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MATHEMATIC

S

Curriculum and Assessment Policy Statement

Further Education and Training PhaseGrades 10-12

National Curriculum Statement (NCS)

CAPS

CurriCulum and assessment PoliCy statement Grades 10-12

matHematiCs

MATHEMATICS GRADES 10-12

CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

department of Basic education

222 Struben StreetPrivate Bag X895Pretoria 0001South AfricaTel: +27 12 357 3000Fax: +27 12 323 0601

120 Plein Street Private Bag X9023Cape Town 8000South Africa Tel: +27 21 465 1701Fax: +27 21 461 8110Website: http://www.education.gov.za

© 2011 department of Basic education

isBn: 978-1-4315-0573-9

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Printed by: Government Printing Works


CAPS

AGRICULTURAL MANAGEMENT PRACTICES GRADES 10-12

CAPS

FOREWORD by thE ministER

Our national curriculum is the culmination of our efforts over a period of seventeen years to transform the curriculum bequeathed to us by apartheid. From the start of democracy we have built our curriculum on the values that inspired our Constitution (Act 108 of 1996). the Preamble to the Constitution states that the aims of the Constitution are to:

• heal thedivisionsof thepastandestablishasocietybasedondemocraticvalues, social justice and fundamental human rights;

• improvethequalityoflifeofallcitizensandfreethepotentialofeachperson;

• laythefoundationsforademocraticandopensocietyinwhichgovernmentisbasedonthewillofthepeopleandeverycitizenisequallyprotectedbylaw;and

• buildaunitedanddemocraticSouthAfricaabletotakeitsrightfulplaceasasovereignstateinthefamilyofnations.

Education and the curriculum have an important role to play in realising these aims.

in 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience ofimplementationpromptedareviewin2000.Thisledtothefirstcurriculumrevision:theRevised National Curriculum Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).

Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National Curriculum Statement (2002) to produce this document.

From 2012 the two 2002 curricula, for Grades R-9 and Grades 10-12 respectively, are combined in a single document andwillsimplybeknownastheNational Curriculum Statement Grades R-12. the National Curriculum Statement for Grades R-12 buildsonthepreviouscurriculumbutalsoupdatesitandaimstoprovideclearerspecificationofwhatis to be taught and learnt on a term-by-term basis.

the National Curriculum Statement Grades R-12 accordingly replaces the subject statements, Learning Programme Guidelines and subject Assessment Guidelines with the

(a) Curriculum and Assessment Policy statements (CAPs) for all approved subjects listed in this document;

(b) National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and

(c) National Protocol for Assessment Grades R-12.

MRS ANGIE MOTSHEKGA, MP MINISTER OF BASIC EDUCATION


CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)


1CAPS

CoNTeNTS

seCtion 1: introduCtion to tHe CurriCulum and assessment PoliCy statements .. 3

1.1 Background ....................................................................................................................................................3

1.2 overview ..........................................................................................................................................................3

1.3 General aims of the south african Curriculum ............................................................................................4

1.4 time allocation ................................................................................................................................................6

1.4.1 Foundation Phase ...................................................................................................................................6

1.4.2 Intermediate Phase .................................................................................................................................6

1.4.3 Senior Phase...........................................................................................................................................7

1.4.4 Grades 10-12 ..........................................................................................................................................7

seCtion 2: introduCtion to matHematiCs .................................................................................. 8

2.1 What is mathematics?.....................................................................................................................................8

2.2 SpecificAims ...................................................................................................................................................8

2.3 SpecificSkills ..................................................................................................................................................8

2.4 Focus of Content areas ..................................................................................................................................9

2.5 Weighting of Content areas ...........................................................................................................................9

2.6 mathematics in the Fet ................................................................................................................................10

seCtion 3: oVerVieW oF toPiCs Per term and annual teaCHinG Plans ....................... 11

3.1 SpecificationofcontenttoshowProgression ...........................................................................................11

3.1.1 overview of topics .................................................................................................................................12

3.2 Contentclarificationwithteachingguidelines ...........................................................................................16

3.2.1 Allocation of teaching time ....................................................................................................................16

3.2.2 Sequencing and pacing of topics ..........................................................................................................18

3.2.3 Topic allocation per term .......................................................................................................................21

Grade 10 Term: 1 ..................................................................................................................................21

Grade 10 Term: 2 ..................................................................................................................................24

Grade 10 Term: 3 ..................................................................................................................................26

Grade 10 Term: 4 ..................................................................................................................................29

Grade 11 Term: 1 ..................................................................................................................................30

Grade 11 Term: 2 ..................................................................................................................................32

Grade 11 Term: 3 ..................................................................................................................................34


2 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

Grade 11 Term: 4 ..................................................................................................................................39

Grade 12 Term:1 ...................................................................................................................................40

Grade 12 Term: 2 ..................................................................................................................................44

Grade 12 Term: 3 ..................................................................................................................................48

Grade 12 Term: 4 ..................................................................................................................................50

seCtion 4: assessment in matHematiCs .................................................................................... 51

4.1. introduction ...................................................................................................................................................51

4.2. informal or daily assessment ......................................................................................................................51

4.3. Formal assessment ......................................................................................................................................52

4.4. Programme of assessment ..........................................................................................................................53

4.5. recording and reporting ..............................................................................................................................55

4.6. moderation of assessment ..........................................................................................................................56

4.7. General ...........................................................................................................................................................56


3CAPS

SeCTIoN 1

introduCtion to tHe CurriCulum and assessment PoliCy statements For matHematiCs Grades 10-12

1.1 Background

The National Curriculum Statement Grades R-12 (NCS) stipulates policy on curriculum and assessment in the schooling sector.

To improve implementation, the National Curriculum Statement was amended, with the amendments coming into effect in January 2012. A single comprehensive Curriculum and Assessment Policy document was developed for each subject to replace Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines in Grades R-12.

1.2 overview

(a) The National Curriculum Statement Grades R-12 (January 2012) represents a policy statement for learning and teaching in South African schools and comprises the following:

(i) Curriculum and Assessment Policy Statements for each approved school subject;

(ii) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and

(iii) The policy document, National Protocol for Assessment Grades R-12 (January 2012).

(b) The National Curriculum Statement Grades R-12 (January 2012) replaces the two current national curricula statements, namely the

(i) Revised National Curriculum Statement Grades R-9, Government Gazette No. 23406 of 31 May 2002, and

(ii) National Curriculum Statement Grades 10-12 Government Gazettes, No. 25545 of 6 October 2003 and No. 27594 of 17 May 2005.

(c) The national curriculum statements contemplated in subparagraphs b(i) and (ii) comprise the following policy documents which will be incrementally repealed by the National Curriculum Statement Grades R-12 (January 2012) during the period 2012-2014:

(i) The Learning Area/Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines for Grades R-9 and Grades 10-12;

(ii) The policy document, National Policy on assessment and qualifications for schools in the GeneralEducation and Training Band, promulgated in Government Notice No. 124 in Government Gazette No. 29626 of 12 February 2007;

(iii) The policy document, the National Senior Certificate: A qualification at Level 4 on the NationalQualificationsFramework(NQF),promulgatedinGovernmentGazetteNo.27819of20July2005;



(iv) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardinglearnerswithspecialneeds, published in Government Gazette, No.29466 of 11 December 2006, is incorporated in the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and

(v) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardingtheNationalProtocolfor Assessment (Grades R-12), promulgated in Government Notice No.1267 in Government Gazette No. 29467 of 11 December 2006.

(d) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, and the sections on the Curriculum and Assessment Policy as contemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the National Curriculum Statement Grades R-12. It will therefore, in terms of section 6A of the South African Schools Act, 1996(ActNo.84of1996,) form the basis for the Minister of Basic education to determine minimum outcomes and standards, as well as the processes and procedures for the assessment of learner achievement to be applicable to public and independent schools.

1.3 General aims of the south african Curriculum

(a) The National Curriculum Statement Grades R-12 gives expression to the knowledge, skills and values worth learning in South African schools. This curriculum aims to ensure that children acquire and apply knowledge and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge in local contexts, while being sensitive to global imperatives.

(b) The National Curriculum Statement Grades R-12 serves the purposes of:

• equipping learners, irrespective of their socio-economic background, race, gender, physical ability or intellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningful participation in society as citizens of a free country;

• providing access to higher education;

• facilitating the transition of learners from education institutions to the workplace; and

• providing employers with a sufficient profile of a learner’s competences.

(c) The National Curriculum Statement Grades R-12 is based on the following principles:

• Social transformation: ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of the population;

• Active and critical learning: encouraging an active and critical approach to learning, rather than rote and uncritical learning of given truths;

• High knowledge and high skills: the minimum standards of knowledge and skills to be achieved at each grade are specified and set high, achievable standards in all subjects;

• Progression: content and context of each grade shows progression from simple to complex;


5CAPS

• Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social and environmental justice and human rights as defined in the Constitution of the Republic of South Africa. The National Curriculum Statement Grades R-12 is sensitive to issues of diversity such as poverty, inequality, race, gender, language, age, disability and other factors;

• Valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country as important contributors to nurturing the values contained in the Constitution; and

• Credibility, quality and efficiency: providing an education that is comparable in quality, breadth and depth to those of other countries.

(d) The National Curriculum Statement Grades R-12 aims to produce learners that are able to:

• identify and solve problems and make decisions using critical and creative thinking;

• work effectively as individuals and with others as members of a team;

• organise and manage themselves and their activities responsibly and effectively;

• collect, analyse, organise and critically evaluate information;

• communicate effectively using visual, symbolic and/or language skills in various modes;

• use science and technology effectively and critically showing responsibility towards the environment and the health of others; and

• demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.

(e) Inclusivity should become a central part of the organisation, planning and teaching at each school. This can only happen if all teachers have a sound understanding of how to recognise and address barriers to learning, and how to plan for diversity.

The key to managing inclusivity is ensuring that barriers are identified and addressed by all the relevant support structures within the school community, including teachers, District-Based Support Teams, Institutional-Level Support Teams, parents and Special Schools as Resource Centres. To address barriers in the classroom, teachers should use various curriculum differentiation strategies such as those included in the Department of Basic Education’s Guidelines for Inclusive Teaching and Learning (2010).



1.4 time allocation

1.4.1 Foundation Phase

(a) The instructional time in the Foundation Phase is as follows:

suBJeCtGrade r (Hours)

Grades 1-2 (Hours)

Grade 3 (Hours)

Home Language 10 8/7 8/7

First Additional Language 2/3 3/4

Mathematics 7 7 7

Life Skills

• Beginning Knowledge

• Creative Arts

• Physical education

• Personal and Social Well-being

6

(1)

(2)

(2)

(1)

6

(1)

(2)

(2)

(1)

7

(2)

(2)

(2)

(1)

total 23 23 25

(b) Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.

(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours for Additional Language in Grades 1-2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional Language.

(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R-2 and 2 hours as indicated by the hours in brackets for Grade 3.

1.4.2 intermediate Phase

(a) The instructional time in the Intermediate Phase is as follows:

suBJeCt Hours

Home Language 6

First Additional Language 5

Mathematics 6

Natural Sciences and Technology 3,5

Social Sciences 3

Life Skills

• Creative Arts

• Physical education

• Personal and Social Well-being

4

(1,5)

(1)

(1,5)

total 27,5


7CAPS

1.4.3 senior Phase

(a) The instructional time in the Senior Phase is as follows:

suBJeCt Hours

Home Language 5

First Additional Language 4

Mathematics 4,5

Natural Sciences 3

Social Sciences 3

Technology 2

economic Management Sciences 2

Life orientation 2

Creative Arts 2

total 27,5

1.4.4 Grades 10-12

(a) The instructional time in Grades 10-12 is as follows:

suBJeCt time alloCation Per Week (Hours)

Home Language 4.5

First Additional Language 4.5

Mathematics 4.5

Life orientation 2

A minimum of any three subjects selected from Group B Annexure B, Tables B1-B8 of the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, subject to the provisos stipulated in paragraph 28 of the said policy document.

12 (3x4h)

total 27,5

The allocated time per week may be utilised only for the minimum required NCS subjects as specified above, and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wish to offer additional subjects, additional time must be allocated for the offering of these subjects



SeCTIoN 2

introduction

In Chapter 2, the Further Education and Training (FET) Phase Mathematics CAPS provides teachers with a definition of mathematics, specific aims, specific skills, focus of content areas and the weighting of content areas.

2.1 What is mathematics?

mathematics is a language that makes use of symbols and notations for describing numerical, geometric and graphical relationships. It is a human activity that involves observing, representing and investigating patterns and qualitative relationships in physical and social phenomena and between mathematical objects themselves. It helps to develop mental processes that enhance logical and critical thinking, accuracy and problem solving that will contribute in decision-making.Mathematical problem solving enables us to understand the world (physical, social and economic) around us, and, most of all, to teach us to think creatively.

2.2 SpecificAims

1. To develop fluency in computation skills without relying on the usage of calculators.

2. Mathematical modeling is an important focal point of the curriculum. Real life problems should be incorporated into all sections whenever appropriate. examples used should be realistic and not contrived. Contextual problems should include issues relating to health, social, economic, cultural, scientific, political and environmental issues whenever possible.

3. To provide the opportunity to develop in learners the ability to be methodical, to generalize, make conjectures and try to justify or prove them.

4. To be able to understand and work with number system.

5. To show Mathematics as a human creation by including the history of Mathematics.

6. To promote accessibility of Mathematical content to all learners. It could be achieved by catering for learners with different needs.

7. To develop problem-solving and cognitive skills. Teaching should not be limited to “how”but should rather feature the “when” and “why” of problem types. Learning procedures and proofs without a good understanding of why they are important will leave learners ill-equipped to use their knowledge in later life.

8. To prepare the learners for further education and training as well as the world of work.

2.3 SpecificSkills

To develop essential mathematical skills the learner should:

• develop the correct use of the language of Mathematics;

• collect, analyse and organise quantitative data to evaluate and critique conclusions;


9CAPS

• use mathematical process skills to identify, investigate and solve problems creatively and critically;

• use spatial skills and properties of shapes and objects to identify, pose and solve problems creatively and critically;

• participate as responsible citizens in the life of local, national and global communities; and

• communicate appropriately by using descriptions in words, graphs, symbols, tables and diagrams.

2.4 Focus of Content areas

Mathematics in the FeT Phase covers ten main content areas. each content area contributes towards the acquisition of the specific skills. The table below shows the main topics in the FET Phase.

the main topics in the Fet mathematics Curriculum

1. Functions

2. number Patterns, sequences, series

3. Finance, growth and decay

4. algebra

5. differential Calculus

6. Probability

7. euclidean Geometry and measurement

8. analytical Geometry

9. trigonometry

10. statistics

2.5 Weighting of Content areas

The weighting of mathematics content areas serves two primary purposes: firstly the weighting gives guidance on the amount of time needed to address adequately the content within each content area; secondly the weighting gives guidance on the spread of content in the examination (especially end of the year summative assessment).



Weighting of Content areas

description Grade 10 Grade 11 Grade. 12

PaPer 1 (Grades 12:bookwork: maximum 6 marks)

Algebra and equations (and inequalities) 30 ± 3 45 ± 3 25 ± 3

Patterns and Sequences 15 ± 3 25 ± 3 25 ± 3

Finance and Growth 10 ± 3

Finance, growth and decay 15 ± 3 15 ± 3

Functions and Graphs 30 ± 3 45 ± 3 35 ± 3

Differential Calculus 35 ± 3

Probability 15 ± 3 20 ± 3 15 ± 3

total 100 150 150

PaPer 2: Grades 11 and 12: theorems and/or trigonometric proofs: maximum 12 marks

description Grade 10 Grade 11 Grade 12

Statistics 15 ± 3 20 ± 3 20 ± 3

Analytical Geometry 15 ± 3 30 ± 3 40 ± 3

Trigonometry 40 ± 3 50 ± 3 40 ± 3

euclidean Geometry and Measurement 30 ± 3 50 ± 3 50 ± 3

total 100 150 150

2.6 mathematics in the Fet

The subject Mathematics in the Further education and Training Phase forges the link between the Senior Phase and the Higher/Tertiary education band. All learners passing through this phase acquire a functioning knowledge of the Mathematics that empowers them to make sense of society. It ensures access to an extended study of the mathematical sciences and a variety of career paths.

In the FeT Phase, learners should be exposed to mathematical experiences that give them many opportunities to develop their mathematical reasoning and creative skills in preparation for more abstract mathematics in Higher/Tertiary education institutions.


11CAPS

SeCTIoN 3

introduction

Chapter 3 provides teachers with:

• specification of content to show progression;

• clarification of content with teaching guidelines; and

• allocation of time.

3.1 SpecificationofContenttoshowProgression

The specification of content shows progression in terms of concepts and skills from Grade 10 to 12 for each content area. However, in certain topics the concepts and skills are similar in two or three successive grades. The clarification of content gives guidelines on how progression should be addressed in these cases. The specification of content should therefore be read in conjunction with the clarification of content.



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)n

(b)

App

ly k

now

ledg

e of

geo

met

ric s

erie

s to

sol

ve

annu

ity a

nd b

ond

repa

ymen

t pro

blem

s.

The

impl

icat

ions

of fl

uctu

atin

g fo

reig

n ex

chan

ge

rate

s.Th

e ef

fect

of d

iffer

ent p

erio

ds o

f com

poun

ding

gr

owth

and

dec

ay (i

nclu

ding

effe

ctiv

e an

d no

min

al

inte

rest

rate

s).

Crit

ical

ly a

naly

se d

iffer

ent l

oan

optio

ns.


13CAPS

4. a

lGeB

ra (a

) U

nder

stan

d th

at re

al n

umbe

rs c

an b

e irr

atio

nal

or ra

tiona

l.Ta

ke n

ote

that

ther

e ex

ist n

umbe

rs o

ther

than

th

ose

on th

e re

al n

umbe

r lin

e, th

e so

-cal

led

non-

real

num

bers

. It

is p

ossi

ble

to s

quar

e ce

rtain

non

-re

al n

umbe

rs a

nd o

btai

n ne

gativ

e re

al n

umbe

rs a

s an

swer

s.

Nat

ure

of ro

ots.

