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ZIMBABWE
MINISTRY OF PRIMARY AND SECONDARY EDUCATION
PURE MATHEMATICS SYLLABUS
FORMS 5 - 6
2015 - 2022
Curriculum Development and Technical ServicesP. O. Box MP 133Mount Pleasant
Harare
© All Rrights Reserved2015
i
Pure Mathematics Syllabus Forms 5 - 6
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 5 to 6 Pure Mathematics• Representatives of the following organisations:
- Zimbabwe School Examinations Council (ZIMSEC)- United Nations International Children’s Emergency Fund (UNICEF)- United Nations Educational Scientific and Cultural Organisation (UNESCO)- Representatives from higher and tertiary educational institutions
Pure Mathematics Syllabus Forms 5 - 6
ii
CONTENTS
ACKNOWLEDGEMENTS ...................................................................................................................i
CONTENTS .........................................................................................................................................ii
1.0 PREAMBLE ..................................................................................................................................1
2.0 PRESENTATION OF SYLLABUS ................................................................................................1
3.0 AIMS ..............................................................................................................................................2
4.0 SYLLABUS OBJECTIVES ...........................................................................................................2
5.0 METHODOLOGY AND TIME ALLOCATION ................................................................................2
6.0 SYLLABUS TOPICS .....................................................................................................................3
7.0 SCOPE AND SEQUENCE ............................................................................................................4
FORM FIVE (5) SYLLABUS ...............................................................................................................10
8.0 COMPETENCY MATRIX ...............................................................................................................10
FORM SIX (6) SYLLABUS .................................................................................................................21
9.0 ASSESSMENT .............................................................................................................................29
1
Pure Mathematics Syllabus Forms 5 - 6
1.0 PREAMBLE
1.1 Introduction
In developing the Form 5 to 6 Pure Mathematics sylla-bus, attention was paid to the need to provide continuity of pure mathematical concepts and lay foundations for further studies. It is meant for learners who have the abil-ity and interest in studying Pure Mathematics. The two year learning phase will provide learners with opportuni-ties to apply pure mathematical concepts, principles and skills in other learning areas.
The intention is to provide wider opportunities for learn-ers who wish to acquire competences in scientifically and technologically based areas required for the national human capital development needs and enterprising ac-tivities in the 21st century. In learning Pure Mathematics, learners should be helped to acquire a variety of skills, knowledge and processes, and develop a positive atti-tude towards the learning area. These will enhance the ability to investigate and interpret numerical and spatial relationships as well as patterns that exist in mathe-matics and in the world in general. The syllabus also caters for learners with diverse needs to experience Pure Mathematics as relevant and worthwhile. It also desires to produce a learner with the ability to communicate mathematical ideas and information effectively.
1.2 Rationale
Pure Mathematics is the science of abstract concepts in the context of number, time, and space. It uses logic and reasoning to construct new mathematical structures by building on existing ones, and to discover new patterns within, and relationships among mathematical structures. Pure Mathematics is underpinned in abstraction and proof. Typically, the Pure Mathematician finds joy and ful-fillment in the intrinsic value of her/his constructions and discoveries, with little or no regard to their applications in life. However, examples abound of instances where Pure Mathematics discoveries initially born and existing only in the abstract, have eventually been found to have important applications in life. These life examples are in the areas of science, technology and engineering, as well as finance, banking and commerce, among others. Given the Pure Mathematician’s interest and ability in abstraction and pattern discovery, such a professional is increasingly in demand in such activities as meteorology, investment forecasting, and risk analysis. Thus teaching and learning Pure Mathematics should not be construed as a luxury, but a 21st Century necessity.
The teaching and learning process in Pure Mathematics at the Form 5 and 6 levels is also expected to enhance learners’ confidence and sense of self fulfillment, inter-connectedness and intellectual honesty, hence contrib-uting to their growth in the acquisition of Unhu/ Ubuntu /Vumunhu values.
1.3 Summary of Content
The syllabus will cover the theoretical and practical aspects of Pure Mathematics. The learning area will cover: algebra, geometry and calculus.
1.4 Assumptions
The syllabus assumes that the learner has:
1.4.1 passed at least one of the following at form 4: Mathematics, Pure Mathematics and Addition-al Mathematics
1.4.2 interest in studying Pure Mathematics form 5 - 6
1.5 Cross cutting Themes
The following are some of the cross cutting themes in the teaching and learning of Pure Mathematics: -
1.5.1 Business and financial literacy1.5.2 Disaster and risk management1.5.3 Collaboration 1.5.4 Environmental issues1.5.5 Enterprise skills 1.5.6 HIV and AIDS1.5.7 Unhu/Ubuntu/ Vumunhu1.5.8 ICT 1.5.9 Gender
2.0 PRESENTATION OF SYLLABUSThe Pure Mathematics syllabus is a document covering Forms 5 and 6. It contains the preamble, aims, syllabus objectives, methodology and time allocation, syllabus topics, scope and sequence, competency matrix and as-sessment. The syllabus also suggests a list of resources that could be used during teaching and learning process.
2
3.0 AIMSThis syllabus is intended to provide a guideline for Forms 5 - 6 learners which will enable them to:
3.1 acquire enterprising skills through modelling, research and project based learning
3.2 develop the abilities to reason logically, to communicate mathematically, and to learn co-operatively and independently
3.3 develop an appreciation of the applicability, creativity and power of pure mathematics in solving a broad range of problems
3.4 understand the nature of Pure Mathematics and its relationship to other branches of math-ematics and STEM in general.
3.5 appreciate the use of ICT tools in solving pure mathematical problems
3.6 engage, persevere, collaborate and show intellectual honesty in performing tasks in Pure Mathematics, in the spirit of Unhu/ Ubuntu/Vu-munhu
4.0 SYLLABUS OBJECTIVESBy the end of the two year learning period, the learners should be able to:
4.1 make use of a variety of mathematical skills (including graphing, proving, modelling, finding pattern and problem
solving) in the learning and application of Pure Mathematics.
4.2 communicate pure mathematical ideas and information
4.3 produce imaginative and creative work aris-ing from pure mathematical ideas
4.4 choose strategies to construct arguments and proofs in both concrete and abstract set-tings
4.5 construct and use mathematical models in solving problems in life
4.6 apply pure mathematical ideas in other branches of mathematics and STEM in gener-al.
4.7 demonstrate perseverance, diligence, coop-eration and intellectual honesty.
4.8 use ICT tools to solve pure mathematical problems.
4.9 conduct research projects including those related to enterprise
5.0 METHODOLOGY AND TIME ALLOCATION
5.1 Methodology
A constructivist based teaching and learning approach is recommended for the Form 5 and 6 Pure Mathemat-ics Syllabus. The theoretical basis for this approach is that: in a conducive environment with appropriate stimuli, learners’ capacity to build on their pre-requisite knowledge and create new mathematical knowledge is enhanced. A conducive environment in this context is one that encourages: creativity and originality; a free ex-change of ideas and information; inclusivity and respect for each other’s’ views, regardless of personal circum-stances (in terms of, for example: gender, appearance, disability and religious beliefs); collaboration and cooper-ation; intellectual honesty; diligence and persistence; and Unhu/ Ubuntu /Vumunhu. This is particularly important in a learning area like mathematics, given the negative attitudes associated with its teaching and learning.
Providing appropriate stimuli has to do with posing relevant challenges that excite learners, and help to make learning Pure Mathematics an enjoyable, fulfilling experience. Such challenges could be posed in the form of problems that encourage learners to create new (to them) mathematical knowledge/ideas in line with the teacher expectations and even beyond. New knowledge acquired in such a manner tends to be deep rooted and meaningful to learners, hence enhancing their ability to apply it within the learning area and in life. Definitely spoon feeding is not and cannot be an appropriate stim-ulus, as it does not help learners to develop critical think-ing, creativity, and the ability to think outside the box, which are critical for self-reliance, national sustainable development and global competitiveness. Thus learners need to be active participants and decision makers in the pure mathematics teaching and learning process, with the teacher playing a facilitator role.Pre-requisite knowledge and skills refers to what the learners should already know and can do, which can form a strong basis on which to construct the expected new knowledge. Thus the Pure Mathematics teacher needs to carefully analyse the new concepts and prin-ciples she/he intends to introduce, identify the relevant pre-requisite knowledge, assess to identify any gaps, and take appropriate steps to fill such gaps. The following, is a list of teaching and learning methods that are consistent with, and supportive of the above approach:
Pure Mathematics Syllabus Forms 5 - 6
Pure Mathematics Syllabus Forms 5 - 6
3
5.1.1 Guided discovery 5.1.2 Group work5.1.3 Interactive e-learning5.1.4 Problem solving5.1.5 Discussion5.1.6 Modelling
5.2 Time Allocation
10 periods of 35 minutes each per week should be allocated. Learners are expected to participate in the following activities: -
- Mathematics Olympiads- Mathematics and Science exhibitions- Mathematics seminars- Mathematical tours to tertiary and other institutions.
