
nd a
GP
Expl
orin
g w
ays
of fi
ndin
g th
e fo
rmul
ae o
f the
sum
of
the
first
n
term
s of
an
AP a
nd a
GP
and
solv
ing
prob
lem
s
Diff
eren
tiatin
g AP
s fro
m G
Ps
D
iscu
ssin
g ap
plic
atio
ns o
f APs
and
G
Ps in
life
IC
T to
ols
Rel
evan
t tex
ts
17
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
8: B
INO
MIA
L EX
PAN
SIO
N
TOPI
C 9
: TR
IGO
NO
MET
RY
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
38
TOPI
C 8
: BIN
OM
IAL
EXPA
NSI
ON
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Bino
mia
l exp
ansi
on
co
nstru
ct a
Pas
cal’s
Tria
ngle
expa
nd (𝑎𝑎
+𝑏𝑏)
n usi
ng P
asca
l’s
Tria
ngle
solv
e pr
oble
ms
invo
lvin
g ex
pans
ion
of (𝑎𝑎
+𝑏𝑏)
n
Pa
scal
’s T
riang
le
Ex
pans
ion
of (𝑎𝑎
+𝑏𝑏)
n whe
re n
is a
pos
itive
in
tege
r
C
onst
ruct
ing
Pasc
al’s
Tria
ngle
Mak
ing
use
of th
e Pa
scal
’s T
riang
le
to e
xpan
d (𝑎𝑎
+𝑏𝑏)
n whe
re n
is a
po
sitiv
e in
tege
r
Solv
ing
prob
lem
s in
volv
ing
expa
nsio
n of
(𝑎𝑎+𝑏𝑏)
n
R
elev
ant t
exts
ICT
tool
s
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
39
TOPI
C 9
: TR
IGO
NO
MET
RY
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Plan
e Tr
igon
omet
ry
de
fine
a ra
dian
use
the
corre
ct ra
dian
not
atio
n
co
nver
t deg
rees
to ra
dian
s an
d ra
dian
s to
deg
rees
find
the
leng
th o
f an
arc
find
area
of a
sec
tor
and
a se
gmen
t
solv
e pr
oble
ms
invo
lvin
g le
ngth
of
arcs
, are
as o
f sec
tors
and
seg
men
ts
R
adia
ns
Le
ngth
of a
n ar
c
Area
of a
sec
tor
Ar
ea o
f a s
egm
ent
D
iscu
ssin
g ra
dian
s an
d de
gree
s
and
thei
r rel
atio
nshi
p
U
sing
the
corre
ct ra
dian
not
atio
n
C
onve
rting
deg
rees
to ra
dian
s an
d ra
dian
s to
deg
rees
Der
ivin
g an
d us
ing
the
form
ulae
for
leng
th o
f an
arc
D
eriv
ing
and
usin
g th
e fo
rmul
ae fo
r th
e ar
ea o
f a s
ecto
r and
seg
men
t
Solv
ing
prob
lem
s in
volv
ing
leng
th o
f ar
cs, a
reas
of s
ecto
rs a
nd
segm
ents
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
Geo
-boa
rd
G
eom
etric
al
inst
rum
ents
Trig
onom
etric
al
func
tions
use
the
nota
tion
sin-1
x, ta
n-1x
and
cos-1
x to
sol
ve p
robl
ems
Solv
e tri
gono
met
rical
equ
atio
ns
Eq
uatio
ns
D
iscu
ssin
g th
e no
tatio
n si
n-1x,
tan-1
x an
d co
s-1x
Fi
ndin
g al
l the
sol
utio
ns, w
ithin
a
spec
ified
inte
rval
of t
he e
quat
ions
si
n(kx
)=c,
cos
(kx)
=c a
nd ta
n(kx
)=c
Ap
plyi
ng tr
igon
omet
rical
equ
atio
ns
in s
olvi
ng li
fe p
robl
ems
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
24
Lear
ners
sho
uld
be a
ble
to:
Kno
wle
dge,
Atti
tude
s}
ACTI
VITI
ES