(a)

Sim

plify

exp

ress

ions

usi

ng th

e la

ws

of

expo

nent

s fo

r rat

iona

l exp

onen

ts.

(b)

est

ablis

h be

twee

n w

hich

two

inte

gers

a g

iven

si

mpl

e su

rd li

es.

(c) R

ound

real

num

bers

to a

n ap

prop

riate

deg

ree

of a

ccur

acy

(to a

giv

en n

umbe

r of d

ecim

al

digi

ts).

(a) A

pply

the

law

s of

exp

onen

ts to

exp

ress

ions

in

volv

ing

ratio

nal e

xpon

ents

.

(b) A

dd, s

ubtra

ct, m

ultip

ly a

nd d

ivid

e si

mpl

e su

rds.

Dem

onst

rate

an

unde

rsta

ndin

g of

the

defin

ition

of

a lo

garit

hm a

nd a

ny la

ws

need

ed to

sol

ve re

al li

fe

prob

lem

s.

Man

ipul

ate

alge

brai

c ex

pres

sion

s by

:

•m

ultip

lyin

g a

bino

mia

l by

a tri

nom

ial;

•fa

ctor

isin

g tri

nom

ials

;

•fa

ctor

isin

g th

e di

ffere

nce

and

sum

s of

two

cube

s;

•fa

ctor

isin

g by

gro

upin

g in

pai

rs; a

nd

•si

mpl

ifyin

g, a

ddin

g an

d su

btra

ctin

g al

gebr

aic

fract

ions

with

den

omin

ator

s of

cub

es (l

imite

d to

sum

and

diff

eren

ce o

f cub

es).

Rev

ise

fact

oris

atio

n.•

Take

not

e an

d un

ders

tand

, the

Rem

aind

er a

nd

Fact

or T

heor

ems

for p

olyn

omia

ls u

p to

the

third

deg

ree.

•Fa

ctor

ise

third

-deg

ree

poly

nom

ials

(inc

ludi

ng

exam

ples

whi

ch re

quire

the

Fact

or T

heor

em).

Sol

ve:

•lin

ear e

quat

ions

;

•qu

adra

tic e

quat

ions

;

•lit

eral

equ

atio

ns (c

hang

ing

the

subj

ect o

f a

form

ula)

;

•ex

pone

ntia

l equ

atio

ns;

•lin

ear i

nequ

aliti

es;

•sy

stem

of l

inea

r equ

atio

ns; a

nd

•w

ord

prob

lem

s.

Sol

ve:

•qu

adra

tic e

quat

ions

;

•qu

adra

tic in

equa

litie

s in

one

var

iabl

e an

d in

terp

ret t

he s

olut

ion

grap

hica

lly; a

nd

•eq

uatio

ns in

two

unkn

owns

, one

of w

hich

is

linea

r the

oth

er q

uadr

atic

, al

gebr

aica

lly o

r gr

aphi

cally

.



5. d

iFFe

ren

tia

l C

alC

ulu

s

(a)

An

intu

itive

und

erst

andi

ng o

f the

con

cept

of a

lim

it.

(b)

Diff

eren

tiatio

n of

spe

cifie

d fu

nctio

ns fr

om fi

rst

prin

cipl

es.

(c)

Use

of t

he s

peci

fied

rule

s of

diff

eren

tiatio

n.

(d)

The

equa

tions

of t

ange

nts

to g

raph

s.

(e)

The

abili

ty to

ske

tch

grap

hs o

f cub

ic fu

nctio

ns.

(f) P

ract

ical

pro

blem

s in

volv

ing

optim

izat

ion

and

rate

s of

cha

nge

(incl

udin

g th

e ca

lcul

us o

f m

otio

n).

6. P

ro

Ba

Bil

ity

(a) C

ompa

re th

e re

lativ

e fre

quen

cy o

f an

expe

rimen

tal o

utco

me

with

the

theo

retic

al

prob

abili

ty o

f the

out

com

e.

(b)

Venn

dia

gram

s as

an

aid

to s

olvi

ng p

roba

bilit

y pr

oble

ms.

(c) M

utua

lly e

xclu

sive

eve

nts

and

com

plem

enta

ry

even

ts.

(d)

The

iden

tity

for a

ny tw

o ev

ents

A a

nd B

:P

(A o

r B) =

P(A

) + (B

) - P

(A a

nd B

)

(a) D

epen

dent

and

inde

pend

ent e

vent

s.

(b) V

enn

diag

ram

s or

con

tinge

ncy

tabl

es a

nd

tree

diag

ram

s as

aid

s to

sol

ving

pro

babi

lity

prob

lem

s (w

here

eve

nts

are

not n

eces

saril

y in

depe

nden

t).

(a) G

ener

alis

atio

n of

the

fund

amen

tal c

ount

ing

prin

cipl

e.

(b) P

roba

bilit

y pr

oble

ms

usin

g th

e fu

ndam

enta

l co

untin

g pr

inci

ple.

7. e

uC

lid

ean

Geo

met

ry a

nd

mea

sur

emen

t

(a) R

evis

e ba

sic

resu

lts e

stab

lishe

d in

ear

lier

grad

es.

(b) I

nves

tigat

e lin

e se

gmen

ts jo

inin

g th

e m

id-

poin

ts o

f tw

o si

des

of a

tria

ngle

.

(c) P

rope

rties

of s

peci

al q

uadr

ilate

rals

.

(a) I

nves

tigat

e an

d pr

ove

theo

rem

s of

the

geom

etry

of c

ircle

s as

sum

ing

resu

lts fr

om

earli

er g

rade

s, to

geth

er w

ith o

ne o

ther

resu

lt co

ncer

ning

tang

ents

and

radi

i of c

ircle

s.

(b) S

olve

circ

le g

eom

etry

pro

blem

s, p

rovi

ding

re

ason

s fo

r sta

tem

ents

whe

n re

quire

d.

(c) P

rove

ride

rs.

(a) R

evis

e ea

rlier

(Gra

de 9

) wor

k on

the

nece

ssar

y an

d su

ffici

ent c

ondi

tions

for

poly

gons

to b

e si

mila

r.

(b) P

rove

(acc

eptin

g re

sults

est

ablis

hed

in e

arlie

r gr

ades

):

•th

at a

line

dra

wn

para

llel t

o on

e si

de o

f a

trian

gle

divi

des

the

othe

r tw

o si

des

prop

ortio

nally

(and

the

Mid

-poi

nt T

heor

em

as a

spe

cial

cas

e of

this

theo

rem

);

•th

at e

quia

ngul

ar tr

iang

les

are

sim

ilar;

•th

at tr

iang

les

with

sid

es in

pro

porti

on a

re

sim

ilar;

•th

e P

ytha

gore

an T

heor

em b

y si

mila

r tri

angl

es; a

nd

•rid

ers.


15CAPS

Sol

ve p

robl

ems

invo

lvin

g vo

lum

e an

d su

rface

ar

ea o

f sol

ids

stud

ied

in e

arlie

r gra

des

as w

ell a

s sp

here

s, p

yram

ids

and

cone

s an

d co

mbi

natio

ns o

f th

ose

obje

cts.

R

evis

e G

rade

10

wor

k.

8. t

riG

on

om

etry

(a)

Defi

nitio

ns o

f th

e tri

gono

met

ric r

atio

s si

n θ,

cos θ

and

tan θ

in a

righ

t-ang

led

trian

gles

.

(b) E

xten

d th

e de

finiti

ons

of s

in θ

, cos

θ a

nd

tan θ

to 0

o ≤ θ≤360

o .

(c)

Der

ive

and

use

valu

es o

f th

e tri

gono

met

ric

ratio

s (w

ithou

t usi

ng a

cal

cula

tor f

or th

e

spec

ial a

ngle

s θ

∈ {0

o ;30o ;4

5o ;60o ;9

0o }

(d)

Defi

ne th

e re

cipr

ocal

s of

trig

onom

etric

ratio

s.

(a)

Der

ive

and

use

the

iden

titie

s:

sin θ

cos θ

tan θ=

and

sin

2 θ+s

in2 θ=1.

(b) D

eriv

e th

e re

duct

ion

form

ulae

. (c

) Det

erm

ine

the

gene

ral s

olut

ion

and

/ or s

peci

fic

solu

tions

of t

rigon

omet

ric e

quat

ions

.(d

) est

ablis

h th

e si

ne, c

osin

e an

d ar

ea ru

les.

Pro

of a

nd u

se o

f the

com

poun

d an

gle

and

doub

le a

ngle

iden

titie

s

So

Sol

ve p

robl

ems

in tw

o di

men

sion

s.S

olve

pro

blem

s in

2-d

imen

sion

s.

Sol

ve p

robl

ems

in tw

o an

d th

ree

dim

ensi

ons.

9. a

na

lyti

Ca

l G

eom

etry

Rep

rese

nt g

eom

etric

figu

res

in a

Car

tesi

an c

o-or

dina

te s

yste

m, a

nd d

eriv

e an

d ap

ply,

for a

ny

two

poin

ts (x

1 ; y

1) an

d (x

2 ; y

2), a

form

ula

for

calc

ulat

ing:

•th

e di

stan

ce b

etw

een

the

two

poin

ts;

•th

e gr

adie

nt o

f the

line

seg

men

t joi

ning

the

poin

ts;

•co

nditi

ons

for p

aral

lel a

nd p

erpe

ndic

ular

line

s;

and

•th

e co

-ord

inat

es o

f the

mid

-poi

nt o

f the

line

se

gmen

t joi

ning

the

poin

ts.

Use

a C

arte

sian

co-

ordi

nate

sys

tem

to d

eriv

e an

d ap

ply

:•

the

equa

tion

of a

line

thro

ugh

two

give

n po

ints

;•

the

equa

tion

of a

line

thro

ugh

one

poin

t and

pa

ralle

l or p

erpe

ndic

ular

to a

giv

en li

ne; a

nd•

the

incl

inat

ion

of a

line

.

Use

a tw

o-di

men

sion

al C

arte

sian

co-

ordi

nate

sy

stem

to d

eriv

e an

d ap

ply:

•th

e eq

uatio

n of

a c

ircle

(any

cen

tre);

and

•th

e eq

uatio

n of

a ta

ngen

t to

a ci

rcle

at a

giv

en

poin

t on

the

circ

le.

10. s

tati

stiC

s

(a)

Col

lect

, org

anis

e an

d in

terp

ret u

niva

riate

nu

mer

ical

dat

a in

ord

er to

det

erm

ine:

•m

easu

res

of c

entra

l ten

denc

y;

•fiv

e nu

mbe

r sum

mar

y;•

box

and

whi

sker

dia

gram

s; a

nd•

mea

sure

s of

dis

pers

ion.

(a)

Rep

rese

nt m

easu

res

of c

entra

l ten

denc

y an

d

disp

ersi

on in

uni

varia

te n

umer

ical

dat

a by

:•

usin

g og

ives

; and

•ca

lcul

atin

g th

e va

rianc

e an

d st

anda

rd

devi

atio

n of

set

s of

dat

a m

anua

lly (f

or

smal

l set

s of

dat

a) a

nd u

sing

cal

cula

tors

(fo

r lar

ger s

ets

of d

ata)

and

repr

esen

ting

resu

lts g

raph

ical

ly.(b

) Rep

rese

nt S

kew

ed d

ata

in b

ox a

nd w

hisk

er

diag

ram

s, a

nd fr

eque

ncy

poly

gons

. Ide

ntify

ou

tlier

s.

(a) R

epre

sent

biv

aria

te n

umer

ical

dat

a as

a

scat

ter p

lot a

nd s

ugge

st in

tuiti

vely

and

by

sim

ple

inve

stig

atio

n w

heth

er a

line

ar, q

uadr

atic

or

exp

onen

tial f

unct

ion

wou

ld b

est fi

t the

dat

a.

(b) U

se a

cal

cula

tor t

o ca

lcul

ate

the

linea

r re

gres

sion

line

whi

ch b

est fi

ts a

giv

en s

et o

f bi

varia

te n

umer

ical

dat

a.

(c) U

se a

cal

cula

tor t

o ca

lcul

ate

the

corr

elat

ion

co-e

ffici

ent o

f a s

et o

f biv

aria

te n

umer

ical

dat

a an

d m

ake

rele

vant

ded

uctio

ns.



3.2 ContentClarificationwithteachingguidelines

In Chapter 3, content clarification includes:

• teaching guidelines;

• sequencing of topics per term; and

• pacing of topics over the year.

• each content area has been broken down into topics. The sequencing of topics within terms gives an idea of how content areas can be spread and re-visited throughout the year.

• The examples discussed in the Clarification Column in the annual teaching plan which follows are by no means a complete representation of all the material to be covered in the curriculum. They only serve as an indication of some questions on the topic at different cognitive levels. Text books and other resources should be consulted for a complete treatment of all the material.

• The order of topics is not prescriptive, but ensure that part of trigonometry is taught in the first term and more than six topics are covered / taught in the first two terms so that assessment is balanced between paper 1 and 2.


17CAPS

3.2.1 allocation of teaching time

Time allocation for Mathematics: 4 hours and 30 minutes, e.g. six forty five-minutes periods, per week in grades 10, 11 and 12.

terms Grade 10 Grade 11 Grade 12

no. ofweeks

no. of weeks

no. of weeks

term 1Algebraic expressions

exponents

Number patterns

equations and inequalities

Trigonometry

3

2

1

2

3

exponents and surds

equations and inequalities

Number patterns

Analytical Geometry

3

3

2

3

Patterns, sequences and

series

Functions and inverse

functions

exponential and

logarithmic functions

Finance, growth and decay

Trigonometry - compound

angles

3

3

1

2

2

term 2Functions

Trigonometric functions

euclidean Geometry

MID-YeAR eXAMS

4

1

3

3

Functions

Trigonometry (reduction

formulae, graphs,

equations)

MID-YeAR eXAMS

4

4

3

Trigonometry 2D and 3D

Polynomial functions

Differential calculus

Analytical Geometry

MID-YeAR eXAMS

2

1

3

2

3

term 3Analytical Geometry

Finance and growth

Statistics

Trigonometry

euclidean Geometry

Measurement

2

2

2

2

1

1

Measurement

euclidean Geometry

Trigonometry (sine, area,

cosine rules)

Probability

Finance, growth and decay

1

3

2

2

2

Geometry

Statistics (regression and

correlation)

Counting and Probability

Revision

TRIAL eXAMS

2

2

2

1

3

term 4 Probability

Revision

eXAMS

2

4

3

Statistics

Revision

eXAMS

3

3

3

Revision

eXAMS

3

6

The detail which follows includes examples and numerical references to the overview.



3.2.

2 se

quen

cing

and

Pac

ing

of t

opic

s

mat

Hem

atiC

s: G

ra

de

10 P

aC

e se

tter

1te

rm

1

Wee

ksW

eek

1W

eek

2W

eek

3W

eek

4W

eek

5W

eek

6W

eek

7W

eek

8W

eek

9W

eek

10

Wee

k

11

topi

csA

lgeb

raic

exp

ress

ions

exp

onen

tsN

umbe

r pa

ttern

se

quat

ions

and

ineq

ualit

ies

Trig

onom

etry

ass

essm

ent

Inve

stig

atio

n or

pro

ject

Test

dat

e co

mpl

eted

2te

rm

2

Wee

ksW

eek

1W

eek

2W

eek

3W

eek

4W

eek

5W

eek

6W

eek

7W

eek

8W

eek

9W

eek

10

Wee

k

11

topi

csFu

nctio

nsTr

igon

omet

ric

func

tions

euc

lidea

n G

eom

etry

ass

essm

ent

Ass

ignm

ent /

Tes

tM

ID-Y

eA

R e

XA

MIN

ATIo

Nd

ate

com

plet

ed3

ter

m 3

Wee

ksW

eek

1W

eek

2W

eek

3W

eek

4W

eek

5W

eek

6W

eek

7W

eek

8W

eek

9W

eek

10

topi

csA

naly

tical

Geo

met

ryFi

nanc

e an

d gr

owth

Sta

tistic

sTr

igon

omet

rye

uclid

ean

Geo

met

ryM

easu

rem

ent

ass

essm

ent

Test

Test

dat

e co

mpl

eted

4te

rm

4P

aper

1: 2

hou

rsP

aper

2: 2

hou

rs

Wee

ksW

eek

1

Wee

k

2W

eek

3

Wee

k

4W

eek

5

Wee

k

6W

eek

7

Wee

k 8

Wee

k 9

Wee

k

10A

lgeb

raic

ex

pres

sion

s an

d eq

uatio

ns (a

nd

ineq

ualit

ies)