6.0 SYLLABUS TOPICSThe following topics will be covered from form 5 – 6:
6.1 Algebra6.2 Geometry and vectors6.3 Series and Sequences 6.4 Trigonometry 6.5 Calculus6.6 Numerical methods 6.7 Complex numbers
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
4
7.0
SC
OPE
AN
D S
EQU
ENC
E
TOPI
C 1
: ALG
EBR
A
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
7
6.2
G
eom
etry
and
vec
tors
6.
3
Serie
s an
d Se
quen
ces
6.
4
Trig
onom
etry
6.
5
Cal
culu
s 6.
6
Num
eric
al m
etho
ds
6.7
C
ompl
ex n
umbe
rs
7.0
SC
OPE
AN
D S
EQU
ENC
E TO
PIC
1: A
LGEB
RA
SUB
TO
PIC
FO
RM 5
FO
RM 6
Indi
ces
and
prop
ortio
nalit
y
Rat
iona
l ind
ices
Gen
eral
law
s of
indi
ces
D
irect
, inv
erse
, joi
nt a
nd p
artia
l var
iatio
ns
Poly
nom
ials
Poly
nom
ial o
pera
tions
Qua
drat
ic o
pera
tions
Fact
or a
nd re
mai
nder
theo
rem
s
Iden
titie
s, e
quat
ions
and
ineq
ualit
ies
Id
entit
ies
Eq
uatio
ns
Pa
rtial
frac
tions
Ineq
ualit
ies
Func
tions
Loga
rithm
ic fu
nctio
ns
Ex
pone
ntia
l fun
ctio
ns
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
4 5
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
8
R
atio
nal f
unct
ions
Mod
ulus
func
tions
Rel
atio
ns
R
elat
ions
Dom
ain,
co-
dom
ain,
and
rang
e
Func
tions
Type
s of
func
tions
(inj
ectiv
e, b
iject
ive,
sur
ject
ive)
Inve
rse
C
ompo
site
func
tion
Mat
rices
Ty
pes
of M
atric
es
Ba
sic
oper
atio
n (u
p to
3 x
3)
D
eter
min
ant a
nd in
vers
e
Sy
stem
s of
line
ar e
quat
ions
Tran
sfor
mat
ions
Mat
hem
atic
al in
duct
ion
Proo
f by
Indu
ctio
n
Con
ject
ure
Gro
ups
Bina
ry o
pera
tions
Basi
c pr
oper
ties
of a
gro
up
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
6
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
9
TOPI
C 2
: G
EOM
ETRY
AN
D V
ECTO
RS
SUB
TO
PIC
FO
RM 5
FO
RM 6
Gra
phs
and
coor
dina
te g
eom
etry
Cur
ve s
ketc
hing
Coo
rdin
ate
geom
etry
Para
met
ric e
quat
ions
Vect
ors
(up
to th
ree
dim
ensi
ons)
Vect
or n
otat
ion
Ve
ctor
ope
ratio
ns
Ty
pes
of v
ecto
rs
M
agni
tude
of a
vec
tor
D
ot (s
cala
r)pro
duct
Area
of p
lane
sha
pes
Ve
ctor
equ
atio
n of
a s
traig
ht li
ne
Eq
uatio
n of
a p
lane
Cro
ss p
rodu
ct
TOPI
C 3
: S
ERIE
S AN
D S
EQU
ENC
ES
SUB
TO
PIC
FO
RM 5
FO
RM 6
Sequ
ence
s
Sequ
ence
s
Arith
met
ic a
nd G
eom
etric
pro
gres
sion
s
Serie
s
,
n! a
nd (𝑛𝑛𝑟𝑟)
not
atio
n
Arith
met
ic a
nd G
eom
etric
pro
gres
sion
s
Bi
nom
ial e
xpan
sion
St
anda
rd re
sults
Met
hod
of d
iffer
ence
s
M
acla
urin
’s s
erie
s
Tayl
or’s
ser
ies
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
6 7
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
10
TOPI
C 4
: TR
IGO
NO
MET
RY
SUB
TO
PIC
FO
RM 5
FO
RM 6
Plan
e Tr
igon
omet
ry
R
adia
ns a
nd d
egre
es
Ar
c le
ngth
Sect
or a
rea
Se
gmen
ts
Trig
onom
etric
al F
unct
ions
Gra
phs
of T
rigon
omet
rical
func
tions
Trig
onom
etric
al e
quat
ions
Trig
onom
etric
al id
entit
ies
(exc
ludi
ng h
alf a
ngle
id
entit
ies)
TOPI
C 4
: TR
IGO
NO
MET
RY
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
8
TOPI
C 5
: CA
LCU
LUS
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
11
TOPI
C 5
: CAL
CU
LUS
SUB
TO
PIC
FO
RM 5
FO
RM 6
Diff
eren
tiatio
n
Firs
t prin
cipl
es d
iffer
entia
tion
Po
lyno
mia
ls, r
atio
nal f
unct
ions
, nat
ural
loga
rithm
s,
expo
nent
ials
, trig
onom
etric
al fu
nctio
ns
Su
ms,
diff
eren
ces,
pro
duct
s, q
uotie
nts
and
com
posi
tes
Impl
icit
and
para
met
ric
G
radi
ent,
tang
ents
, nor
mal
s, ra
tes
of c
hang
e an
d st
atio
nary
poi
nts
Inte
grat
ion
In
defin
ite In
tegr
al o
f Pol
ynom
ials
, Rat
iona
l fun
ctio
ns,
expo
nent
ials
(eax
+b),
Trig
onom
etric
al fu
nctio
ns w
ith
stan
dard
inte
gral
s an
d th
ose
that
can
be
redu
ced
to
stan
dard
inte
gral
Inte
grat
ion
by re
cogn
ition
, by
parts
and
by
subs
titut
ion
D
efin
ite In
tegr
al
Ap
plic
atio
n of
inte
grat
ion
to a
reas
and
vol
umes
1st O
rder
Diff
eren
tial e
quat
ions
R
ates
of c
hang
e
Sepa
ratio
n of
Var
iabl
es
So
lutio
n by
Inte
grat
ion
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
8 9
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
12
TOPI
C 6
: N
UM
ERIC
AL M
ETH
OD
S
SUB
TO
PIC
FO
RM 5
FO
RM 6
Num
eric
al M
etho
ds
Erro
rs
Ite
rativ
e m
etho
ds
N
ewto
n –
Rap
hson
met
hod
Trap
eziu
m ru
le
TOPI
C 7
: C
OM
PLEX
NU
MB
ERS
SUB
TO
PIC
FO
RM 5
FO
RM 6
Com
plex
Num
bers
Parts
of a
com
plex
num
ber
C
onju
gate
, mod
ulus
and
arg
umen
t
Ope
ratio
ns
Ar
gand
dia
gram
Eq
uatio
ns (u
p to
ord
er 5
)
Pola
r for
m
(r (c
os+
i sin
) =
rei)
Lo
ci
D
e M
oivr
e’s
Theo
rem
nth ro
ots
of u
nit
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
10
FOR
M F
IVE
(5) S
YLLA
BU
S
8.0
C
OM
PETE
NC
Y M
ATR
IX8.
