policy statements math gr 10 12

8/9/2019 Policy Statements Math Gr 10 12

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MA

THEMATICS

Curriculum and Assessment

Policy Statement

Further Education and Training Phase

Grades 10-12

National Curriculum Statement (NCS)


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CAPS

CURRICULUM AND ASSESSMENT POLICY STATEMENT

GRADES 10-12

MATHEMATICS


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MATHEMATICS GRADES 10-12

CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

Department of Basic Education

222 Struben Street

Private Bag X895Pretoria 0001

South Africa

Tel: +27 12 357 3000

Fax: +27 12 323 0601

120 Plein Street Private Bag X9023

Cape Town 8000

South Africa

Tel: +27 21 465 1701

Fax: +27 21 461 8110

Website: http://www.education.gov.za

2011 Department of Basic Education

ISBN: 978-1-4315-0573-9

Design and Layout by: Ndabase Printing Solution

Printed by: Government Printing Works


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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 the divisions of the past and establish a society based on democratic

values, social justice and fundamental human rights;

improve the quality of life of all citizens and free the potential of each person;

lay the foundations for a democratic and open society in which government is

based on the will of the people and every citizen is equally protected by law;

and

build a united and democratic South Africa able to take its rightful place as a sovereign state in the family ofnations.

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

of implementation prompted a review in 2000. This led to the rst curriculum revision: the Revised 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-9and Grades 10-12respectively, are combined in a single document

and will simply be known as the National Curriculum Statement Grades R-12. TheNational Curriculum Statement for

Grades R-12 builds on the previous curriculum but also updates it and aims to provide clearer specication of what

is to be taught and learnt on a term-by-term basis.

The National Curriculum Statement Grades R-12accordingly 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.

MRSANGIE MOTSHEKGA, MP

MINISTER OF BASIC EDUCATION


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CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)


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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 Specic Aims...................................................................................................................................................8

2.3 Specic Skills..................................................................................................................................................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 Specication of content to show Progression...........................................................................................11

3.1.1 Overview of topics .................................................................................................................................12

3.2 Content clarication with teaching guidelines...........................................................................................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


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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


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3CAPS

SECTION 1

INTRODUCTION TO THE CURRICULUM AND ASSESSMENT POLICY STATEMENTS FOR


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 qualications for schools in the General

Education 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 Certicate: A qualication at Level 4 on the NationalQualications Framework (NQF), promulgated in Government Gazette No.27819 of 20 July 2005;


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(iv) The policy document, An addendum to the policy document, the National Senior Certicate: A

qualication at Level 4 on the National Qualications Framework (NQF), regarding learners with special

needs,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 Certicate: A

qualication at Level 4 on the National Qualications Framework (NQF), regarding the National Protocolfor 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 ofsection 6A of the South African Schools Act,

1996 (Act No. 84 of 1996,)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-12gives 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-fullment, 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 sufcient prole of a learners 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 specied and set high, achievable standards in all subjects;

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


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Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social and

environmental justice and human rights as dened 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 efciency: 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 identied 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 Educations Guidelines for Inclusive Teaching and Learning(2010).


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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 inbrackets 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


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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 specied 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


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SECTION 2

Introduction

In Chapter 2, the Further Education and Training (FET) Phase Mathematics CAPS provides teachers with a denition

of mathematics, specic aims, specic 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 Specic Aims

1. To develop uency 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, scientic, political and environmental issues

whenever possible.

3. To provide the opportunity to develop in learners the ability to be methodical, to generalize, make conjecturesand 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 howbut should rather

feature the whenand whyof problem types. Learning procedures and proofs without a good understanding

of why they are important will leave learners ill-equipped to usetheir knowledge in later life.

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

2.3 Specic Skills

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;


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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 specic 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: rstly the weighting gives guidance on

the amount of time needed to address adequately the content within each content area; secondlythe weighting gives

guidance on the spread of content in the examination (especially end of the year summative assessment).


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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.


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11CAPS

SECTION 3

Introduction

Chapter 3 provides teachers with:

specication of content to show progression;

clarication of content with teaching guidelines; and

allocation of time.

