ZIMBABWE

MINISTRY OF PRIMARY AND SECONDARY EDUCATION

ADDITIONAL MATHEMATICS

SYLLABUS

FORMS 5 - 6

2015 - 2022Curriculum Development and Technical Services

P. O. Box MP 133Mount Pleasant

Harare

© All Rrights Reserved2015

Additional Mathematics Syllabus Forms 5 - 6

i

ACKNOWLEDGEMENTSThe Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued contribution in the production of this syllabus:

• National Mathematics panel• Zimbabwe School Examinations Council (ZIMSEC)• United Nations International Children’s Emergency Fund (UNICEF)• UnitedNationsEducationalScientificandCulturalOrganisation(UNESCO)• Representatives from Higher and Tertiary institutions

ii

Additional Mathematics Syllabus Forms 5 - 6

CONTENTSACKNOWLEDGEMENTS .............................................................................................................i

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

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

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

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

4.0 OBJECTIVES ..........................................................................................................................1

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

6.0 TOPICS ...................................................................................................................................3

7.0 SCOPE AND SEQUENCE ......................................................................................................4

8.0 COMPETENCY MATRIX .........................................................................................................15

FORM FIVE (5) ..............................................................................................................................15

FORM SIX (6) ................................................................................................................................29

9.0 ASSESSMENT ........................................................................................................................50

1

1.0 PREAMBLE

1.1 INTRODUCTION

The Form 5 – 6 Additional Mathematics syllabus builds on the Form 3 - 4 Additional Mathematics syllabus and is designed to cater for the needs of post Form 4, mathematically outstanding learners. The teaching and learning that is based on the syllabus provides further opportunities for such learners to enjoy doing and using mathematics and, in the process developing a deeper appreciation and understanding of the nature of mathematics, its pivotal role in Science, Technology, Engineering and Mathematics (STEM) and life in general and hence promoting sustainable development. The intentionistoprovideafirmbasisonwhichtopursuefurther studies in mathematics and related areas which are critical for national development and global compet-itiveness in the 21st century. In addition to providing a firmbase,thelearningareaisalsoexpectedtoenhancelearners’confidenceandsenseofselffulfilment,collegiality and intellectual honesty, hence contributing to their growth in the acquisition of Unhu/Ubuntu//Vumunhu values.

1.2 RATIONALE

In its socio-economic transformation agenda, Zimbabwe has embarked on an industrialisation development strategy, where high level mathematical knowledge and skills are a prerequisite. To this end, Additional Math-ematics learners are expected to emerge with a solid basis for further studies in STEM, and with enhanced mathematical competencies. These include abstract and analytical thinking, logical reasoning, designing algorithms, communicating mathematical information effectively, conjecturing and proving conjectures, modelling life phenomena into mathematical language in order to better understand those phenomena and to solve related problems and applying mathematics in a wide variety of contexts. It is from the pool of individuals with such competencies that some of Zimbabwe’s most creative thinkers, innovators, inventors and mathemati-cally literate entrepreneurs are expected to emerge. This is critical for sustainable development.

1.3 SUMMARY OF CONTENT

The Form 5- 6 Additional Mathematics syllabus will cover the theoretical concepts and their applications. This two year learning area consists of Pure Mathematics, Mechanics and Statistics.

1.4 ASSUMPTIONS

The syllabus assumes that the learner:

• hasatalentinmathematics• hasahighpassinMathematicsorapassineither

Pure Mathematics or Additional Mathematics at Form 4.

• IsexcellinginPureMathematicsatForm5

1.5 CROSS- CUTTING ISSUES

The following are some of the cross cutting themes catered for in the teaching and learning of Additional Mathematics:-

• Businessandfinancialliteracy• Disasterandriskmanagement• Communication• Teambuilding• Problemsolving• Environmentalissues• Enterpriseskills• InformationCommunicationandTechnology(ICT)• HIV&AIDS

2.0 PRESENTATION OF SYLLABUSThe Additional Mathematics syllabus is a single document covering Form 5–6. It contains the preamble, aims, objectives, syllabus topics, scope and sequence, competency matrix and assessment procedures. The syllabus also suggests a list of resources to be used during the teaching and learning process.

3.0 AIMSThe syllabus will enable learners to:

3.1 further develop mathematical knowledge and skillsinawaythatpromotesfulfilmentanden-joymentandlaysafirmfoundationforfurtherstudies and lifelong learning

3.2 acquire an additional range of mathematical skills, particularly those applicable to other learning areas and various life contexts, in-cluding enterprise

3.3 enhanceconfidence,criticalthinking,innova-tiveness, creativity and problem solving skills for sustainable development

Additional Mathematics Syllabus Forms 5 - 6

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3.4 develop a greater appreciation of the role of mathematics in personal, community and na-tional development in line with Unhu/Ubuntu/Vumunhu

3.5 further develop an appreciation for and ability to use I.C.T tools in solving problems in math-ematical and other contexts

3.6 develop the ability to communicate mathemati-cal ideas and to learn cooperatively

4.0 OBJECTIVESThe learners should be able to:

4.1 use mathematical skills and techniques that are necessary for further studies

4.2 use mathematical models to solve problems in life and for sustainable development

4.3 use I.C.T tools in solving problems in mathe-matical and other contexts

4.4 demonstrate expertise, perseverance, coop-eration and intellectual honesty for personal, community and national development

4.5 interpret mathematical results and their impli-cations in life

4.6 communicate mathematical results and their implications in life

4.7 draw inferences through correct manipulation of data

4.8 conduct research projects including those related to enterprise

4.9 apply relevant mathematical notations and terms in problem solving

4.10 present data through appropriate presenta-tions

4.11 apply mathematical skills in other learning areas

4.12 conduct mathematical proofs

5.0 METHODOLOGY AND TIME ALLOCATION

5.1 Methodology

A constructivist based teaching and learning approach is recommended for the Form 5 – 6 Additional Mathematics 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

exchange of ideas and information; inclusivity and respect for each other’s views, regardless of personal circumstances (in terms of, for example: gender, ap-pearance, disability and religious beliefs); collaboration and cooperation; 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 rel-evant challenges that excite learners, and help to make learningAdditionalMathematicsanenjoyable,fulfillingexperience. Such challenges could be posed in the form of problems that encourage learners to create new mathematical 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 thelearningareaandinlife.Definitelyspoonfeedingisnot and cannot be an appropriate stimulus, as it does not help learners to develop critical thinking, 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 Additional Mathematics teaching and learning process, with the teacher playing the facilitator’s 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 Additional Mathematics teacher needs to carefully analyse the new concepts and principles he/she intends to introduce, identify the relevant pre-requisite knowledge, assess to identify any gaps,andtakeappropriatestepstofillsuchgaps.The following, is a list of teaching and learning approach-es that are consistent with, and supportive of the above approach:

5.1.1 Guided discovery 5.1.2 Group work5.1.3 Interactive e-learning5.1.4 Problem solving5.1.5 Discussion5.1.6 Modelling5.1.7 Visual tactile

The above suggested methods should be enhanced through the application of multi-sensory (inclusive) approaches.

Additional Mathematics Syllabus Forms 5 - 6

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5.2 Time Allocation

10 periods of 35 minutes each per week should be allocated. Learners are expected to participate in the following activities:-

- MathematicsOlympiads- Mathematics and Science exhibitions- Mathematics seminars- Mathematical tours to tertiary and other institu-

tions

6.0 TOPICSThe following topics will be covered from Form 5 - 6

6.1 Pure Mathematics

6.1.1 Algebra6.1.2 Series6.1.3 Trigonometry 6.1.4 Mathematical Induction6.1.5 Geometry and Vectors

6.1.6 Calculus

6.2 Mechanics

6.2.1 Particle dynamics6.2.2 Elasticity6.2.3 Energy, work and power6.2.4 Circular motion6.2.5 Simple harmonic motion

6.3 Statistics

6.3.1 Probability 6.3.2 Random Variables6.3.3 Sampling and estimation6.3.4 Statistical inference6.3.5 Bivariate data

Additional Mathematics Syllabus Forms 5 - 6

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FORM

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Addi

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8.0

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MAT

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TOPI

C 1

: A

LGEB

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27

8.0

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MAT

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FIV

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)

