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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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MATHEMATICS GRADES 10-12
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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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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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 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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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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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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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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4.ALGEB
RA (a
)Un
ders
tan
dtha
trea
lnum
bersc
an
be
irra
tiona
l
orra
tiona
l.
Ta
keno
tetha
tthereex
istnum
berso
ther
than
thoseon
therea
lnum
ber
line,
theso-ca
llednon-
rea
lnum
bers.
Itisposs
ibletosquarecerta
innon
-
rea
lnum
bersan
do
btainnega
tiverea
lnum
bersa
s
answers.
Na
tureo
fro
ots
.
(a)Simp
lifyexpress
ionsus
ing
the
lawso
f
exponen
tsforra
tiona
lexponen
ts.
(b)Es
tablishbe
tweenw
hichtwoin
tegersag
iven
simp
lesurd
lies.
(c)Roun
drea
lnum
bers
toanappropria
tedegree
ofaccuracy
(toag
ivennum
ber
ofdec
ima
l
digits
).
(a)App
lyth
elawso
fexponen
tstoexpress
ions
invo
lvingra
tiona
lexponen
ts.
(b)Add
,su
btrac
t,mu
ltiplyan
ddivides
imp
lesurds.
Demonstrateanunderstandingofthedenitionof
alogari
thman
dany
lawsnee
de
dtoso
lverea
llife
pro
blems.
Man
ipu
latea
lge
bra
icexpress
ionsb
y:
mu
ltiplyinga
binom
ialbya
trino
mial;
fac
toris
ing
trinom
ials;
fac
toris
ing
the
differencean
dsumso
ftwo
cu
bes;
fac
toris
ing
bygroup
ing
inpa
irs;an
d
simp
lify
ing,
addingan
dsu
btrac
tinga
lge
bra
ic
frac
tionsw
ithdenom
ina
torsofcu
bes
(limite
d
tosuman
ddifferenceo
fcu
bes
).
Rev
ise
factorisa
tion.
Ta
keno
tean
dun
ders
tan
d,
the
Rema
inderan
d
Fac
tor
Theorems
forp
olynom
ialsup
tothe
thirddegree.
Fac
torise
third-degree
po
lynom
ials(inc
luding
examp
lesw
hichrequire
the
Fac
tor
Theorem
).
So
lve:
linearequa
tions;
qua
dra
ticequa
tions;
litera
lequa
tions
(chang
ing
thesu
bjec
to
fa
formu
la);
exponen
tia
lequa
tions;
linear
inequa
lities;
sys
temo
flinearequa
tions;and
wordpro
blems.
So
lve:
qua
drat
icequa
tions;
qua
drat
icinequa
lities
inonevaria
blean
d
interpre
ttheso
lutiongrap
hica
lly;an
d
equa
tion
sintwoun
knowns,
oneo
fw
hichis
linearth
eo
therqua
dra
tic,
alge
bra
ica
llyor
grap
hica
lly.
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14 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
5.DIFFER
ENTIALCALCULUS
(a)An
intuitiveun
ders
tandingo
ftheconcep
to
fa
limit
.
(b)Differentiationofspeciedfunctionsfromrst
princ
iples.
(c)Useofthespeciedru
lesofdifferentiation.
(d)Theequa
tionso
ftangen
tstograp
hs.
(e)Thea
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
there
lative
frequency
ofan
experimen
talou
tcomew
iththe
theore
tica
l
pro
ba
bilityo
ftheou
tcome.
(b)Venn
diagramsasana
idtosolv
ingpro
ba
bility
pro
blems.
(c)Mu
tua
llyexc
lus
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
lvingpro
ba
bility
pro
blem
s(whereeven
tsareno
tnecessari
ly
indepen
den
t).
(a)Genera
lisa
tiono
fthefun
damen
talcoun
ting
princ
iple
.
(b)Pro
ba
bilitypro
blemsu
sing
the
fun
damen
tal
coun
tingprinc
iple
.
7.EUCLIDEANGEOMETRYANDMEASUREMENT
(a)Rev
ise
bas
icresu
ltses
tablishedinearl
ier
gra
des.
(b)Inves
tiga
telinesegmen
tsjoinin
gthem
id-
po
intso
ftwos
ideso
fa
triangle.
(c)Propert
ieso
fspec
ialqua
dri
latera
ls.
(a)Inves
tiga
tean
dprove
theoremso
fthe
geometryo
fc
irc
lesassum
ingresu
lts
from
earl
ierg
rades,
toge
therw
ithoneo
therresult
concern
ing
tangen
tsan
dra
diio
fc
irc
les.
(b)So
lvecirc
legeome
trypro
blems,
prov
iding
reasons
fors
tatemen
tsw
henrequ
ire
d.
(c)Proveri
ders.
(a)Rev
iseearl
ier
(Gra
de9)workon
the
necessaryandsufcie
ntconditionsfor
po
lygons
tobes
imilar
.
(b)Prove
(accep
tingresu
ltses
tablishe
dinearl
ier
gra
des
):
tha
ta
line
drawnpara
lleltoones
ideo
f
atriang
ledividest
heo
ther
twos
ides
proport
iona
lly(and
the
Mid-po
intTheorem
asaspec
ialcaseo
fthistheorem
);
tha
tequ
iangu
lartr
iang
lesares
imilar;
tha
ttriang
lesw
iths
ides
inproport
ionare
similar;
the
Py
thagoreanT
heorem
bys
imilar
triang
les;an
d
riders.
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MATHEMATICS GRADES 10-12
16 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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.
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MATHEMATICS GRADES 10-12
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.
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MATHEMATICS GRADES 10-12
18 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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
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MATHEMATICS GRADES 10-12
19CAPS
MATHEMATICS:GRADE11PACESETTER
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
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MATHEMATICS GRADES 10-12
20 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
MATHEMATICS:GRADE12PACESETTER
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
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MATHEMATICS GRADES 10-12
22 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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)
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MATHEMATICS GRADES 10-12
24 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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)
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MATHEMATICS GRADES 10-12
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
)
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MATHEMATICS GRADES 10-12
26 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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).
-
8/9/2019 Policy Statements Math Gr 10 12
32/62
MATHEMATICS GRADES 10-12
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