3.1 Specication of Content to show Progression

The specication 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 clarication

of content gives guidelines on how progression should be addressed in these cases. The specication of content

should therefore be read in conjunction with the clarication of content.


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13CAPS

4.ALGEB

RA (a

)Un

ders

tan

dtha

trea

lnum

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an

be

irra

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l

orra

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l.

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ther

than

thoseon

therea

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line,

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llednon-

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lnum

bers.

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ibletosquarecerta

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-

rea

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do

btainnega

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s

answers.

Na

tureo

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ots

.

(a)Simp

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ionsus

ing

the

lawso

f

exponen

tsforra

tiona

lexponen

ts.

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tablishbe

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hichtwoin

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iven

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lnum

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toanappropria

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ofaccuracy

(toag

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ber

ofdec

ima

l

digits

).

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lyth

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tstoexpress

ions

invo

lvingra

tiona

lexponen

ts.

(b)Add

,su

btrac

t,mu

ltiplyan

ddivides

imp

lesurds.

Demonstrateanunderstandingofthedenitionof

alogari

thman

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de

dtoso

lverea

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pro

blems.

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ipu

latea

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y:

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ialbya

trino

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fac

toris

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toris

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bes;

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toris

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).

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ise

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ders

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the

Rema

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Fac

tor

Theorems

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torise

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hichrequire

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).

So

lve:

linearequa

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qua

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exponen

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blems.

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lve:

qua

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qua

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oneo

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5.DIFFER

ENTIALCALCULUS

(a)An

intuitiveun

ders

tandingo

ftheconcep

to

fa

limit

.

(b)Differentiationofspeciedfunctionsfromrst

princ

iples.

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lesofdifferentiation.

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tionso

ftangen

tstograp

hs.

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bilitytos

ke

tchgrap

hso

fcu

bicfunc

tions.

(f)Prac

tica

lpro

blems

invo

lvingop

tim

iza

tionan

d

rateso

fc

hange

(inclu

ding

theca

lcu

luso

f

mo

tion

).

6.PROBA

BILITY

(a)Compare

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lative

frequency

ofan

experimen

talou

tcomew

iththe

theore

tica

l

pro

ba

bilityo

ftheou

tcome.

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diagramsasana

idtosolv

ingpro

ba

bility

pro

blems.

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tua

llyexc

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iveeven

tsan

dc

omp

lemen

tary

even

ts.

(d)The

iden

tityforany

twoevents

Aan

dB:

P(AorB)=P(A)+(B)-P(AandB)

(a)Dependen

tan

dindepen

den

teven

ts.

(b)Venn

dia

gramsorcon

tingency

tablesan

d

tree

diagramsasa

ids

toso

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ba

bility

pro

blem

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ly

indepen

den

t).

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lisa

tiono

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damen

talcoun

ting

princ

iple

.

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ba

bilitypro

blemsu

sing

the

fun

damen

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coun

tingprinc

iple

.

7.EUCLIDEANGEOMETRYANDMEASUREMENT

(a)Rev

ise

bas

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tablishedinearl

ier

gra

des.

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tiga

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triangle.

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tean

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fthe

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irc

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from

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henrequ

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iseearl

ier

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the

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po

lygons

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imilar

.

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(accep

tingresu

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tablishe

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ier

gra

des

):

tha

ta

line

drawnpara

lleltoones

ideo

f

atriang

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heo

ther

twos

ides

proport

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lly(and

the

Mid-po

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);

tha

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imilar;

tha

ttriang

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iths

ides

inproport

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similar;

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Py

thagoreanT

heorem

bys

imilar

triang

les;an

d

riders.


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3.2 Content Clarication with teaching guidelines

In Chapter 3, content clarication 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 Clarication 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 rst term and more

than six topics are covered / taught in the rst two terms so that assessment is balanced between paper 1 and 2.


22/62


17CAPS

3.2.1 Allocation of Teaching Time

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

11 and 12.

Terms Grade 10 Grade 11 Grade 12

No. of

weeks

No. of

weeks

No. of

weeks

Term 1

Algebraic expressions

Exponents

Number patterns

Equations andinequalities

Trigonometry

3

2

1

2

3

Exponents and surds

Equations andinequalities

Number patterns

Analytical Geometry

3

3

2

3

Patterns, sequences and

series

Functions and inverse

functions

Exponential and

logarithmic functions

Finance, growth anddecay

Trigonometry - compound

angles

3

3

1

2

2

Term 2

Functions

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 3

Analytical 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 anddecay

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.