1 C
OM
PETE
NC
Y M
ATR
IX: F
OR
M 5
SYL
LAB
US
TOPI
C 1
: ALG
EBR
A
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
13
FORM
FIV
E (5
) SYL
LAB
US
8.0
C
OM
PETE
NC
Y M
ATR
IX
8.1
CO
MPE
TEN
CY
MAT
RIX
: FO
RM
5 S
YLLA
BUS
TOPI
C 1
: ALG
EBR
A
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
Indi
ces
and
prop
ortio
nalit
y
stat
e th
e la
ws
of in
dice
s
use
law
s of
indi
ces
to s
olve
pr
oble
ms
so
lve
prob
lem
s in
volv
ing
dire
ct, i
nver
se, p
artia
l and
join
t va
riatio
n
R
atio
nal i
ndic
es
G
ener
al la
ws
of in
dice
s
D
irect
, inv
erse
, par
tial a
nd
join
t var
iatio
ns
Ap
plyi
ng la
ws
of in
dice
s to
sol
ve
prob
lem
s (in
clud
ing
life
prob
lem
s)
Mod
ellin
g si
tuat
ions
invo
lvin
g va
riatio
n an
d so
lvin
g re
late
d pr
oble
ms
IC
T to
ols
Br
aille
mat
eria
ls
and
equi
pmen
t
Talk
ing
book
s or
so
ftwar
e
Rel
evan
t tex
ts
Poly
nom
ials
carr
y ou
t pol
ynom
ial
oper
atio
ns o
f add
ition
, su
btra
ctio
n, m
ultip
licat
ion
and
divi
sion
com
plet
e th
e sq
uare
of a
qu
adra
tic p
olyn
omia
l
use
the
rem
aind
er a
nd fa
ctor
th
eore
ms
Po
lyno
mia
l ope
ratio
ns
Qua
drat
ic o
pera
tions
Fa
ctor
and
rem
aind
er
theo
rem
s
Pe
rform
ing
oper
atio
ns w
ith
poly
nom
ials
C
ompl
etin
g th
e sq
uare
and
sol
ving
th
e re
late
d pr
oble
ms
Der
ivin
g fa
ctor
and
rem
aind
er
theo
rem
s
Appl
ying
the
fact
or a
nd re
mai
nder
th
eore
ms
in s
olvi
ng p
robl
ems
IC
T to
ols
Br
aille
mat
eria
ls
and
equi
pmen
t
Talk
ing
book
s or
so
ftwar
e
Rel
evan
t tex
ts
Iden
titie
s, e
quat
ions
an
d In
equa
litie
s
dist
ingu
ish
betw
een
an
equa
tion
and
an id
entit
y
find
unkn
own
coef
ficie
nts
in
poly
nom
ials
usi
ng id
entit
ies
so
lve
sim
ulta
neou
s eq
uatio
ns
deco
mpo
se ra
tiona
l po
lyno
mia
ls in
to p
artia
l fra
ctio
ns
Id
entit
ies
Eq
uatio
ns
Parti
al fr
actio
ns
D
iscu
ssin
g th
e di
ffere
nce
betw
een
iden
titie
s an
d eq
uatio
ns
Fi
ndin
g un
know
n co
effic
ient
s in
po
lyno
mia
ls u
sing
iden
titie
s
Solv
ing
sim
ulta
neou
s eq
uatio
ns (a
t le
ast o
ne is
line
ar a
nd a
t mos
t one
qu
adra
tic)
Ex
pres
sing
ratio
nal p
olyn
omia
ls
in p
artia
l fra
ctio
ns (i
nclu
ding
im
prop
er fr
actio
ns)
IC
T to
ols
Br
aille
mat
eria
ls
and
equi
pmen
t
Talk
ing
book
s or
so
ftwar
e
Rel
evan
t tex
ts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
10 11
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
14
us
e th
e di
scrim
inan
t to
dete
rmin
e th
e nu
mbe
r of r
eal
root
s of
qua
drat
ic e
quat
ions
solv
e pr
oble
ms
invo
lvin
g th
e us
e of
the
disc
rimin
ant
so
lve
poly
nom
ial e
quat
ions
us
ing
the
fact
or th
eore
m
so
lve
prob
lem
s us
ing
fact
or
and
rem
aind
er th
eore
ms
so
lve
ineq
ualit
ies
In
equa
litie
s
D
eter
min
ing
the
num
ber o
f rea
l ro
ots
of q
uadr
atic
equ
atio
ns u
sing
th
e di
scrim
inan
t
Solv
ing
prob
lem
s us
ing
the
disc
rimin
ant
St
atin
g an
d us
ing
fact
or a
nd
rem
aind
er th
eore
ms
to s
olve
eq
uatio
ns
So
lvin
g pr
oble
ms
invo
lvin
g in
equa
litie
s (in
clud
ing
ratio
nal
ineq
ualit
ies)
Mod
ellin
g si
tuat
ions
invo
lvin
g eq
uatio
ns a
nd in
equa
litie
s an
d so
lvin
g re
late
d pr
oble
ms
Func
tions
defin
e th
e fu
nctio
n as
a
map
ping
sket
ch s
impl
e gr
aphs
of
func
tions
for a
giv
en d
omai
n
ex
plai
n ex
pone
ntia
l gro
wth
an
d de
cay
so
lve
equa
tion
of th
e fo
rm a
x =
b,
usi
ng lo
garit
hms
solv
e in
equa
litie
s of
the
form
ax
≤ b
, or a
x ≥
b,
usin
g lo
garit
hms
us
e lo
garit
hms
to tr
ansf
orm
a
give
n re
latio
nshi
p to
a li
near
fo
rm
de
scrib
e th
e m
eani
ng o
f ab
solu
te v
alue
not
atio
n
solv
e eq
uatio
ns a
nd
ineq
ualit
ies
invo
lvin
g th
e ab
solu
te v
alue
Lo
garit
hmic
func
tions
Ex
pone
ntia
l fun
ctio
ns
R
atio
nal f
unct
ions
Mod
ulus
func
tions
D
iscu
ssin
g th
e fu
nctio
n as
a
map
ping
Sket
chin
g si
mpl
e gr
aphs
of
func
tions
D
iscu
ssin
g ex
ampl
es o
f exp
onen
tial
grow
th a
nd d
ecay
in li
fe
M
odel
ling
situ
atio
ns to
sol
ve
prob
lem
s in
volv
ing
expo
nent
ial
grow
th a
nd d
ecay
Sol
ving
equ
atio
ns a
nd in
equa
litie
s us
ing
loga
rithm
s
Tr
ansf
orm
ing
give
n re
latio
nshi
ps to
lin
ear f
orm
to fi
nd u
nkno
wn
cons
tant
s (in
clud
ing
sket
chin
g lin
ear g
raph
s)
M
odel
ling
situ
atio
ns to
sol
ve
prob
lem
s in
volv
ing
the
use
of
loga
rithm
s
Dis
cuss
ing
the
abso
lute
val
ue
nota
tion
IC
T to
ols
Br
aille
mat
eria
ls
and
equi
pmen
t
Talk
ing
book
s or
so
ftwar
e
Rel
evan
t tex
ts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
12
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
15
So
lvin
g eq
uatio
ns a
nd in
equa
litie
s in
volv
ing
the
mod
ulus
func
tion
Rel
atio
ns
de
fine
a re
latio
n
de
fine
dom
ain,
co-
dom
ain
and
rang
e
desc
ribe
type
s of
rela
tions
defin
e a
func
tion
di
stin
guis
h am
ong
the
follo
win
g ty
pes
of fu
nctio
ns:
one
to o
ne/in
ject
ive,
bije
ctiv
e an
d su
rject
ive
fin
d th
e in
vers
e of
a g
iven
fu
nctio
n
illust
rate
in g
raph
ical
term
s th
e re
latio
n be
twee
n a
one
to o
ne
func
tion
and
its in
vers
e
illust
rate
rela
tions
hip
amon
gst
the
grap
hs o
f 𝑦𝑦
= 𝑓𝑓
(𝑥𝑥) a
nd
𝑦𝑦=
| 𝑓𝑓(𝑥𝑥
)| 𝑦𝑦
=𝑎𝑎𝑓𝑓
( 𝑥𝑥) ,
𝑦𝑦=𝑓𝑓(𝑥𝑥)
+𝑎𝑎,
𝑦𝑦=
𝑓𝑓(𝑥𝑥
+𝑎𝑎)
, 𝑦𝑦
=𝑓𝑓(𝑎𝑎𝑥𝑥
) and
𝑦𝑦
=𝑎𝑎𝑓𝑓
(𝑥𝑥+𝑏𝑏)
find
com
posi
te fu
nctio
ns
R
elat
ions
Dom
ain,
co-
dom
ain,
and
ra
nge
Func
tions
Type
s of
func
tion
(inje
ctiv
e,
bije
ctiv
e, s
urje
ctiv
e)
Inve
rse
C
ompo
site
func
tion
D
iscu
ssin
g re
latio
ns, d
omai
n, c
o-do
mai
n an
d ra
nge
D
escr
ibin
g ty
pes
of re
latio
ns
Def
inin
g a
func
tion
D
iscu
ssin
g di
ffere
nces
am
ong
the
follo
win
g ty
pes
of fu
nctio
ns:
inje
ctiv
e, b
iject
ive
and
surje
ctiv
e
Fi
ndin
g th
e in
vers
e of
a g
iven
fu
nctio
n
Illus
tratin
g in
gra
phic
al te
rms
the
rela
tion
betw
een
a on
e to
one
fu
nctio
n an
d its
inve
rse
Ill
ustra
ting
rela
tions
hip
amon
gst t
he
grap
hs o
f
𝑦𝑦 =
𝑓𝑓(𝑥𝑥
) and
𝑦𝑦=
| 𝑓𝑓(𝑥𝑥
)| 𝑦𝑦
=𝑎𝑎𝑓𝑓
( 𝑥𝑥) ,
𝑦𝑦=𝑓𝑓(𝑥𝑥)
+𝑎𝑎,
𝑦𝑦=
𝑓𝑓(𝑥𝑥
+𝑎𝑎)
, 𝑦𝑦
=𝑓𝑓(𝑎𝑎𝑥𝑥
) and
𝑦𝑦=
𝑎𝑎𝑓𝑓(𝑥𝑥
+𝑏𝑏)
Find
ing
com
posi
te fu
nctio
ns
M
odel
ling
situ
atio
ns in
volv
ing
rela
tions
and
sol
ving
rela
ted
prob
lem
s
IC
T to
ols
Br
aille
mat
eria
ls
and
equi
pmen
t
Talk
ing
book
s or
so
ftwar
e
Rel
evan
t tex
ts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
12 13
TOPI
C 2
: GEO
MET
RY A
ND
