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MATHEMATIC
S
Curriculum and Assessment Policy Statement
Further Education and Training PhaseGrades 10-12
National Curriculum Statement (NCS)
CAPS
CurriCulum and assessment PoliCy statement Grades 10-12
matHematiCs
MATHEMATICS GRADES 10-12
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
department of Basic education
222 Struben StreetPrivate Bag X895Pretoria 0001South AfricaTel: +27 12 357 3000Fax: +27 12 323 0601
120 Plein Street Private Bag X9023Cape Town 8000South Africa Tel: +27 21 465 1701Fax: +27 21 461 8110Website: http://www.education.gov.za
© 2011 department of Basic education
isBn: 978-1-4315-0573-9
Design and Layout by: Ndabase Printing Solution
Printed by: Government Printing Works
MATHEMATICS GRADES 10-12
CAPS
AGRICULTURAL MANAGEMENT PRACTICES GRADES 10-12
CAPS
FOREWORD by thE ministER
Our national curriculum is the culmination of our efforts over a period of seventeen years to transform the curriculum bequeathed to us by apartheid. From the start of democracy we have built our curriculum on the values that inspired our Constitution (Act 108 of 1996). the Preamble to the Constitution states that the aims of the Constitution are to:
• heal thedivisionsof thepastandestablishasocietybasedondemocraticvalues, social justice and fundamental human rights;
• improvethequalityoflifeofallcitizensandfreethepotentialofeachperson;
• laythefoundationsforademocraticandopensocietyinwhichgovernmentisbasedonthewillofthepeopleandeverycitizenisequallyprotectedbylaw;and
• buildaunitedanddemocraticSouthAfricaabletotakeitsrightfulplaceasasovereignstateinthefamilyofnations.
Education and the curriculum have an important role to play in realising these aims.
in 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience ofimplementationpromptedareviewin2000.Thisledtothefirstcurriculumrevision:theRevised National Curriculum Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).
Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National Curriculum Statement (2002) to produce this document.
From 2012 the two 2002 curricula, for Grades R-9 and Grades 10-12 respectively, are combined in a single document andwillsimplybeknownastheNational Curriculum Statement Grades R-12. the National Curriculum Statement for Grades R-12 buildsonthepreviouscurriculumbutalsoupdatesitandaimstoprovideclearerspecificationofwhatis to be taught and learnt on a term-by-term basis.
the National Curriculum Statement Grades R-12 accordingly replaces the subject statements, Learning Programme Guidelines and subject Assessment Guidelines with the
(a) Curriculum and Assessment Policy statements (CAPs) for all approved subjects listed in this document;
(b) National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(c) National Protocol for Assessment Grades R-12.
MRS ANGIE MOTSHEKGA, MP MINISTER OF BASIC EDUCATION
MATHEMATICS GRADES 10-12
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
MATHEMATICS GRADES 10-12
1CAPS
CoNTeNTS
seCtion 1: introduCtion to tHe CurriCulum and assessment PoliCy statements .. 3
1.1 Background ....................................................................................................................................................3
1.2 overview ..........................................................................................................................................................3
1.3 General aims of the south african Curriculum ............................................................................................4
1.4 time allocation ................................................................................................................................................6
1.4.1 Foundation Phase ...................................................................................................................................6
1.4.2 Intermediate Phase .................................................................................................................................6
1.4.3 Senior Phase...........................................................................................................................................7
1.4.4 Grades 10-12 ..........................................................................................................................................7
seCtion 2: introduCtion to matHematiCs .................................................................................. 8
2.1 What is mathematics?.....................................................................................................................................8
2.2 SpecificAims ...................................................................................................................................................8
2.3 SpecificSkills ..................................................................................................................................................8
2.4 Focus of Content areas ..................................................................................................................................9
2.5 Weighting of Content areas ...........................................................................................................................9
2.6 mathematics in the Fet ................................................................................................................................10
seCtion 3: oVerVieW oF toPiCs Per term and annual teaCHinG Plans ....................... 11