expo

nent

sN

umbe

r Pat

tern

s Fu

nctio

ns a

nd g

raph

sFi

nanc

e an

d gr

owth

P

roba

bilit

y

30 10 30 15 15

euc

lidea

n ge

omet

ry

and

mea

sure

men

t

Ana

lytic

al g

eom

etry

Trig

onom

etry

Sta

tistic

s

20 15 50 15

topi

csP

roba

bilit

yR

evis

ion

Adm

in

ass

essm

ent

Test

exa

min

atio

ns

dat

e co

mpl

eted

Tota

l mar

ks10

0To

tal m

arks

100


19CAPS

mat

Hem

atiC

s: G

ra

de

11 P

aC

e se

tter

1te

rm

1

Wee

ksW

eek

1W

eek

2W

eek

3W

eek

4W

eek

5W

eek

6W

eek

7W

eek

8W

eek

9W

eek

10

Wee

k

11to

pics

exp

onen

ts a

nd s

urds

equ

atio

ns a

nd in

equa

litie

sN

umbe

r pat

tern

sA

naly

tical

Geo

met

rya

sses

smen

tIn

vest

igat

ion

or p

roje

ctTe

std

ate

com

plet

ed2

ter

m 2

Wee

ksW

eek

1W

eek

2W

eek

3W

eek

4W

eek

5W

eek

6W

eek

7W

eek

8W

eek

9W

eek

10

Wee

k

11to

pics

Func

tions

Trig

onom

etry

(red

uctio

n fo

rmul

ae, g

raph

s, e

quat

ions

)a

sses

smen

tA

ssig

nmen

t / T

est

MID

-Ye

AR

eX

AM

INAT

IoN

dat

e co

mpl

eted

3te

rm

3W

eeks

Wee

k 1

Wee

k 2

Wee

k 3

Wee

k 4

Wee

k 5

Wee

k 6

Wee

k 7

Wee

k 8

Wee

k 9

Wee

k 1

0to

pics

Mea

sure

men

te

uclid

ean

Geo

met

ryTr

igon

omet

ry (s

ine,

cos

ine

and

area

rule

s)Fi

nanc

e, g

row

th a

nd d

ecay

Pro

babi

lity

ass

essm

ent

Test

Test

dat

e co

mpl

eted

4te

rm

4P

aper

1: 3

hou

rsP

aper

2: 3

hou

rs

Wee

ksW

eek

1

Wee

k

2W

eek

3

Wee

k

4W

eek

5

Wee

k

6W

eek

7

Wee

k

8W

eek

9W

eek

10

Alg

ebra

ic e

xpre

ssio

ns

and

equa

tions

(and

in

equa

litie

s)N

umbe

r pat

tern

sFu

nctio

ns a

nd g

raph

s Fi

nanc

e, g

row

th a

nd d

ecay

Pro

babi

lity

45 25 45 15 20

euc

lidea

n G

eom

etry

and

mea

sure

men

tA

naly

tical

geo

met

ryTr

igon

omet

ry

Sta

tistic

s

40 30 60 20

topi

csS

tatis

tics

Rev

isio

nFI

NA

L e

XA

MIN

ATIo

NA

dmin

ass

essm

ent

Test

dat

e co

mpl

eted

Tota

l mar

ks15

0To

tal m

arks

150



mat

Hem

atiC

s: G

ra

de

12 P

aC

e se

tter

1te

rm

1W

eeks

Wee

k 1

Wee

k 2

Wee

k 3

Wee

k 4

Wee

k 5

Wee

k 6

Wee

k 7

Wee

k 8

Wee

k 9

Wee

k 1

0W

eek

11

topi

csN

umbe

r pat

tern

s, s

eque

nces

and

ser

ies

Func

tions

: For

mal

defi

nitio

n; in

vers

esFu

nctio

ns:

expo

nent

ial

and

loga

rithm

ic

Fina

nce,

gro

wth

and

dec

ayTr

igon

omet

ry

ass

essm

ent

Test

Inve

stig

atio

n or

pro

ject

Ass

ignm

ent

dat

e co

mpl

eted

2te

rm

2W

eeks

Wee

k 1

Wee

k 2

Wee

k 3

Wee

k 4

Wee

k 5

Wee

k 6

Wee

k 7

Wee

k 8

Wee

k 9

Wee

k 1

0W

eek

11

topi

csTr

igon

omet

ryFu

nctio

ns:

poly

nom

ials

Diff

eren

tial C

alcu

lus

Ana

lytic

al G

eom

etry

ass

essm

ent

Test

MID

-Ye

AR

eX

AM

INAT

IoN

dat

e co

mpl

eted

3te

rm

3W

eeks

Wee

k 1

Wee

k 2

Wee

k 3

Wee

k 4

Wee

k 5

Wee

k 6

Wee

k 7

Wee

k 8

Wee

k 9

Wee

k 1

0to

pics

Geo

met

ryS

tatis

tics

Cou

ntin

g an

d P

roba

bilit

yR

evis

ion

tria

l eX

am

inat

ion

ass

essm

ent

Test

dat

e co

mpl

eted

4te

rm

4P

aper

1: 3

hou

rsP

aper

2: 3

hou

rs

Wee

ksW

eek

1

Wee

k

2W

eek

3

Wee

k

4W

eek

5

Wee

k

6W

eek

7

Wee

k

8W

eek

9W

eek

10

Alg

ebra

ic e

xpre

ssio

ns

and

equa

tions

(and

ineq

ualit

ies)

Num

ber p

atte

rns

Func

tions

and

gra

phs

Fina

nce,

gro

wth

and

dec

ay

Diff

eren

tial C

alcu

lus

Cou

ntin

g an

d pr

obab

ility

25 25 35 15 35 15

euc

lidea

n G

eom

etry

and

mea

sure

men

t

Ana

lytic

al G

eom

etry

Trig

onom

etry

Sta

tistic

s

50 40 40 20

topi

csR

evis

ion

FIN

AL

eX

AM

INAT

IoN

Adm

ina

sses

smen

t

dat

e co

mpl

eted

Tota

l mar

ks15

0To

tal m

arks

150


21CAPS

3.2.

3 to

pic

allo

catio

n pe

r ter

m

Gr

ad

e 10

: ter

m 1

no

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

Whe

re a

n ex

ampl

e is

giv

en, t

he c

ogni

tive

dem

and

is s

ugge

sted

: kno

wle

dge

(k),

rout

ine

proc

edur

e (r

), co

mpl

ex p

roce

dure

(C) o

r pro

blem

-sol

ving

(P)

3a

lgeb

raic

ex

pres

sion

s

1.

Und

erst

and

that

real

num

bers

can

be

ratio

nal o

r irr

atio

nal.

2.

est

ablis

h be

twee

n w

hich

two

inte

gers

a g

iven

sim

ple

surd

lies

.3.

R

ound

real

num

bers

to a

n ap

prop

riate

deg

ree

of

accu

racy

. 4.

M

ultip

licat

ion

of a

bin

omia

l by

a tri

nom

ial.

5.

Fact

oris

atio

n to

incl

ude

type

s ta

ught

in g

rade

9 a

nd:

•tri

nom

ials

•gr

oupi

ng in

pai

rs•

sum

and

diff

eren

ce o

f tw

o cu

bes

6.

Sim

plifi

catio

n of

alg

ebra

ic fr

actio

ns u

sing

fact

oriz

atio

n w

ith d

enom

inat

ors

of c

ubes

(lim

ited

to s

um a

nd

diffe

renc

e of

cub

es).

exam

ples

to il

lust

rate

the

diffe

rent

cog

nitiv

e le

vels

invo

lved

in fa

ctor

isat

ion:

1.

Fact

oris

e fu

lly:

1.1.

m

2 - 2

m +

1 (r

evis

ion)

Le

arne

rs m

ust b

e ab

le to

reco

gnis

e th

e si

mpl

est

p

erfe

ct s

quar

es.

(R

)1.

2.

2x2 -

x -

3

This

type

is ro

utin

e an

d ap

pear

s in

all

text

s.

(R)

1.3.

13

y 2+

18-

y2 2

Le

arne

rs a

re re

quire

d to

wor

k w

ith fr

actio

ns a

nd

ide

ntify

w

hen

an e

xpre

ssio

n ha

s be

en “f

ully

fact

oris

ed”.

(R

)

2.

Sim

plify

(C

)

2ex

pone

nts

1.

Rev

ise

law

s of

exp

onen

ts le

arnt

in G

rade

9 w

here

€

x,y

>0

and

€

m,

€

n ∈ Z:

•

€

xm×xn

=xm

+n

•

€

xm÷xn

=xm

−n

•

€

(xm)n

=xm

n

•

€

xm×ym

=(xy)

m

Als

o by

defi

nitio

n:

•,

€

x≠0 ,

and

•

€

x0=1 ,

€

x≠0

2.

Use

the

law

s of

exp

onen

ts to

sim

plify

exp

ress

ions

and

so

lve

equa

tions

, acc

eptin

g th

at th

e ru

les

also

hol

d fo

r

€

m,

€

n ∈

Q.

exam

ples

:1.

Sim

plify

: (3

x 52 )3 -

75

A si

mpl

e tw

o-st

ep p

roce

dure

is in

volv

ed.

(R

)

2. S

impl

ify

Ass

umin

g th

is ty

pe o

f que

stio

n ha

s no

t bee

n ta

ught

,

sp

ottin

g th

at th

e nu

mer

ator

can

be

fact

oris

ed a

s a

diffe

renc

e of

squ

ares

requ

ires

insi

ght.

(P

)3.

S

olve

for

x :

3.1

12

5,0

2=

x

(R

)

3.2

€

2x3 2

=54

(R

)

3.3

(C

)

3.4

(C

)



Gr

ad

e 10

: ter

m 1

no

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

1n

umbe

rs a

nd

patte

rns

Pat

tern

s: In

vest

igat

e nu

mbe

r pat

tern

s le

adin

g to

thos

e w

here

ther

e is

a c

onst

ant d

iffer

ence

bet

wee

n co

nsec

utiv

e te

rms,

and

the

gene

ral t

erm

(with

out u

sing

a fo

rmul

a-se

e co

nten

t ove

rvie

w) i

s th

eref

ore

linea

r.

Com

men

t:

• A

rithm

etic

seq

uenc

e is

don

e in

Gra

de 1

2, h

ence

is

not u

sed

in

Gra

de 1

0.

exam

ples

:1.

D

eter

min

e th

e 5th

and

the

nth te

rms

of th

e nu

mbe

r pat

tern

10;

7; 4

; 1; …

. The

re is

an

alg

orith

mic

app

roac

h to

ans

wer

ing

such

que

stio

ns.

(R

)

2.

If th

e pa

ttern

MAT

HS

MAT

HS

MAT

HS

… is

con

tinue

d in

this

way

, wha

t will

the

267th

le

tter b

e? It

is n

ot im

med

iate

ly o

bvio

us h

ow o

ne s

houl

d pr

ocee

d, u

nles

s si

mila

r qu

estio

ns h

ave

been

tack

led.

(P

)

2eq

uatio

ns a

nd

ineq

ualit

ies

1.

Rev

ise

the

solu

tion

of li

near

equ

atio

ns.

2.

Sol

ve q

uadr

atic

equ

atio

ns (b

y fa

ctor

isat

ion)

.

3.

Sol

ve s

imul

tane

ous

linea

r equ

atio

ns in

two

unkn

owns

.

4.

Sol

ve w

ord

prob

lem

s in

volv

ing

linea

r, qu

adra

tic o

r si

mul

tane

ous

linea

r equ

atio

ns.

5.

Sol

ve li

tera

l equ

atio

ns (c

hang

ing

the

subj

ect o

f a

form

ula)

.

6.

Sol

ve li

near

ineq

ualit

ies

(and

sho

w s

olut

ion

grap

hica

lly).

Inte

rval

not

atio

n m

ust b

e kn

own.

exam

ples

:

1.

Sol

ve fo

r x:

(R

)

2.

Sol

ve fo

r m:

2m2 -

m =

1

(R)

3.

Sol

ve fo

r x a

nd y

: x +

2y

= 1;

1

23

=+

yx

(C

)

4.

Sol

ve fo

r r in

term

s of

V, ∏

and

h: V

=∏

r2 h

(R

)

5.

Sol

ve fo

r x:

-1 ≤

2 -

3x ≤

8

(

C)


23CAPS

Gr

ad

e 10

: ter

m 1

no

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3tr

igon

omet

ry

1.

Defi

ne th

e tri

gono

met

ric ra

tios

sin

θ, c

os θ

and

tan θ,

us

ing

right

-ang

led

trian

gles

.

2.

Ext

end

the

defin

ition

s of

sin

θ, c

os θ

and

tan θ

for

00 ≤ θ

≤ 3

600 .

3.

Defi

ne th

e re

cipr

ocal

s of

the

trigo

nom

etric

ratio

s

cose

c θ,

sec

θ a

nd c

ot θ

, usi

ng ri

ght-a

ngle

d tri

angl

es

(thes

e th

ree

reci

proc

als

shou

ld b

e ex

amin

ed in

gra

de

10 o

nly)

.

4.

Der

ive

valu

es o

f the

trig

onom

etric

ratio

s fo

r the

spe

cial

ca

ses

(with

out u

sing

a c

alcu

lato

r)

θ∈

{00 ;

300 ;

450 ;

600 ;

900 }.

5.

Sol

ve tw

o-di

men

sion

al p

robl

ems

invo

lvin

g rig

ht-a

ngle

d tri

angl

es.

6.

Sol

ve s

impl

e tri

gono

met

ric e

quat

ions

for a

ngle

s be

twee

n 00 a

nd 9

00 .

7.

Use

dia

gram

s to

det

erm

ine

the

num

eric

al v

alue

s of

ra

tios

for a

ngle

s fro

m 0

0 to

3600 .

Com

men

t: It

is im

porta

nt to

stre

ss th

at:

• si

mila

rity

of tr

iang

les

is fu

ndam

enta

l to

the

trigo

nom

etric

ratio

s si

n θ,

cos

θ a

nd ta

n θ;

• tri

gono

met

ric ra

tios

are

inde

pend

ent o

f the

leng

ths

of th

e si

des

of a

sim

ilar

right

-ang

led

tria

ngle

and

dep

end

(uni

quel

y) o

nly

on th

e an

gles

, hen

ce w

e co

nsid

er

them

as

func

tions

of t

he a

ngle

s;

• do

ublin

g a

ratio

has

a d

iffer

ent e

ffect

from

dou

blin

g an

ang

le, f

or e

xam

ple,

gen

eral

ly

2sin

θ≠

sin

2θ;a

nd

• S

olve

equ

atio

n of

the

form

c

x=

sin

, or

cx=

cos

2, o

r c

x=

2ta

n, w

here

c is

a

cons

tant

.

exam

ples

:

1.

If 5s

in θ+4=0

and

00 ≤

θ ≤

270

0 , c

alcu

late

the

valu

e of

sin

2 θ+c

os2 θw

ithou

t us

ing

a ca

lcul

ator

.

(R

)

2.

Let A

BC

D b

e a

rect

angl

e, w

ith A

B =

2cm

. Let

E b

e on

AD

suc

h th

at A

EB

ˆˆ= E =

450

and

BÊ

C =

750 .

Det

erm

ine

the

area

of t

he re

ctan

gle.

(P

)

3.

Det

erm

ine

the

leng

th o

f the

hyp

oten

use

of a

righ

t-ang

led

trian

gle

AB

C, w

here

EB

ˆˆ= =

900 ,

DA

ˆˆ= =

300 a

nd A

B =

10c

m

(K

)

4.

Sol

ve fo

r x:

for

(C)

ass

essm

ent t

erm

1:

1. I

nves

tigat

ion

or p

roje

ct (o

nly

one

proj

ect p

er y

ear)

(at l

east

50

mar

ks)

e

xam

ple

of a

n in

vest

igat

ion:

Im

agin

e a

cube

of w

hite

woo

d w

hich

is d

ippe

d in

to re

d pa

int s

o th

at th

e su

rface

is re

d, b

ut th

e in

side

stil

l whi

te. I

f one

cut

is m

ade,

par

alle

l to

each

face

of t

he c

ube

(and

thro

ugh

the

cent

re o

f the

cub

e), t

hen

ther

e w

ill b

e 8

smal

ler c

ubes

. eac

h of

the

smal

ler c

ubes

will

hav

e 3

red

face

s an

d 3

whi

te fa

ces.

Inve

stig

ate

the

num

ber o

f sm

alle

r cub

es w

hich

will

hav

e 3,

2,

1 a

nd 0

red

face

s if

2/3/

4/…

/n e

qual

ly s

pace

d cu

ts a

re m

ade

para

llel t

o ea

ch fa

ce. T

his

task

pro

vide

s th

e op

portu

nity

to in

vest

igat

e, ta

bula

te re

sults

, mak

e co

njec

ture

s an

d ju

stify

or

pro

ve th

em.

2.

Test

(at l

east

50

mar

ks a

nd 1

hou

r). M

ake

sure

all

topi

cs a

re te

sted

.

C

are

need

s to

be

take

n to

set

que

stio

ns o

n al

l fou

r cog

nitiv

e le

vels

: ap

prox

imat

ely

20%

kno

wle

dge,

app

roxi

mat

ely

35%

rout

ine

proc

edur

es, 3

0% c

ompl

ex p

roce

dure

s an

d 15

%

prob

lem

-sol

ving

.



Gr

ad

e 10

: ter

m 2

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

(4 +

1)

5Fu

nctio

ns

1.

The

conc

ept o

f a fu

nctio

n, w

here

a

certa

in q

uant

ity (o

utpu

t val

ue) u

niqu

ely

depe

nds

on a

noth

er q

uant

ity (i

nput

va

lue)

. Wor

k w

ith re

latio

nshi

ps b

etw

een

varia

bles

usi

ng ta

bles

, gra

phs,

wor

ds a

nd

form

ulae

. Con

vert

flexi

bly

betw

een

thes

e re

pres

enta

tions

.

Not

e: th

at th

e gr

aph

defin

ed b

yy

x=

shou

ld b

e kn

own

from

Gra

de 9

.

2.

Poi

nt b

y po

int p

lotti

ng o

f bas

ic g

raph

s

defin

ed b

y 2 x

y=

, x

y1

=an

d x

by=

;

0>

b a

nd

to d

isco

ver s

hape

, dom

ain

(inpu

t val

ues)

, ran

ge (o

utpu

t val

ues)

, as

ympt

otes

, axe

s of

sym

met

ry, t

urni

ng

poin

ts a

nd in

terc

epts

on

the

axes

(whe

re

appl

icab

le).

3.

Inve

stig

ate

the

effe

ct o

f q

xf

ay

+=

)(

. and

qx

fa

y+

=)

(.

on

the

grap

hs d

efine

d by

q

xf

ay

+=

)(

.,

whe

re

xx

f=

)(

, ,

)(

2 xx

f=

xx

f1

)(

=

and

,)

(x

bx

f=

,0

>b

4.

Poi

nt b

y po

int p

lotti

ng o

f bas

ic g

raph

s

defin

ed b

y ,

and

fo

r

5. S

tudy

the

effe

ct o

f a

and

qx

fa

y+

=)

(.

on

the

grap

hs

defin

ed b

y:

; ; a

nd w

here

q

xf

ay

+=

)(

. , q

xf

ay

+=

)(

. ∈

Q fo

r .

6.

Ske

tch

grap

hs, fi

nd th

e eq

uatio

ns o

f giv

en

grap

hs a

nd in

terp

ret g

raph

s.

not

e: S

ketc

hing

of t

he g

raph

s m

ust b

e ba

sed

on

the

obse

rvat

ion

of n

umbe

r 3 a

nd 5

.