VEC
TOR
S Pu
re M
athe
mat
ics S
ylla
bus F
orm
5–
6 20
16
1
6 TO
PIC
2: G
EOM
ETR
Y AN
D V
ECTO
RS
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
and
Coo
rdin
ate
geom
etry
sk
etch
gra
phs
of th
e fo
rm
y
= f
(x),
whe
re f
(x) =
kxn
and
n =
1 2 or
n is
an
inte
ger,
and
whe
re f(
x) is
a
quad
ratic
or c
ubic
pol
ynom
ial
lo
cate
sol
utio
ns o
f equ
atio
ns a
nd
ineq
ualit
ies
usin
g sk
etch
es o
f gr
aphs
find
equa
tions
of p
aral
lel a
nd
perp
endi
cula
r stra
ight
line
s
calc
ulat
e th
e di
stan
ce b
etw
een
two
poin
ts
redu
ce a
n eq
uatio
n to
app
ropr
iate
lin
ear f
orm
in s
olvi
ng p
robl
ems
(suc
h as
y =
ax2 +
b w
hen
y is
pl
otte
d ag
ains
t x2
)
fin
d th
e eq
uatio
n of
a c
ircle
defin
e a
curv
e us
ing
para
met
ric
equa
tions
C
urve
ske
tchi
ng
C
oord
inat
e ge
omet
ry
Pa
ram
etric
equ
atio
ns
Sk
etch
ing
grap
hs o
f the
form
y =
f (x
), w
here
f (x
) = k
xn a
nd
n =
1 2 or
n is
an
inte
ger,
and
whe
re f(
x) is
a
quad
ratic
or c
ubic
pol
ynom
ial
Ex
plor
ing
solu
tions
of e
quat
ions
and
in
equa
litie
s by
ske
tchi
ng g
raph
s
Find
ing
equa
tions
of p
aral
lel a
nd
perp
endi
cula
r lin
es
C
ompu
ting
the
dist
ance
bet
wee
n tw
o po
ints
(inc
ludi
ng p
erpe
ndic
ular
di
stan
ce o
f a p
oint
from
a s
traig
ht
line)
Red
ucin
g eq
uatio
ns to
app
ropr
iate
lin
ear f
orm
in s
olvi
ng p
robl
ems
(suc
h as
y
= ax
2 + b
whe
n y
is p
lotte
d ag
ains
t x2
)
Find
ing
equa
tions
of c
ircle
s
Def
inin
g a
curv
e us
ing
para
met
ric
equa
tions
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Vect
ors
(up
to th
ree
dim
ensi
ons)
de
fine
posi
tion
and
free
vect
or
carr
y ou
t add
ition
, sub
tract
ion
and
scal
ar m
ultip
licat
ion
of v
ecto
rs
us
e un
it, d
ispl
acem
ent a
nd p
ositi
on
vect
or to
sol
ve p
robl
ems
Ve
ctor
not
atio
n
Ve
ctor
ope
ratio
ns
Ty
pes
of v
ecto
rs
D
iscu
ssin
g th
e us
e of
pos
ition
and
fre
e ve
ctor
s in
life
Car
ryin
g ou
t vec
tor o
pera
tions
Usi
ng u
nit,
disp
lace
men
t and
pos
ition
ve
ctor
s to
sol
ve p
robl
ems
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
14
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
19
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
and
of (1
+ x
)n , w
here
n is
a
ratio
nal n
umbe
r and
| 𝑥𝑥| <
1
so
lve
prob
lem
s in
volv
ing
serie
s
(a +
b) n
whe
re n
is a
pos
itive
in
tege
r, an
d of
(1 +
x) n
, whe
re n
is a
ra
tiona
l num
ber a
nd
| 𝑥𝑥| <
1
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
serie
s an
d ex
plor
ing
thei
r app
licat
ions
in li
fe
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
14 15
TOPI
C 3
: SER
IES
AN
D S
EQU
ENC
ES Pu
re M
athe
mat
ics S
ylla
bus F
orm
5–
6 20
16
1
8 TO
PIC
3: S
ERIE
S AN
D S
EQU
ENC
ES
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
fine
a se
quen
ce
use
sequ
ence
def
initi
ons
such
as
Un =
n2 a
nd
Un+
1 = 2
Un t
o ca
lcul
ate
succ
essi
ve
term
s
dist
ingu
ish
amon
g pe
riodi
c,
osci
llatin
g, c
onve
rgin
g, a
nd
dive
rgin
g se
quen
ces
defin
e ar
ithm
etic
and
geo
met
ric
prog
ress
ions
find
the
gene
ral t
erm
s an
d ot
her
term
s of
arit
hmet
ic a
nd g
eom
etric
pr
ogre
ssio
ns
so
lve
prob
lem
s in
volv
ing
sequ
ence
s
Se
quen
ces
Ar
ithm
etic
and
geo
met
ric
prog
ress
ions
D
iscu
ssin
g th
e m
eani
ng a
nd v
alue
of
sequ
ence
s in
life
Cal
cula
ting
succ
essi
ve te
rms
usin
g se
quen
ce d
efin
ition
suc
h as
Un =
n2
and
Un+
1 = 2
Un
D
iscu
ssin
g th
e be
havi
our o
f per
iodi
c,
osci
llatin
g, c
onve
rgin
g, a
nd d
iver
ging
se
quen
ces
Dis
cuss
ing
exam
ples
of a
rithm
etic
an
d ge
omet
ric p
rogr
essi
ons
Fi
ndin
g th
e ge
nera
l ter
ms
and
othe
r te
rms
of a
rithm
etic
and
geo
met
ric
prog
ress
ions
Rep
rese
ntin
g lif
e ph
enom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g se
quen
ces
and
expl
orin
g th
eir
appl
icat
ions
in li
fe
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Serie
s
use ,
n! a
nd (𝑛𝑛 𝑟𝑟)
not
atio
n
fin
d th
e su
m o
f giv
en a
rithm
etic
an
d ge
omet
ric te
rms
fin
d su
m to
infin
ity o
f giv
en
conv
ergi
ng g
eom
etric
ser
ies
ex
pand
exp
ress
ions
of
(a +
b)
n whe
re n
is a
pos
itive
inte
ger,
,
n! a
nd (𝑛𝑛𝑟𝑟)
not
atio
n
Ar
ithm
etic
and
geo
met
ric
prog
ress
ions
Bi
nom
ial e
xpan
sion
U
sing
the ,
n! a
nd (𝑛𝑛𝑟𝑟)
not
atio
n to
so
lve
prob
lem
s
Com
putin
g th
e su
m o
f giv
en
arith
met
ic a
nd g
eom
etric
term
s
Find
ing
sum
to in
finity
of g
iven
co
nver
ging
geo
met
ric s
erie
s
Expa
ndin
g ex
pres
sion
s of
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
16
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
19
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
and
of (1
+ x
)n , w
here
n is
a
ratio
nal n
umbe
r and
| 𝑥𝑥| <
1
so
lve
prob
lem
s in
volv
ing
serie
s
(a +
b) n
whe
re n
is a
pos
itive
in
tege
r, an
d of
(1 +
x) n
, whe
re n
is a
ra
tiona
l num
ber a
nd
| 𝑥𝑥| <
1
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
serie
s an
d ex
plor
ing
thei
r app
licat
ions
in li
fe
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
16 17
TOPI
C 4
: TR
IGO
NO
MET
RY Pu
re M
athe
mat
ics S
ylla
bus F
orm
5–
6 20
16
2
0 TO
PIC
4: T
RIG
ON
OM
ETRY
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
di
stin
guis
h be
twee
n ra
dian
s an
d de
gree
s
co
nver
t deg
rees
to ra
dian
s an
d vi
ce v
ersa
ca
lcul
ate
arc
leng
th a
nd
sect
or a
rea
so
lve
prob
lem
s in
volv
ing
leng
ths
of a
rcs,
are
as o
f se
ctor
s an
d se
gmen
ts
us
e sm
all a
ngle
ap
prox
imat
ion
for s
in x
, cos
x
and
tan
x
R
adia
ns a
nd d
egre
es
Ar
c le
ngth
Se
ctor
are
a
Se
gmen
ts
D
iscu
ssin
g th
e co
ncep
t of r
adia
ns a
nd
degr
ees,
thei
r rel
atio
nshi
ps a
nd th
e si
gnifi
canc
e of
usi
ng ra
dian
s
D
eriv
ing
and
usin
g th
e fo
rmul
ae fo
r len
gth
of
an a
rc a
nd th
e ar
ea o
f a s
ecto
r
Solv
ing
prob
lem
s in
volv
ing
leng
ths
of a
rcs,
ar
eas
of s
ecto
rs a
nd s
egm
ents
R
ecal
ling
and
usin
g sm
all a
ngle
ap
prox
imat
ion
for s
in x
, cos
x a
nd t
an x
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Trig
onom
etric
al
Func
tions
sket
ch th
e gr
aphs
of
trigo
nom
etric
al fu
nctio
ns
tran
sfor
m th
e gr
aphs
of
trigo
nom
etric
al fu
nctio
ns
sk
etch
gra
phs
of in
vers
e tri
gono
met
rical
rela
tions
so
lve
trigo
nom
etric
al
equa
tions
prov