3.1 SpecificationofcontenttoshowProgression ...........................................................................................11
3.1.1 overview of topics .................................................................................................................................12
3.2 Contentclarificationwithteachingguidelines ...........................................................................................16
3.2.1 Allocation of teaching time ....................................................................................................................16
3.2.2 Sequencing and pacing of topics ..........................................................................................................18
3.2.3 Topic allocation per term .......................................................................................................................21
Grade 10 Term: 1 ..................................................................................................................................21
Grade 10 Term: 2 ..................................................................................................................................24
Grade 10 Term: 3 ..................................................................................................................................26
Grade 10 Term: 4 ..................................................................................................................................29
Grade 11 Term: 1 ..................................................................................................................................30
Grade 11 Term: 2 ..................................................................................................................................32
Grade 11 Term: 3 ..................................................................................................................................34
MATHEMATICS GRADES 10-12
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
MATHEMATICS GRADES 10-12
3CAPS
SeCTIoN 1
introduCtion to tHe CurriCulum and assessment PoliCy statements For matHematiCs Grades 10-12
1.1 Background
The National Curriculum Statement Grades R-12 (NCS) stipulates policy on curriculum and assessment in the schooling sector.
To improve implementation, the National Curriculum Statement was amended, with the amendments coming into effect in January 2012. A single comprehensive Curriculum and Assessment Policy document was developed for each subject to replace Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines in Grades R-12.
1.2 overview
(a) The National Curriculum Statement Grades R-12 (January 2012) represents a policy statement for learning and teaching in South African schools and comprises the following:
(i) Curriculum and Assessment Policy Statements for each approved school subject;
(ii) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(iii) The policy document, National Protocol for Assessment Grades R-12 (January 2012).
(b) The National Curriculum Statement Grades R-12 (January 2012) replaces the two current national curricula statements, namely the
(i) Revised National Curriculum Statement Grades R-9, Government Gazette No. 23406 of 31 May 2002, and
(ii) National Curriculum Statement Grades 10-12 Government Gazettes, No. 25545 of 6 October 2003 and No. 27594 of 17 May 2005.
(c) The national curriculum statements contemplated in subparagraphs b(i) and (ii) comprise the following policy documents which will be incrementally repealed by the National Curriculum Statement Grades R-12 (January 2012) during the period 2012-2014:
(i) The Learning Area/Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines for Grades R-9 and Grades 10-12;
(ii) The policy document, National Policy on assessment and qualifications for schools in the GeneralEducation and Training Band, promulgated in Government Notice No. 124 in Government Gazette No. 29626 of 12 February 2007;
(iii) The policy document, the National Senior Certificate: A qualification at Level 4 on the NationalQualificationsFramework(NQF),promulgatedinGovernmentGazetteNo.27819of20July2005;
MATHEMATICS GRADES 10-12
4 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
(iv) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardinglearnerswithspecialneeds, published in Government Gazette, No.29466 of 11 December 2006, is incorporated in the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(v) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardingtheNationalProtocolfor Assessment (Grades R-12), promulgated in Government Notice No.1267 in Government Gazette No. 29467 of 11 December 2006.
(d) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, and the sections on the Curriculum and Assessment Policy as contemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the National Curriculum Statement Grades R-12. It will therefore, in terms of section 6A of the South African Schools Act, 1996(ActNo.84of1996,) form the basis for the Minister of Basic education to determine minimum outcomes and standards, as well as the processes and procedures for the assessment of learner achievement to be applicable to public and independent schools.
1.3 General aims of the south african Curriculum
(a) The National Curriculum Statement Grades R-12 gives expression to the knowledge, skills and values worth learning in South African schools. This curriculum aims to ensure that children acquire and apply knowledge and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge in local contexts, while being sensitive to global imperatives.