23/62



3.2.2Seq

uencingandPacingofTopics

MATHEMATICS:GRADE10PACESETTER

1

TERM1

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

WEEK

11

Topics

Alge

bra

icexpressions

Exponents

Num

ber

pa

tterns

Equa

tion

san

dinequa

lities

Trigonome

try

Assessm

ent

Inves

tiga

tionorpro

jec

t

Tes

t

Date

completed

2

TERM2

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

WEEK

11

Topics

Func

tions

Trigonome

tric

func

tions

Euc

lidean

Ge

ome

try

Assessm

ent

Ass

ignmen

t/Tes

t

MID-Y

EA

REXAMINATION

Date

completed

3

TERM3

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

Topics

Ana

lytica

lGeome

try

Financean

dgrow

th

Statis

tics

Trigonome

try

Euc

lidean

Geom

etry

Measuremen

t

Assessm

ent

Tes

t

Tes

t

Date

completed

4

TERM4

Pap

er

1:

2hours

Paper

2:

2hours

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

WEEK5

WEEK6

WEEK7

WE

EK8

WEEK9

WEEK

10

Alge

bra

ic

expressions

an

dequa

tions

(an

d

inequa

litie

s)

exponents

Num

berP

atterns

Func

tions

an

dgrap

hs

Financean

dgrow

th

Pro

ba

bility

30

10

30

15

15

Euc

lideangeome

try

an

dmeasureme

nt

Ana

lytica

lgeome

try

Trigonome

try

Statis

tics

20

15

50

15

Topics

Pro

ba

bility

Rev

ision

Adm

in

Assessm

ent

Test

Exam

ina

tions

Date

completed

To

talmark

s

100

To

talm

arks

100


24/62


19CAPS


1

TERM1

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

WEEK

11

Topics

Exponen

tsan

dsurds

Equa

tions

an

dinequa

lities

Num

berpa

tterns

Analy

tica

lGeome

try

Assessm

ent

Inves

tiga

tionorpro

jec

t

Tes

t

Date

completed

2

TERM2

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

WEEK

11

Topics

Func

tions

T

rigonome

try

(re

duc

tion

formu

lae,

grap

hs,

equa

tions

)

Assessm

ent

Ass

ignmen

t/Tes

t

MID-Y

EA

REXAMINATION

Date

completed

3

TERM3

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

Topics

Measuremen

t

Eu

clidean

Geome

try

Trigonome

try

(sine,

cos

inean

d

arearu

les

)

Finance,

grow

than

ddecay

P

roba

bility

Assessm

ent

Tes

t

Tes

t

Date

completed

4

TERM4

Paper

1:

3hours

Paper

2:

3hours

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

WEEK5

WEEK6

WEEK7

W

EEK8

WEEK9

WEEK

10

Alge

bra

ic

express

ions

an

dequa

tions

(an

d

inequa

litie

s)

Num

berpa

tterns

Func

tions

an

dgrap

hs

Finance,g

row

than

ddecay

Pro

ba

bility

45

25

45

15

20

Euc

lidea

nGeome

try

an

dmea

suremen

t

Ana

lytica

lgeome

try

Trigonom

etry

Statis

tics

40

30

60

20

Topics

Statis

tics

Rev

ision

FINALE

XAMINATION

Adm

in

Assessm

ent

Tes

t

Date

completed

T

otalmarks

150

Totalmarks

150


25/62




1

TERM1

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

WEEK

11

Topics

Num

berpa

tterns,

sequence

san

dseries

Functions:Form

aldenition;inverses

Func

tion

s:

exponen

tia

l

and

logari

thm

ic

Finance,

grow

than

ddecay

Trigonome

try

Assessm

ent

Tes

t

Inves

tiga

tionorpro

jec

t

Ass

ignmen

t

Date

completed

2

TERM2

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

WEEK

11

Topics

Trigonome

try

Func

tions:

po

lynom

ials

Differen

tia

lCa

lcu

lus

Ana

lytical

Geome

try

Assessm

ent

Tes

t

MID-Y

EA

REXAMINATION

Date

completed

3

TERM3

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

W

EEK5

WEEK6

WEEK

7

WEEK8

WEEK9

WEEK10

Topics

Geome

try

Statis

tics

Coun

tingan

dPro

ba

bility

Rev

isio

n

TRIALEXAMINATION

Assessm

ent

Tes

t

Date

completed

4

TERM4

Paper

1:

3hours

Paper

2:

3hours

Weeks

WEEK1

WEEK2

WEEK3

WEEK4

WEEK5

WEEK6

WEEK7

W

EEK8

WEEK9

WEEK

10

Alge

bra

ic

express

ions

an

dequat

ions

(an

d

inequa

litie

s)

Num

berpa

tterns

Func

tions

an

dgrap

hs

Finance,g

row

than

ddecay

Differentia

lCa

lcu

lus

Coun

tingan

dpro

ba

bility

25

25

35

15

35

15

Euc

lidea

nGeome

try

an

dmea

suremen

t

Ana

lytica

lGeome

try

Trigonom

etry

Statis

tics

50

40

40

20

Topics

Rev

ision

FINALEXAMINATION

Adm

in

Assessm

ent

Date

completed

To

talmark

s

150

To

talma

rks

150


26/62


27/62



GR

ADE10:TERM1

Noof

Weeks

Topic

Curriculumstatement

Clarication

1

Numbersand

patterns

Pa

tterns:

Investiga

tenum

berpa

tterns

lea

ding

tothose

where

there

isa

cons

tan

tdifference

be

tweenconsecu

tive

terms,

an

dthegenera

lterm

(withou

tus

inga

formu

la-s

ee

con

ten

toverv

iew

)isthere

fore

linear.

Comment:

Ari

thme

ticsequence

isdone

inGra

de

12

,hence

isno

tuse

din

Gra

de

10

.

Examples:

1.

De

term

ine

the

5th

an

dthe

nth

termso

fthenum

berpa

ttern

10;7

;4;

1;.

There

is

ana

lgori

thm

icapproach

toansweringsuc

hques

tions.

(R)

2.

Ifthepa

ttern

MATHSMAT

HSMATHS

i

scon

tinue

dinthisway

,w

ha

tw

illthe

267th

letter

be

?Itisno

timmed

iatelyo

bv

ious

howones

hou

ldprocee

d,

un

lesss

imilar

ques

tions

have

been

tack

led

.

(P)

2

Equationsand

Inequalities

1.

Rev

ise

theso

lutiono

flinearequa

tions.

2.

So

lvequa

dra

ticequa

tions

(by

fac

torisa

tion

).

3.

So

lves

imulta

neous

linearequa

tions

intwoun

know

ns.

4.

So

lvewordp

roblems

invo

lving

linear,qua

dra

ticor

simu

ltaneous

linearequa

tions.

5.

So

lve

literale

qua

tions

(chang

ing

thesu

bjec

to

fa

formu

la).

6.

So

lve

linear

inequa

lities

(an

ds

howso

lutiongraphica

lly).

Interva

lnota

tionmus

tbe

known.

Examples:

1.

So

lve

forx:

(R)

2.

So

lve

form:2m2-m=1

(R)

3.

So

lve

forxan

dy:x+2y=

1;

1

2

3

=

+

y

x

(C)

4.

So

lve

forr

intermso

fV,an

dh:

V=r2h

(R)

5.

So

lve

forx:-12-3x

8

(C)


28/62


29/62



GR

ADE10:TERM2

Weeks

Topic

C

urriculumstatement

Clarication

(4+1)

5

Functions

1.

Theconce

pto

fa

func

tion,

wherea

certa

inquan

tity(ou

tpu

tva

lue

)un

ique

ly

depen

dso

nano

therquan

tity(inpu

t

va

lue

).Workw

ithre

lations

hips

be

tween

varia

blesus

ing

tables,

grap

hs,

wordsan

d

formulae.

Convertexiblybetweenthese

representa

tions.

Note:that

thegraphdenedbyy

x=

shou

ldbe

known

from

Gra

de

9.

2.