e tri
gono
met
rical
id
entit
ies
so
lve
prob
lem
s us
ing
trigo
nom
etric
al id
entit
ies
G
raph
s of
Tr
igon
omet
rical
fu
nctio
ns
Tr
igon
omet
rical
eq
uatio
ns
Tr
igon
omet
rical
id
entit
ies
(exc
ludi
ng
half
angl
e id
entit
ies)
Sk
etch
ing
and
trans
form
ing
the
grap
hs o
f tri
gono
met
rical
func
tions
Sk
etch
ing
and
trans
form
ing
grap
hs o
f inv
erse
tri
gono
met
rical
rela
tions
Fi
ndin
g so
lutio
ns o
f trig
onom
etric
al e
quat
ions
Pr
ovin
g tri
gono
met
rical
iden
titie
s
So
lvin
g pr
oble
ms
invo
lvin
g tri
gono
met
rical
id
entit
ies
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
trigo
nom
etric
al fu
nctio
ns a
nd e
xplo
ring
thei
r ap
plic
atio
ns in
life
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
18
TOPI
C 5
: C
ALC
ULU
S Pu
re M
athe
mat
ics S
ylla
bus F
orm
5–
6 20
16
2
1 TO
PIC
5:
CAL
CU
LUS
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
Diff
eren
tiatio
n
diffe
rent
iate
from
firs
t prin
cipl
es
excl
udin
g lo
garit
hmic
and
ex
pone
ntia
l fun
ctio
ns
diffe
rent
iate
pol
ynom
ials
, rat
iona
l fu
nctio
ns, n
atur
al lo
garit
hms,
ex
pone
ntia
ls a
nd tr
igon
omet
rical
fu
nctio
ns
diffe
rent
iate
sum
s, d
iffer
ence
s,
prod
ucts
, quo
tient
s an
d co
mpo
site
fu
nctio
ns
ca
rry
out i
mpl
icit
and
para
met
ric
diffe
rent
iatio
n
lo
cate
sta
tiona
ry p
oint
s
di
stin
guis
h be
twee
n m
axim
a,
min
ima
and
poin
t of i
nfle
xion
solv
e pr
oble
ms
invo
lvin
g di
ffere
ntia
tion
Fi
rst p
rinci
ples
di
ffere
ntia
tion
Po
lyno
mia
ls, r
atio
nal
func
tions
, nat
ural
lo
garit
hms,
ex
pone
ntia
ls,
trigo
nom
etric
al fu
nctio
ns
Su
ms,
diff
eren
ces,
pr
oduc
ts, q
uotie
nts
and
com
posi
tes
Impl
icit
and
para
met
ric
Gra
dien
t, ta
ngen
ts,
norm
al, r
ates
of c
hang
e an
d st
atio
nary
poi
nts
D
iffer
entia
ting
from
firs
t prin
cipl
es:
poly
nom
ials
, rat
iona
l fun
ctio
ns,
trigo
nom
etric
al fu
nctio
ns e
xclu
ding
lo
garit
hmic
and
exp
onen
tial f
unct
ions
Diff
eren
tiatin
g po
lyno
mia
ls, r
atio
nal
func
tions
, nat
ural
loga
rithm
s,
expo
nent
ials
and
trig
onom
etric
al
func
tions
D
iffer
entia
ting
sum
s, d
iffer
ence
s,
prod
ucts
, quo
tient
s an
d co
mpo
site
fu
nctio
ns
C
arry
ing
out i
mpl
icit
and
para
met
ric
diffe
rent
iatio
n
Lo
catin
g st
atio
nary
poi
nts
and
dist
ingu
ishi
ng b
etw
een
max
ima,
m
inim
a an
d po
int o
f inf
lexi
on
So
lvin
g pr
oble
ms
invo
lvin
g di
ffere
ntia
tion
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
diffe
rent
iatio
n an
d ex
plor
ing
thei
r ap
plic
atio
ns in
life
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Inte
grat
ion
in
tegr
ate
poly
nom
ials
, rat
iona
l fu
nctio
ns, e
xpon
entia
ls,
trigo
nom
etric
al fu
nctio
ns
In
defin
ite In
tegr
al o
f Po
lyno
mia
ls, R
atio
nal
func
tions
, exp
onen
tials
(e
ax+b
), tri
gono
met
rical
fu
nctio
ns w
ith s
tand
ard
inte
gral
s an
d th
ose
that
Fi
ndin
g In
tegr
als
of
poly
nom
ials
, ra
tiona
l fun
ctio
ns, e
xpon
entia
ls a
nd
trigo
nom
etric
al fu
nctio
ns
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
18 19
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
22
inte
grat
e by
reco
gniti
on, b
y su
bstit
utio
n an
d by
par
ts
eval
uate
def
inite
inte
gral
s
find
area
s an
d vo
lum
es
can
be re
duce
d to
st
anda
rd in
tegr
al
Inte
grat
ion
by
reco
gniti
on, p
arts
and
su
bstit
utio
n
Def
inite
Inte
gral
Appl
icat
ion
of in
tegr
atio
n to
are
as a
nd v
olum
es
In
tegr
atin
g by
reco
gniti
on, b
y su
bstit
utio
n an
d by
par
ts
Eval
uatin
g de
finite
inte
gral
s
Appl
ying
inte
grat
ion
to fi
nd a
reas
and
vo
lum
es
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
inte
grat
ion
and
expl
orin
g th
eir
appl
icat
ions
in li
fe
R
elev
ant t
exts
TOPI
C 6
: NU
MER
ICA
L M
ETH
OD
S: to
be
cove
red
in fo
rm s
ix
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
20
TOPI
C 7
: CO
MPL
EX N
UM
BER
S
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
23
TOPI
C 6
: NU
MER
ICAL
MET
HO
DS:
to b
e co
vere
d in
form
six
TOPI
C 7
: CO
MPL
EX N
UM
BER
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
Com
plex
Num
bers
find
the
conj
ugat
es, m
odul
i and
ar
gum
ents
of c
ompl
ex n
umbe
rs
ca
rry
out o
pera
tions
with
com
plex
nu
mbe
rs
repr
esen
t com
plex
num
bers
on
an
Arga
nd d
iagr
am
In
terp
rete
geo
met
ric e
ffect
s of
:
- co
njug
atin
g a
com
plex
nu
mbe
r -
addi
ng, s
ubtra
ctin
g,
mul
tiply
ing
and
divi
ding
co
mpl
ex n
umbe
rs
Pa
rts o
f a c
ompl
ex
num
ber
C
onju
gate
, mod
ulus
an
d ar
gum
ent
O
pera
tions
Arga
nd d
iagr
am
Fi
ndin
g co
njug
ates
, mod
ulus
and
ar
gum
ent o
f com
plex
num
bers
Addi
ng, s
ubtra
ctin
g, m
ultip
lyin
g an
d di
vidi
ng c
ompl
ex n
umbe
rs
Rep
rese
ntin
g co
mpl
ex n
umbe
rs o
n an
Arg
and
diag
ram
Inte
rpre
ting
geom
etric
effe
cts
of:
-
conj
ugat
ing
a co
mpl
ex
num
ber
- a
ddin
g, s
ubtra
ctin
g,
mul
tiply
ing
and
divi
ding
co
mpl
ex n
umbe
rs
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
20 21
FOR
M S
IX (6
) SYL
LAB
US
8.2
CO
MPE
TEN
CY
MAT
RIX
: FO
RM
6 S
YLLA
BU
S
TOPI
C 1
: A
LGEB
RA
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
24
FORM
SIX
(6) S
YLLA
BU
S
8.2
CO
MPE
TEN
CY
MAT
RIX
: FO
RM
6 S
YLLA
BUS
TOPI
C 1
: AL
GEB
RA
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
Mat
rices
iden
tify
null
mat
rix, i
dent
ity m
atrix
, si
ngul
ar a
nd n
on-s
ingu
lar m
atrix
carr
y ou
t bas
ic o
pera
tions
of
mat
rices
ca
lcul
ate
dete
rmin
ant o
f a s
quar
e m
atrix
(up
to 3
x 3
)
find
inve
rse
of a
3 x
3 n
on- s
ingu
lar
mat
rix
ap
ply
the
resu
lt (A
B)-1
= B-1
A-1 fo
r no
n-si
ngul
ar m
atric
es to
sol
ve
prob
lem
s
cons
truct
2 x
2 m
atric
es to
repr
esen
t en
larg
emen
t, ro
tatio
n, re
flect
ion,
st
retc
h an
d sh
ear t
rans
form
atio
ns
us
e a
2 x
2 m
atrix
to re
pres
ent
certa
in g
eom
etric
al tr
ansf
orm
atio
n in
th
e x
– y
plan
e
us
e th
e co
mpo
site
tran
sfor
mat
ion
AB a
nd A
n in
prob
lem
sol
ving
deriv
e th
e re
latio
nshi
p be
twee
n th
e ar
ea s
cale
-fact
or o
f a tr
ansf
orm
atio
n an
d th
e de
term
inan
t of t
he
corre
spon
ding
mat
rix
Ty
pes
of m
atric
es
Basi
c op
erat
ion
(up
to
3 x
3)
D
eter
min
ant a
nd
inve
rse
Syst
ems
of li
near
eq
uatio
ns
Tran
sfor
mat
ions
D
iscu
ssin
g nu
ll m
atrix