RES
OU
RC
ES
Bino
mia
l exp
ansi
on
co
nstru
ct a
Pas
cal’s
Tria
ngle
expa
nd (𝑎𝑎
+𝑏𝑏)
n usi
ng P
asca
l’s
Tria
ngle
solv
e pr
oble
ms
invo
lvin
g ex
pans
ion
of ( 𝑎𝑎
+𝑏𝑏)
n
Pa
scal
’s T
riang
le
Ex
pans
ion
of (𝑎𝑎
+𝑏𝑏)
n
whe
re n
is a
pos
itive
in
tege
r
C
onst
ruct
ing
Pasc
al’s
Tria
ngle
Mak
ing
use
of th
e Pa
scal
’s T
riang
le
to e
xpan
d (𝑎𝑎
+𝑏𝑏)
n whe
re n
is a
po
sitiv
e in
tege
r
Solv
ing
prob
lem
s in
volv
ing
expa
nsio
n of
(𝑎𝑎+𝑏𝑏)
n
R
elev
ant t
exts
ICT
tool
s
TOPI
C 9
: TR
IGO
NO
MET
RY
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Plan
e Tr
igon
omet
ry
de
fine
a ra
dian
use
the
corre
ct ra
dian
not
atio
n
co
nver
t deg
rees
to ra
dian
s an
d ra
dian
s to
deg
rees
find
the
leng
th o
f an
arc
find
area
of a
sec
tor
and
a se
gmen
t
solv
e pr
oble
ms
invo
lvin
g le
ngth
of
arc
s, a
reas
of s
ecto
rs a
nd
segm
ents
R
adia
ns
Le
ngth
of a
n ar
c
Area
of a
sec
tor
Ar
ea o
f a s
egm
ent
D
iscu
ssin
g ra
dian
s an
d de
gree
s a
nd th
eir
rela
tions
hip
Usi
ng th
e co
rrect
radi
an
nota
tion
Con
verti
ng d
egre
es to
ra
dian
s an
d ra
dian
s to
de
gree
s
Der
ivin
g an
d us
ing
the
form
ulae
for l
engt
h of
an
arc
D
eriv
ing
and
usin
g th
e fo
rmul
ae fo
r the
are
a of
a
sect
or a
nd s
egm
ent
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
Geo
-boa
rd
G
eom
etric
al
inst
rum
ents
18
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
10:
LO
GA
RIT
HM
IC A
ND
EXP
ON
ENTI
AL
FUN
CTI
ON
S
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
40
TOPI
C 1
0: L
OG
ARIT
HMIC
AN
D E
XPO
NEN
TIAL
FU
NC
TIO
NS
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, K
now
ledg
e, A
ttitu
des}
SU
GG
ESTE
D N
OTE
S AN
D
ACTI
VITI
ES
SUG
GES
TED
R
ESO
UR
CES
Loga
rithm
s
de
fine
the
natu
ral l
ogar
ithm
sket
ch th
e gr
aph
of th
e fo
rm
y=ln
(ax+
b)
us
e lo
garit
hms
to s
olve
equ
atio
ns o
f th
e fo
rm a
x =
b
N
atur
al lo
garit
hms
Eq
uatio
ns o
f the
form
a x
= b
D
iscu
ssin
g th
e na
tura
l log
arith
ms
in
rela
tion
to lo
garit
hms
in g
ener
al
Sk
etch
ing
the
grap
hs o
f the
form
y=
ln(a
x+b)
Solv
ing
equa
tions
of t
he fo
rm a
x =
b
usin
g lo
garit
hms
IC
T to
ols
Rel
evan
t tex
ts
G
eo-b
oard
Expo
nent
ial
func
tions
expl
ain
the
conc
ept o
f exp
onen
tial
grow
th a
nd d
ecay
sket
ch th
e gr
aph
of th
e ex
pone
ntia
l fu
nctio
n
solv
e eq
uatio
ns in
volv
ing
expo
nent
ial g
row
th a
nd d
ecay
form
ulat
e eq
uatio
ns in
volv
ing
expo
nent
ial g
row
th a
nd d
ecay
Ex
pone
ntia
l gro
wth
and
de
cay
D
iscu
ssin
g th
e co
ncep
t of
expo