Com

men

ts:

• A

mor

e fo

rmal

defi

nitio

n of

a fu

nctio

n fo

llow

s in

Gra

de 1

2. A

t thi

s le

vel i

t is

enou

gh to

inve

stig

ate

the

way

(uni

que)

out

put v

alue

s de

pend

on

how

inpu

t val

ues

vary

. The

term

s in

depe

nden

t (in

put)

and

depe

nden

t (ou

tput

) var

iabl

es m

ight

be

usef

ul.

• A

fter s

umm

arie

s ha

ve b

een

com

pile

d ab

out b

asic

feat

ures

of p

resc

ribed

gra

phs

and

the

effe

cts

of p

aram

eter

s a

and

q ha

ve b

een

inve

stig

ated

: a: a

ver

tical

stre

tch

(and

/or a

refle

ctio

n ab

out t

he

x-ax

is) a

nd q

a v

ertic

al s

hift.

The

follo

win

g ex

ampl

es m

ight

be

appr

opria

te:

• R

emem

ber t

hat g

raph

s in

som

e pr

actic

al a

pplic

atio

ns m

ay b

e ei

ther

dis

cret

e or

con

tinuo

us.

exam

ples

:

1.

Ske

tche

d be

low

are

gra

phs

of

qxa

xf

+=

)(

and

.

The

horiz

onta

l asy

mpt

ote

of b

oth

grap

hs is

the

line

y =

1.

Det

erm

ine

the

valu

es o

f a

, b

, n

, q

and

t.

(C)

Ox

y

(1;

-1)

(2;

0)

2.

Ske

tch

the

grap

h de

fined

by

fo

r

(R)


25CAPS

Gr

ad

e 10

: ter

m 2

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3eu

clid

ean

Geo

met

ry

1.

Rev

ise

basi

c re

sults

est

ablis

hed

in e

arlie

r gr

ades

rega

rdin

g lin

es, a

ngle

s an

d tri

angl

es, e

spec

ially

the

sim

ilarit

y an

d co

ngru

ence

of t

riang

les.

2.

Inve

stig

ate

line

segm

ents

join

ing

the

mid

-po

ints

of t

wo

side

s of

a tr

iang

le.

3.

Defi

ne th

e fo

llow

ing

spec

ial q

uadr

ilate

rals

: th

e ki

te, p

aral

lelo

gram

, rec

tang

le, r

hom

bus,

sq

uare

and

trap

eziu

m. I

nves

tigat

e an

d m

ake

conj

ectu

res

abou

t the

pro

perti

es o

f th

e si

des,

ang

les,

dia

gona

ls a

nd a

reas

of

thes

e qu

adril

ater

als.

Pro

ve th

ese

conj

ectu

res.

Com

men

ts:

•Tr

iang

les

are

sim

ilar i

f the

ir co

rres

pond

ing

angl

es a

re e

qual

, or i

f the

ratio

s of

thei

r sid

es a

re

equa

l: Tr

iang

les

AB

Can

d D

EF

are

sim

ilar i

fD

Aˆ

ˆ=

,

EB

ˆˆ=

and

FC

ˆˆ=

. The

y ar

e al

so

sim

ilar i

f .

•W

e co

uld

defin

e a

para

llelo

gram

as

a qu

adril

ater

al w

ith tw

o pa

irs o

f opp

osite

sid

es p

aral

lel.

Then

we

inve

stig

ate

and

prov

e th

at th

e op

posi

te s

ides

of t

he p

aral

lelo

gram

are

equ

al, o

ppos

ite

angl

es o

f a p

aral

lelo

gram

are

equ

al, a

nd d

iago

nals

of a

par

alle

logr

am b

isec

t eac

h ot

her.

•It

mus

t be

expl

aine

d th

at a

sin

gle

coun

ter e

xam

ple

can

disp

rove

a C

onje

ctur

e, b

ut n

umer

ous

spec

ific

exam

ples

sup

porti

ng a

con

ject

ure

do n

ot c

onst

itute

a g

ener

al p

roof

.

exam

ple:

In q

uadr

ilate

ral K

ITe

, KI =

Ke

and

IT =

eT.

The

dia

gona

ls in

ters

ect a

t M. P

rove

that

:

1.

IM =

Me

and

(R)

2.

KT

is p

erpe

ndic

ular

to Ie

.

(

P)

As

it is

not

obv

ious

, firs

t pro

ve th

at

.

3m

id-y

ear

exam

inat

ions

ass

essm

ent t

erm

2:

1. A

ssig

nmen

t / te

st (a

t lea

st 5

0 m

arks

)

2. M

id-y

ear e

xam

inat

ion

(at l

east

100

mar

ks)

o

ne p

aper

of

2 h

ours

(100

mar

ks) o

r Tw

o pa

pers

- on

e, 1

hou

r (50

mar

ks) a

nd th

e ot

her,

1 ho

ur (5

0 m

arks

)



Gr

ad

e 10

: ter

m 3

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2a

naly

tical

G

eom

etry

Rep

rese

nt g

eom

etric

figu

res

on a

Car

tesi

an

co-o

rdin

ate

syst

em.

Der

ive

and

appl

y fo

r any

two

poin

ts

);

(1

1y

xan

d )

;(

22

yx

the

form

ulae

for

calc

ulat

ing

the:

1.

dist

ance

bet

wee

n th

e tw

o po

ints

;

2.

grad

ient

of t

he li

ne s

egm

ent c

onne

ctin

g th

e tw

o po

ints

(and

from

that

iden

tify

para

llel

and

perp

endi

cula

r lin

es);

and

3.

coor

dina

tes

of th

e m

id-p

oint

of t

he li

ne

segm

ent j

oini

ng th

e tw

o po

ints

.

exam

ple:

Con

side

r the

poi

nts

)5;2(P

and

in th

e C

arte

sian

pla

ne.

1.1.

Cal

cula

te th

e di

stan

ce P

Q.

(K)

1.2

Fin

d th

e co

ordi

nate

s of

R if

M

is th

e m

id-p

oint

of P

R.

(R

)

1.3

Det

erm

ine

the

coor

dina

tes

of S

if P

QR

S is

a p

aral

lelo

gram

. (C

)

1.4

Is

PQ

RS

a re

ctan

gle?

Why

or w

hy n

ot?

(R

)

2Fi

nanc

e an

d gr

owth

Use

the

sim

ple

and

com

poun

d

grow

th fo

rmul

ae

and

ni

PA

)1(+

=] to

sol

ve p

robl

ems,

incl

udin

g an

nual

inte

rest

, hire

pur

chas

e,

infla

tion,

pop

ulat

ion

grow

th a

nd o

ther

real

-lif

e pr

oble

ms.

Und

erst

and

the

impl

icat

ion

of

fluct

uatin

g fo

reig

n ex

chan

ge ra

tes

(e.g

. on

the

petro

l pric

e, im

ports

, exp

orts

, ove

rsea

s tra

vel).


27CAPS

Gr

ad

e 10

: ter

m 3

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2st

atis

tics

1. R

evis

e m

easu

res

of c

entra

l ten

denc

y in

un

grou

ped

data

.

2. M

easu

res

of c

entra

l ten

denc

y in

gro

uped

da

ta:

ca

lcul

atio

n of

mea

n es

timat

e of

gro

uped

an

d un

grou

ped

data

and

iden

tifica

tion

of

mod

al in

terv

al a

nd in

terv

al in

whi

ch th

e m

edia

n lie

s.

3.

Rev

isio

n of

rang

e as

a m

easu

re o

f di

sper

sion

and

ext

ensi

on to

incl

ude

perc

entil

es, q

uarti

les,

inte

rqua

rtile

and

sem

i in

terq

uarti

le ra

nge.

4.

Five

num

ber s

umm

ary

(max

imum

, min

imum

an

d qu

artil

es) a

nd b

ox a

nd w

hisk

er

diag

ram

.

5.

Use

the

stat

istic

al s

umm

arie

s (m

easu

res

of c

entra

l ten

denc

y an

d di

sper

sion

), an

d gr

aphs

to a

naly

se a

nd m

ake

mea

ning

ful

com

men

ts o

n th

e co

ntex

t ass

ocia

ted

with

th

e gi

ven

data

.

Com

men

t:In

gra

de 1

0, th

e in

terv

als

of g

roup

ed d

ata

shou

ld b

e gi

ven

usin

g in

equa

litie

s, th

at is

, in

the

form

0≤

x<20

rath

er th

an in

the

form

0-1

9, 2

0-29

, …

exam

ple:

The

mat

hem

atic

s m

arks

of 2

00 g

rade

10

lear

ners

at a

sch

ool c

an b

e su

mm

aris

ed a

s fo

llow

s:

Perc

enta

ge o

btai

ned

num

ber o

f can

dida

tes

0≤x<

204

20≤x

<30

10

30≤x

<40

37

40≤x

<50

43

50≤x

<60

36

60≤x

<70

26

70≤x

<80

24

80≤x

<100

20

1.

Cal

cula

te th

e ap

prox

imat

e m

ean

mar

k fo

r the

exa

min

atio

n.

(R

)

2.

Iden

tify

the

inte

rval

in w

hich

eac

h of

the

follo

win

g da

ta it

ems

lies:

2.1.

th

e m

edia

n;

(R

)

2.2.

th

e lo

wer

qua

rtile

;

(R

)

2.3.

th

e up

per q

uarti

le; a

nd

(R)

2.4.

the

thirt

ieth

per

cent

ile.

(R)



Gr

ad

e 10

: ter

m 3

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2tr

igon

omet

ry

Pro

blem

s in

two

dim

ensi

ons.

exam

ple:

Two

flagp

oles

are

30

m a

part.

The

one

has

hei

ght 1

0 m

, whi

le th

e ot

her h

as h

eigh

t 15

m. T

wo

tig

ht ro

pes

conn

ect t

he to

p of

eac

h po

le to

the

foot

of t

he o

ther

. At w

hat h

eigh

t abo

ve th

e

grou

nd d

o th

e tw

o ro

pes

inte

rsec

t? W

hat i

f the

pol

es w

ere

at d

iffer

ent d

ista

nce

apar

t?

(P)

1eu

clid

ean

Geo

met

ry

Sol

ve p

robl

ems

and

prov

e rid

ers

usin

g th

e pr

oper

ties

of p

aral

lel l

ines

, tria

ngle

s an

d qu

adril

ater

als.

Com

men

t:U

se c

ongr

uenc

y an

d pr

oper

ties

of q

uads

, esp

. par

alle

logr

ams.

exam

ple:

eFG

H is

a p

aral

lelo

gram

. Pro

ve th

at M

FNH

is a

par

alle

logr

am.

N

M

HE

FG

(C)

2m

easu

rem

ent

1.

Rev

ise

the

volu

me

and

surfa

ce a

reas

of

right

-pris

ms

and

cylin

ders

.

2.

Stu

dy th

e ef

fect

on

volu

me

and

surfa

ce

area

whe

n m

ultip

lyin

g an

y di

men

sion

by

a co

nsta

nt fa

ctor

k.

3.

Cal

cula

te th

e vo

lum

e an

d su

rface

are

as o

f sp

here

s, ri

ght p

yram

ids

and

right

con

es.

exam

ple:

The

heig

ht o

f a c

ylin

der i

s 10

cm

, and

the

radi

us o

f the

circ

ular

bas

e is

2 c

m. A

hem

isph

ere

is

atta

ched

to o

ne e

nd o

f the

cyl

inde

r and

a c

one

of h

eigh

t 2 c

m to

the

othe

r end

. Cal

cula

te th

e vo

lum

e an

d su

rface

are

a of

the

solid

, cor

rect

to th

e ne

ares

t cm

3 and

cm

2 , res

pect

ivel

y.

(R

)

Com

men

ts:

• In

cas

e of

pyr

amid

s, b

ases

mus

t eith

er b

e an

equ

ilate

ral t

riang

le o

r a s

quar

e.

• P

robl

em ty

pes

mus

t inc

lude

com

posi

te fi

gure

.

ass

essm

ent t

erm

3: T

wo

(2) T

ests

(at l

east

50

mar

ks a

nd 1

hou

r) c

over

ing

all t

opic

s in

app

roxi

mat

ely

the

ratio

of t

he a

lloca

ted

teac

hing

tim

e.


29CAPS

Gr

ad

e 10

: ter

m 4

no

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2Pr

obab

ility

1. T

he u

se o

f pro

babi

lity

mod

els

to

com

pare

the

rela

tive

frequ

ency

of

even

ts w

ith th

e th

eore

tical

prob

abili

ty.

2. T

he u

se o

f Ven

n di

agra

ms

to s

olve

prob

abili

ty p

robl

ems,

der

ivin

g an

d

a

pply

ing

the

follo

win

g fo

r any

two

e

vent

s A

and

B in

a s

ampl

e sp

ace

S:

AP

(or

a

nd);

B

A

and

B a

re m

utua

lly e

xclu

sive

if

AP

(an

d;0

)=

B

A an

d B

are

com

plem

enta

ry if

they

are

mut

ually

exc

lusi

ve ;

and

.1)

()

(=

+B

PA

P

Then

()

(P

BP

=no

t .

Com

men

t: •

It ge

nera

lly ta

kes

a ve

ry la

rge

num

ber o

f tria

ls b

efor

e th

e re

lativ

e fre

quen

cy o

f a c

oin

falli

ng

head

s up

whe

n to

ssed

app

roac

hes

0,5.

exam

ple:

In a

sur

vey

80 p

eopl

e w

ere

ques

tione

d to

find

out

how

man

y re

ad n

ewsp

aper

S o

r D o

r bot

h. T

he s

urve

y re

veal

ed th

at 4

5 re

ad D

, 30

read

S a

nd 1

0 re

ad n

eith

er.

Use

a V

enn

diag

ram

to fi

nd h

ow m

any

read

1.

S o

nly;

(C)

2.

D o

nly;

and

(C)

3.

both

D a

nd S

.

(C

)

4r

evis

ion

Com

men

t:Th

e va

lue

of w

orki

ng th

roug

h pa

st p

aper

s ca

nnot

be

over

em

phas

ised

.

3ex

amin

atio

ns

ass

essm

ent t

erm

41.

Tes

t (at

leas

t 50

mar

ks)

2. e

xam

inat

ion

Pap

er 1

: 2 h

ours

(100

mar

ks m

ade

up a

s fo

llow

s: 1

5±3

on n

umbe

r pat

tern

s, 3

0±3

on a

lgeb

raic

exp

ress

ions

, equ

atio

ns a

nd in

equa

litie

s , 3

0±3

on fu

nctio

ns, 1

0±3

on fi

nanc

e an

d

gro

wth

and

15±

3 on

pro

babi

lity.

Pap

er 2

: 2 h

ours

(100

mar

ks m

ade

up a

s fo

llow

s: 4

0±3

on tr

igon

omet

ry, 1

5±3

on A

naly

tical

Geo

met

ry, 3

0±3

on e

uclid

ean

Geo

met

ry a

nd M

easu

rem

ent,

and

15±3

on

Sta

tistic

s



Gr

ad

e 11

: ter

m 1

no

fWee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

Whe

re a

n ex

ampl

e is

giv

en, t

he c

ogni

tive

dem

and

is s

ugge

sted

: kno

wle

dge

(k),

rout

ine

proc

edur

e (r

), co

mpl

ex p

roce

dure

(C) o

r pro

blem

sol

ving

(P)

3ex

pone

nts

and

surd

s

1.

Sim

plify

exp

ress

ions

and

sol

ve e

quat

ions

us

ing

the

law

s of

exp

onen

ts fo

r ra

tiona

l ex

pone

nts

whe

re

;

qp

qp

xx

=0

;0>

>q

x.

2.

Add

, sub

tract

, mul

tiply

and

div

ide

sim

ple

surd

s.

3.

Sol

ve s

impl

e eq

uatio

ns in

volv

ing

surd

s.

exam

ple:

1.

Det

erm

ine

the

valu

e of

23

9.

(R)

2.

Sim

plify

:

(R)

3.

Sol

ve fo

r x

: .

(P

)

3eq

uatio

ns a

nd

ineq

ualit

ies

1.

Com

plet

e th

e sq

uare

.

2.

Qua

drat

ic e

quat

ions

(by

fact

oris

atio

n an

d by

usi

ng th

e qu

adra

tic fo

rmul

a).

3.

Qua

drat

ic in

equa

litie

s in

one

unk

now

n (In

terp

ret s

olut

ions

gra

phic

ally

).

NB

: It i

s re

com

men

ded

that

the

solv

ing

of

equa

tions

in tw

o un

know

ns is

impo

rtant

to

be u

sed

in o

ther

equ

atio

ns li

ke h

yper

bola

- st

raig

ht li

ne a

s th

is is

nor

mal

in th

e ca

se o

f gr

aphs

.

4.

equ

atio

ns in

two

unkn

owns

, one

of w

hich

is

linea

r and

the

othe

r qua

drat

ic.

5.

Nat

ure

of ro

ots.

exam

ple:

1.

I hav

e 12

met

res

of fe

ncin

g. W

hat a

re th

e di

men

sion

s of

the

larg

est r

ecta

ngul

ar a

rea

I can

en

clos

e w

ith th

is fe

ncin

g by

usi

ng a

n ex

istin

g w

all a

s on

e si

de?H

int:

let t

he le

ngth

of t

he e

qual

si

des

of th

e re

ctan

gle

be x

met

res

and

form

ulat

e an

exp

ress

ion

for t

he a

rea

of th

e re

ctan

gle.

(C)

(

With

out t

he h

int t

his

wou

ld p

roba

bly

be p

robl

em s

olvi

ng.)

2.1.

Sho

w th

at th

e ro

ots

of

are

irrat

iona

l.

(R)

2.2.

Sho

w th

at

01

2=

++

xx

has

no

real

root

s.

(R

)

3.

Sol

ve fo

r x

: .

(R

)

4.

Sol

ve fo

r x

:

.

(

R)

5.

Two

mac

hine

s, w

orki

ng to

geth

er, t

ake

2 ho

urs

24 m

inut

es to

com

plet

e a

job.

Wor

king

on

its

own,

one

mac

hine

take

s 2

hour

s lo

nger

than

the

othe

r to

com

plet

e th

e jo

b. H

ow lo

ng d

oes

th

e sl

ower

mac

hine

take

on

its o

wn?