, ide
ntity
mat
rix,
sing
ular
and
non
-sin
gula
r mat
rix
Ad
ding
, sub
tract
ing
and
mul
tiply
ing
mat
rices
C
alcu
latin
g de
term
inan
t of a
squ
are
mat
rix (u
p to
3 x
3)
Fi
ndin
g in
vers
e of
3 x
3 n
on- s
ingu
lar
mat
rices
Usi
ng th
e re
sult
(AB)
-1=
B-1A-1
for n
on-
sing
ular
mat
rices
to s
olve
pro
blem
s
C
onst
ruct
ing
2 x
2 m
atric
es to
re
pres
ent e
nlar
gem
ent,
rota
tion,
re
flect
ion,
stre
tch
and
shea
r tra
nsfo
rmat
ions
Usi
ng a
2 x
2 m
atrix
to re
pres
ent
certa
in g
eom
etric
al
trans
form
atio
ns in
the
x –
y pl
ane
Usi
ng th
e co
mpo
site
tran
sfor
mat
ion
AB
and
An in
prob
lem
sol
ving
Der
ivin
g an
d di
scus
sing
the
rela
tions
hip
betw
een
the
area
sca
le-
fact
or o
f a tr
ansf
orm
atio
n an
d th
e
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or
softw
are
R
elev
ant
text
s
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
22
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
25
so
lve
sim
ulta
neou
s eq
uatio
ns in
2 o
r 3
unkn
owns
by
redu
cing
them
to th
e m
atrix
equ
atio
n of
the
form
(AX
=b)
dete
rmin
ant o
f the
cor
resp
ondi
ng
mat
rix
So
lvin
g si
mul
tane
ous
equa
tions
in 2
or
3 un
know
ns b
y re
duci
ng th
em to
the
mat
rix e
quat
ion
form
(Ax
=b)
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
mat
rices
and
exp
lorin
g th
eir
appl
icat
ions
in li
fe
Mat
hem
atic
al
Indu
ctio
n
desc
ribe
the
proc
ess
of
mat
hem
atic
al in
duct
ion
prov
e by
mat
hem
atic
al in
duct
ion
to
esta
blis
h a
give
n re
sult
us
e th
e st
rate
gy o
f con
duct
ing
limite
d tri
als
to fo
rmul
ate
a co
njec
ture
and
pro
ve it
by
the
met
hod
of in
duct
ion
Pr
oof b
y In
duct
ion
Con
ject
ure
D
iscu
ssin
g th
e pr
oces
ses
of
mat
hem
atic
al in
duct
ion
Prov
ing
by m
athe
mat
ical
indu
ctio
n to
es
tabl
ish
give
n re
sults
Usi
ng th
e st
rate
gy o
f con
duct
ing
limite
d tri
als
to fo
rmul
ate
conj
ectu
re
and
prov
ing
it by
the
met
hod
of
indu
ctio
n
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or
softw
are
R
elev
ant
text
s
Gro
ups
de
fine
a bi
nary
ope
ratio
n
defin
e cl
osur
e, c
omm
utat
ion,
as
soci
atio
n, d
istri
butio
n, id
entit
y an
d in
vers
e el
emen
t
defin
e a
grou
p
use
the
basi
c pr
oper
ties
to s
how
that
a
give
n st
ruct
ure
is, o
r is
not,
a gr
oup
so
lve
prob
lem
s in
volv
ing
bina
ry
oper
atio
ns a
nd p
rope
rties
of a
gro
up
Bi
nary
ope
ratio
ns
Ba
sic
prop
ertie
s of
a
grou
p
D
efin
ing
a bi
nary
ope
ratio
n
Dis
cuss
ing
clos
ure,
com
mut
atio
n,
asso
ciat
ion,
dis
tribu
tion,
iden
tity
and
inve
rse
elem
ent
D
iscu
ssin
g a
grou
p
Usi
ng th
e ba
sic
prop
ertie
s to
sho
w th
at
a gi
ven
stru
ctur
e is
, or i
s no
t, a
grou
p
Solv
ing
prob
lem
s in
volv
ing
bina
ry
oper
atio
ns a
nd p
rope
rties
of a
gro
up
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or
softw
are
R
elev
ant
text
s
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
22 23
TOPI
C 2
: G
EOM
ETRY
AN
D V
ECTO
RS
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
26
TOPI
C 2
: G
EOM
ETR
Y AN
D V
ECTO
RS
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
(up
to
thre
e di
men
sion
s)
fin
d ve
ctor
and
Car
tesi
an
equa
tions
of a
stra
ight
line
in 3
D
fin
d th
e cr
oss
prod
uct o
f giv
en
vect
ors
us
e cr
oss
prod
uct t
o fin
d ar
ea o
f pl
ane
shap
es
find
vect
or, p
aram
etric
and
C
arte
sian
equ
atio
ns o
f a p
lane
find
the
angl
e be
twee
n a
line
and
a pl
ane,
two
lines
and
two
plan
es
de
term
ine
whe
ther
two
lines
are
pa
ralle
l, in
ters
ectin
g or
ske
wed
dete
rmin
e w
heth
er tw
o lin
es
inte
rsec
t
find
the
perp
endi
cula
r dis
tanc
e fro
m a
poi
nt to
a s
traig
ht li
ne a
nd
the
coor
dina
tes
of th
e fo
ot o
f the
pe
rpen
dicu
lar
de
term
ine
whe
ther
a li
ne li
es in
, is
para
llel t
o or
inte
rsec
ts a
pla
ne
fin
d th
e po
int o
f int
erse
ctio
n of
a
line
and
a pl
ane
find
the
line
of in
ters
ectio
n of
two
plan
es
fin
d th
e pe
rpen
dicu
lar d
ista
nce
from
a p
oint
to a
pla
ne
so
lve
prob
lem
s in
volv
ing
lines
and
pl
anes
Ve
ctor
equ
atio
n of
a
stra
ight
line
Eq
uatio
n of
a p
lane
C
ross
pro
duct
Fi
ndin
g ve
ctor
and
Car
tesi
an e
quat
ions
of
a s
traig
ht li
ne in
3D
Find
ing
the
cros
s pr
oduc
t of g
iven
ve
ctor
s
Usi
ng c
ross
pro
duct
to fi
nd a
rea
of p
lane
sh
apes
Fi
ndin
g ve
ctor
, par
amet
ric a
nd C
arte
sian
eq
uatio
ns o
f a p
lane
Find
ing
the
angl
e be
twee
n a
line
and
a pl
ane,
two
lines
and
two
plan
es
D
eter
min
ing
whe
ther
two
lines
are
pa
ralle
l, in
ters
ectin
g or
ske
wed
Det
erm
inin
g w
heth
er tw
o lin
es in
ters
ect
Find
ing
the
perp
endi
cula
r dis
tanc
e fro
m
a po
int t
o a
stra
ight
line
and
the
coor
dina
tes
of th
e fo
ot o
f the
pe
rpen
dicu
lar
D
eter
min
ing
whe
ther
a li
ne li
es in
, is
para
llel t
o or
inte
rsec
ts a
pla
ne
Fi
ndin
g th
e po
int o
f int
erse
ctio
n of
a li
ne
and
a pl
ane
Find
ing
the
line
of in
ters
ectio
n of
two
plan
es
Fi
ndin
g th
e pe
rpen
dicu
lar d
ista
nce
from
a
poin
t to
a pl
ane
So
lvin
g pr
oble
ms
invo
lvin
g lin
es a
nd
plan
es
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant t
exts
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
24
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
27
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
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
vect
ors
and
expl
orin
g th
eir a
pplic
atio
ns in
life
TOPI
C 3
SER
IES
AND
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
Serie
s
use
stan
dard
resu
lts fo
r r, r
2 and
r
3 to
find
rela
ted
sum
s
use
the
met
hod
of d
iffer
ence
s to
ob
tain
the
sum
of f
inite
ser
ies
u
se T
aylo
r’s a
nd M
acla
urin
’s
serie
s fo
r app
roxi
mat
ion
so
lve
prob
lem
s in
volv
ing
met
hod
of d
iffer
ence
s as
wel
l as
Tayl
or’s
an
d M
acla
urin
’s s
erie
s
St
anda
rd re
sults
M
etho
d of
diff
eren
ces
M
acla
urin
’s s
erie
s
Tayl
or’s
ser
ies
Fi
ndin
g re
late
d su
ms
usin
g st
anda
rd
resu
lts fo
r r, r
2 and
r3
Obt
aini
ng th
e su
m o
f fin
ite s
erie
s us
ing
the
met
hod
of d
iffer
ence
s
U
sing
Tay
lor’s
and
Mac
laur
in’s
ser
ies
for a
ppro
xim
atio
n
So
lvin
g pr
oble
ms
invo
lvin
g m
etho
d of
di
ffere
nces
as
wel
l as
Tayl
or’s
and
M
acla
urin
’s s
erie
s
Rep
rese
ntin
g lif
e ph