nent
ial g
row
th a
nd d
ecay
Sket
chin
g th
e gr
aph
of th
e ex
pone
ntia
l fun
ctio
n an
d co
mpa
re
with
the
loga
rithm
ic fu
nctio
n
Fo
rmul
atin
g eq
uatio
ns in
volv
ing
expo
nent
ial g
row
th a
nd d
ecay
Solv
ing
equa
tions
invo
lvin
g ex
pone
ntia
l gro
wth
and
dec
ay
IC
T to
ols
Rel
evan
t tex
ts
G
eo-b
oard
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
41
TOPI
C 1
1: D
IFFE
REN
TIAT
ION
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, Kno
wle
dge,
At
titud
es}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Diff
eren
tiatio
n
fin
d th
e eq
uatio
n of
a ta
ngen
t and
a
norm
al to
qua
drat
ic a
nd c
ubic
cur
ves
dete
rmin
e st
atio
nary
poi
nts
and
thei
r na
ture
find
the
rate
of c
hang
e of
one
va
riabl
e w
ith re
spec
t to
anot
her
so
lve
prob
lem
s in
volv
ing
rate
s of
ch
ange
Ap
plic
atio
n of
diff
eren
tiatio
n to
gra
dien
ts, t
ange
nts
and
norm
als,
sta
tiona
ry p
oint
s,
rate
s of
cha
nge,
vel
ocity
and
ac
cele
ratio
n
D
eter
min
ing
equa
tions
of
tang
ents
and
nor
mal
s to
qu
adra
tic a
nd c
ubic
cur
ves
Dis
cuss
ing
the
natu
re o
f, an
d so
lvin
g pr
oble
ms
invo
lvin
g,
stat
iona
ry p
oint
s
Cal
cula
ting
the
rate
of c
hang
e of
on
e va
riabl
e w
ith re
spec
t to
anot
her
So
lvin
g pr
oble
ms
invo
lvin
g ra
tes
of c
hang
e in
life
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
19
Pure Mathematics Syllabus Forms 3 - 4TO
PIC
12:
INTE
GR
ATIO
N
TOPI
C 1
3: N
UM
ERIC
AL
MET
HO
DS
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
42
TOPI
C 1
2: IN
TEG
RAT
ION
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, Kno
wle
dge,
At
titud
es}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Inte
grat
ion
co
mpu
te a
rea
boun
ded
by
acur
vean
d a
linep
aral
lel t
o th
e co
ordi
nate
axe
s
ca
lcul
atet
he v
olum
e of
revo
lutio
n ab
out o
ne o
f the
axe
s
Ar
ea
Vo
lum
e
Expl
orin
g w
ays
of fi
ndin
g ar
ea
boun
ded
by a
cur
ve a
nd a
line
pa
ralle
l to
the
coor
dina
te a
xes
Expl
orin
g w
ays
of fi
ndin
g th
e vo
lum
e of
revo
lutio
n ab
out o
ne
of th
e ax
es
So
lvin
g pr
oble
ms
invo
lvin
g us
e of
inte
grat
ion
in d
eter
min
ing
area
s an
d vo
lum
es
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
Pure
Mat
hem
atics
Syl
labu
s For
m 3
– 4
201
6
43
TOPI
C 1
3: N
UM
ERIC
AL M
ETH
OD
S
SUB
TO
PIC
O
BJE
CTI
VES
Le
arne
rs s
houl
d be
abl
e to
: C
ON
TEN
T: {S
kills
, Kno
wle
dge,
At
titud
es}
SUG
GES
TED
NO
TES
AND
AC
TIVI
TIES
SU
GG
ESTE
D
RES
OU
RC
ES
Num
eric
al m
etho
ds
lo
cate
the
posi
tion
of ro