Po

intbyp

ointp

lottingo

fbas

icgrap

hs

denedby

2x

y=

,

x

y

1

=

an

d

xb

y=

;

0

>

b

and

to

discovers

hape,

doma

in

(inpu

tvalu

es

),range

(ou

tpu

tva

lues

),

asymp

tote

s,

axeso

fsymme

try,

turn

ing

po

intsand

intercep

tson

theaxes

(where

app

lica

ble

).

3.

Inves

tigate

thee

ffec

to

faan

dqon

the

graphsde

nedby

q

xfa

y

+

=

)

(

.

,

where

x

xf

=)

(

,

,

)

(

2x

xf

=

x

xf

1

)

(

=

an

d

,

)(

xb

xf

=

,0

>

b

4.

Po

intbyp

ointp

lottingo

fbas

icgrap

hs

denedby

,

an

d

for

5.

Study

thee

ffec

to

faan

dqon

thegrap

hs

denedby

:

;

;an

d

wherea,q

Qfor

.

6.Sketchgraphs,ndtheequationsofgiven

grap

hsan

dinterpre

tgrap

hs.

Note:

Ske

tchingo

fthegrap

hsmus

tbe

base

d

on

theo

bserva

tiono

fnum

ber

3an

d5

.

Comments:

AmoreformaldenitionofafunctionfollowsinGrade12.Atthislevelit

isenoughtoinvestigate

theway

(un

ique

)ou

tpu

tva

lues

depen

don

how

inpu

tva

luesvary.

Thete

rms

indepen

den

t(inpu

t)

an

ddepen

den

t(ou

tpu

t)varia

blesm

ightbeuse

ful.

Aftersummaries

have

beencomp

ileda

bou

tbas

icfea

tureso

fprescri

bed

grap

hsan

dthee

ffec

ts

ofparametersaandqhavebeeninvestigated:a:averticalstretch(and/orareectionaboutthe

x-ax

is)an

dqavert

ica

ls

hift.Thefo

llow

ingexamp

lesm

ightbeappropria

te:

Remem

ber

tha

tgrap

hs

insomepr

ac

tica

lapp

lica

tionsmay

bee

ither

discre

teorcon

tinuous.

Examples:

1.

Ske

tche

dbe

lowaregrap

hso

f

q

xa

xf

+

=)

(

an

d

.

The

horizon

talasymp

toteo

fbo

thg

rap

hs

isthe

liney=

1.

De

term

ine

theva

lueso

fa,

b,n,qan

dt.

(C)

O

x

y

(1;-1)

(2;0)

2.

Sketchthegraphdenedby

for

(R)


30/62


25CAPS

GR

ADE10:TERM2

Weeks

Topic

C

urriculumstatement

Clarication

3

Euclidean

Geometry

1.

Rev

ise

ba

sicresu

ltses

tablishe

dinearl

ier

gra

desregard

ing

lines,

ang

lesan

d

triang

les,espec

iallythes

imilari

tyan

d

congruenc

eo

ftriang

les.

2.

Inves

tigate

linesegmen

tsjoining

them

id-

po

intsoftwos

ideso

fa

triang

le.

3.Denethe

followingspecialquadrilaterals:

the

kite,p

ara

llelogram,

rec

tang

le,

rhom

bus,

squarean

dtrapez

ium.

Inves

tiga

tean

d

ma

kecon

jec

turesa

bou

tthepropert

ieso

f

thes

ides,

ang

les,

diagona

lsan

dareas

ofthesequa

dri

latera

ls.

Prove

these

con

jec

ture

s.

Comments:

Triang

lesares

imilar

ifthe

ircorrespon

dingang

lesareequa

l,or

iftherat

ioso

fthe

irs

idesare

equa

l:Triang

lesABCan

dDEF

ares

imilar

if

D

A

=

,

E

B

=

an

d

F

C

=

.Theyarea

lso

similar

if

.

Wecoulddeneaparallelograma

saquadrilateralwithtwopairsofopp

ositesidesparallel.

Thenwe

inves

tiga

tean

dprove

tha

ttheoppos

ites

ideso

fthepara

llelogr

amareequa

l,oppos

ite

ang

leso

fapara

llelogramareequ

al,an

ddiagona

lso

fapara

llelogramb

isec

teac

ho

ther.