enom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g se
ries
and
expl
orin
g th
eir a
pplic
atio
ns in
life
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant
text
s
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
27
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
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
vect
ors
and
expl
orin
g th
eir a
pplic
atio
ns in
life
TOPI
C 3
SER
IES
AND
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
Serie
s
use
stan
dard
resu
lts fo
r r, r
2 and
r
3 to
find
rela
ted
sum
s
use
the
met
hod
of d
iffer
ence
s to
ob
tain
the
sum
of f
inite
ser
ies
u
se T
aylo
r’s a
nd M
acla
urin
’s
serie
s fo
r app
roxi
mat
ion
so
lve
prob
lem
s in
volv
ing
met
hod
of d
iffer
ence
s as
wel
l as
Tayl
or’s
an
d M
acla
urin
’s s
erie
s
St
anda
rd re
sults
M
etho
d of
diff
eren
ces
M
acla
urin
’s s
erie
s
Tayl
or’s
ser
ies
Fi
ndin
g re
late
d su
ms
usin
g st
anda
rd
resu
lts fo
r r, r
2 and
r3
Obt
aini
ng th
e su
m o
f fin
ite s
erie
s us
ing
the
met
hod
of d
iffer
ence
s
U
sing
Tay
lor’s
and
Mac
laur
in’s
ser
ies
for a
ppro
xim
atio
n
So
lvin
g pr
oble
ms
invo
lvin
g m
etho
d of
di
ffere
nces
as
wel
l as
Tayl
or’s
and
M
acla
urin
’s s
erie
s
Rep
rese
ntin
g lif
e ph
enom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g se
ries
and
expl
orin
g th
eir a
pplic
atio
ns in
life
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or s
oftw
are
R
elev
ant
text
s
TOPI
C 3
SER
IES
AN
D S
EQU
ENC
ES
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
25
TOPI
C 4
: TR
IGO
NO
MET
RY: c
over
ed in
form
five
TOPI
C 5
: CA
LCU
LUS
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
28
TOPI
C 4
: TR
IGO
NO
MET
RY: c
over
ed in
form
five
TOPI
C 5
: CAL
CU
LUS
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
1st O
rder
Diff
eren
tial
equa
tions
form
ulat
e a
stat
emen
t inv
olvi
ng a
ra
te o
f cha
nge
as a
diff
eren
tial
equa
tion
so
lve
diffe
rent
ial e
quat
ions
by
inte
grat
ion
in th
e ca
se w
here
va
riabl
es a
re s
epar
able
sket
ch ty
pica
l exa
mpl
es o
f a fa
mily
of
cur
ves
repr
esen
ting
a ge
nera
l so
lutio
n of
a d
iffer
entia
l equ
atio
n
fin
d a
parti
cula
r sol
utio
n of
a
diffe
rent
ial e
quat
ion
give
n in
itial
co
nditi
ons
solv
e pr
oble
ms
invo
lvin
g 1st
ord
er
diffe
rent
ial e
quat
ion
R
ates
of c
hang
e
Se
para
tion
of V
aria
bles
Solu
tion
by In
tegr
atio
n
Fo
rmul
atin
g st
atem
ents
invo
lvin
g ra
tes
of c
hang
e as
diff
eren
tial
equa
tions
Solv
ing
diffe
rent
ial e
quat
ions
by
inte
grat
ion
in th
e ca
se w
here
va
riabl
es a
re s
epar
able
Sket
chin
g ty
pica
l exa
mpl
es o
f a
fam
ily o
f cur
ves
repr
esen
ting
a ge
nera
l sol
utio
n of
a d
iffer
entia
l eq
uatio
n
Fi
ndin
g pa
rticu
lar s
olut
ions
of
diffe
rent
ial e
quat
ions
giv
en in
itial
co
nditi
ons
Solv
ing
prob
lem
s in
volv
ing
1st o
rder
di
ffere
ntia
l equ
atio
ns
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
1st
orde
r diff
eren
tial e
quat
ions
and
ex
plor
ing
thei
r app
licat
ions
in li
fe
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or
softw
are
R
elev
ant
text
s
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
25 26
TOPI
C 6
: N
UM
ERIC
AL
MET
HO
DS
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
29
TOPI
C 6
: 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
, 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
Num
eric
al
Met
hods
defin
e er
ror
di
stin
guis
h be
twee
n ab
solu
te e
rror a
nd
rela
tive
erro
r
estim
ate
erro
rs in
cal
cula
tion
incl
udin
g th
e us
e of
𝜕𝜕𝜕𝜕≈
𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝜕𝜕𝜕𝜕
appr
oxim
ate
the
root
of a
n eq
uatio
n by
gr
aphi
cal m
eans
or s
ign
chan
ge
deriv
e a
conv
ergi
ng it
erat
ive
form
ula
for
solv
ing
a gi
ven
equa
tion
solv
e th
e eq
uatio
n us
ing
itera
tive
proc
edur
e
de
rive
the
New
ton
– R
aphs
on fo
rmul
a
solv
e eq
uatio
ns u
sing
the
New
ton
– R
aphs
on m
etho
d
re
cogn
ise
case
s w
here
the
itera
tive
met
hod
may
fail
to c
onve
rge
to th
e re
quire
d ro
ot
solv
e pr
oble
ms
invo
lvin
g th
e us
e of
ite
rativ
e pr
oced
ures
in ro
ot fi
ndin
g
deriv
e th
e tra
pezi
um ru
le
es
timat
e th
e ar
ea u
nder
a c
urve
usi
ng
the
trape
zium
rule
Er
rors
Ite
rativ
e m
etho
ds
New
ton
– R
aphs
on
met
hod
Tr
apez
ium
rule
D
efin
ing
erro
r
Dis
tingu
ishi
ng b
etw
een
abso
lute
er
ror a
nd re
lativ
e er
ror
Es
timat
ing
erro
rs in
cal
cula
tions
in
clud
ing
the
use
of 𝜕𝜕𝜕𝜕≈
𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝜕𝜕𝜕𝜕
Appr
oxim
atin
g th
e ro
ot o
f an
equa
tion
by g
raph
ical
mea
ns o
r sig
n ch
ange
Der
ivin
g a
conv
ergi
ng it
erat
ive
form
ula
for s
olvi
ng a
giv
en e
quat
ion
Solv
ing
equa
tions
usi
ng it
erat
ive
proc
edur
e
D
eriv
ing
the
New
ton
– R
aphs
on
form
ula
So
lvin
g eq
uatio
ns u
sing
the
New
ton
– R
aphs
on m
etho
d
R
ecog
nisi
ng c
ases
whe
re th
e ite
rativ
e m
etho
d m
ay fa
il to
co
nver
ge to
the
requ
ired
root
Solv
ing
prob
lem
s in
volv
ing
the
use
of it
erat
ive
proc
edur
es in
root
fin
ding
D
eriv
ing
the
trape
zium
rule
Estim
atin
g th
e ar
ea u
nder
a c
urve
us
ing
the
trape
zium
rule
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or
softw
are
R
elev
ant
text
s
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
27
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
30
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
ex
plai
n ho
w to
set
bou
nds
for t
he a
rea
unde
r the
cur
ve u
sing
rect
angl
e or
tra
pezi
a
solv
e pr
oble
ms
invo
lvin
g th
e tra
pezi
um
rule
Ex
plai
ning
how
to s
et b
ound
s fo
r th
e ar
ea u
nder
the
curv
e us
ing
rect
angl
e or
trap
ezia
Solv
ing
prob
lem
s in
volv
ing
the
trape
zium
rule
Rep
rese
ntin
g lif
e ph
enom
ena
usin
g m
athe
mat
ical
mod
els
invo
lvin
g nu
mer
ical
met
hods
and
exp
lorin
g th
eir a
pplic
atio
ns in
life
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
27 28
TOPI
C 7
: C
OM
PLEX
NU
MB
ERS
Pure
Mat
hem
atics
Syl
labu
s For
m 5
– 6
2016
31
TOPI
C 7
: C
OM
PLEX
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
Com
plex
N
umbe
rs
so
lve
poly
nom
ial e
quat
ions
with
at l
east
on
e pa
ir of
non
- rea
l roo
ts
ex
pres
s co
mpl
ex n
umbe
rs in
pol
ar fo
rm
carr
y ou
t ope
ratio
ns o
f com
plex
nu
mbe