PUR

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Pa

rtial

Fra

ctio

ns

ObliqueAsymptotes

G

raph

s

Ex

pres

sing

ratio

nal f

unct

ions

in

parti

al fr

actio

ns

Ex

plor

ing

and

dete

rmin

ing

key

feat

ures

of r

atio

nal f

unct

ion

grap

hs, i

nclu

ding

obl

ique

asym

ptot

es in

cas

es w

here

degr

ee o

f num

erat

or a

nd

deno

min

ator

are

at m

ost

two

IC

T to

ols

R

elev

ant t

exts

G

eo-b

oard

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

16

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

28

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

sk

etch

gra

phs

of ra

tiona

l

func

tions

so

lve

prob

lem

s in

volv

ing

ratio

nal f

unct

ions

Sk

etch

ing

grap

hs o

f rat

iona

l

func

tions

, inc

ludi

ng th

e

dete

rmin

atio

n of

obl

ique

asym

ptot

es

So

lvin

g p

robl

ems

invo

lvin

g

ratio

nal f

unct

ions

MAT

RIC

ES A

ND

LIN

EAR

SP

ACES

defin

e th

e sy

stem

s of

line

ar

equa

tions

de

term

ine

cons

iste

ncy

or

inco

nsis

tenc

y of

sys

tem

s of

linea

r equ

atio

ns

in

terp

ret g

eom

etric

ally

the

cons

iste

ncy

or in

cons

iste

ncy

of s

yste

ms

of li

near

equ

atio

ns

re

late

to s

ingu

larit

y th

e

corre

spon

ding

squ

are

mat

rix

of a

sys

tem

of l

inea

r

equa

tions

so

lve

linea

r equ

atio

ns o

f

cons

iste

nt s

yste

ms

so

lve

prob

lem

s in

volv

ing

Li

near

equ

atio

ns

Sp

aces

and

sub

spac

es

Discussingthesystem

soflinear

equa

tions

Discussinganddeterm

iningthe

cons

iste

ncy

or in

cons

iste

ncy

of

syst

ems

of li

near

equ

atio

ns

In

terp

retin

g ge

omet

rical

ly th

e

cons

iste

ncy

or in

cons

iste

ncy

of

syst

ems

of li

near

equ

atio

ns

R

elat

ing

to s

ingu

larit

y th

e

corre

spon

ding

squ

are

mat

rix o

f a

syst

em o

f lin

ear e

quat

ions

So

lvin

g lin

ear e

quat

ions

of

cons

iste

nt s

yste

ms

So

lvin

g pr

oble

ms

invo

lvin

g

syst

ems

of li

near

equ

atio

ns

IC

T to

ols

R

elev

ant

text

s

En

viro

nmen

t

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

16 17

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

29

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

syst

ems

of li

near

equ

atio

ns

de

fine

a lin

ear s

pace

and

a

sub-

spac

e

so

lve

prob

lem

s in

volv

ing

linea

r spa

ces

and

sub-

spac

es

Discussingpropertiesoflinear

spac

es a

nd s

ub-s

pace

s

So

lvin

g pr

oble

ms

invo

lvin

g li

near

spac

es a

nd s

ub-s

pace

s

GR

OU

PS

de

fine

a gr

oup

de

term

ine

whe

ther

or n

ot a

give

n st

ruct

ure

is a

gro

up

de

fine

the

orde

r of t

he g

roup

and

elem

ents

of a

gro

up

de

fine

a su

bgro

up

de

term

ine

whe

ther

or n

ot a

give

n st

ruct

ure

is a

sub

gro

up

in s

impl

e ca

ses

st

ate

the

LaG

rang

e’s

theo

rem

ap

ply

the

LaG

rang

e’s

theo

rem

con

cern

ing

the

orde

r

Pr

oper

ties

Orderofelements

Si

mpl

e su

bgro

ups

La

Gra

nge’

s th

eore

m

St

ruct

ure

of fi

nite

gro

ups

Is

omor

phis

m

Discussinggroupsand

dete

rmin

ing

whe

ther

or n

ot a

give

n st

ruct

ure

is a

gro

up

Determiningtheordero

fagroup

and

the

orde

r of e

lem

ents

of a

grou

p

Discussingsubgroupsand

dete

rmin

ing

whe

ther

or n

ot a

give

n st

ruct

ure

is a

sub

grou

p in

sim

ple

case

s

Discussingandapplyingthe

LaG

rang

e’s

theo

rem

con

cern

ing

IC

T to

ols

R

elev

ant

text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

18

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

30

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

of a

sub

grou

p of

a fi

nite

grou

p

de

fine

a cy

clic

gro

up

de

mon

stra

te fa

milia

rity

with

the

stru

ctur

e of

a fi

nite

gro

up

up to

ord

er 7

de

fine

isom

orph

ism

bet

wee

n

grou

ps

de

term

ine

whe

ther

or n

ot

give

n fin

ite g

roup

s ar

e

isom

orph

ic

so

lve

prob

lem

s in

volv

ing

grou

ps

the

orde

r of a

sub

grou

p of

a fi

nite

grou

p

Discussingandfindingexamples

of c

yclic

gro

ups

Ex

plor

ing

prop

ertie

s of

stru

ctur

es

of f

inite

gro

ups

up to

ord

er 7

Discussinganddeterm

ining

whe

ther

or n

ot g

iven

fini

te g

roup

s

are

isom

orph

ic

So

lvin

g pr

oble

ms

invo

lvin

g

grou

ps

18 19

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 2

: SE

RIE

S

31

TOPI

C 2

: SE

RIE

S

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

SUM

MAT

ION

OF

SER

IES

us

e th

e st

anda

rd re

sults

to

find

rela

ted

sum

s

de

rive

the

met

hod

of

diffe

renc

es

fin

d th

e su

m o

f fin

ite s

erie

s

usin

g m

etho

d of

diff

eren

ces

de

term

ine

the

sum

to in

finity

of a

con

verg

ent s

erie

s by

cons

ider

ing

the

sum

to n

term

s

so

lve

prob

lem

s in

volv

ing

serie

s

St

anda

rd re

sults

(∑𝒓𝒓,∑𝒓𝒓𝟐𝟐

,∑𝒓𝒓𝟑𝟑

)