ots
by
sign
cha
nge
solv
e eq
uatio
ns b
y th
e bi
sect
ion
met
hod
us
e si
mpl
e ite
rativ
e pr
oced
ures
and
the
New
ton-
Rap
hson
met
hod
to s
olve
eq
uatio
ns
es
timat
e ar
eas
unde
r cur
ves
usin
g th
e Tr
apez
ium
Rul
e
Si
mpl
e ite
rativ
e pr
oced
ures
New
ton-
Rap
hson
met
hod
Trap
eziu
m R
ule
D
eter
min
ing
the
exis
tenc
e of
ro
ots
with
in a
n in
terv
al
U
sing
the
bise
ctio
n m
etho
dto
solv
e eq
uatio
ns to
a s
peci
fic
degr
ee o
f acc
urac
y
So
lvin
g eq
uatio
ns u
sing
sim
ple
itera
tive
proc
edur
es a
nd th
e N
ewto
n-R
aphs
on m
etho
d
Det
erm
inin
gest
imat
es o
f are
a un
der c
urve
s an
d re
late
d ar
eas
in li
fe b
y th
e Tr
apez
ium
Rul
e
IC
T to
ols
Rel
evan
t tex
ts
En
viro
nmen
t
Num
eric
al m
etho
ds•
loca
te th
e po
sitio
n of
root
s by
sig
n ch
ange
•
solv
e eq
uatio
ns b
y th
e bi
sect
ion
met
hod
• us
e si
mpl
e ite
rativ
e pr
oced
ures
an
d th
e N
ewto
n-R
aphs
on m
etho
d to
sol
ve e
quat
ions
•
estim
ate
area
s un
der c
urve
s us
ing
the
Trap
eziu
m R
ule
• Si
mpl
e ite
rativ
e pr
oced
ures
•
New
ton-
Rap
hson
met
hod
• Tr
apez
ium
Rul
e
• D
eter
min
ing
the
exis
tenc
e of
ro
ots
with
in a
n in
terv
al
• U
sing
the
bise
ctio
n m
etho
d to
so
lve
equa
tions
to a
spe
cific
de
gree
of a
ccur
acy
• So
lvin
g eq
uatio
ns u
sing
sim
ple
itera
tive
proc
edur
es a
nd th
e N
ewto
n-R
aphs
on m
etho
d•
Det
erm
inin
g es
timat
es o
f are
a un
der c
urve
s an
d re
late
d ar
eas
in
life
by th
e Tr
apez
ium
Rul
e
• IC
T to
ols
• R
elev
ant t
exts
• En
viro
nmen
t
20
Pure Mathematics Syllabus Forms 3 - 4
9.0 ASSESSMENT
(a) ASSESSMENT OBJECTIVES
(b) SCHEME OF ASSESSMENT
The assessment will test candidate’s ability to:-
• use Mathematical symbols, terms and definitions correctly in problem solving• sketch graphs accurately • use appropriate formulae,algorithms and strategies, to solve routine and non-routine problems in Pure Mathe-
matics• demonstrate the appropriate and accurate use of ICT tools in problem solving • translate Mathematical information from one form to another accurately • demonstrate an appreciation of Mathematical concepts and processes • demonstrate an ability to solve problems systematically• apply Mathematical reasoning and communicate mathematical ideas clearly• model information from other forms to Mathematical form and vice versa • conduct research projects including those related to enterprise
The Form 3 - 4Pure Mathematics assessment will be based on 30% Continuous Assessment and 70% Summative
Assessment.