rs e
xpre
ssed
in p
olar
form
illust
rate
equ
atio
ns a
nd in
equa
litie
s in
volv
ing
com
plex
num
bers
by
mea
ns o
f lo
ci in
an
Arga
nd d
iagr
am
de
rive
the
deM
oivr
e’s
Theo
rem
prov
e th
e de
Moi
vre’
s Th
eore
m
pr
ove
trigo
nom
etric
al id
entit
ies
usin
g de
Moi
vre’
s Th
eore
m
so
lve
equa
tions
usi
ng th
e de
Moi
vre’
s Th
eore
m
solv
e pr
oble
ms
invo
lvin
g co
mpl
ex
num
bers
Eq
uatio
ns (u
p to
ord
er 5
)
Po
lar f
orm
(r
(cos
+i s
in
) = re
i)
Lo
ci
deM
oivr
e’s
Theo
rem
nth
root
s of
uni
t
So
lvin
g po
lyno
mia
l equ
atio
ns w
ith a
t le
ast o
ne p
air o
f non
- rea
l roo
ts
Ex
pres
sing
com
plex
num
bers
in p
olar
fo
rm
D
ivid
ing
and
mul
tiply
ing
com
plex
nu
mbe
rs e
xpre
ssed
in p
olar
form
Illus
tratin
g eq
uatio
ns a
nd in
equa
litie
s in
volv
ing
com
plex
num
bers
by
mea
ns
of lo
ci in
an
Arga
nd d
iagr
am
D
eriv
ing
and
dis
cuss
ing
the
deM
oivr
e’s
Theo
rem
Prov
ing
the
deM
oivr
e’s
Theo
rem
Prov
ing
trigo
nom
etric
al id
entit
ies
usin
g de
Moi
vre’
s Th
eore
m
So
lvin
g eq
uatio
ns u
sing
the
deM
oivr
e’s
Theo
rem
Solv
ing
prob
lem
s in
volv
ing
com
plex
nu
mbe
rs
R
epre
sent
ing
life
phen
omen
a us
ing
mat
hem
atic
al m
odel
s in
volv
ing
com
plex
num
bers
and
exp
lorin
g th
eir
appl
icat
ions
in li
fe
IC
T to
ols
Br
aille
m
ater
ials
and
eq
uipm
ent
Ta
lkin
g bo
oks
or
softw
are
R
elev
ant
text
s
9.0
ASS
ESSM
ENT
9.
1 As
sess
men
t Obj
ectiv
es
The
ass
essm
ent w
ill te
st c
andi
date
’s a
bilit
y to
:
9.1.
1 us
e m
athe
mat
ical
sym
bols
, ter
ms
and
defin
ition
s ap
prop
riate
ly
9.1.
2 sk
etch
gra
phs
accu
rate
ly
29
9.0 ASSESSMENT
9.1 Assessment Objectives
The assessment will test candidate’s ability to:
9.1.1 use mathematical symbols, terms and definitions appropriately 9.1.2 sketch graphs accurately 9.1.3 use appropriate formulae, algorithms and strategies to solve routine and non-routine problems in Pure Mathe-
matics 9.1.4 solve problems in Pure Mathematics systematically9.1.5 apply mathematical reasoning and communicate mathematical ideas clearly 9.1.6 conduct mathematical proofs in the expected manner9.1.7 construct and use appropriate mathematical models for a given life situation 9.1.8 conduct research projects (including those related to enterprise) accurately and systematically.
9.2 Scheme of Assessment
Form 5 - 6 Pure Mathematics assessment will be based on 30% continuous assessment and 70% summative assess-ment.The syllabus’ scheme of assessment caters for all learners. Arrangements, accommodations and modifications must be visible in both continuous and summative assessments to enable candidates with special needs to access assess-ments 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 (tran-sitory or permanent) may be eligible to receive an award based on the assessment they would have taken.
a) Continuous Assessment
Continuous assessment for Form 5 – 6 will consists of topic tasks, written tests, end of term examinations, project and profiling to measure soft skills.
i. Topic Tasks These are activities that teachers use in their day to day teaching. These should include practical activities, assign-ments and group work activities.
ii. Written TestsThese 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 or provincial level.iv. Project This should be done from term two to term five. Summary of Continuous Assessment TasksFrom term two to five, candidates are expected to have done the following recorded tasks:• 1 Topic task per term• 2 Written tests per term• 1 End of term test per term• 1 Project in five termsDetailed Continuous Assessment Tasks Table
Pure Mathematics Syllabus Forms 5 - 6
30
Pure Mathematics Syllabus Form 5– 6 2016 33
Summary of Continuous Assessment Tasks
From term two to five, candidates are expected to have done the following recorded tasks:
1 Topic task per term 2 Written tests per term 1 End of term test per term 1 Project in five terms
Detailed Continuous Assessment Tasks Table
Term Number of Topic Tasks
Number of Written Tests
Number of End of Term Tests
Project Total
2 1 2 1 1
3 1 2 1
4 1 2 1
5 1 2 1
Weighting 25% 25% 25% 25% 100%
Actual Weight 7.5% 7.5% 7.5% 7.5% 30%
Specification Grid for Continuous Assessment
Component Skills
Topic Tasks Written Tests End of Term Project
Skill 1
Knowledge
Comprehensive
50% 50% 50% 20%
Skill 2
Application
40% 40% 40% 40%
Pure Mathematics Syllabus Form 5– 6 2016 33
Summary of Continuous Assessment Tasks
From term two to five, candidates are expected to have done the following recorded tasks:
1 Topic task per term 2 Written tests per term 1 End of term test per term 1 Project in five terms
Detailed Continuous Assessment Tasks Table
Term Number of Topic Tasks
Number of Written Tests
Number of End of Term Tests
Project Total
2 1 2 1 1
3 1 2 1
4 1 2 1
5 1 2 1
Weighting 25% 25% 25% 25% 100%
Actual Weight 7.5% 7.5% 7.5% 7.5% 30%
Specification Grid for Continuous Assessment
Component Skills
Topic Tasks Written Tests End of Term Project
Skill 1
Knowledge
Comprehensive
50% 50% 50% 20%
Skill 2
Application
40% 40% 40% 40%
Pure Mathematics Syllabus Form 5– 6 2016 34
Analysis
Skill 3
Synthesis
Evaluation
10% 10% 10% 40%
Total 100% 100% 100% 100%
Actual weighting
7.5% 7.5% 7.5% 7.5%
9.3 Assessment Model Learners will be assessed using both continuous and summative assessments.
a)
Assessment of learner performance in Pure Mathematics
100%
Continuous assessment 30%
Profiling
Continuous assessment mark
30%
Profile
End of term Tests 7.5%
Written Tests
7.5%
Topic Tasks 7.5%
+ +
Summative assessment 70%
Examination mark
70%
Paper 1 35%
Paper 2 35%
Project
7.5%
Specification Grid for Continuous Assessment
Pure Mathematics Syllabus Forms 5 - 6
31
Assessment of learner performance in Pure Mathematics100%
Continuous assessment 30 %
Continuous assessment mark =30 %
FINAL MARKS 100 %
Summative Assessment70 %
Summative Assessment mark= 70 %
Topic Tasks 7.5%
Profiling
Profile
ExitProfile
Written Tests 7.5%
End of term Tests
7.5%
Project7.5%
Paper 1 35%
Paper 2 35%
9.3 Assessment modelLearners will be assessed using both continuous and summative assessments
Pure Mathematics Syllabus Forms 5 - 6
32
Pure
Mat
hem
atic
s Sy
llabu
s Fo
rms
5 - 6
33