Met

hod

of d

iffer

ence

s

Su

m to

infin

ity

Fi

ndin

g re

late

d su

ms

usin

g th

e

stan

dard

resu

lts

Ex

plor

ing

and

deriv

ing

the

met

hod

of d

iffer

ence

s

U

sing

met

hod

of d

iffer

ence

s to

find

the

sum

of f

inite

ser

ies

C

ompu

ting

the

sum

to in

finity

of a

conv

erge

nt s

erie

s by

con

side

ring

the

sum

to n

term

s

So

lvin

g p

robl

ems

invo

lvin

g se

ries

R

epre

sent

ing

life

phe

nom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g se

ries

and

expl

orin

g

thei

r app

licat

ions

in li

fe

IC

T to

ols

R

elev

ant

text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

20

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 3

: TR

IGO

NO

MET

RY

32

TOPI

C 3

: TR

IGO

NO

MET

RY

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

HYP

ERB

OLI

C

FUN

CTI

ON

S

defin

e th

e si

x hy

perb

olic

func

tions

in te

rms

of

expo

nent

ials

sk

etch

the

grap

hs o

f

hype

rbol

ic fu

nctio

ns

de

rive

iden

titie

s in

volv

ing

hype

rbol

ic f

unct

ions

us

e hy

perb

olic

iden

titie

s in

solv

ing

prob

lem

s

de

note

the

prin

cipa

l val

ues

of

the

inve

rse

hype

rbol

ic

rela

tions

usi

ng th

e in

vers

e

nota

tions

de

rive

hype

rbol

ic e

xpre

ssio

ns

in te

rms

of lo

garit

hms

us

e hy

perb

olic

exp

ress

ions

in

term

s of

loga

rithm

s to

sol

ve

prob

lem

s

Si

x hy

perb

olic

func

tions

Id

entit

ies

In

vers

e no

tatio

n

Discussingthesixhyperbolic

func

tions

in te

rms

of e

xpon

entia

ls

Sk

etch

ing

the

grap

hs o

f

hype

rbol

ic fu

nctio

ns

Derivingandusingidentities

invo

lvin

g hy

perb

olic

fun

ctio

ns to

solv

e pr

oble

ms

U

sing

the

inve

rse

nota

tions

to

deno

te th

e pr

inci

pal v

alue

s of

the

inve

rse

hype

rbol

ic re

latio

ns

Derivingandusinghyperbolic

expr

essi

ons

in te

rms

of lo

garit

hms

to s

olve

pro

blem

s

So

lvin

g pr

oble

ms

invo

lvin

g

hype

rbol

ic f

unct

ions

R

epre

sent

ing

life

phe

nom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g se

ries

and

expl

orin

g

IC

T to

ols

R

elev

ant

text

s

En

viro

nmen

t

R

esou

rce

pers

ons

Brai

lle

mat

eria

ls

Ta

lkin

g bo

oks

20 21

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 5

: M

ATH

EMAT

ICA

L IN

DU

CTI

ON

33

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

so

lve

prob

lem

s in

volv

ing

hype

rbol

ic fu

nctio

ns

thei

r app

licat

ions

in li

fe

TOPI

C 5

: M

ATH

EMAT

ICAL

IND

UC

TIO

N

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

MAT

HEM

ATIC

AL

IND

UC

TIO

N

de

scrib

e th

e pr

oces

s of

mat

hem

atic

al in

duct

ion

pr

ove

by

mat

hem

atic

al

indu

ctio

n to

est

ablis

h a

give

n

resu

lt

us

e th

e st

rate

gy o

f con

duct

ing

limite

d tri

als

to fo

rmul

ate

a

conj

ectu

re a

nd p

rovi

ng it

by

the

met

hod

of in

duct

ion

Pr

oof b

y in

duct

ion

C

onje

ctur

e

Discussingtheprocessesof

mat

hem

atic

al in

duct

ion

Pr

ovin

g b

y m

athe

mat

ical

indu

ctio

n to

est

ablis

h g

iven

resu

lts

C

ondu

ctin

g lim

ited

trial

s to

form

ulat

e c

onje

ctur

e an

d pr

ovin

g

it by

the

met

hod

of in

duct

ion

IC

T To

ols

R

elev

ant

Text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

33

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

so

lve

prob

lem

s in

volv

ing

hype

rbol

ic fu

nctio

ns

thei

r app

licat

ions

in li

fe

TOPI

C 5

: M

ATH

EMAT

ICAL

IND

UC

TIO

N

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

MAT

HEM

ATIC

AL

IND

UC

TIO

N

de

scrib

e th

e pr

oces

s of

mat

hem

atic

al in

duct

ion

pr

ove

by

mat

hem

atic

al

indu

ctio

n to

est

ablis

h a

give

n

resu

lt

us

e th

e st

rate

gy o

f con

duct

ing

limite

d tri

als

to fo

rmul

ate

a

conj

ectu

re a

nd p

rovi

ng it

by

the

met

hod

of in

duct

ion

Pr

oof b

y in

duct

ion

C

onje

ctur

e

Discussingtheprocessesof

mat

hem

atic

al in

duct

ion

Pr

ovin

g b

y m

athe

mat

ical

indu

ctio

n to

est

ablis

h g

iven

resu

lts

C

ondu

ctin

g lim

ited

trial

s to

form

ulat

e c

onje

ctur

e an

d pr

ovin

g

it by

the

met

hod

of in

duct

ion

IC

T To

ols

R

elev

ant

Text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

22

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 6

: G

EOM

ETRY

AN

D V

ECTO

RS

34

TOPI

C 6

: G

EOM

ETR

Y AN

D V

ECTO

RS

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

POLA

R C

OO

RD

INAT

ES

ex

plai

n th

e re

latio

nshi

p

betw

een

Car

tesi

an a

nd p

olar

coor

dina

tes

for

r

≥ 0

co

nver

t equ

atio

ns o

f cur

ves

from

Car

tesi

an to

pol

ar a

nd

vice

ver

sa

sk

etch

sim

ple

pola

r cur

ves

for

0 ≤

𝜃𝜃<

2𝜋𝜋 o

r - 𝜋𝜋

< 𝜃𝜃

≤ 𝜋𝜋

,

show

ing

sign

ifica

nt fe

atur

es

such

as

sym

met

ry, t

he fo

rm o

f

the

curv

e at

the

pole

and

leas

t/gre

ates

t val

ues

of r

C

arte

sian

and

pol

ar

coor

dina

tes

Po

lar c

oord

inat

es c

urve

s

Ar

ea o

f a s

ecto

r

Discussingtheappropriatenessof

usin

g C

arte

sian

or p

olar

coor

dina

tes

C

onve

rting

equ

atio

ns o

f cur

ves

from

Car

tesi

an to

pol

ar a

nd v

ice

vers

a

Sk

etch

ing

sim

ple

pola

r cur

ves

for

0 ≤

𝜃𝜃<

2𝜋𝜋 o

r

- 𝜋𝜋

< 𝜃𝜃

≤ 𝜋𝜋

,

show

ing

sign

ifica

nt fe

atur

es s

uch

as s

ymm

etry

, the

form

of t

he

curv

e at

the

pole

and

leas

t/gre

ates

t val

ues

of r

IC

T To

ols

R

elev

ant

Text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

22 23

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

35

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

de

rive

the

form

ula

𝟏𝟏 𝟐𝟐∫

𝒓𝒓𝟐𝟐𝜷𝜷 𝜶𝜶

d𝜽𝜽 fo

r the

are

a of

a s

ecto

r in

sim

ple

case

s

us

e th

e fo

rmul

a

𝟏𝟏 𝟐𝟐∫

𝒓𝒓𝟐𝟐𝜷𝜷 𝜶𝜶

d𝜽𝜽 fo

r the

are

a of

a s

ecto

r in

sim

ple

case

s

so

lve

prob

lem

s in

volv

ing

pola

r

coor

dina

tes

Derivingandusingtheform

ula

𝟏𝟏 𝟐𝟐∫

𝒓𝒓𝟐𝟐𝜷𝜷 𝜶𝜶

d𝜽𝜽

for t

he a

rea

of a

sec

tor

in s

impl

e ca

ses

So

lvin

g pr

oble

ms

invo

lvin

g po

lar

coor

dina

tes

R

epre

sent

ing

life

phe

nom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g po

lar c

oord

inat

es a

nd

expl

orin

g th

eir a

pplic

atio

ns in

life

VEC

TOR

GEO

MET

RY

de

term

ine

the

vect

or p

rodu

ct

of tw

o gi

ven

vect

ors

ca

lcul

ate

the

tripl

e sc

alar

prod

uct

of g

iven

vec

tors

in

terp

ret t

he tr

iple

sca

lar

prod

uct a

nd c

ross

pro

duct

in

geom

etric

al te

rms

so

lve

prob

lem

s co

ncer

ning

dist

ance

s, a

ngle

s an

d

inte

rsec

tions

usi

ng e

quat

ions

of li

nes

and

plan

es.

Tr

iple

sca

lar p

rodu

ct

C

ross

pro

duct

Eq

uatio

ns o

f lin

es a

nd p

lane

s

C

alcu

latin

g th

e ve

ctor

pro

duct

of

two

give

n ve

ctor

s

C

ompu

ting

the

tripl

e sc

alar

prod

uct

of g

iven

vec

tors

Discussingthetriplescalarand

cros

s pr

oduc

t in

geom

etric

al

term

s

So

lvin

g pr

oble

ms

conc

erni

ng

dist

ance

s, a

ngle

s an

d

inte

rsec

tions

usi

ng e

quat

ions

of

lines

and

pla

nes.