(

P)

2n

umbe

r pa

ttern

s

Pat

tern

s: In

vest

igat

e nu

mbe

r pat

tern

s le

adin

g to

thos

e w

here

ther

e is

a c

onst

ant s

econ

d di

ffere

nce

betw

een

cons

ecut

ive

term

s, a

nd th

e ge

nera

l ter

m is

ther

efor

e qu

adra

tic.

exam

ple:

In th

e fir

st s

tage

of t

he W

orld

Cup

Soc

cer F

inal

s th

ere

are

team

s fro

m fo

ur d

iffer

ent c

ount

ries

in e

ach

grou

p. e

ach

coun

try in

a g

roup

pla

ys e

very

oth

er c

ount

ry in

the

grou

p on

ce. H

ow m

any

mat

ches

are

ther

e fo

r eac

h gr

oup

in th

e fir

st s

tage

of t

he fi

nals

? H

ow m

any

gam

es w

ould

ther

e

be if

ther

e w

ere

five

team

s in

eac

h gr

oup?

Six

team

s? n

team

s?

(

P)


31CAPS

Gr

ad

e 11

: ter

m 1

no

fWee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3a

naly

tical

G

eom

etry

Der

ive

and

appl

y:1.

th

e eq

uatio

n of

a li

ne th

ough

two

give

n po

ints

;2.

th

e eq

uatio

n of

a li

ne th

roug

h on

e po

int a

nd

para

llel o

r per

pend

icul

ar to

a g

iven

line

; and

3.

the

incl

inat

ion

(θ) o

f a li

ne, w

here

is th

e gr

adie

nt o

f the

line

exam

ple:

G

iven

the

poin

ts A

(2;5

) ; B

(-3;

-4) a

nd C

(4;-2

) det

erm

ine:

1.

the

equa

tion

of th

e lin

e A

B;

and

(R

)

2.

the

size

of

CA

Bˆ

.

(

C)

ass

essm

ent t

erm

1:

1.

A

n In

vest

igat

ion

or a

pro

ject

(a

max

imum

of o

ne p

roje

ct in

a y

ear)

(at l

east

50

mar

ks)

Not

ice

that

an

assi

gnm

ent i

s ge

nera

lly a

n ex

tend

ed p

iece

of w

ork

unde

rtake

n at

hom

e. L

inea

r pro

gram

min

g qu

estio

ns c

an b

e us

ed a

s pr

ojec

ts.

exam

ple

of a

n as

sign

men

t: r

atio

s an

d eq

uatio

ns in

two

varia

bles

.(T

his

assi

gnm

ent b

rings

in a

n el

emen

t of h

isto

ry w

hich

cou

ld b

e ex

tend

ed to

incl

ude

one

or tw

o an

cien

t pai

ntin

gs a

nd e

xam

ples

of a

rchi

tect

ure

whi

ch a

re in

the

shap

e of

a re

ctan

gle

with

the

ratio

of s

ides

equ

al to

the

gold

en ra

tio.)

Task

1

If 2x

2 - 3

xy +

y2 =

0 th

en (2

x - y

)(x-

y) =

0 s

o 2y

x=

or

yx=

. Hen

ce th

e ra

tio

21=

yx o

r 11

=yx

. In

the

sam

e w

ay fi

nd th

e po

ssib

le v

alue

s of

the

ratio

yx

if it

is g

iven

that

2x2 -

5xy

+ y

2 = 0

Task

M

ost p

aper

is c

ut to

inte

rnat

iona

lly a

gree

d si

zes:

A0,

A1,

A2,

…, A

7 w

ith th

e pr

oper

ty th

at th

e A

1 sh

eet i

s ha

lf th

e si

ze o

f the

A0

shee

t and

sim

ilar t

o th

e A

0

shee

t, th

e A

2 sh

eet i

s ha

lf th

e si

ze o

f the

A1

shee

t and

sim

ilar t

o th

e A

1 sh

eet,

etc.

Fin

d th

e ra

tio o

f the

leng

th

yx= to

the

brea

dth

yx=

of A

0, A

1, A

2, …

, A7

pape

r (in

sim

ples

t sur

d fo

rm).

Task

3Th

e go

lden

rect

angl

e ha

s be

en re

cogn

ised

thro

ugh

the

ages

as

bein

g ae

sthe

tical

ly p

leas

ing.

It c

an b

e se

en in

the

arch

itect

ure

of th

e G

reek

s, in

scu

lptu

res

and

in R

enai

ssan

ce

pain

tings

. Any

gol

den

rect

angl

e w

ith le

ngth

x a

nd b

read

th y

has

the

prop

erty

that

whe

n a

squa

re th

e le

ngth

of t

he s

horte

r sid

e (y

) is

cut f

rom

it, a

noth

er re

ctan

gle

sim

ilar t

o it

is le

ft. T

he

proc

ess

can

be c

ontin

ued

inde

finite

ly, p

rodu

cing

sm

alle

r and

sm

alle

r rec

tang

les.

Usi

ng th

is in

form

atio

n, c

alcu

late

the

ratio

x:yin

sur

d fo

rm.

exa

mpl

e of

pro

ject

: Col

lect

the

heig

hts

of a

t lea

st 5

0 si

xtee

n-ye

ar-o

ld g

irls

and

at le

ast 5

0 si

xtee

n-ye

ar-o

ld b

oys.

Gro

up y

our d

ata

appr

opria

tely

and

use

thes

e tw

o se

ts o

f gro

uped

dat

a to

dra

w fr

eque

ncy

poly

gons

of t

he re

lativ

e he

ight

s of

boy

s an

d of

girl

s, in

diff

eren

t col

ours

, on

the

sam

e sh

eet o

f gra

ph p

aper

. Ide

ntify

the

mod

al in

terv

als,

the

inte

rval

s in

whi

ch th

e m

edia

ns li

e an

d th

e ap

prox

imat

e m

eans

as

calc

ulat

ed fr

om th

e fre

quen

cies

of t

he g

roup

ed d

ata.

By

how

muc

h do

es th

e ap

prox

imat

e m

ean

heig

ht o

f you

r sam

ple

of s

ixte

en-y

ear-

old

girls

diff

er fr

om th

e ac

tual

mea

n? C

omm

ent o

n th

e sy

mm

etry

of t

he tw

o fre

quen

cy p

olyg

ons

and

any

othe

r asp

ects

of t

he d

ata

whi

ch a

re il

lust

rate

d by

the

frequ

ency

pol

ygon

s.2.

Te

st (

at le

ast 5

0 m

arks

and

1 h

our)

. Mak

e su

re a

ll to

pics

are

test

ed.

Car

e ne

eds

to b

e ta

ken

to a

sk q

uest

ions

on

all f

our c

ogni

tive

leve

ls: a

ppro

xim

atel

y 20

% k

now

ledg

e, a

ppro

xim

atel

y 35

% ro

utin

e pr

oced

ures

, 30%

com

plex

pro

cedu

res

and

15

% p

robl

em-s

olvi

ng.



Gr

ad

e 11

: ter

m 2

no

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

4Fu

nctio

ns

1.

Rev

ise

the

effe

ct o

f the

par

amet

ers

a an

d q

and

inve

stig

ate

the

effe

ct o

f p o

n th

e gr

aphs

of

the

func

tions

defi

ned

by:

1.1.

q

px

ax

fy

++

==

2 )(

)(

1.2.

q

px

ax

fy

++

==

)(

1.3.

q

ba

xf

yp

x+

==

+.

)(

whe

re

b>0,b≠1

2.

Inve

stig

ate

num

eric

ally

the

aver

age

grad

ient

bet

wee

n tw

o po

ints

on

a cu

rve

and

deve

lop

an in

tuiti

ve u

nder

stan

ding

of t

he

conc

ept o

f the

gra

dien

t of a

cur

ve a

t a p

oint

.

3.

Poi

nt b

y po

int p

lotti

ng o

f bas

ic g

raph

s

defin

ed b

y ,

and

fo

r

€

θ∈[−360°;360

°]

4.

Inve

stig

ate

the

effe

ct o

f the

par

amet

er k

on th

e gr

aphs

of t

he fu

nctio

ns d

efine

d by

€

y=sin(kx)

, an

d

.

5.

Inve

stig

ate

the

effe

ct o

f the

par

amet

er

p on

the

grap

hs o

f the

func

tions

defi

ned

by

),si

n(p

xy

+=

,),

cos(

px

y+

= a

nd

),ta

n(p

xy

+=

.

6.

Dra

w s

ketc

h gr

aphs

defi

ned

by:

𝑦=

𝑎 𝑠𝑖

𝑛 𝑘

(𝑥+

𝑝),

𝑦=𝑎

𝑐𝑜𝑠

𝑘 (𝑥

+𝑝)

and

𝑦=𝑎

𝑡𝑎 𝑛

𝑘 (𝑥

+𝑝)

at m

ost t

wo

para

met

ers

at a

tim

e.

Com

men

t: •

onc

e th

e ef

fect

s of

the

para

met

ers

have

bee

n es

tabl

ishe

d, v

ario

us p

robl

ems

need

to b

e se

t: dr

awin

g sk

etch

gra

phs,

det

erm

inin

g th

e de

finin

g eq

uatio

ns o

f fun

ctio

ns fr

om s

uffic

ient

dat

a,

mak

ing

dedu

ctio

ns fr

om g

raph

s. R

eal l

ife a

pplic

atio

ns o

f the

pre

scrib

ed fu

nctio

ns s

houl

d be

st

udie

d.

• Tw

o pa

ram

eter

s at

a ti

me

can

be v

arie

d in

test

s or

exa

min

atio

ns.

exam

ple:

Ske

tch

the

grap

hs d

efine

d by

a

nd

€

f(x)

=cos(2x

−120°)

on th

e sa

me

set o

f axe

s, w

here

.

(C

)


33CAPS

Gr

ad

e 11

: ter

m 2

no

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

4tr

igon

omet

ry

1.

Der

ive

and

use

the

iden

titie

s

kan

odd

inte

ger;

and

.2.

D

eriv

e an

d us

e re

duct

ion

form

ulae

to

sim

plify

the

follo

win

g ex

pres

sion

s:

2.1.

;

2.2.

2.3.

an

d

2.4.

.

3.

Det

erm

ine

for w

hich

val

ues

of a

var

iabl

e an

id

entit

y ho

lds.

4.

Det

erm

ine

the

gene

ral s

olut

ions

of

trigo

nom

etric

equ

atio

ns. A

lso,

det

erm

ine

solu

tions

in s

peci

fic in

terv

als.

Com

men

t:•

Teac

hers

sho

uld

expl

ain

whe

re re

duct

ion

form

ulae

com

e fro

m.

exam

ples

:

1.

Pro

ve th

at

. (R

)

2.

For w

hich

val

ues

of

is

und

efine

d?

(R)

3.

Sim

plify

€

cos180°−x

() sin

x−90

°(

) −1

tan2540°

+x

() sin90

°+x

() cos

−x

()

(R)

4.

Det

erm

ine

the

gene

ral s

olut

ions

of

. (C

)

3m

id-y

ear

exam

inat

ions

ass

essm

ent t

erm

2:

1.

Ass

ignm

ent

( at l

east

50

mar

ks)

2.

Mid

-yea

r exa

min

atio

n:

Pap

er 1

: 2 h

ours

(100

mar

ks m

ade

up a

s fo

llow

s: g

ener

al a

lgeb

ra (2

5±3)

equ

atio

ns a

nd in

equa

litie

s (3

5±3)

; num

ber p

atte

rns

(15±

3); f

unct

ions

(25±

3)

Pap

er 2

: 2 h

ours

(100

mar

ks m

ade

up a

s fo

llow

s: a

naly

tical

geo

met

ry (3

0±3)

and

trig

onom

etry

(70

±3))

.



Gr

ad

e 11

: ter

m 3

no.

of

wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

1m

easu

rem

ent

1.

Rev

ise

the

Gra

de 1

0 w

ork.

3eu

clid

ean

Geo

met

ry

Acc

ept r

esul

ts e

stab

lishe

d in

ear

lier g

rade

s

as a

xiom

s an

d al

so th

at a

tang

ent t

o a

circ

le

is p

erpe

ndic

ular

to th

e ra

dius

, dra

wn

to th

e

poin

t of c

onta

ct.

Then

inve

stig

ate

and

prov

e th

e th

eore

ms

of

the

geom

etry

of c

ircle

s:

•Th

e lin

e dr

awn

from

the

cent

re o

f a c

ircle

pe

rpen

dicu

lar t

o a

chor

d bi

sect

s th

e ch

ord;

•Th

e pe

rpen

dicu

lar b

isec

tor o

f a c

hord

pa

sses

thro

ugh

the

cent

re o

f the

circ

le;

•Th

e an

gle

subt

ende

d by

an

arc

at th

e ce

ntre

of a

circ

le is

dou

ble

the

size

of t

he

angl

e su

bten

ded

by th

e sa

me

arc

at th

e ci

rcle

(on

the

sam

e si

de o

f the

cho

rd a

s th

e ce

ntre

);

•A

ngle

s su

bten

ded

by a

cho

rd o

f the

circ

le,

on th

e sa

me

side

of t

he c

hord

, are

equ

al;

•Th

e op

posi

te a

ngle

s of

a c

yclic

qua

drila

tera

l ar

e su

pple

men

tary

;

•Tw

o ta

ngen

ts d

raw

n to

a c

ircle

from

the

sam

e po

int o

utsi

de th

e ci

rcle

are

equ

al in

le

ngth

;

•Th

e an

gle

betw

een

the

tang

ent t

o a

circ

le

and

the

chor

d dr

awn

from

the

poin

t of

cont

act i

s eq

ual t

o th

e an

gle

in th

e al

tern

ate

segm

ent.

Use

the

abov

e th

eore

ms

and

thei

r

conv

erse

s, w

here

they

exi

st, t

o so

lve

rider

s.

Com

men

ts:

Pro

ofs

of th

eore

ms

can

be a

sked

in e

xam

inat

ions

, but

thei

r con

vers

es

(whe

reve

r the

y ho

ld) c

anno

t be

aske

d.

exam

ple:

1.

AB

and

CD

are

two

chor

ds o

f a c

ircle

with

cen

tre o

. M i

s on

AB

and

N is

on

CD

suc

h th

at

OM

⊥ A

B a

nd O

N ⊥

CD

. Als

o, A

B =

50m

m, O

M =

40m

m a

nd O

N =

20m

m. D

eter

min

e th

e

radi

us o

f the

circ

le a

nd th

e le

ngth

of C

D.

(

C)

2.

O is

the

cent

re o

f the

circ

le b

elow

and

x

O2

ˆ 1=

.

2.1.

D

eter

min

e 2

O a

nd M

in te

rms

of x

.

(R

)

2.2.

D

eter

min

e 1

K a

nd

2K

in te

rms

of x

.

(R

)

2.3.

D

eter

min

eM

Kˆ

ˆ 1+

. Wha

t do

you

notic

e?

(R)

2.4.

Writ

e do

wn

your

obs

erva

tion

rega

rdin

g th

e m

easu

res

of

2K

and

M.

(R)


35CAPS

Gr

ad

e 11

: ter

m 3

no.

of

wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3.

O is

the

cent

re o

f the

circ

le a

bove

and

MP

T is

a ta

ngen

t. A

lso,

.

Det

erm

ine,

with

reas

ons,

y

x, a

nd z

.

(C)

2

y

3 z

O

B

T M

A

P x

4. G

iven

: ,

and

2

2ˆ

ˆB

A=

. .

Pro

ve th

at:

4.1

PA

L is

a ta

ngen

t to

circ

le A

BC

;

(P

)

4.2

AB

is a

tang

ent t

o ci

rcle

AD

P.

(P)



Gr

ad

e 11

: ter

m 3

no.

of

wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

5.

In th

e ac

com

pany

ing

figur

e, tw

o ci

rcle

s in

ters

ect a

t F a

nd D

.

BFT

is a

tang

ent t

o th

e sm

alle

r circ

le a

t F. S

traig

ht li

ne A

FE is

dra

wn

such

that

FD

= F

E. C

DE

is a

stra

ight

line

and

cho

rd A

C a

nd B

F cu

t at K

.

Pro

ve th

at:

5.1

BT

// C

E

(C)

5.2

BC

EF

is a

par

alle

logr

am

(

P)

5.3

AC

= B

F

(

P)


37CAPS

Gr

ad

e 11

: ter

m 3

no.

of

wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2tr

igon

omet

ry

1.

Pro

ve a

nd a

pply

the

sine

, cos

ine

and

area

ru

les.

2.

Sol

ve p

robl

ems

in tw

o di

men

sion

s us

ing

the

sine

, cos

ine

and

area

rule

s.

Com

men

t:•

The

proo

fs o

f the

sin

e, c

osin

e an

d ar

ea ru

les

are

exam

inab

le.

exam

ple:

In

D is

on

BC

, AD

C =

θ, D

A =

DC

= r,

BD

= 2

r, AC=k

, and

.

Sho

w th

at

.

(P)

2Fi

nanc

e, g

row

th

and

deca

y

1.

Use

sim

ple

and

com

poun

d de

cay

form

ulae

:

A =

P(1

- in

) and

A =

P(1

- i)n

to s

olve

pro

blem

s (in

clud

ing

stra

ight

line

de

prec

iatio

n an

d de

prec

iatio

n on

a re

duci

ng

bala

nce)

.

2.

The

effe

ct o

f diff

eren

t per

iods

of c

ompo

und

grow

th a

nd d

ecay

, inc

ludi

ng n

omin

al a

nd

effe

ctiv

e in

tere

st ra

tes.

exam

ples

:

1.

The

valu

e of

a p

iece

of e

quip

men

t dep

reci

ates

from

R10

000

to R

5 00

0 in

four

yea

rs.

Wha

t is

the

rate

of d

epre

ciat

ion

if ca

lcul

ated

on

the:

1.1

stra

ight

line

met

hod;

and

(R)

1.2

redu

cing

bal

ance

?

(C)

2.