Itmus

tbeexp

laine

dtha

tas

ing

lecoun

terexamp

lecan

disprovea

Conjec

ture,

bu

tnumerous

specicexamplessupportingaconjecturedonotconstituteageneralproof.

Example:

Inqua

dri

latera

lKITE

,KI=

KEan

dIT=

ET

.The

diagona

lsintersec

ta

tM

.Prove

tha

t:

1.

IM=

MEan

d

(R)

2.

KTisperpen

dicu

lar

toIE

.

(P)

Asitisnotobvious,rstprovethat

.

3

Mid-year

examinations

Assessm

entterm2:

1.

Ass

ign

men

t/tes

t(atleas

t50marks

)

2.

Mid-ye

arexam

ina

tion

(atleas

t100marks)

Onepapero

f2hours

(100marks

)or

Twopapers-one,

1hour

(50marks

)an

dtheo

ther,

1hour

(50marks

)


31/62



GR

ADE10:TERM3

Weeks

Topic

C

urriculumstatement

Clarication

2

Analytical

Geometry

Representge

ometricguresonaCartesian

co-ord

ina

tesys

tem.

Derivean

dapp

lyforany

twopo

ints

)

;

(

1

1

yx

and

)

;

(

2

2

y

x

the

formu

lae

for

ca

lcu

latingth

e:

1.

distanceb

etween

the

twopo

ints;

2.

gra

diento

fthe

linesegmen

tconnec

ting

the

twopo

ints

(an

dfrom

tha

tiden

tifypara

llel

an

dperpe

ndicu

lar

lines

);an

d

3.

coord

inateso

fthem

id-po

into

fthe

line

segment

joining

the

twopo

ints

.

Example:

Cons

ider

thepo

ints

)5;2(

P

an

d

in

the

Cartes

ianp

lane.

1.1.

Ca

lcu

latethe

distance

PQ

.

(K)

1.2

Findthecoord

ina

teso

fRifM

is

them

id-po

into

fPR

.

(R)

1.3

De

term

ine

thecoord

ina

teso

fSifPQRSisapara

llelogram.

(C)

1.4

IsPQRSarec

tang

le?Whyorw

hyno

t?

(R)

2

Financeand

growth

Use

thes

imp

lean

dcompoun

d

grow

thformu

lae

an

d

ni

P

A

)

1(

+

=

] toso

lvepro

blems,

inc

ludingann

ua

linteres

t,hirepurc

hase,

ination,populationgrowthandotherreal-

lifepro

blems.

Un

ders

tan

dthe

imp

lica

tiono

f

uctuatingforeignexchangerates(e.g.onthe

pe

tro

lprice,imports,

exports,

overseas

trave

l).


32/62


27CAPS

GR

ADE10:TERM3

Weeks

Topic

C

urriculumstatement

Clarication

2

Statistics

1.

Rev

iseme

asureso

fcen

tra

lten

dency

in

ungroupe

dda

ta.

2.

Measures

ofcen

tra

lten

dency

ingroupe

d

da

ta:

ca

lcu

lationo

fmeanes

tima

teo

fgroupe

d

andungro

upeddataandidenticationof

mo

da

linterva

lan

dinterva

linw

hichthe

me

dianlie

s.

3.

Rev

isiono

frangeasameasureo

f

dispers

ion

an

dex

tens

ion

toinc

lude

percen

tile

s,

quart

iles,

interquart

ilean

dsem

i

interquart

ilerange.

4.

Fivenum

bersummary

(max

imum,

minimum

an

dquart

iles

)an

dboxan

dw

hisker

diagram.

5.

Use

thes

tatis

tica

lsummaries

(measures

ofcen

tral

ten

dencyan

ddispers

ion

),an

d

grap

hsto

ana

lysean

dma

kemean

ing

ful

commentson

thecon

tex

tassoc

iatedw

ith

theg

iven

da

ta.

Comment:

Ingra

de

10

,the

interva

lso

fgrouped

da

tas

hou

ldbeg

ivenus

ing

inequa

litie

s,

tha

tis

,inthe

form

0x

policy statements math gr 10 12

Documents