IC

T To

ols

R

elev

ant

Text

s

En

viro

nmen

t

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

24

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

36

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Rep

rese

ntin

g li

fe p

heno

men

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g ve

ctor

geo

met

ry a

nd

expl

orin

g th

eir a

pplic

atio

ns in

life

TOPI

C 7

: C

ALC

ULU

S

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

DIF

FER

ENTI

ATIO

N

AND

INTE

GR

ATIO

N

de

rive

an e

xpre

ssio

n fo

r 𝑑𝑑2𝑦𝑦

𝑑𝑑𝑥𝑥2

in c

ases

whe

re th

e re

latio

n

betw

een 𝑥𝑥

and 𝑦𝑦

is d

efin

ed

impl

icitl

y or

par

amet

rical

ly

de

duce

the

rela

tions

hip

betw

een

the

sign

of 𝑑𝑑2

𝑦𝑦𝑑𝑑𝑥𝑥

2 and

H

ighe

r ord

er d

iffer

entia

tion

C

onca

vity

R

educ

tion

form

ulae

Ar

c le

ngth

s

Su

rface

are

as o

f rev

olut

ion

DifferentiationandIntegration

of in

vers

e tr

igon

omet

ric

Derivinganexpressionfor𝑑𝑑

2 𝑦𝑦 𝑑𝑑𝑥𝑥2

in

case

s w

here

the

rela

tion

betw

een

𝑥𝑥 an

d 𝑦𝑦i

s de

fined

impl

icitl

y or

para

met

rical

ly

Ex

plor

ing

and

dedu

cing

the

rela

tions

hip

betw

een

the

sign

of

IC

T To

ols

R

elev

ant

Text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

36

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

Rep

rese

ntin

g li

fe p

heno

men

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g ve

ctor

geo

met

ry a

nd

expl

orin

g th

eir a

pplic

atio

ns in

life

TOPI

C 7

: C

ALC

ULU

S

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

DIF

FER

ENTI

ATIO

N

AND

INTE

GR

ATIO

N

de

rive

an e

xpre

ssio

n fo

r 𝑑𝑑2𝑦𝑦

𝑑𝑑𝑥𝑥2

in c

ases

whe

re th

e re

latio

n

betw

een 𝑥𝑥

and 𝑦𝑦

is d

efin

ed

impl

icitl

y or

par

amet

rical

ly

de

duce

the

rela

tions

hip

betw

een

the

sign

of 𝑑𝑑2

𝑦𝑦𝑑𝑑𝑥𝑥

2 and

H

ighe

r ord

er d

iffer

entia

tion

C

onca

vity

R

educ

tion

form

ulae

Ar

c le

ngth

s

Su

rface

are

as o

f rev

olut

ion

DifferentiationandIntegration

of in

vers

e tr

igon

omet

ric

Derivinganexpressionfor𝑑𝑑

2 𝑦𝑦 𝑑𝑑𝑥𝑥2

in

case

s w

here

the

rela

tion

betw

een

𝑥𝑥 an

d 𝑦𝑦i

s de

fined

impl

icitl

y or

para

met

rical

ly

Ex

plor

ing

and

dedu

cing

the

rela

tions

hip

betw

een

the

sign

of

IC

T To

ols

R

elev

ant

Text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

TOPI

C 7

: C

ALC

ULU

S

24 25

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

37

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

conc

avity

de

term

ine

the

poin

ts o

f

infle

xion

usi

ng 𝑑𝑑2

𝑦𝑦𝑑𝑑𝑥𝑥

2

de

rive

the

deriv

ativ

es o

f

inve

rse

trigo

nom

etric

and

hype

rbol

ic fu

nctio

ns

ap

ply

the

deriv

ativ

es o

f

inve

rse

trigo

nom

etric

and

hype

rbol

ic fu

nctio

ns in

prob

lem

sol

ving

fin

d de

finite

or i

ndef

inite

inte

gral

s us

ing

appr

opria

te

trigo

nom

etric

or h

yper

bolic

subs

titut

ion

in

tegr

ate

ratio

nal f

unct

ions

by

mea

ns o

f dec

ompo

sitio

n in

to

parti

al fr

actio

ns

de

rive

redu

ctio

n fo

rmul

ae fo

r

the

eval

uatio

n of

def

inite

inte

gral

s in

sim

ple

case

s

fin

d de

finite

inte

gral

s us

ing

func

tions

and

hyp

erbo

lic

func

tions

𝑑𝑑2𝑦𝑦

𝑑𝑑𝑥𝑥2

and

conc

avity

Fi

ndin

g po

ints

of i

nfle

xion

usi

ng

𝑑𝑑2𝑦𝑦

𝑑𝑑𝑥𝑥2

Ex

plor

ing

and

deriv

ing

the

deriv

ativ

es o

f inv

erse

trigo

nom

etric

and

hyp

erbo

lic

func

tions

Ap

plyi

ng th

e de

rivat

ives

of i

nver

se

trigo

nom

etric

and

hyp

erbo

lic

func

tions

in p

robl

em s

olvi

ng

Fi

ndin

g de

finite

or i

ndef

inite

inte

gral

s us

ing

appr

opria

te

trigo

nom

etric

or h

yper

bolic

subs

titut

ion

In

tegr

atin

g ra

tiona

l fun

ctio

ns b

y

mea

ns o

f dec

ompo

sitio

n in

to

parti

al fr

actio

ns

Ex

plor

ing

and

deriv

ing

redu

ctio

n

form

ulae

for t

he e

valu

atio

n of

defin

ite in

tegr

als

in s

impl

e ca

ses

Fi

ndin

g de

finite

inte

gral

s us

ing

26

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

38

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

redu

ctio

n fo

rmul

a

fin

d ar

c le

ngth

s fo

r cur

ves

with

equ

atio

ns in

Car

tesi

an

coor

dina

tes

incl

udin

g us

e of

a

para

met

er o

r in

pola

r for

m

fin

d th

e ar

ea o

f sur

face

of

revo

lutio

n w

hen

an a

rc is

rota

ted

abou

t one

of t

he

coor

dina

te a

xes,

giv

en th

at

the

equa

tion

of th

e cu

rve

cont

aini

ng th

e ar

c is

in

Car

tesi

an o

r par

amet

ric fo

rm

so

lve

prob

lem

s in

volv

ing

diffe

rent

iatio

n an

d in

tegr

atio

n

redu

ctio

n fo

rmul

a

Fi

ndin

g ar

c le

ngth

s fo

r cur

ves

with

equa

tions

in C

arte

sian

coor

dina

tes

incl

udin

g us

e of

a

para

met

er o

r in

pola

r for

m

Determiningtheareaofsurfaceof

revo

lutio

n w

hen

an a

rc is

rota

ted

abou

t one

of t

he c

oord

inat

e ax

es,

give

n th

at th

e eq

uatio

n of

the

curv

e co

ntai

ning

the

arc

is in

Car

tesi

an o

r par

amet

ric fo

rm

So

lvin

g pr

oble

ms

invo

lvin

g

diffe

rent

iatio

n an

d in

tegr

atio

n

R

epre

sent

ing

life

phe

nom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g di

ffere

ntia

tion

and

inte

grat

ion

and

expl

orin

g th

eir

appl

icat

ions

in li

fe

DIF

FER

ENTI

AL

EQU

ATIO

NS

fin

d th

e ge

nera

l sol

utio

n of

a

first

ord

er li

near

diff

eren

tial

equa

tion

by m

eans

of a

n

Fi

rst o

rder

diff

eren

tial

equa

tions

Se

cond

ord

er d

iffer

entia

l

Determininggeneralsolutionsof

first

ord

er li

near

diff

eren

tial

equa

tions

by

mea

ns o

f int

egra

ting

IC

T To

ols

R

elev

ant

Text

s

26 27

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

39

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

inte

grat

ing

fact

or

de

fine

a ‘c

ompl

emen

tary

func

tion’

and

a ‘p

artic

ular

inte

gral

’ in

the

cont

ext o

f

linea

r diff

eren

tial e

quat

ions

us

e a

give

n su

bstit

utio

n to

redu

ce a

firs

t ord

er d

iffer

entia

l

equa

tion

to li

near

form

or t

o a

form

in w

hich

var

iabl

es a

re

sepa

rabl

e

fin

d th

e co

mpl

imen

tary

func

tion

of a

firs

t or s

econ

d

orde

r lin

ear d

iffer

entia

l

equa

tion

with

con

stan

t

coef

ficie

nts

de

term

ine

a pa

rticu

lar i

nteg

ral

for a

firs

t or s

econ

d or

der

linea

r diff

eren

tial e

quat

ion

in

the

case

whe

re 𝑎𝑎𝑎𝑎

+ 𝑏𝑏

or

𝑎𝑎𝑒𝑒𝑏𝑏𝑏𝑏

or 𝑎𝑎

𝑎𝑎𝑎𝑎𝑎𝑎 (𝑝𝑝𝑎𝑎

) +

𝑏𝑏𝑎𝑎𝑏𝑏𝑏𝑏

(𝑝𝑝𝑎𝑎)

is a

sui

tabl

e fo

rm.

equa

tions

C

ompl

emen

tary

func

tion

G

ener

al a

nd P

artic

ular

inte

gral

s

Su

bstit

utio

n

Pa

rticu

lar s

olut

ion

fact

ors

Discussingco

mpl

emen

tary

func

tions

and

par

ticul

ar in

tegr

als

in th

e co

ntex

t of l

inea

r diff

eren

tial

equa

tions

Ap

plyi

ng g

iven

sub

stitu

tions

to

redu

ce f

irst o

rder

diff

eren

tial

equa

tions

to li

near

form

or t

o

form

s in

whi

ch v

aria

bles

are

sepa

rabl

e

Fi

ndin

g c

ompl

imen

tary

func

tions

of fi

rst o

r sec

ond

orde

r lin

ear

diffe

rent

ial e

quat

ions

with

cons

tant

coe

ffici

ents

Determiningparticularintegrals

for f

irst o

r sec

ond

orde

r lin

ear

diffe

rent

ial e

quat

ions

in th

e ca

se

whe

re 𝑎𝑎𝑎𝑎

+ 𝑏𝑏

or 𝑎𝑎

𝑒𝑒𝑏𝑏𝑏𝑏

or

𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

(𝑝𝑝𝑎𝑎)

+ 𝑏𝑏𝑎𝑎

𝑏𝑏𝑏𝑏 (𝑝𝑝

𝑎𝑎) is

a

suita

ble

form

.

Fi

ndin

g ap

prop

riate

coe

ffici

ents

of

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

28

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

40

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

fin

d th

e ap

prop

riate

coe

ffici

ent

(s) o

f a fi

rst o

r sec

ond

orde

r

diffe

rent

ial e

quat

ion

give

n a

suita

ble

form

of a

par

ticul

ar

inte

gral

fin

d a

parti

cula

r sol

utio

n to

a

diffe

rent

ial e

quat

ion

usin

g

initi

al c

ondi

tions

in

terp

ret p

artic

ular

sol

utio

ns in

the

cont

ext o

f pro

blem

s

mod

elle

d by

diff

eren

tial

equa

tions

so

lve

prob

lem

s in

volv

ing

diffe

rent

ial e

quat

ions

first

or s

econ

d or

der d

iffer

entia

l

equa

tions

giv

en s

uita

ble

form

s of

parti

cula

r int

egra

ls

Determiningparticularsolutionsto

diffe

rent

ial e

quat

ions

usi

ng in

itial

cond

ition

s

In

terp

retin

g pa

rticu

lar s

olut

ions

in

the

cont

ext o

f pro

blem

s m

odel

led

by d

iffer

entia

l equ

atio

ns

So

lvin

g pr

oble

ms

invo

lvin

g

diffe

rent

ial e

quat

ions

R

epre

sent

ing

life

phe

nom

ena

usin

g m

athe

mat

ical

mod

els

invo

lvin

g di

ffere

ntia

l equ

atio

ns

and

expl

orin

g th

eir a

pplic

atio

ns in

life

28 29

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

FOR

M S

IX (6

)

MEC

HA

NIC

S

TOPI

C 1

: PA

RTI

CLE

DYN

AM

ICS

41

FORM

SIX

(6)

MEC

HAN

ICS

TOPI

C 1

: PA

RTI

CLE

DYN

AMIC

S

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

KIN

EMAT

ICS

OF

MO

TIO

N

us

e di

ffere

ntia

tion

and

inte

grat

ion

with

resp

ect t

o

time

to s

olve

pro

blem

s

conc

erni

ng d

ispl

acem

ent,

velo

city

and

acc

eler

atio

n

sk

etch

the

grap

hs o

f: (x

-t), (

s-

M

otio

n in

a s

traig

ht li

ne

Ve

loci

ty

Ac

cele

ratio

n

Displacem

ent-

tim

e ve

loci

ty-

time

and

acce

lera

tion-

time

grap

hs

Discussingdistance(x)

disp

lace

men

t(s),

spee

d,

velo

city

(v) a

nd a

ccel

erat

ion(

a)

So

lvin

g pr

oble

ms

conc

erni

ng

disp

lace

men

t, ve

loci

ty a

nd

acce

lera

tion

usin

g di

ffere

ntia

tion

IC

T to

ols

G

eo-b

oard

En

viro

nmen

t

R

elev

ant t

exts

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

30

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

42

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

t), (v

-t) a

nd (a

-t)

in

terp

ret t

he (x

-t), (

s-t),

(v-t)

and

(a-t)

gra

phs

de

rive

the

equa

tions

of

mot

ion

of a

par

ticle

with

cons

tant

acc

eler

atio

n in

a

stra

ight

line

us

e th

e eq

uatio

ns o

f mot

ion

of a

par

ticle

with

con

stan

t

acce

lera

tion

in a

stra

ight

line

to s

olve

kin

emat

ics

prob

lem

s

so

lve

prob

lem

s in

volv

ing

kine

mat

ics

of m

otio

n in

a

stra

ight

line

incl

udin

g ve

rtica

l

mot

ion

unde

r gra

vity

Eq

uatio

n of

mot

ion

for

cons

tant

line

ar a

ccel

erat

ion

Ve

rtica

l mot

ion

unde

r gra

vity

M

otio

n an

d co

nsta

nt v

eloc

ity

and

inte

grat

ion

Sk

etch

ing

(x-t)

, (s-

t), (

v-t)

and

(a-

t) g

raph

s

In

terp

retin

g th

e (x

-t),

(s-t)

, (v-

t) an

d (a

-t) g

raph

s

Derivingtheequationsofm

otion

of a

par

ticle

with

con

stan

t

acce

lera

tion

in a

stra

ight

line

So

lvin

g ki

nem

atic

s pr

oble

ms

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g ki

nem

atic

s of

mot

ion

in

a st

raig

ht li

ne a

nd e

xplo

ring

thei

r

appl

icat

ions

in li

fe

30 31

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

43

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

NEW

TON

’S L

AWS

OF

MO

TIO

N

st

ate

New

ton’

s la

ws

of

mot

ion

ap

ply

New

ton’