Whi

ch is

the

bette

r inv

estm

ent o

ver a

yea

r or l

onge

r: 10

,5%

p.a

. com

poun

ded

daily

or

10,5

5% p

.a. c

ompo

unde

d m

onth

ly?

(R)

3.

R50

000

is in

vest

ed in

an

acco

unt w

hich

offe

rs 8

% p

.a. i

nter

est c

ompo

unde

d qu

arte

rly fo

r th

e fir

st 1

8 m

onth

s. T

he in

tere

st th

en c

hang

es to

6%

p.a

. com

poun

ded

mon

thly.

Tw

o ye

ars

af

ter t

he m

oney

is in

vest

ed, R

10 0

00 is

with

draw

n. H

ow m

uch

will

be

in th

e ac

coun

t afte

r 4

year

s?

(

C)

Com

men

t:•

The

use

of a

tim

elin

e to

sol

ve p

robl

ems

is a

use

ful t

echn

ique

.

• S

tress

the

impo

rtanc

e of

not

wor

king

with

roun

ded

answ

ers,

but

of u

sing

the

max

imum

acc

urac

y af

ford

ed b

y th

e ca

lcul

ator

righ

t to

the

final

ans

wer

whe

n ro

undi

ng m

ight

be

appr

opria

te.



Gr

ad

e 11

: ter

m 3

no.

of

wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2Pr

obab

ility

1.

Rev

ise

the

addi

tion

rule

for m

utua

lly

excl

usiv

e ev

ents

:

𝑃

(𝐴 𝑜𝑟

𝐵)=

𝑃𝐴 +

𝑃(𝐵)

,

the

com

plem

enta

ry ru

le:

𝑃

(𝑛 𝑜𝑡

𝐴 )=

1−𝑃(

𝐴 )an

d th

e id

entit

y

P

(A o

r B) =

P(A

) + P

(B) -

P(A

and

B)

2.

Iden

tify

depe

nden

t and

inde

pend

ent e

vent

s an

d th

e pr

oduc

t rul

e fo

r ind

epen

dent

ev

ents

:

𝑃

(𝐴 𝑎 𝑛

𝑑 𝐵)

=𝑃(

𝐴 )×

𝑃(𝐵)

.

3.

The

use

of V

enn

diag

ram

s to

sol

ve

prob

abili

ty p

robl

ems,

der

ivin

g an

d

appl

ying

form

ulae

for a

ny th

ree

even

ts A

, B a

nd C

in a

sam

ple

spac

e S

.

4.

Use

tree

dia

gram

s fo

r the

pro

babi

lity

of

cons

ecut

ive

or s

imul

tane

ous

even

ts w

hich

ar

e no

t nec

essa

rily

inde

pend

ent.

Com

men

t:

• Ve

nn D

iagr

ams

or C

ontin

genc

y ta

bles

can

be

used

to s

tudy

dep

ende

nt a

nd in

depe

nden

t ev

ents

.

exam

ples

:

1. P

(A) =

0,4

5, P

(B) =

0,3

and

P(A

or B

) = 0

,615

. Are

the

even

ts A

and

B m

utua

lly e

xclu

sive

, in

depe

nden

t or n

eith

er m

utua

lly e

xclu

sive

nor

inde

pend

ent?

(R)

2. W

hat i

s th

e pr

obab

ility

of t

hrow

ing

at le

ast o

ne s

ix in

four

rolls

of a

regu

lar s

ix s

ided

die

?

(C

)

3. I

n a

grou

p of

50

lear

ners

, 35

take

Mat

hem

atic

s an

d 30

take

His

tory

, whi

le 1

2 ta

ke n

eith

er

of th

e tw

o. If

a le

arne

r is

chos

en a

t ran

dom

from

this

gro

up, w

hat i

s th

e pr

obab

ility

that

he

/she

take

s bo

th M

athe

mat

ics

and

His

tory

?

(C)

4. A

stu

dy w

as d

one

to te

st h

ow e

ffect

ive

thre

e di

ffere

nt d

rugs

, A, B

and

C w

ere

in re

lievi

ng

head

ache

s. o

ver t

he p

erio

d co

vere

d by

the

stud

y, 8

0 pa

tient

s w

ere

give

n th

e op

portu

nity

to

use

all

two

drug

s. T

he fo

llow

ing

resu

lts w

ere

obta

ined

:from

at l

east

one

of t

he d

rugs

?

(R

)

40 re

porte

d re

lief f

rom

dru

g A

35 re

porte

d re

lief f

rom

dru

g B

40 re

porte

d re

lief f

rom

dru

g C

21 re

porte

d re

lief f

rom

bot

h dr

ugs

A an

d C

18 re

porte

d re

lief f

rom

dru

gs B

and

C

68 re

porte

d re

lief f

rom

at l

east

one

of t

he d

rugs

7 re

porte

d re

lief f

rom

all

thre

e dr

ugs.

4.1

Rec

ord

this

info

rmat

ion

in a

Ven

n di

agra

m.

(

C)

4.2

How

man

y su

bjec

ts g

ot n

o re

lief f

rom

any

of t

he d

rugs

?

(K)

4.3

How

man

y su

bjec

ts g

ot re

lief f

rom

dru

gs A

and

B,

but n

ot C

?

(R

)

4.4

Wha

t is

the

prob

abili

ty th

at a

rand

omly

cho

sen

subj

ect g

ot re

lief f

rom

at l

east

one

of t

he

drug

s?

(R

)


39CAPS

Gr

ad

e 11

: ter

m 4

no.

of

wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3st

atis

tics

1.

His

togr

ams

2.

Freq

uenc

y po

lygo

ns

3.

ogi

ves

(cum

ulat

ive

frequ

ency

cur

ves)

4.

Varia

nce

and

stan

dard

dev

iatio

n of

un

grou

ped

data

5.

Sym

met

ric a

nd s

kew

ed d

ata

6.

Iden

tifica

tion

of o

utlie

rs

Com

men

ts:

•Va

rianc

e an

d st

anda

rd d

evia

tion

may

be

calc

ulat

ed u

sing

cal

cula

tors

.

•P

robl

ems

shou

ld c

over

topi

cs re

late

d to

hea

lth, s

ocia

l, ec

onom

ic, c

ultu

ral,

polit

ical

and

en

viro

nmen

tal i

ssue

s.

•Id

entifi

catio

n of

out

liers

sho

uld

be d

one

in th

e co

ntex

t of a

sca

tter p

lot a

s w

ell a

s th

e bo

x an

d w

hisk

er d

iagr

ams.

3r

evis

ion

3ex

amin

atio

ns

ass

essm

ent t

erm

4:

1.

Test

(at l

east

50

mar

ks)

2.

exa

min

atio

n (3

00 m

arks

)

Pap

er 1

: 3 h

ours

(150

mar

ks m

ade

up a

s fo

llow

s: (2

5±3)

on

num

ber p

atte

rns,

on

(45±

3) e

xpon

ents

and

sur

ds, e

quat

ions

and

ineq

ualit

ies,

(45±

3) o

n fu

nctio

ns, (

15±3

) on

finan

ce

grow

th a

nd d

ecay

, (20

±3) o

n pr

obab

ility

).

Pap

er 2

: 3 h

ours

(150

mar

ks m

ade

up a

s fo

llow

s: (5

0±3)

on

trigo

nom

etry

, (30

±3) o

n A

naly

tical

Geo

met

ry, (

50±3

) on

euc

lidea

n G

eom

etry

and

Mea

sure

men

t, (2

0±3)

on

Sta

tistic

s.



Gr

ad

e 12

: ter

m 1

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3Pa

ttern

s,

sequ

ence

s,

serie

s

1.

Num

ber p

atte

rns,

incl

udin

g ar

ithm

etic

and

ge

omet

ric s

eque

nces

and

ser

ies

2.

Sig

ma

nota

tion

3.

Der

ivat

ion

and

appl

icat

ion

of th

e fo

rmul

ae

for t

he s

um o

f arit

hmet

ic a

nd g

eom

etric

se

ries:

3.1

;

;

3.2

; a

nd

3.3

,

Com

men

t:D

eriv

atio

n of

the

form

ulae

is e

xam

inab

le.

exam

ples

:1.

Writ

e do

wn

the

first

five

term

s of

the

sequ

ence

with

gen

eral

term

.

(K)

2. C

alcu

late

.

(R)

3. D

eter

min

e th

e 5th

term

of t

he g

eom

etric

seq

uenc

e of

whi

ch th

e 8th

term

is 6

and

the

12th

term

is 1

4.

(

C)

4. D

eter

min

e th

e la

rges

t val

ue o

f n

suc

h th

at

.

(R

)

5. S

how

that

1

999

9,0

.

=.

(P

)

3Fu

nctio

ns

1.

Defi

nitio

n of

a fu

nctio

n.

2.

Gen

eral

con

cept

of t

he in

vers

e of

a fu

nctio

n an

d ho

w th

e do

mai

n of

the

func

tion

may

ne

ed to

be

rest

ricte

d (in

ord

er to

obt

ain

a on

e-to

-one

func

tion)

to e

nsur

e th

at th

e in

vers

e is

a fu

nctio

n.3.

D

eter

min

e an

d sk

etch

gra

phs

of th

e in

vers

es o

f the

func

tions

defi

ned

by

Focu

s on

the

follo

win

g ch

arac

teris

tics:

do

mai

n an

d ra

nge,

inte

rcep

ts w

ith th

e ax

es,

turn

ing

poin

ts, m

inim

a, m

axim

a,as

ympt

otes

(hor

izon

tal a

nd v

ertic

al),

shap

e an

d sy

mm

etry

, ave

rage

gra

dien

t (av

erag

e ra

te o

f cha

nge)

, int

erva

ls o

n w

hich

the

func

tion

incr

ease

s /d

ecre

ases

.

exam

ples

:

1.

Con

side

r the

func

tion

fw

here

.

1.1

W

rite

dow

n th

e do

mai

n an

d ra

nge

of f

.

(K

)

1.2

S

how

that

f is

a o

ne-to

-one

rela

tion.

(R)

1.3

D

eter

min

e th

e in

vers

e fu

nctio

n .

(

R)

1.4

S

ketc

h th

e gr

aphs

of t

he fu

nctio

ns

f,

and

x

y=

line

on th

e sa

me

set o

f axe

s.

W

hat d

o yo

u no

tice?

(R

)

2.

Rep

eat Q

uest

ion

1 fo

r the

func

tion

and

.

(C)

Cau

tion:

1. D

o no

t con

fuse

the

inve

rse

func

tion

with

the

reci

proc

al

)(1 x

f. F

or e

xam

ple,

for t

he fu

nctio

n w

here

x

xf

=)

(, t

he re

cipr

ocal

is

x1, w

hile

fo

r

€

x≥0 .

2.

Not

e th

at th

e no

tatio

n is

use

d on

ly fo

r one

-to-o

ne re

latio

n an

d m

ust n

ot b

e

used

for i

nver

ses

of m

any-

to-o

ne re

latio

ns, s

ince

in th

ese

case

s th

e in

vers

es a

re n

ot fu

nctio

ns.


41CAPS

Gr

ad

e 12

: ter

m 1

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3Pa

ttern

s,

sequ

ence

s,

serie

s

1.

Num

ber p

atte

rns,

incl

udin

g ar

ithm

etic

and

ge

omet

ric s

eque

nces

and

ser

ies

2.

Sig

ma

nota

tion

3.

Der

ivat

ion

and

appl

icat

ion

of th

e fo

rmul

ae

for t

he s

um o

f arit

hmet

ic a

nd g

eom

etric

se

ries:

3.1

;

;

3.2

; a

nd

3.3

,

Com

men

t:D

eriv

atio

n of

the

form

ulae

is e

xam

inab

le.

exam

ples

:1.

Writ

e do

wn

the

first

five

term

s of

the

sequ

ence

with

gen

eral

term

.

(K)

2. C

alcu

late

.

(R)

3. D

eter

min

e th

e 5th

term

of t

he g

eom

etric

seq

uenc

e of

whi

ch th

e 8th

term

is 6

and

the

12th

term

is 1

4.

(

C)

4. D

eter

min

e th

e la

rges

t val

ue o

f n

suc

h th

at

.

(R

)

5. S

how

that

1

999

9,0

.

=.

(P

)

3Fu

nctio

ns

1.

Defi

nitio

n of

a fu

nctio

n.

2.

Gen

eral

con

cept

of t

he in

vers

e of

a fu

nctio

n an

d ho

w th

e do

mai

n of

the

func

tion

may

ne

ed to

be

rest

ricte

d (in

ord

er to

obt

ain

a on

e-to

-one

func

tion)

to e

nsur

e th

at th

e in

vers

e is

a fu

nctio

n.3.

D

eter

min

e an

d sk

etch

gra

phs

of th

e in

vers

es o

f the

func

tions

defi

ned

by

Focu

s on

the

follo

win

g ch

arac

teris

tics:

do

mai

n an

d ra

nge,

inte

rcep

ts w

ith th

e ax

es,

turn

ing

poin

ts, m

inim

a, m

axim

a,as

ympt

otes

(hor

izon

tal a

nd v

ertic

al),

shap

e an

d sy

mm

etry

, ave

rage

gra

dien

t (av

erag

e ra

te o

f cha

nge)

, int

erva

ls o

n w

hich

the

func

tion

incr

ease

s /d

ecre

ases

.

exam

ples

:

1.

Con

side

r the

func

tion

fw

here

.

1.1

W

rite

dow

n th

e do

mai

n an

d ra

nge

of f

.

(K

)

1.2

S

how

that

f is

a o

ne-to

-one

rela

tion.

(R)

1.3

D

eter

min

e th

e in

vers

e fu

nctio

n .

(

R)

1.4

S

ketc

h th

e gr

aphs

of t

he fu

nctio

ns

f,

and

x

y=

line

on th

e sa

me

set o

f axe

s.

W

hat d

o yo

u no

tice?

(R

)

2.

Rep

eat Q

uest

ion

1 fo

r the

func

tion

and

.

(C)

Cau

tion:

1. D

o no

t con

fuse

the

inve

rse

func

tion

with

the

reci

proc

al

)(1 x

f. F

or e

xam

ple,

for t

he fu

nctio

n w

here

x

xf

=)

(, t

he re

cipr

ocal

is

x1, w

hile

fo

r

€

x≥0 .

2.

Not

e th

at th

e no

tatio

n is

use

d on

ly fo

r one

-to-o

ne re

latio

n an

d m

ust n

ot b

e

used

for i

nver

ses

of m

any-

to-o

ne re

latio

ns, s

ince

in th

ese

case

s th

e in

vers

es a

re n

ot fu

nctio

ns.

Gr

ad

e 12

: ter

m 1

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

1

Func

tions

:

expo

nent

ial a

nd

loga

rithm

ic

1.

Rev

isio

n of

the

expo

nent

ial f

unct

ion

and

the

expo

nent

ial l

aws

and

grap

h of

the

func

tion

defin

ed b

y w

here

a

nd

2.

Und

erst

and

the

defin

ition

of a

loga

rithm

: ,

whe

re

and

.

3.

The

grap

h of

the

func

tion

defin

ex

yb

log

=

for b

oth

the

case

s 1

0<

<b

and

1

>b

.

Com

men

t:

The

four

loga

rithm

ic la

ws

that

will

be

appl

ied,

onl

y in

the

cont

ext o

f rea

l-life

pro

blem

s

rela

ted

to fi

nanc

e, g

row

th a

nd d

ecay

, are

:

;

;

; a

nd

BA

AB

log

log

log

=.

They

follo

w fr

om th

e ba

sic

expo

nent

ial l

aws

(term

1 o

f gra

de 1

0).

• M

anip

ulat

ion

invo

lvin

g th

e lo

garit

hmic

law

s w

ill n

ot b

e ex

amin

ed.

Cau

tion:

1.

Mak

e su

re le

arne

rs k

now

the

diffe

renc

e be

twee

n th

e tw

o fu

nctio

ns d

efine

d by

x

yb

= a

nd

by

x=

whe

re b

is a

pos

itive

(con

stan

t) re

al n

umbe

r.

2. M

anip

ulat

ion

invo

lvin

g th

e lo

garit

hmic

law

s w

ill n

ot b

e ex

amin

ed.

exam

ples

:

1.

Sol

ve f

orx

:

(R)

2.

Let

x ax

f=)

(,

.0

>a

2.1

Det

erm

ine

aif

the

grap

h of

fgo

es th

roug

h th

e po

int

(R

)

2.2

Det

erm

ine

the

func

tion

.

(R

)

2.3

For

whi

ch v

alue

s of

xis

?

(C)

2.4

Det

erm

ine

the

func

tion

h if

the

grap

h of

h

is th

e re

flect

ion

of th

e gr

aph

of f

thro

ugh

the

y-a

xis.

(C

)

2.5

Det

erm

ine

the

func

tion

kif

the

grap

h of

kis

the

refle

ctio

n of

the

grap

h of

f

thro

ugh

the

x-a

xis.

(C

)

2.6

Det

erm

ine

the

func

tion

p if

the

grap

h of

p

is o

btai

ned

by s

hifti

ng th

e gr

aph

of f

two

units

to th

e le

ft.

(C)

2.7

Writ

e do

wn

the

dom

ain

and

rang

e fo

r eac

h of

the

func

tions

,k

and

p.

(R

)

2.8

Rep

rese

nt a

ll th

ese

func

tions

gra

phic

ally.

(R)



Gr

ad

e 12

: ter

m 1

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2

Fina

nce,

gr

owth

and

de

cay

1.

Sol

ve p

robl

ems

invo

lvin

g pr

esen

t val

ue a

nd

futu

re v

alue

ann

uitie

s.

2.

Mak

e us

e of

loga

rithm

s to

cal

cula

te

the

valu

e of

n, t

he ti

me

perio

d, in

the

equa

tions

ni

PA

)1(+

= o

r.

3.

Crit

ical

ly a

naly

se in

vest

men

t and

loan

op

tions

and

mak

e in

form

ed d

ecis

ions

as

to

best

opt

ion(

s) (i

nclu

ding

pyr

amid

).

