pure mathematics syllabus - globtorch mathematics forms 3 - 4.pdf · pure mathematics syllabus...

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)

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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


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

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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.

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elev

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tool

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Pure

Mat

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Syl

labu

s For

m 3

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12

TOPI

C 2

: PO

LYN

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C 3

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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


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


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


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


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


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


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


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


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


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


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


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


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


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


(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

22


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


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


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%

23


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%

25


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pure mathematics syllabus - globtorch mathematics forms 3 - 4.pdf · pure mathematics syllabus...

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