s la

ws

of

mot

ion

to th

e lin

ear m

otio

n of

a bo

dy o

f con

stan

t mas

s

mov

ing

unde

r the

act

ion

of

cons

tant

forc

es

so

lve

prob

lem

s us

ing

the

rela

tions

hip

betw

een

mas

s

and

wei

ght

so

lve

prob

lem

s in

volv

ing

the

mot

ion

of tw

o pa

rticl

es,

conn

ecte

d by

a li

ght

inex

tens

ible

stri

ng w

hich

may

pass

ove

r a fi

xed,

sm

ooth

,

light

pul

ley

or p

eg

m

odel

the

mot

ion

of th

e bo

dy

mov

ing

verti

cally

or o

n an

incl

ined

pla

ne a

s m

otio

n w

ith

cons

tant

acc

eler

atio

n

so

lve

prob

lem

s in

volv

ing

N

ewto

n’s

law

s of

mot

ion

M

otio

n ca

used

by

a se

t of

forc

es

C

once

pt o

f mas

s an

d

wei

ght

M

otio

n of

con

nect

ed

obje

cts

D

iscu

ssin

g th

e N

ewto

n’s

law

s

of m

otio

n

Ap

plyi

ng N

ewto

n’s

law

s of

mot

ion

to th

e lin

ear m

otio

n of

a

body

of c

onst

ant m

ass

mov

ing

unde

r the

act

ion

of c

onst

ant

forc

es

So

lvin

g pr

oble

ms

usin

g th

e

rela

tions

hip

betw

een

mas

s an

d

wei

ght

So

lvin

g pr

oble

ms

invo

lvin

g th

e

mot

ion

of tw

o pa

rticl

es,

conn

ecte

d by

a li

ght

inex

tens

ible

stri

ng w

hich

may

pass

ove

r a fi

xed,

sm

ooth

, lig

ht

pulle

y or

peg

So

lvin

g pr

oble

ms

invo

lvin

g

New

ton’

s la

ws

of m

otio

n

M

odel

ling

the

mot

ion

of a

bod

y

mov

ing

verti

cally

or o

n an

incl

ined

pla

ne a

s m

otio

n w

ith

IC

T to

ols

G

eo-b

oard

En

viro

nmen

t

R

elev

ant t

exts

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

32

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

44

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

New

ton’

s la

ws

of m

otio

n co

nsta

nt a

ccel

erat

ion

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g N

ewto

n’s

law

s of

mot

ion

and

expl

orin

g th

eir

appl

icat

ions

in li

fe

MO

TIO

N O

F A

PRO

JEC

TILE

mod

el th

e m

otio

n of

a

proj

ectil

e as

a p

artic

le

mov

ing

with

con

stan

t

acce

lera

tion

so

lve

prob

lem

s on

the

mot

ion

of p

roje

ctile

s us

ing

horiz

onta

l

and

verti

cal e

quat

ions

of

mot

ion

fin

d th

e m

agni

tude

and

the

Pr

ojec

tile

- M

otio

n of

a p

roje

ctile

- Ve

loci

ty a

nd

disp

lace

men

ts

R

ange

on

horiz

onta

l pla

ne

G

reat

est h

eigh

t

M

axim

um ra

nge

C

arte

sian

equ

atio

n of

a

traje

ctor

y of

a p

roje

ctile

M

odel

ling

the

mot

ion

of a

proj

ectil

e as

a p

artic

le m

ovin

g

with

con

stan

t acc

eler

atio

n

Ap

plyi

ng h

oriz

onta

l and

ver

tical

equa

tions

of m

otio

n in

sol

ving

prob

lem

s on

the

mot

ion

of

proj

ectil

es

C

alcu

latin

g th

e m

agni

tude

and

the

dire

ctio

n of

the

velo

city

at a

IC

T to

ols

G

eo-b

oard

En

viro

nmen

t

R

elev

ant t

exts

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

32 33

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

45

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

dire

ctio

n of

the

velo

city

at a

give

n tim

e or

pos

ition

fin

d th

e ra

nge

on th

e

horiz

onta

l pla

ne a

nd h

eigh

t

reac

hed

de

rive

form

ulae

for g

reat

est

heig

ht a

nd m

axim

um ra

nge

de

rive

the

Car

tesi

an e

quat

ion

of a

traj

ecto

ry o

f a p

roje

ctile

so

lve

prob

lem

s us

ing

the

Car

tesi

an e

quat

ion

of a

traje

ctor

y of

a p

roje

ctile

give

n tim

e or

pos

ition

Fi

ndin

g th

e ra

nge

on th

e

horiz

onta

l pla

ne a

nd h

eigh

t

reac

hed

Derivingform

ulaeforgreatest

heig

ht a

nd m

axim

um ra

nge

DerivingtheCartesiane

quat

ion

of a

traj

ecto

ry o

f a p

roje

ctile

So

lvin

g pr

oble

ms

usin

g C

arte

sian

equa

tion

of a

traj

ecto

ry o

f a

proj

ectil

e

34

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 2

: EL

AST

ICIT

Y

46

TOPI

C 2

: EL

ASTI

CIT

Y

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

:

CO

NTE

NT

(Atti

tude

s, S

kills

and

K

now

ledg

e)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

ELAS

TIC

ITY

de

fine

elas

ticity

in s

tring

s an

d

sprin

gs

ex

plai

n H

ooke

’s la

w

ca

lcul

ate

mod

ulus

of e

last

icity

so

lve

prob

lem

s in

volv

ing

forc

es d

ue to

ela

stic

stri

ngs

or

sprin

gs in

clud

ing

thos

e w

here

cons

ider

atio

n of

wor

k an

d

ener

gy a

re n

eede

d

Pr

oper

ties

of e

last

ic s

tring

s

and

sprin

gs

W

ork

done

in s

tretc

hing

a

strin

g

El

astic

pot

entia

l ene

rgy

M

echa

nica

l ene

rgy

C

onse

rvat

ion

of m

echa

nica

l

ener

gy

Discussingelasticityinstringsand

sprin

gs

Ex

plai

ning

Hoo

ke’s

law

C

ondu

ctin

g ex

perim

ents

to v

erify

Hoo

ke’s

law

C

alcu

latin

g m

odul

us o

f ela

stic

ity

So

lvin

g pr

oble

ms

invo

lvin

g fo

rces

due

to e

last

ic s

tring

s or

spr

ings

incl

udin

g th

ose

whe

re

cons

ider

atio

n of

wor

k an

d en

ergy

are

need

ed

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g el

astic

ity a

nd e

xplo

ring

thei

r app

licat

ions

in li

fe

IC

T to

ols

R

elev

ant

text

s

En

viro

nmen

t

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

34 35

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

48

TOPI

C 4

: C

IRC

ULA

R M

OTI

ON

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

CIR

CU

LAR

MO

TIO

N

(Ver

tical

and

Hor

izon

tal)

de

rive

the

form

ula

for s

peed

,

velo

city

and

acc

eler

atio

n of

a

parti

cle

mov

ing

in a

circ

le

ex

plai

n th

e co

ncep

t of

angu

lar s

peed

for a

par

ticle

mov

ing

in a

circ

le w

ith

cons

tant

spe

ed

di

stin

guis

h be

twee

n

horiz

onta

l and

ver

tical

mot

ion

ca

lcul

ate

ang

ular

spe

ed fo

r a

parti

cle

mov

ing

in a

circ

le

with

con

stan

t spe

ed

ca

lcul

ate

acce

lera

tion

of a

parti

cle

mov

ing

in a

circ

le

with

con

stan

t spe

ed

so

lve

prob

lem

s w

hich

can

be

mod

elle

d as

the

mot

ion

of a

parti

cle

mov

ing

in a

horiz

onta

l circ

le w

ith c

onst

ant

spee

d

An

gula

r spe

ed a

nd v

eloc

ity

H

oriz

onta

l and

ver

tical

circ

ular

mot

ion

A

ccel

erat

ion

of a

par

ticle

mov

ing

on a

circ

le

M

otio

n in

a c

ircle

with

cons

tant

spe

ed

C

entri

peta

l for

ce

R

elat

ion

betw

een

angu

lar

and

linea

r spe

ed

C

onic

al p

endu

lum

Ba

nked

trac

ks

Ex

plor

ing

and

deriv

ing

the

form

ula

for s

peed

, vel

ocity

and

acce

lera

tion

of a

par

ticle

mov

ing

in a

circ

le

Discussingtheconceptof

angu

lar s

peed

for a

par

ticle

mov

ing

in a

circ

le w

ith c

onst

ant

spee

d

Distinguishingbetweenthe

conc

epts

of h

oriz

onta

l and

verti

cal m

otio

n in

a c

ircle

C

ompu

ting

ang

ular

spe

ed fo

r a

parti

cle

mov

ing

in a

circ

le w

ith

cons

tant

spe

ed

C

alcu

latin

g ac

cele

ratio

n of

a

parti

cle

mov

ing

in a

circ

le w

ith

cons

tant

spe

ed

So

lvin

g pr

oble

ms

whi

ch c

an b

e

mod

elle

d as

the

mot

ion

of a

parti

cle

mov

ing

in a

hor

izon

tal

IC

T to

ols

R

elev

ant t

exts

En

viro

nmen

t

Si

mpl

e

pend

ulum

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

TOPI

C 3

: EN

ERG

Y W

OR

K

36

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

48

TOPI

C 4

: C

IRC

ULA

R M

OTI

ON

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

CIR

CU

LAR

MO

TIO

N

(Ver

tical

and

Hor

izon

tal)