Com

men

t:D

eriv

atio

n of

the

form

ulae

for p

rese

nt a

nd fu

ture

val

ues

usin

g th

e ge

omet

ric s

erie

s

form

ula,

sh

ould

be

part

of th

e te

achi

ng p

roce

ss to

ens

ure

that

the

lear

ners

und

erst

and

whe

re th

e fo

rmul

ae c

ome

from

.

The

two

annu

ity fo

rmul

ae:

€

F=x[(1

+i)

n−1]

i a

nd

hol

d on

ly w

hen

paym

ent c

omm

ence

s on

e pe

riod

from

the

pres

ent a

nd e

nds

afte

r n

perio

ds.

Com

men

t: Th

e us

e of

a ti

mel

ine

to a

naly

se p

robl

ems

is a

use

ful t

echn

ique

.

exam

ples

:

Giv

en th

at a

pop

ulat

ion

incr

ease

d fro

m 1

20 0

00 to

214

000

in 1

0 ye

ars,

at w

hat a

nnua

l (c

ompo

und)

rate

did

the

popu

latio

n gr

ow?

(R)

1.

In

orde

r to

buy

a ca

r, Jo

hn ta

kes

out a

loan

of R

25 0

00 fr

om th

e ba

nk. T

he b

ank

char

ges

an

ann

ual i

nter

est r

ate

of 1

1%, c

ompo

unde

d m

onth

ly. T

he in

stal

men

ts s

tart

a m

onth

afte

r he

has

rece

ived

the

mon

ey fr

om th

e ba

nk.

1.1

Cal

cula

te h

is m

onth

ly in

stal

men

ts if

he

has

to p

ay b

ack

the

loan

ove

r a p

erio

d of

5 y

ears

. (

R)

1.2

Cal

cula

te th

e ou

tsta

ndin

g ba

lanc

e of

his

loan

afte

r tw

o ye

ars

(imm

edia

tely

afte

r the

24th

in

stal

men

t).

(C

)

2tr

igon

omet

ry

Com

poun

d an

gle

iden

titie

s:

; ;

;

;

; and

.

2. A

ccep

ting

, der

ive

the

othe

r com

poun

d an

gle

id

entit

ies.

(C

)

3. D

eter

min

e th

e ge

nera

l sol

utio

n of

0co

s2

sin

=+

xx

.

(R

)

4.

Pro

ve th

at

.

(C

)


43CAPS

Gr

ad

e 12

: ter

m 1

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

ass

essm

ent t

erm

1:

1.

Inve

stig

atio

n or

pro

ject

. (a

t lea

st 5

0 m

arks

)

onl

y on

e in

vest

igat

ion

or p

roje

ct p

er y

ear i

s re

quire

d.

• e

xam

ple

of a

n in

vest

igat

ion

whi

ch re

vise

s th

e si

ne, c

osin

e an

d ar

ea ru

les:

Gra

de 1

2 In

vest

igat

ion:

Pol

ygon

s w

ith 1

2 M

atch

es

• H

ow m

any

diffe

rent

tria

ngle

s ca

n be

mad

e w

ith a

per

imet

er o

f 12

mat

ches

?

• W

hich

of t

hese

tria

ngle

s ha

s th

e gr

eate

st a

rea?

• W

hat r

egul

ar p

olyg

ons

can

be m

ade

usin

g al

l 12

mat

ches

?

• In

vest

igat

e th

e ar

eas

of p

olyg

ons

with

a p

erim

eter

of 1

2 m

atch

es in

an

effo

rt to

est

ablis

h th

e m

axim

um a

rea

that

can

be

encl

osed

by

the

mat

ches

.

Any

ext

ensi

ons

or g

ener

alis

atio

ns th

at c

an b

e m

ade,

bas

ed o

n th

is ta

sk, w

ill e

nhan

ce y

our i

nves

tigat

ion.

But

you

nee

d to

stri

ve fo

r qua

lity,

rath

er th

an s

impl

y

prod

ucin

g a

larg

e nu

mbe

r of t

rivia

l obs

erva

tions

.

ass

essm

ent:

The

focu

s of

this

task

is o

n m

athe

mat

ical

pro

cess

es. S

ome

of th

ese

proc

esse

s ar

e: s

peci

alis

ing,

cla

ssify

ing,

com

parin

g, in

ferr

ing,

est

imat

ing,

gen

eral

isin

g, m

akin

g

conj

ectu

res,

val

idat

ing,

pro

ving

and

com

mun

icat

ing

mat

hem

atic

al id

eas.

2.

Ass

ignm

ent

or T

est.

(at l

east

50

mar

ks)

3.

Test

. (at

leas

t 50

mar

ks)



Gr

ad

e 12

: ter

m 2

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2tr

igon

omet

ryco

ntin

ued

1.

Sol

ve p

robl

ems

in tw

o an

d th

ree

dim

ensi

ons.

exam

ples

:

a

150°

yx

PQ

R

T

1.

is a

tow

er. I

ts fo

ot,

P, a

nd th

e po

ints

Q a

ndR

are

on

the

sam

e ho

rizon

tal p

lane

.

From

Q th

e an

gle

of e

leva

tion

to th

e to

p of

the

build

ing

is x

. Fur

ther

mor

e,

,

y an

d th

e di

stan

ce b

etw

een

Pan

d R

is a

met

res.

Pro

ve th

at

(C

)

2.

In

, . P

rove

that

:

2.1

Bc

Cb

aco

sco

s+

=w

here

and

.

(R)

2.2

(on

cond

ition

that

).

(P)

2.3

(on

cond

ition

that

).

(P)

2.4

Cb

aB

ac

Ac

bc

ba

cos

)(

cos

)(

cos

)(

++

++

+=

++

.

( P

)

1Fu

nctio

ns:

poly

nom

ials

Fact

oris

e th

ird-d

egre

e po

lyno

mia

ls. A

pply

th

e R

emai

nder

and

Fac

tor T

heor

ems

to

poly

nom

ials

of d

egre

e at

mos

t 3 (n

o pr

oofs

re

quire

d).

Any

met

hod

may

be

used

to fa

ctor

ise

third

deg

ree

poly

nom

ials

but

it s

houl

d in

clud

e ex

ampl

es

whi

ch re

quire

the

Fact

or T

heor

em.

exam

ples

:

1. S

olve

for

:x

(

R)

2. If

is

div

ided

by

, the

rem

aind

er is

.

D

eter

min

e th

e va

lue

of p

.

(P)


45CAPS

Gr

ad

e 12

: ter

m 2

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

3d

iffer

entia

lC

alcu

lus

1.

An

intu

itive

und

erst

andi

ng o

f the

lim

it co

ncep

t, i

n th

e co

ntex

t of a

ppro

xim

atin

g th

e ra

te o

f cha

nge

or g

radi

ent o

f a fu

nctio

n at

a p

oint

.

2.

Use

lim

its to

defi

ne th

e de

rivat

ive

of a

func

tion

fat

any

x:

.

Gen

eral

ise

to fi

nd th

e de

rivat

ive

of f

at

any

poin

t x

in th

e do

mai

n of

f, i

.e.,

defin

e

the

deriv

ativ

e fu

nctio

n )

('x

fof

the

func

tion

)(xf

. Und

erst

and

intu

itive

ly th

at

)('af

is

the

grad

ient

of t

he ta

ngen

t to

the

grap

h of

fat

the

poin

t with

x-c

oord

inat

ea

.

3.

Usi

ng th

e de

finiti

on (fi

rst p

rinci

ple)

, fin

d th

e

deriv

ativ

e,

)('x

f fo

r a, b

and

cco

nsta

nts:

3.1

3.2

;

3.3

xax

f=

)(

; an

d

3.3

cx

f=)

(.

Com

men

t: D

iffer

entia

tion

from

firs

t prin

cipl

es w

ill b

e ex

amin

ed o

n an

y of

the

type

s

desc

ribed

in 3

.1, 3

.2 a

nd 3

.3.

exam

ples

:

1.

In e

ach

of th

e fo

llow

ing

case

s, fi

nd th

e de

rivat

ive

of

)(xf

at th

e po

int w

here

, u

sing

th

e de

finiti

on o

f the

der

ivat

ive:

1.1

2)

(2+

=x

xf

(R)

1.2

(R)

1.3

(R)

1.4

(C

)

Cau

tion:

Car

e sh

ould

be

take

n no

t to

appl

y th

e su

m ru

le fo

r diff

eren

tiatio

n 4.

1 in

a s

imila

r way

to p

rodu

cts.

• D

eter

min

e .

• D

eter

min

e .

• W

rite

dow

n yo

ur o

bser

vatio

n.

2. U

se d

iffer

entia

tion

rule

s to

do

the

follo

win

g:

2.1

Det

erm

ine

)('x

f if

(R

)

2.2

Det

erm

ine

)('x

f if

x

xx

f3 )2

()

(+

=

(C

)

(P

)



Gr

ad

e 12

: ter

m 2

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

4.

Use

the

form

ula

(fo

r

a

ny re

al n

umbe

r n) t

oget

her w

ith th

e ru

les

4.1

an

d

4.2

(k a

con

stan

t)

5.

Find

equ

atio

ns o

f tan

gent

s to

gra

phs

of

func

tions

.

6.

Intro

duce

the

seco

nd d

eriv

ativ

e

of

)(xf

and

how

it

dete

rmin

es th

e co

ncav

ity o

f a fu

nctio

n.

7. S

ketc

h gr

aphs

of c

ubic

pol

ynom

ial f

unct

ions

us

ing

diffe

rent

iatio

n to

det

erm

ine

the

co-

ordi

nate

of s

tatio

nary

poi

nts,

and

poi

nts

of in

flect

ion

(whe

re c

onca

vity

cha

nges

). A

lso,

det

erm

ine

the

x-in

terc

epts

of t

he

grap

h us

ing

the

fact

or th

eore

m a

nd o

ther

te

chni

ques

.

8. S

olve

pra

ctic

al p

robl

ems

conc

erni

ng

optim

isat

ion

and

rate

of c

hang

e, in

clud

ing

calc

ulus

of m

otio

n.

2.3

Det

erm

ine

if

(R)

2.4

Det

erm

ine

if

(C

)

3.

Det

erm

ine

the

equa

tion

of th

e ta

ngen

t to

the

grap

h de

fined

by

)2(

)12(

2+

+=

xx

y

whe

re43

=x

.

(C)

4.

Ske

tch

the

grap

h de

fined

by

by:

4.1

findi

ng th

e in

terc

epts

with

the

axes

;

(C

)

4.2

findi

ng m

axim

a, m

inim

a an

d th

e co

-ord

inat

e of

the

poin

t of i

nflec

tion;

(R

)

4.3

look

ing

at th

e be

havi

our o

f y a

s an

d as

.

(P

)

(Rem

embe

r: To

und

erst

and

poin

ts o

f infl

ectio

n, a

n un

ders

tand

ing

of c

onca

vity

is n

eces

sary

. Th

is is

whe

re th

e se

cond

der

ivat

ive

play

s a

role

.)

5.

The

radi

us o

f the

bas

e of

a c

ircul

ar c

ylin

dric

al c

an is

xcm

, and

its

volu

me

is 4

30 c

m3 .

5.1

Det

erm

ine

the

heig

ht o

f the

can

in te

rms

of x

.

(R

)

5.2

Det

erm

ine

the

area

of t

he m

ater

ial n

eede

d to

man

ufac

ture

the

can

(that

is, d

eter

min

e

the

tota

l sur

face

are

a of

the

can)

in te

rms

of x

.

(C)

5.3

Det

erm

ine

the

valu

e of

x fo

r whi

ch th

e le

ast a

mou

nt o

f mat

eria

l is

need

ed to

m

anuf

actu

re s

uch

a ca

n.

(C

)

5.4

If th

e co

st o

f the

mat

eria

l is

R50

0 pe

r m2

, wha

t is

the

cost

of t

he c

heap

est c

an

(labo

ur e

xclu

ded)

?

(P)


47CAPS

Gr

ad

e 12

: ter

m 2

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2a

naly

tical

Geo

met

ry1.

Th

e eq

uatio

n d

efine

s

a ci

rcle

with

radi

us r

and

cent

re)

;(

ba

.

2.

Det

erm

inat

ion

of th

e eq

uatio

n of

a ta

ngen

t to

a g

iven

circ

le.

exam

ples

:

1.

Det

erm

ine

the

equa

tion

of th

e ci

rcle

with

cen

tre

and

radi

us6

(K)

2.

Det

erm

ine

the

equa

tion

of th

e ci

rcle

whi

ch h

as th

e lin

e se

gmen

t with

end

poin

ts

)3;5(

and

as d

iam

eter

.

(R

)

3.

Det

erm

ine

the

equa

tion

of a

circ

le w

ith a

radi

us o

f 6

units

, whi

ch in

ters

ects

the

x-a

xis

at

and

the

y-a

xis

at

)3;0(. H

ow m

any

such

circ

les

are

ther

e?

(P

)

4.

Det

erm

ine

the

equa

tion

of th

e ta

ngen

t tha

t tou

ches

the

circ

le d

efine

d by

at

the

poin

t .

(C)

5.

The

line

with

the

equa

tion

2+

=x

yin

ters

ects

the

circ

le d

efine

d by

at

Aan

d B

.

5.1

Det

erm

ine

the

co-o

rdin

ates

of

Aan

d B

.

(R

)

5.2

Det

erm

ine

the

leng

th o

f cho

rd

.

(K

)

5.3

Det

erm

ine

the

co-o

rdin

ates

of

,M

the

mid

poin

t of

.

(K

)

5.4

Sho

w th

at

, whe

re O

is th

e or

igin

.

(

C)

5.5

Det

erm

ine

the

equa

tions

of t

he ta

ngen

ts to

the

circ

le a

t the

poi

nts

A

and

B.

(C

)

5.6

Det

erm

ine

the

co-o

rdin

ates

of t

he p

oint

Cw

here

the

two

tang

ents

in 5

.5 in

ters

ect.

(C

)

5.7

Ver

ify th

at

.

(R)

5.8

Det

erm

ine

the

equa

tions

of t

he tw

o ta

ngen

ts to

the

circ

le, b

oth

para

llel t

o th

e lin

e

with

the

equa

tion

.

(P)

3m

id-y

ear

exam

inat

ions

ass

essm

ent t

erm

2:

1. A

ssig

nmen

t (at

leas

t 50

mar

ks)

2. e

xam

inat

ion

(300

mar

ks)



Gr

ad

e 12

ter

m 3

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2eu

clid

ean

Geo

met

ry

1. R

evis

e ea

rlier

wor

k on

the

nece

ssar

y an

d su

ffici

ent c

ondi

tions

for p

olyg

ons

to b

e si

mila

r. 2.

Pro

ve (a

ccep

ting

resu

lts e

stab

lishe

d in

ea

rlier

gra

des)

:•

that

a li

ne d

raw

n pa

ralle

l to

one

side

of

a tr

iang

le d

ivid

es th

e ot

her t

wo

side

s pr

opor

tiona

lly (a

nd th

e M

id-p

oint

Th

eore

m a

s a

spec

ial c

ase

of th

is

theo

rem

) ;•

that

equ

iang

ular

tria

ngle

s ar

e si

mila

r;•

that

tria

ngle

s w

ith s

ides

in p

ropo

rtion

are

si

mila

r; an

d •

the

Pyt

hago

rean

The

orem

by

sim

ilar

trian

gles

.

exam

ple:

Con

side

r a ri

ght t

riang

le A

BC

with

. L

et

and

.

Let

Dbe

on

suc

h th

at

. Det

erm

ine

the

leng

th o

f in

term

s of

aan

d c

.

(P)

1st

atis

tics

(reg

ress

ion

and

corr

elat

ion)

1. R

evis

e sy

mm

etric

and

ske

wed

dat

a.2.

U

se s

tatis

tical

sum

mar

ies,

sca

tterp

lots

, re

gres

sion

(in

parti

cula

r the

leas

t squ

ares

re

gres

sion

line

) and

cor

rela

tion

to a

naly

se

and

mak

e m

eani

ngfu

l com

men

ts o

n th

e co

ntex

t ass

ocia

ted

with

giv

en b

ivar

iate

da

ta, i

nclu

ding

inte

rpol

atio

n, e

xtra

pola

tion

and

disc

ussi

ons

on s

kew

ness

.

exam

ple:

The

follo

win

g ta

ble

sum

mar

ises

the

num

ber o

f rev

olut

ions

x (p

er m

inut

e) a

nd th

e co

rres

pond

ing

pow

er o

utpu

t y (h

orse

pow

er) o

f a D

iese

l eng

ine:

x40

050

060

070

075

0

y58

010

3014

2018

8021

00

1. F

ind

the

leas

t squ

ares

regr

essi

on li

ne

(K)

2. U

se th

is li

ne to

est

imat

e th

e po

wer

out

put w

hen

the

engi

ne ru

ns a

t 800

m.

(R

)3.

Rou

ghly

how

fast

is th

e en

gine

runn

ing

whe

n it

has

an o

utpu

t of 1

200

hors

e po

wer

?

(R

)


49CAPS

Gr

ad

e 12

ter

m 3

no.

of

Wee

ksto

pic

Cur

ricul

um s

tate

men

tClarifi

catio

n

2C

ount

ing

and

prob

abili

ty

1. R

evis

e:•

depe

nden

t and

inde

pend

ent e

vent

s;•

the

prod

uct r

ule

for i

ndep

ende

nt e

vent

s:

P(A

and

B) =

P(A

) × P

(B).

•th

e su

m ru

le fo

r mut

ually

exc

lusi

ve

even

ts A

and

B:

AP

(or

)

()

()

BP

AP

B+

=

•th

e id

entit

y:

AP

(or

an

d)

B

•th

e co

mpl

emen

tary

rule

:

(P

not

2. p

roba

bilit

y pr

oble

ms

usin

g Ve

nn d

iagr

ams,

tre

es, t

wo-

way

con

tinge

ncy

tabl

es a

nd

othe

r tec

hniq

ues

(like

the

fund

amen

tal

coun

ting

prin

cipl

e) to

sol

ve p

roba

bilit

y pr

oble

ms

(whe

re e

vent

s ar

e no

t nec

essa

rily

inde

pend

ent).

3. A

pply

the

fund

amen

tal c

ount

ing

prin

cipl

e to

so

lve

prob

abili

ty p

robl

ems.

exam

ples

:1.