The syllabus’ scheme of assessment caters for all learners and does not condone direct or indirect discrimination.Arrangements, accommodations and modifications must be visible in 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 candidates 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 (transitory or permanent) may be eligible to receive an award based on the assessment they would have taken
Continuous AssessmentContinuous assessment will consists of topic tasks, written tests and end of term examinations:i) Topic Tasks These are activities that teachers use in their day to day teaching. These may include projects, assignments and team work activities.
ii) Written Tests
These are tests set by the teacher to assess the concepts covered during a given period of up to a month. The tests should consist of short structured questions as well as long structured questions.
iii) End of term examinationsThese are comprehensive tests of the whole term’s or year’s work. These can be set at school/district/provincial level.
Summary of Continuous Assessment TasksFrom term one to five, candidates are expected to have done at least the following recorded tasks per term:
• 1 Topic task• 1 Written test• 1 End of term test
21
Pure Mathematics Syllabus Forms 3 - 4
Detailed Continuous Assessment Tasks Table
Pure Mathematics Syllabus Form 3 – 4 2016 25
iii) End of term examinations
These are comprehensive tests of the whole term’s or year’s work. These can be set at school/district/provincial level.
Summary of Continuous Assessment Tasks
From term one to five, candidates are expected to have done at least the following recorded tasks per term:
1 Topic task 1 Written test 1 End of term test
Detailed Continuous Assessment Tasks Table
Term Number of Topic Tasks
Number of Written Tests
Number of End Of Term Tests
Total
1 1 1 1
2 1 1 1
3 1 1 1
4 1 1 1
5 1 1 1
Weighting 25% 25% 50% 100%
Actual Weight 7.5% 7.5% 15% 30%
Comment: Term 6 is for the National Examination
c) Specification Grid
Pure Mathematics Syllabus Form 3 – 4 2016 26
(c) Specification Grid
Specification grid for continuous assessment
Component Skills
Topic Tasks Written Tests End of Term
Skill 1
Knowledge
Comprehension
30% 30% 30%
Skill 2
Application
Analysis
50% 50% 50%
Skill 3
Synthesis
Evaluation
20% 20% 20%
Total
100%
100%
100%
Actual weighting
7.5% 7.5% 15%
Summative Assessment
The examination will consist of 2 papers: paper 1 and paper 2, each to be written in 2½ hours
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Pure Mathematics Syllabus Forms 3 - 4
P1 P2 TotalWeighting 50% 50% 100%Actual weighting 35% 35% 70%Type of paper Approximately 15 Short Answer
Questions, where candidates anwer all questions
16 Questions where candidates answer any 10, each question carrying 10 marks
Marks 100 100
Summative Assessment
The examination will consist of 2 papers: paper 1 and paper 2, each to be written in 2½ hours
Specification Grid for Summative Assessment
Pure Mathematics Syllabus Form 3 – 4 2016 27
The tables below shows the information on weighting and types of papers to be offered.
P1 P2 Total
Weighting 50% 50% 100%
Actual weighting
35% 35% 70%
Type of Paper Approximately 15 Short Answer Questions, where candidates answer all questions
16questions where candidates answer any 10, each question carrying 10 marks
Marks 100 100
Specification Grid for Summative Assessment
P1 P2 Total
Pure Mathematics Syllabus Form 3 – 4 2016 28
Skill 1
Knowledge &
Comprehension
50% 30% 80%
Skill 2
Application &
Analysis
40% 50% 90%
Skill 3
Synthesis &
Evaluation
10% 20% 30%
Total 100% 100% 200%
Weighting 50% 50% 100%
(d) Assessment Model
Learners will be assessed using both continuous and summative assessments.
Assessment of learner performance in Pure Mathematics
100%
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Pure Mathematics Syllabus Forms 3 - 4
d) Assessment Model
Assessment of learner performance in Pure Mathematics100%
Continuous assessment 30%
Continuous assessment 30%
FINAL MARK 100%
Examination Mark 100%
Summative assessment 70%
Profiling
Profile
Exit Profile
Topic Tasks 7.5%
Written Tests 7.5%
End of term Tests 15%
Paper 1 35%
Paper 2 35%
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Pure Mathematics Syllabus Forms 3 - 4
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Pure Mathematics Syllabus Forms 3 - 4