de

rive

the

form

ula

for s

peed

,

velo

city

and

acc

eler

atio

n of

a

parti

cle

mov

ing

in a

circ

le

ex

plai

n th

e co

ncep

t of

angu

lar s

peed

for a

par

ticle

mov

ing

in a

circ

le w

ith

cons

tant

spe

ed

di

stin

guis

h be

twee

n

horiz

onta

l and

ver

tical

mot

ion

ca

lcul

ate

ang

ular

spe

ed fo

r a

parti

cle

mov

ing

in a

circ

le

with

con

stan

t spe

ed

ca

lcul

ate

acce

lera

tion

of a

parti

cle

mov

ing

in a

circ

le

with

con

stan

t spe

ed

so

lve

prob

lem

s w

hich

can

be

mod

elle

d as

the

mot

ion

of a

parti

cle

mov

ing

in a

horiz

onta

l circ

le w

ith c

onst

ant

spee

d

An

gula

r spe

ed a

nd v

eloc

ity

H

oriz

onta

l and

ver

tical

circ

ular

mot

ion

A

ccel

erat

ion

of a

par

ticle

mov

ing

on a

circ

le

M

otio

n in

a c

ircle

with

cons

tant

spe

ed

C

entri

peta

l for

ce

R

elat

ion

betw

een

angu

lar

and

linea

r spe

ed

C

onic

al p

endu

lum

Ba

nked

trac

ks

Ex

plor

ing

and

deriv

ing

the

form

ula

for s

peed

, vel

ocity

and

acce

lera

tion

of a

par

ticle

mov

ing

in a

circ

le

Discussingtheconceptof

angu

lar s

peed

for a

par

ticle

mov

ing

in a

circ

le w

ith c

onst

ant

spee

d

Distinguishingbetweenthe

conc

epts

of h

oriz

onta

l and

verti

cal m

otio

n in

a c

ircle

C

ompu

ting

ang

ular

spe

ed fo

r a

parti

cle

mov

ing

in a

circ

le w

ith

cons

tant

spe

ed

C

alcu

latin

g ac

cele

ratio

n of

a

parti

cle

mov

ing

in a

circ

le w

ith

cons

tant

spe

ed

So

lvin

g pr

oble

ms

whi

ch c

an b

e

mod

elle

d as

the

mot

ion

of a

parti

cle

mov

ing

in a

hor

izon

tal

IC

T to

ols

R

elev

ant t

exts

En

viro

nmen

t

Si

mpl

e

pend

ulum

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

TOPI

C 4

: C

IRC

ULA

R M

OTI

ON

36 37

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

49

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

so

lve

prob

lem

s w

hich

can

be

mod

elle

d as

the

mot

ion

of a

parti

cle

mov

ing

in a

ver

tical

circ

le w

ith c

onst

ant s

peed

fin

d th

e re

latio

nshi

p be

twee

n

angu

lar a

nd li

near

spe

ed

ca

lcul

ate

tens

ion

in a

stri

ng

and

angu

lar s

peed

in a

coni

cal p

endu

lum

so

lve

prob

lem

s in

volv

ing

bank

ed tr

acks

.

so

lve

prob

lem

s w

hich

can

be

mod

elle

d as

the

mot

ion

of a

parti

cle

mov

ing

in a

horiz

onta

l circ

le w

ith c

onst

ant

spee

d us

ing

New

ton’

s

seco

nd la

w

and

verti

cal c

ircle

with

con

stan

t

spee

d

Discussin

g th

e re

latio

nshi

p

betw

een

angu

lar a

nd li

near

spee

d

C

ompu

ting

tens

ion

in a

stri

ng

and

angu

lar s

peed

in a

con

ical

pend

ulum

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g ci

rcul

ar m

otio

n an

d

expl

orin

g th

eir a

pplic

atio

ns in

life

38

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 5

: SI

MPL

E H

AR

MIN

IC M

OTI

ON

50

TOPI

C 5

: SI

MPL

E H

ARM

INIC

MO

TIO

N

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

SIM

PLE

HAR

MO

NIC

M

OTI

ON

de

fine

sim

ple

harm

onic

mot

ion

so

lve

prob

lem

s us

ing

the

stan

dard

sim

ple

harm

onic

mot

ion

form

ula

fo

rmul

ate

diffe

rent

ial

equa

tions

of m

otio

n in

prob

lem

s le

adin

g to

sim

ple

harm

onic

mot

ion

so

lve

diffe

rent

ial e

quat

ions

invo

lvin

g si

mpl

e ha

rmon

ic

mot

ion

to o

btai

n th

e pe

riod

and

ampl

itude

of t

he m

otio

n

Ba

sic

equa

tion

of s

impl

e

harm

onic

mot

ion

Pr

oper

ties

of s

impl

e ha

rmon

ic

mot

ion

Discussingsimpleharm

onic

mot

ion

C

ondu

ctin

g ex

perim

ents

to

dem

onst

rate

sim

ple

harm

onic

mot

ion

usin

g a

pend

ulum

So

lvin

g pr

oble

ms

usin

g th

e

stan

dard

sim

ple

harm

onic

mot

ion

form

ula

Fo

rmul

atin

g di

ffere

ntia

l equ

atio

ns

of m

otio

n in

pro

blem

s le

adin

g to

sim

ple

harm

onic

mot

ion

So

lvin

g di

ffere

ntia

l equ

atio

ns

invo

lvin

g si

mpl

e ha

rmon

ic m

otio

n

to o

btai

n th

e pe

riod

and

ampl

itude

of th

e m

otio

n

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g si

mpl

e ha

rmon

ic m

otio

n

and

expl

orin

g th

eir a

pplic

atio

ns in

IC

T to

ols

R

elev

ant

text

s

En

viro

nmen

t

Pe

ndul

um

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

38 39

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

STAT

ISTI

CS

TOPI

C 1

: PR

OB

AB

ILIT

Y

52

STAT

ISTI

CS

TOPI

C 1

: PR

OB

ABIL

ITY

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

PRO

BAB

ILIT

Y

defin

e pr

obab

ility

key

term

s

ca

lcul

ate

prob

abilit

ies

of

even

ts

so

lve

prob

lem

s in

volv

ing

cond

ition

al p

roba

bilit

y

us

e tre

e di

agra

ms,

Ven

n

diag

ram

s an

d ou

tcom

e

tabl

es to

sol

ve p

robl

ems

us

e th

e no

tatio

ns n

!, n P𝑟𝑟 a

nd

(𝑛𝑛 𝑟𝑟)

de

fine

perm

utat

ions

and

com

bina

tions

so

lve

prob

lem

s in

volv

ing

perm

utat

ions

and

com

bina

tions

Ev

ents

- In

depe

nden

t

- M

utua

lly e

xclu

sive

- Ex

haus

tive

- C

ombi

ned

C

ondi

tiona

l

prob

abilit

y

Tr

ee d

iagr

ams

Outcometables

Ve

nn d

iagr

ams

Pe

rmut

atio

ns a

nd

com

bina

tions

Discussingtheimporta

nceof

prob

abilit

y in

life

C

ompu

ting

prob

abilit

ies

of a

varie

ty o

f eve

nts

Ap

plyi

ng c

ondi

tiona

l pro

babi

lity

conc

epts

in s

olvi

ng p

robl

ems

So

lvin

g pr

oble

ms

usin

g tre

e

diag

ram

s, V

enn

diag

ram

s an

d

outc

ome

tabl

es

C

arry

ing

out e

xper

imen

ts

invo

lvin

g pr

obab

ility

U

sing

the

nota

tions

n!,

n P𝑟𝑟 a

nd

(𝑛𝑛 𝑟𝑟)

Ex

plai

ning

the

mea

ning

s of

perm

utat

ions

and

com

bina

tions

So

lvin

g pr

oble

ms

invo

lvin

g

perm

utat

ions

and

com

bina

tions

IC

T to

ols

R

elev

ant

text

s

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

40

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 2

: R

AN

DO

M V

AR

IAB

LES

54

TOPI

C 2

: R

AND

OM

VAR

IAB

LES

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

RAN

DO

M V

ARIA

BLE

S (d

iscr

ete

and

cont

inuo

us)

de

fine

a ra

ndom

var

iabl

e

co

nstru

ct a

pro

babi

lity

dist

ribut

ion

tabl

e

de

fine

expe

ctat

ion

us

e th

e pr

obab

ility

dens

ity

func

tions

and

cum

ulat

ive

dist

ribut

ion

func

tions

to

calc

ulat

e pr

obab

ilitie

s

ca

lcul

ate

mea

n, m

ode,

med

ian,

sta

ndar

d de

viat

ion,

varia

nce

and

perc

entil

es

us

e in

tegr

atio

n to

cal

cula

te

cum

ulat

ive

dist

ribut

ion

func

tion

from

pro

babi

lity

dens

ity fu

nctio

n

us

e di

ffere

ntia

tion

to

calc

ulat

e pr

obab

ility

dens

ity

func

tion

from

cum

ulat

ive

dist

ribut

ion

func

tion

Pr

obab

ility

dist

ribut

ions

Ex

pect

atio

n

Va

rianc

e

Pr

obab

ility

dens

ity fu

nctio

ns

(pdf

) and

cum

ulat

ive

dist

ribut

ion

func

tions

(cdf

)