How

man

y th

ree-

char

acte

r cod

es c

an b

e fo

rmed

if th

e fir

st c

hara

cter

mus

t be

a le

tter a

nd

the

seco

nd tw

o ch

arac

ters

mus

t be

digi

ts?

(K

) 2.

Wha

t is

the

prob

abili

ty th

at a

rand

om a

rran

gem

ent o

f the

lette

rs B

AFA

NA

star

ts a

nd e

nds

w

ith a

n ‘A

’?

(R

)3.

A d

raw

er c

onta

ins

twen

ty e

nvel

opes

. Eig

ht o

f the

env

elop

es e

ach

cont

ain

five

blue

and

th

ree

red

shee

ts o

f pap

er. T

he o

ther

twel

ve e

nvel

opes

eac

h co

ntai

n si

x bl

ue a

nd tw

o re

d

shee

ts o

f pap

er. o

ne e

nvel

ope

is c

hose

n at

rand

om. A

she

et o

f pap

er is

cho

sen

at ra

ndom

fro

m it

. Wha

t is

the

prob

abili

ty th

at th

is s

heet

of p

aper

is re

d?

(C)

4. A

ssum

ing

that

it is

equ

ally

like

ly to

be

born

in a

ny o

f the

12

mon

ths

of th

e ye

ar, w

hat i

s th

e pr

obab

ility

that

in a

gro

up o

f six

, at l

east

two

peop

le h

ave

birth

days

in th

e sa

me

mon

th?

(P

)

3ex

amin

atio

ns /

r

evis

ion

ass

essm

ent t

erm

3:

1. T

est (

at l

east

50

mar

ks)

2. P

relim

inar

y ex

amin

atio

ns (

300

mar

ks)

impo

rtan

t:Ta

ke n

ote

that

at l

east

one

of t

he e

xam

inat

ions

in te

rms

2 an

d 3

mus

t con

sist

of t

wo

thre

e-ho

ur p

aper

s w

ith th

e sa

me

or v

ery

sim

ilar s

truct

ure

to th

e fin

al N

SC

pap

ers.

The

oth

er

exam

inat

ion

can

be re

plac

ed b

y te

sts

on re

leva

nt s

ectio

ns.



Gr

ad

e 12

: ter

m 4

no

ofW

eeks

topi

cC

urric

ulum

sta

tem

ent

Clarifi

catio

n

3r

evis

ion

6ex

amin

atio

ns

ass

essm

ent t

erm

4:

Fina

l exa

min

atio

n:Pa

per 1

: 150

mar

ks: 3

hou

rs

P

aper

2: 1

50 m

arks

: 3 h

ours

Pat

tern

s an

d se

quen

ces

(2

5±3)

e

uclid

ean

Geo

met

ry a

nd M

easu

rem

ent

(50

±3)

Fina

nce,

gro

wth

and

dec

ay

(15

±3)

A

naly

tical

Geo

met

ry

(40±

3)

Func

tions

and

gra

phs

(35±

3)

Sta

tistic

s an

d re

gres

sion

(2

0±3)

Alg

ebra

and

equ

atio

ns

(2

5±3)

T

rigon

omet

ry

(40±

3)

Cal

culu

s

(35±

3)

Pro

babi

lity

(15±

3)


51CAPS

SeCTIoN 4

4.1 introduction

assessment is a continuous planned process of identifying, gathering and interpreting information about the performance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence of achievement; evaluating this evidence; recording the findings and using this information to understand and assist in the learner’s development to improve the process of learning and teaching.

Assessment should be both informal (Assessment for Learning) and formal (Assessment of Learning). In both cases regular feedback should be provided to learners to enhance the learning experience.

Although assessment guidelines are included in the Annual Teaching Plan at the end of each term, the following general principles apply:

1. Tests and examinations are assessed using a marking memorandum.

2. Assignments are generally extended pieces of work completed at home. They can be collections of past examination questions, but should focus on the more demanding aspects as any resource material can be used, which is not the case when a task is done in class under strict supervision.

3. At most one project or assignment should be set in a year. The assessment criteria need to be clearly indicated on the project specification. The focus should be on the mathematics involved and not on duplicated pictures and regurgitation of facts from reference material. The collection and display of real data, followed by deductions that can be substantiated from the data, constitute good projects.

4. Investigations are set to develop the skills of systematic investigation into special cases with a view to observing general trends, making conjecures and proving them. To avoid having to assess work which is copied without understanding, it is recommended that while the initial investigation can be done at home, the final write up should be done in class, under supervision, without access to any notes. Investigations are marked using rubrics which can be specific to the task, or generic, listing the number of marks awarded for each skill:

• 40% for communicating individual ideas and discoveries, assuming the reader has not come across the text before. The appropriate use of diagrams and tables will enhance the investigation.

• 35% for the effective consideration of special cases;

• 20% for generalising, making conjectures and proving or disproving these conjectures; and

• 5% for presentation: neatness and visual impact.

4.2 informal or daily assessment

the aim of assessment for learning is to collect continually information on a learner’s achievement that can be used to improve individual] learning.

Informal assessment involves daily monitoring of a learner’s progress. This can be done through observations, discussions, practical demonstrations, learner-teacher conferences, informal classroom interactions, etc. Although informal assessment may be as simple as stopping during the lesson to observe learners or to discuss with learners



how learning is progressing. Informal assessment should be used to provide feedback to the learners and to inform planning for teaching, it need not be recorded. This should not be seen as separate from learning activities taking place in the classroom. Learners or teachers can evaluate these tasks.

Self assessment and peer assessment actively involve learners in assessment. Both are important as these allow learners to learn from and reflect on their own performance. Results of the informal daily assessment activities are not formally recorded, unless the teacher wishes to do so. The results of daily assessment tasks are not taken into account for promotion and/or certification purposes.

4.3 Formal assessment

All assessment tasks that make up a formal programme of assessment for the year are regarded as Formal Assessment. Formal assessment tasks are marked and formally recorded by the teacher for progress and certification purposes. All Formal Assessment tasks are subject to moderation for the purpose of quality assurance.

Formal assessments provide teachers with a systematic way of evaluating how well learners are progressing in a grade and/or in a particular subject. examples of formal assessments include tests, examinations, practical tasks, projects, oral presentations, demonstrations, performances, etc. Formal assessment tasks form part of a year-long formal Programme of Assessment in each grade and subject.Formal assessments in Mathematics include tests, a June examination, a trial examination(for Grade 12), a project or an investigation.

The forms of assessment used should be age- and developmental- level appropriate. The design of these tasks should cover the content of the subject and include a variety of activities designed to achieve the objectives of the subject.

Formal assessments need to accommodate a range of cognitive levels and abilities of learners as shown below:


53CAPS

4.4

Prog

ram

me

of a

sses

smen

t

The

four

cog

nitiv

e le

vels

use

d to

gui

de a

ll as

sess

men

t tas

ks a

re b

ased

on

thos

e su

gges

ted

in th

e TI

MS

S s

tudy

of 1

999.

Des

crip

tors

for e

ach

leve

l and

the

appr

oxim

ate

perc

enta

ges

of ta

sks,

test

s an

d ex

amin

atio

ns w

hich

sho

uld

be a

t eac

h le

vel a

re g

iven

bel

ow:

Cog

nitiv

e le

vels

des

crip

tion

of s

kills

to b

e de

mon

stra

ted

exam

ples

kno

wle

dge 20

%

•S

traig

ht re

call

•Id

entifi

catio

n of

cor

rect

form

ula

on th

e in

form

atio

n sh

eet (

no c

hang

ing

of th

e su

bjec

t)

Use

of m

athe

mat

ical

fact

s

•A

ppro

pria

te u

se o

f mat

hem

atic

al v

ocab

ular

y

1. W

rite

dow

n th

e do

mai

n of

the

func

tion

(Gra

de 1

0)

2. T

he a

ngle

ˆ

AO

Bsu

bten

ded

by a

rc A

Bat

the

cent

re o

of a

circ

le

......

.

rou

tine

Proc

edur

es

35%

•e

stim

atio

n an

d ap

prop

riate

roun

ding

of n

umbe

rs

•P

roof

s of

pre

scrib

ed t

heor

ems

and

deriv

atio

n of

form

ulae

•Id

entifi

catio

n an

d d

irect

use

of c

orre

ct fo

rmul

a on

the

info

rmat

ion

shee

t (no

cha

ngin

g of

the

subj

ect)

•P

erfo

rm w

ell k

now

n pr

oced

ures

•S

impl

e ap

plic

atio

ns a

nd c

alcu

latio

ns w

hich

mig

ht in

volv

e fe

w s

teps

•D

eriv

atio

n fro

m g

iven

info

rmat

ion

may

be

invo

lved

•Id

entifi

catio

n an

d u

se (a

fter c

hang

ing

the

subj

ect)

of c

orre

ct fo

rmul

a

•G

ener

ally

sim

ilar t

o th

ose

enco

unte

red

in c

lass

1.

Sol

ve fo

r

(Gra

de 1

0)

2.

Det

erm

ine

the

gene

ral s

olut

ion

of th

e eq

uatio

n

(

Gra

de 1

1)

2.

Pro

ve th

at th

e an

gle

ˆA

OB

subt

ende

d by

arc

AB

at th

e ce

ntre

o

of a

circ

le is

dou

ble

the

size

of t

he a

ngle

ˆA

CB

whi

ch th

e sa

me

arc

subt

ends

at t

he c

ircle

.

(G

rade

11)

Com

plex

Pro

cedu

res

30%

•P

robl

ems

invo

lve

com

plex

cal

cula

tions

and

/or h

ighe

r ord

er re

ason

ing

•Th

ere

is o

ften

not a

n ob

viou

s ro

ute

to th

e so

lutio

n

•P

robl

ems

need

not

be

base

d on

a re

al w

orld

con

text

•C

ould

invo

lve

mak

ing

sign

ifica

nt c

onne

ctio

ns b

etw

een

diffe

rent

re

pres

enta

tions

•R

equi

re c

once

ptua

l und

erst

andi

ng

1.

Wha

t is

the

aver

age

spee

d co

vere

d on

a ro

und

trip

to a

nd fr

om

a de

stin

atio

n if

the

aver

age

spee

d go

ing

to th

e de

stin

atio

n is

a

nd th

e av

erag

e sp

eed

for t

he re

turn

jour

ney

is

(G

rade

11)

2.

Diff

eren

tiate

x

x2 )2

(+

with

resp

ect t

o x.

(Gra

de 1

2)

Prob

lem

sol

ving

15%

•N

on-r

outin

e pr

oble

ms

(whi

ch a

re n

ot n

eces

saril

y di

fficu

lt)

•H

ighe

r ord

er re

ason

ing

and

proc

esse

s ar

e in

volv

ed

•M

ight

requ

ire th

e ab

ility

to b

reak

the

prob

lem

dow

n in

to it

s co

nstit

uent

pa

rts

Sup

pose

a p

iece

of w

ire c

ould

be

tied

tight

ly a

roun

d th

e ea

rth a

t the

eq

uato

r. Im

agin

e th

at th

is w

ire is

then

leng

then

ed b

y ex

actly

one

met

re

and

held

so

that

it is

stil

l aro

und

the

earth

at t

he e

quat

or. W

ould

a m

ouse

be

abl

e to

cra

wl b

etw

een

the

wire

and

the

earth

? W

hy o

r why

not

?

(A

ny g

rade

)

The

Pro

gram

me

of A

sses

smen

t is

desi

gned

to s

et fo

rmal

ass

essm

ent t

asks

in a

ll su

bjec

ts in

a s

choo

l thr

ough

out t

he y

ear.



a)

num

ber o

f ass

essm

ent t

asks

and

Wei

ghtin

g:

Lear

ners

are

exp

ecte

d to

hav

e se

ven

(7) f

orm

al a

sses

smen

t tas

ks fo

r the

ir sc

hool

-bas

ed a

sses

smen

t. Th

e nu

mbe

r of t

asks

and

thei

r wei

ghtin

g ar

e lis

ted

belo

w:

Gr

ad

e 10

Gr

ad

e 11

Gr

ad

e 12

task

sW

eiG

Ht

(%)

task

sW

eiG

Ht

(%)

task

sW

eiG

Ht

(%)

school-based assessment

term

1

Proj

ect /

inve

stig

atio

nte

st20 10

Proj

ect /

inve

stig

atio

nte

st20 10

test

Proj

ect /

inve

stig

atio

na

ssig

nmen

t

10 20 10

term

2a

ssig

nmen

t/tes

tm

id-y

ear e

xam

inat

ion

10 30a

ssig

nmen

t/tes

tm

id-y

ear e

xam

inat

ion

10 30te

stm

id-y

ear e

xam

inat

ion

10 15

term

3te

stte

st10 10

test

test

10 10te

sttr

ial e

xam

inat

ion

10 25

term

4te

st10

test

10

scho

ol-b

ased

a

sses

smen

t mar

k 10

010

010

0

scho

ol-b

ased

a

sses

smen

t m

ark

(as

% o

f pr

omot

ion

mar

k)

25%

25%

25%

end-

of-y

ear

exam

inat

ions

75%

75%

Prom

otio

n m

ark

100%

100%

not

e:•

Alth

ough

the

proj

ect/i

nves

tigat

ion

is in

dica

ted

in th

e fir

st te

rm, i

t cou

ld b

e sc

hedu

led

in te

rm 2

. Onl

y o

ne

proj

ect/i

nves

tigat

ion

shou

ld b

e se

t per

yea

r.•

Test

s sh

ould

be

at le

ast o

Ne

hou

r lon

g an

d co

unt a

t lea

st 5

0 m

arks

.•

Pro

ject

or i

nves

tigat

ion

mus

t con

tribu

te 2

5% o

f ter

m 1

mar

ks w

hile

the

test

mar

ks c

ontri

bute

75%

of t

he te

rm 1

mar

ks.

The

com

bina

tion

(25%

and

75%

) of t

he m

arks

mus

t app

ear i

n th

e le

arne

r’s re

port.

•N

one

grap

hic

and

none

pro

gram

mab

le c

alcu

lato

rs a

re a

llow

ed (f

or e

xam

ple,

to fa

ctor

ise

, or t

o fin

d ro

ots

of e

quat

ions

) will

be

allo

wed

. Cal

cula

tors

sho

uld

only

be

use

d to

per

form

sta

ndar

d nu

mer

ical

com

puta

tions

and

to v

erify

cal

cula

tions

by

hand

.•

Form

ulasheetm

ustn

otbeprovidedfo

rtestsand

forfi

nalexaminationsinGrades10and

11.


55CAPS

b) examinations:

In Grades 10, 11 and 12, 25% of the final promotion mark is a year mark and 75% is an examination mark.

All assessments in Grade 10 and 11 are internal while in Grade 12 the 25% year mark assessment is internally set and marked but externally moderated and the 75% examination is externally set, marked and moderated.

Mark distribution for Mathematics NCS end-of-year papers: Grades 10-12

PAPeR 1: Grades 12: bookwork: maximum 6 marks

description Grade 10 Grade 11 Grade. 12

Algebra and equations (and inequalities) 30 ± 3 45 ± 3 25 ± 3

Patterns and sequences 15 ± 3 25 ± 3 25 ± 3

Finance and growth 10 ± 3

Finance, growth and decay 15 ± 3 15 ± 3

Functions and graphs 30 ± 3 45 ± 3 35 ± 3

Differential Calculus 35 ± 3

Probability 15 ± 3 20 ± 3 15 ± 3

total 100 150 150

PaPer 2: Grades 11 and 12: theorems and/or trigonometric proofs: maximum 12 marks

description Grade 10 Grade 11 Grade 12

Statistics 15 ± 3 20 ± 3 20 ± 3

Analytical Geometry 15 ± 3 30 ± 3 40 ± 3

Trigonometry 40 ± 3 50 ± 3 40 ± 3

euclidean Geometry and Measurement 30 ± 3 50 ± 3 50 ± 3

total 100 150 150

note: • Modelling as a process should be included in all papers, thus contextual questions can be set on any topic.

• Questions will not necessarily be compartmentalised in sections, as this table indicates. Various topics can be integrated in the same question.

• FormulasheetmustnotbeprovidedfortestsandforfinalexaminationsinGrades10and11.

4.5 recording and reporting

• Recording is a process in which the teacher is able to document the level of a learner’s performance in a specific assessment task.

- It indicates learner progress towards the achievement of the knowledge as prescribed in the Curriculum and Assessment Policy Statements.

- Records of learner performance should provide evidence of the learner’s conceptual progression within a grade and her / his readiness to progress or to be promoted to the next grade.

- Records of learner performance should also be used to monitor the progress made by teachers and learners in the teaching and learning process.

• Reporting is a process of communicating learner performance to learners, parents, schools and other stakeholders. Learner performance can be reported in a number of ways.



- These include report cards, parents’ meetings, school visitation days, parent-teacher conferences, phone calls, letters, class or school newsletters, etc.

- Teachers in all grades report percentages for the subject. Seven levels of competence have been described for each subject listed for Grades R-12. The individual achievement levels and their corresponding percentage bands are shown in the Table below.

Codes and PerCentaGes For reCordinG and rePortinG

ratinG Code desCriPtion oF ComPetenCe PerCentaGe

7 outstanding achievement 80 – 100

6 Meritorious achievement 70 – 79

5 Substantial achievement 60 – 69

4 Adequate achievement 50 – 59

3 Moderate achievement 40 – 49

2 elementary achievement 30 – 39

1 Not achieved 0 - 29

note: the seven-point scale should have clear descriptors that give detailed information for each level.

teachers will record actual marks for the task on a record sheet; and indicate percentages for each subject on the learners’ report cards.

4.6 moderation of assessment

Moderation refers to the process that ensures that the assessment tasks are fair, valid and reliable. Moderation should be implemented at school, district, provincial and national levels. Comprehensive and appropriate moderation practices must be in place to ensure quality assurance for all subject assessments.

4.7 General

This document should be read in conjunction with:

4.7.1 National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R – 12; and

4.7.2 The policy document, National Protocol for Assessment Grades R – 12.

Curriculum and Assessment Policy Statement - Western … · Curriculum and Assessment Policy...

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