M

ean,

med

ian,

mod

e,

stan

dard

dev

iatio

n an

d

perc

entil

es

Discussingexam

plesofrandom

varia

bles

C

onst

ruct

ing

prob

abilit

y

dist

ribut

ion

tabl

es

C

alcu

latin

g m

ean,

mod

e, m

edia

n,

stan

dard

dev

iatio

n, v

aria

nce

and

perc

entil

es

So

lvin

g pr

oble

ms

invo

lvin

g m

ean,

varia

nce

and

stan

dard

dev

iatio

n

Discussingthedifference

betw

een

a di

scre

te ra

ndom

varia

ble

and

a co

ntin

uous

rand

om v

aria

ble

Discussingthesignificanceof

prob

abilit

y de

nsity

func

tion

and

cum

ulat

ive

dist

ribut

ion

func

tion

of

a co

ntin

uous

rand

om v

aria

ble

C

ompu

ting

prob

abilit

ies

usin

g

both

pdf

and

cdf

IC

T to

ols

R

elev

ant t

exts

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

40 41

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

55

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

so

lve

prob

lem

s in

volv

ing

prob

abilit

y de

nsity

func

tion

So

lvin

g pr

oble

ms

invo

lvin

g pd

f

and

cdf

DIS

TRIB

UTI

ON

S

Outlinethecharacteristicsof

Bino

mia

l, Po

isso

n an

d

Nor

mal

dis

tribu

tions

ca

lcul

ate

the

mea

n, v

aria

nce

and

stan

dard

dev

iatio

n of

each

dis

tribu

tion

ca

lcul

ate

prob

abilit

ies

for t

he

dist

ribut

ions

ex

plai

n th

e ch

arac

teris

tics

of

a no

rmal

dis

tribu

tion

curv

e

st

anda

rdiz

e a

rand

om

varia

ble

us

e th

e st

anda

rd n

orm

al

tabl

es to

obt

ain

prob

abilit

ies

ap

prox

imat

e th

e bi

nom

ial

usin

g th

e no

rmal

dis

tribu

tion

Bi

nom

ial d

istri

butio

n

Po

isso

n d

istri

butio

n

N

orm

al d

istri

butio

n

St

anda

rd n

orm

al ta

bles

C

ontin

uity

cor

rect

ion

Li

near

com

bina

tions

of

norm

al a

nd P

oiss

on

dist

ribut

ions

Discussingthecharacteristicsof

Bino

mia

l, Po

isso

n an

d N

orm

al

dist

ribut

ions

C

ompu

ting

the

mea

n, v

aria

nce

and

stan

dard

dev

iatio

n of

eac

h

dist

ribut

ion

C

alcu

latin

g pr

obab

ilitie

s us

ing

the

prob

abilit

y de

nsity

func

tions

of

the

dist

ribut

ions

Discussingthecharacteristicsof

a no

rmal

dis

tribu

tion

curv

e, g

ivin

g

life

exam

ples

St

anda

rdiz

ing

rand

om v

aria

bles

Obtainingprobabilitiesusing

stan

dard

nor

mal

tabl

es

U

sing

the

norm

al d

istri

butio

n

mod

el to

app

roxi

mat

e th

e

IC

T to

ols

R

elev

ant t

exts

En

viro

nmen

t

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

42

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

56

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

whe

re n

is la

rge

enou

gh to

ensu

re th

at 𝑛𝑛𝑛𝑛

> 5

and 𝑛𝑛𝑛𝑛

> 5

and

appl

y co

ntin

uity

corre

ctio

n

us

e th

e no

rmal

dis

tribu

tion

as

a m

odel

to s

olve

pro

blem

s

us

e th

e fo

llow

ing

fact

s to

solv

e pr

oble

ms:

- E(

aX±b

) = a

E(X)

± b

and

Var(a

X±b)

= a

2 Var

(X)

- E(

aX±b

Y) =

aE(

X)±b

E(Y)

- Va

r(aX±

bY) =

a2 V

ar(X

)+

b2 Var

(Y) f

or in

depe

nden

t

X an

d Y

us

e th

e re

sults

that

:

- If

X ha

s a

norm

al

dist

ribut

ion,

then

so

does

aX +

b

- If

X an

d Y

have

inde

pend

ent n

orm

al

dist

ribut

ions

, the

n

aX +

bY

has

a no

rmal

bino

mia

l dis

tribu

tion

U

sing

the

norm

al d

istri

butio

n as

a

mod

el to

sol

ve p

robl

ems

Discussingexam

plesoflinear

com

bina

tions

C

alcu

latin

g pr

obab

ilitie

s, m

ean

and

varia

nce

of a

sum

of t

wo

or

mor

e in

depe

nden

t var

iabl

es fo

r

Pois

son

or n

orm

al d

istri

butio

n

So

lvin

g pr

oble

ms

invo

lvin

g lin

ear

com

bina

tions

and

thei

r

appl

icat

ions

in li

fe

So

lvin

g pr

oble

ms

invo

lvin

g

dist

ribut

ions

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g di

strib

utio

ns a

nd

expl

orin

g th

eir a

pplic

atio

ns in

life

42 43

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

57

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

dist

ribut

ion

- If

X an

d Y

have

inde

pend

ent P

oiss

on

dist

ribut

ions

, the

n X

+ Y

has

a Po

isso

n di

strib

utio

n

so

lve

prob

lem

s in

volv

ing

the

dist

ribut

ions

44

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 3

: SA

MPL

ING

AN

D E

STIM

ATIO

NS

58

TOPI

C 3

: SA

MPL

ING

AN

D E

STIM

ATIO

NS

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

SAM

PLIN

G T

ECH

NIQ

UES

AN

D E

STIM

ATIO

N

di

stin

guis

h be

twee

n a

sam

ple

and

a po

pula

tion

di

stin

guis

h be

twee

n

prob

abilit

y sa

mpl

ing

tech

niqu

es a

nd n

on-

prob

abilit

y sa

mpl

ing

tech

niqu

es

ap

ply

the

sam

plin

g m

etho

ds

to id

entif

y re

pres

enta

tive

sam

ples

ca

lcul

ate

sam

ple

mea

n,

varia

nce

and

stan

dard

devi

atio

n

fin

d th

e un

bias

ed e

stim

ates

of

popu

latio

n pa

ram

eter

s

st

ate

the

Cen

tral L

imit

Theo

rem

re

cogn

ize

that

the

sam

ple

mea

n ca

n be

rega

rded

as

a

rand

om v

aria

ble

Pr

obab

ility

sam

plin

g

tech

niqu

es

N

on-p

roba

bilit

y s

ampl

ing

tech

niqu

es

Es

timat

ion

of p

opul

atio

n

para

met

ers

C

entra

l lim

it th

eore

m

C

onfid

ence

inte

rval

s

Discussingthedifferencebetween

a sa

mpl

e an

d a

popu

latio

n,

prob

abilit

y sa

mpl

ing

and

non-

prob

abilit

y sa

mpl

ing

tech

niqu

es

Id

entif

ying

and

dis

cuss

ing

situ

atio

ns in

whi

ch p

roba

bilit

y an

d

non-

prob

abilit

y sa

mpl

ing

met

hods

are

used

C

arry

ing

out s

ampl

ing

in a

prac

tical

situ

atio

n

C

ompu

ting

sam

ple

mea

n,

varia

nce

and

stan

dard

dev

iatio

n

Determiningtheunbiased

estim

ates

of p

opul

atio

n

para

met

ers

DerivingtheCentra

lLimit

Theo

rem

Ex

plai

ning

how

the

sam

ple

mea

n

can

be re

gard

ed a

s a

rand

om

varia

ble

IC

T to

ols

R

elev

ant t

exts

En

viro

nmen

t

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

44 45

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

59

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

us

e th

e C

entra

l Lim

it Th

eore

m

in s

olvi

ng p

robl

ems

id

entif

y th

e im

plic

atio

ns o

f the

Cen

tral L

imit

Theo

rem

on

smal

l and

larg

e sa

mpl

es

de

term

ine

a co

nfid

ence

inte

rval

for a

pop

ulat

ion

mea

n

in c

ases

whe

re th

e po

pula

tion

is n

orm

ally

dis

tribu

ted

with

know

n va

rianc

e or

whe

re a

larg

e sa

mpl

e w

ith u

nkno

wn

varia

nce

is u

sed

de

term

ine

a co

nfid

ence

inte

rval

for a

pop

ulat

ion

mea

n

in c

ases

whe

re th

e po

pula

tion

is n

orm

ally

dis

tribu

ted

with

unkn

own

varia

nce

whe

re a

smal

l sam

ple

is u

sed

de

term

ine

from

a la

rge

sam

ple

an a

ppro

xim

ate

conf

iden

ce in

terv

al fo

r a

popu

latio

n pr

opor

tion

So

lvin

g pr

oble

ms

usin

g th

e

Cen

tral L

imit

Theo

rem

Discussingtheimplicationsofthe

Cen

tral L

imit

Theo

rem

C

alcu

latin

g co

nfid

ence

inte

rval

s

for p

opul

atio

n m

ean

in c

ases

whe

re th

e po

pula

tion

is n

orm

ally

dist

ribut

ed w

ith k

now

n va

rianc

e or

whe

re a

larg

e sa

mpl

e w

ith

unkn

own

varia

nce

is u

sed

C

ompu

ting

conf

iden

ce in

terv

als

for p

opul

atio

n m

ean

in c

ases

whe

re th

e po

pula

tion

is n

orm

ally

dist

ribut

ed w

ith u

nkno

wn

varia

nce

whe

re a

sm

all s

ampl

e is

use

d

Determining

from

a la

rge

sam

ple

an a

ppro

xim

ate

conf

iden

ce

inte

rval

for a

pop

ulat

ion

prop

ortio

n

So

lvin

g pr

oble

ms

invo

lvin

g

sam

plin

g an

d es

timat

ion

C

ondu

ctin

g fie

ldw

ork

46

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

60

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

so

lve

prob

lem

s in

volv

ing

sam

plin

g an

d es

timat

ion

inve

stig

atio

ns in

volv

ing

sam

plin

g

and

estim

atio

n

46 47

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 4

: ST

ATIS

TIC

AL

INFE

REN

CE

61

TOPI

C 4

: ST

ATIS

TIC

AL IN

FER

ENC

E

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

HYP

OTH

ESIS

TES

TIN

G

fo

rmul

ate

hypo

thes

es

di

stin

guis

h be

twee

n a

type

1

and

a ty

pe 2

erro

r

co

mpu

te p

roba

bilit

ies

of

mak

ing

type

1 a

nd ty

pe 2

erro

rs

ap

ply

a hy

poth

esis

test

in th

e

cont

ext o

f a s

ingl

e

obse

rvat

ion

from

a p

opul

atio

n

whi

ch h

as b

inom

ial

dist

ribut

ion

usin

g ei

ther

the

bino

mia

l dis

tribu

tion

or th

e

norm

al a

ppro

xim

atio

n to

the

bino

mia

l dis

tribu

tion

ap

ply

a hy

poth

esis

test

conc

erni

ng p

opul

atio

n m

ean

usin

g a

sam

ple

draw

n fro

m a

norm

al d

istri

butio

n of

kno

wn

varia

nce

usin

g th

e no

rmal

dist

ribut

ion

N

ull h

ypot

hesi

s

Al

tern

ativ

e hy

poth

esis

Te

st s

tatis

tics

Si

gnifi

canc

e le

vel

H

ypot

hesi

s te

st (1

-tail

and

2-

tail)

Ty

pe 1

and

type

2 e

rrors

z-

test

s

t –

test

s

ch

i-squ

ared

test

s

Discussinghypothesistestingin

rese

arch

C

alcu

latin

g pr

obab

ilitie

s of

mak

ing

type

1 a

nd ty

pe 2

erro

rs

Ap

plyi

ng h

ypot

hesi

s te

sts

in th

e

cont

ext o

f a s

ingl

e ob

serv

atio

n

from

a p

opul

atio

n w

hich

has

bino

mia

l dis

tribu

tion

usin

g ei

ther

the

bino

mia

l dis

tribu

tion

or th

e

norm

al a

ppro

xim

atio

n to

the

bino

mia

l dis

tribu

tion

Discussingthecharacteristicsof

a t a

nd c

hi-s

quar

ed d

istri

butio

n

Fo

rmul

atin

g an

d ap

plyi

ng

hypo

thes

is te

sts

conc

erni

ng

popu

latio

n m

ean

usin

g a

smal

l

sam

ple

draw

n fro

m a

nor

mal

dist

ribut

ion

of u

nkno

wn

varia

nce

usin

g a

t – te

st

IC

T to

ols

R

elev

ant t

exts

En

viro

nmen

t

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

48

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

62

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

de

scrib

e th

e ch

arac

teris

tics

of

a t a

nd c

hi-s

quar

ed

dist

ribut

ion

ap

ply

a hy

poth

esis

test

conc

erni

ng p

opul

atio

n m

ean

usin

g a

smal

l sam

ple

draw

n

from

a n

orm

al d

istri

butio

n of

unkn

own

varia

nce

usin

g a

t –

test

us

e a

chi-s

quar

ed te

st to

test

for i

ndep

ende

nce

in a

cont

inge

ncy

tabl

e

us

e a

chi-s

quar

ed te

st to

car

ry

out t

he g

oodn

ess

of fi

t

anal

ysis

so

lve

prob

lem

s us

ing

an

appr

opria

te te

st

us

ing

chi-s

quar

ed te

sts

to te

st fo

r

inde

pend

ence

in a

con

tinge

ncy

tabl

e

ap

plyi

ng c

hi-s

quar

ed te

sts

to

carr

y ou

t the

goo

dnes

s of

fit

anal

ysis

So

lvin

g pr

oble

ms

invo

lvin

g

hypo

thes

is te

sts

C

ondu

ctin

g re

sear

ch p

roje

cts

invo

lvin

g hy

poth

esis

test

s

48 49

Addi

tiona

l Mat

hem

atic

s Sy

llabu

s Fo

rms

5 - 6

TOPI

C 5

: B

IVA

RIA

TE D

ATA

63

TOPI

C 5

: B

IVAR

IATE

DAT

A

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

BIV

ARIA

TE D

ATA

plot

sca

tter d

iagr

ams

dr

aw li

nes

of b

est f

it

fin

d th

e eq

uatio

ns o

f

regr

essi

on li

nes

ca

lcul

ate

Pear

son`

s pr

oduc

t

mom

ent c

orre

latio

n

coef

ficie

nt (r

)

co

mpu

te th

e co

effic

ient

of

dete

rmin

atio

n (r2 )

so

lve

prob

lem

s in

volv

ing

regr

essi

on a

nd c

orre

latio

n

Sc

atte

r dia

gram

s

R

egre

ssio

n lin

es

Le

ast s

quar

es

Pe

arso

n`s

Prod

uct m

omen

t

corre

latio

n (r)

C

oeffi

cien

t of d

eter

min

atio

n

(r2 )

Pl

ottin

g an

d in

terp

retin

g sc

atte

r

diag

ram

s

Drawinglinesofbestfit

Fi

ndin

g th

e eq

uatio

ns o

f

regr

essi

on li

nes

C

ompu

ting

Pear

son`

s pr

oduc

t

mom

ent c

orre

latio

n co

effic

ient

(r)

In

terp

retin

g th

e va

lue

of

Pear

son`

s pr

oduc

t mom

ent

corre

latio

n co

effic

ient

Discussingthesignificanceof

coef

ficie

nt o

f det

erm

inat

ion

So

lvin

g pr

oble

ms

invo

lvin

g

regr

essi

on a

nd c

orre

latio

n

C

ondu

ctin

g in

vest

igat

ions

invo

lvin

g lin

ear r

elat

ions

hips

R

epre

sent

ing

life

phen

omen

a

usin

g m

athe

mat

ical

mod

els

invo

lvin

g bi

varia

te d

ata

and

IC

T to

ols

R

elev

ant t

exts

En

viro

nmen

t

G

eo-b

oard

Br

aille

mat

eria

ls

Ta

lkin

g bo

oks

64

SUB

TOPI

C

LEAR

NIN

G O

BJE

CTI

VES

Le

arne

rs s

houl

d be

abl

e to

: C

ON

TEN

T (A

ttitu

des,

Ski

lls a

nd

Kno

wle

dge)

SUG

GES

TED

NO

TES

AND

AC

TIVI

TIES

SU

GG

ESTE

D

RES

OU

RC

ES

expl

orin

g th

eir a

pplic

atio

ns in

life

Additional Mathematics Syllabus Forms 5 - 6

9.0 ASSESSMENT

9.1 Assessment Objectives

The assessment will test candidate’s ability to:-

9.1.1 usemathematicalsymbols,termsanddefinitionsappropriately9.1.2 sketch graphs accurately 9.1.3 use appropriate formulae, algorithms and strategies to solve problems in familiar and less familiar contexts 9.1.4 solve problems in Pure Mathematics, Mechanics and Statistics systematically9.1.5 apply mathematical reasoning and communicate mathematical ideas clearly 9.1.6 conduct mathematical proofs rigorously9.1.7 make effective use of a variety of ICT tools in solving problems 9.1.8 construct and use appropriate mathematical models for a given life situation 9.1.9 conduct research projects including those related to enterprise9.1.10 draw inferences through correct manipulation of data.9.1.11 use data correctly to predict trends for planning and decision making purposes9.1.12 construct mathematical arguments through appropriate use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions9.1.13 evaluate mathematical models including an appreciation of the assumptions made and interpret, justify and present the result from a mathematical analysis in a form relevant to the original problem

9.2 Scheme of Assessment

Forms 5 to 6 Additional Mathematics assessment will be based on 30% Continuous Assessment and 70% Summative Assessment.The syllabus’ scheme of assessment is grounded in the principle of equalisation of opportunities hence, doesnotcondonedirectorindirectdiscriminationoflearners.Arrangements,accommodationsandmodificationsmust 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.NBForfurtherdetailsonarrangements,accommodationsandmodificationsrefertotheassessmentprocedurebooklet.

a) Continuous Assessment

Continuous Assessment for Form 5 – 6 will consists of topic tasks, written tests, end of term examinations and projects 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 Tests

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

50

iii) End of term examinations

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

iv) Project

Thisshouldbedonefromtermtwototermfive.

Summary of Continuous Assessment Tasks

Fromtermtwotofive,candidatesareexpectedtohavedonethefollowingrecordedtasks:

• 1topictaskperterm• 2writtentestsperterm• 1endoftermexaminationperterm

Term Number of Topic Tasks

Number of Written Tests

Number of End OfTermExam-ination

Project Total

2 1 2 1 13 1 2 14 1 2 15 1 2 1Actual Weight 3% 8% 9% 10% 30%

Component Skills Topic Tasks Written Tests End of Term ProjectSkill 1Knowledge&Comprehension

50% 50% 50% 20%

Skill 2Application&Analysis

40% 40% 40% 40%

Skill 3Synthesis&Evaluation

10% 10% 10% 40%

Total 100% 100% 100% 100%Actual weighting 3% 8% 9% 10%

Specification Grid for Continuous Assessment

51

Additional Mathematics Syllabus Forms 5 - 6

b. Summative Assessment

The examination will consist of 2 papers: Paper 1 and Paper 2.

69

Actual weighting

3% 8% 9% 10%

b. Summative Assessment

The examination will consist of 2 papers: Paper 1 and Paper 2.

Paper Type of Paper and Topics Marks Duration

1 Pure Mathematics 1 - 10 120 3 hours

2 Mechanics 1 – 5

Statistics 1 – 6

120 3 hours

Paper 1(120 marks)

Pure Mathematics– this is a paper containing about 14 compulsory questions chosen from topics 1 – 6.

Paper 2 (120 marks)

Mechanics and Statistics – this is a paper containing about 14 compulsory questions chosen from topics 1 – 5 of the mechanics section and topics 1 – 5 of the

Statistics section.

Detailed Summative Assessment Table

Paper 1(120 marks)

Pure Mathematics– this is a paper containing about 14 compulsory questions chosen from topics 1 – 6.

Paper 2 (120 marks)

Mechanics and Statistics – this is a paper containing about 14 compulsory questions chosen from topics 1 – 5 of the mechanics section and topics 1 – 5 of the Statistics section.

Detailed Summative Assessment Table

The table below shows the information on types of papers to be offered and their weighting.

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The table below shows the information on types of papers to be offered and their weighting.

P1 P2 Total

Weighting 50% 50% 100%

Actual weighting 35% 35% 70%

Type of Paper PURE MATHEMATICS

Section A (60 Marks)

About 10 compulsory short questions

Section B (60 Marks)

5 compulsory long questions

MECHANICS AND STATISTICS

Section A

MECHANICS-(60 Marks)

About 7 compulsory questions

Section B

STATISTICS- (60 Marks) about 7 compulsory questions

Marks 120 120

Specification Grid for Summative Assessment 52

Additional Mathematics Syllabus Forms 5 - 6

Specification Grid for Summative Assessment

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P1 P2 Total

Skill 1

Knowledge&

Comprehension

50% 36% 86%

Skill 2

Application&

Analysis

40% 36% 76%

Skill 3

Synthesis&

Evaluation

10% 28% 38%

Total 100% 100% 200%

Weighting 35% 35% 70%

9.3 Assessment Model Learners will be assessed using both Continuous and Summative Assessments.

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Additional Mathematics Syllabus Forms 5 - 6

9.3 Assessment Model

Learners will be assessed using both Continuous and Summative Assessments.

Assessment of learner performance in Additional Mathematics

100%

Continuous Assessment 30%

Continuous Assessment Mark = 30%

Final Mark 100%

Summative Assessment 70%

Summative Assessment Mark = 70%

Profiling

Profile

Exit Profile

Topic Tasks3%

Written Tests 8%

End of term

Tests 9%

Project10%

Paper 1 35%

Paper 2 35%

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Additional Mathematics Syllabus Forms 5 - 6

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