(b) The National Curriculum Statement Grades R-12 serves the purposes of:
• equipping learners, irrespective of their socio-economic background, race, gender, physical ability or intellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningful participation in society as citizens of a free country;
• providing access to higher education;
• facilitating the transition of learners from education institutions to the workplace; and
• providing employers with a sufficient profile of a learner’s competences.
(c) The National Curriculum Statement Grades R-12 is based on the following principles:
• Social transformation: ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of the population;
• Active and critical learning: encouraging an active and critical approach to learning, rather than rote and uncritical learning of given truths;
• High knowledge and high skills: the minimum standards of knowledge and skills to be achieved at each grade are specified and set high, achievable standards in all subjects;
• Progression: content and context of each grade shows progression from simple to complex;
MATHEMATICS GRADES 10-12
5CAPS
• Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social and environmental justice and human rights as defined in the Constitution of the Republic of South Africa. The National Curriculum Statement Grades R-12 is sensitive to issues of diversity such as poverty, inequality, race, gender, language, age, disability and other factors;
• Valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country as important contributors to nurturing the values contained in the Constitution; and
• Credibility, quality and efficiency: providing an education that is comparable in quality, breadth and depth to those of other countries.
(d) The National Curriculum Statement Grades R-12 aims to produce learners that are able to:
• identify and solve problems and make decisions using critical and creative thinking;
• work effectively as individuals and with others as members of a team;
• organise and manage themselves and their activities responsibly and effectively;
• collect, analyse, organise and critically evaluate information;
• communicate effectively using visual, symbolic and/or language skills in various modes;
• use science and technology effectively and critically showing responsibility towards the environment and the health of others; and
• demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.
(e) Inclusivity should become a central part of the organisation, planning and teaching at each school. This can only happen if all teachers have a sound understanding of how to recognise and address barriers to learning, and how to plan for diversity.
The key to managing inclusivity is ensuring that barriers are identified and addressed by all the relevant support structures within the school community, including teachers, District-Based Support Teams, Institutional-Level Support Teams, parents and Special Schools as Resource Centres. To address barriers in the classroom, teachers should use various curriculum differentiation strategies such as those included in the Department of Basic Education’s Guidelines for Inclusive Teaching and Learning (2010).
MATHEMATICS GRADES 10-12
6 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
1.4 time allocation
1.4.1 Foundation Phase
(a) The instructional time in the Foundation Phase is as follows:
suBJeCtGrade r (Hours)
Grades 1-2 (Hours)
Grade 3 (Hours)
Home Language 10 8/7 8/7
First Additional Language 2/3 3/4
Mathematics 7 7 7
Life Skills
• Beginning Knowledge
• Creative Arts
• Physical education
• Personal and Social Well-being
6
(1)
(2)
(2)
(1)
6
(1)
(2)
(2)
(1)
7
(2)
(2)
(2)
(1)
total 23 23 25
(b) Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.
(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours for Additional Language in Grades 1-2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional Language.
(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R-2 and 2 hours as indicated by the hours in brackets for Grade 3.
1.4.2 intermediate Phase
(a) The instructional time in the Intermediate Phase is as follows:
suBJeCt Hours
Home Language 6
First Additional Language 5
Mathematics 6
Natural Sciences and Technology 3,5
Social Sciences 3
Life Skills
• Creative Arts
• Physical education
• Personal and Social Well-being
4
(1,5)
(1)
(1,5)
total 27,5
MATHEMATICS GRADES 10-12
7CAPS
1.4.3 senior Phase
(a) The instructional time in the Senior Phase is as follows:
suBJeCt Hours
Home Language 5
First Additional Language 4
Mathematics 4,5
Natural Sciences 3
Social Sciences 3
Technology 2
economic Management Sciences 2
Life orientation 2
Creative Arts 2
total 27,5
1.4.4 Grades 10-12
(a) The instructional time in Grades 10-12 is as follows:
suBJeCt time alloCation Per Week (Hours)
Home Language 4.5
First Additional Language 4.5
Mathematics 4.5
Life orientation 2
A minimum of any three subjects selected from Group B Annexure B, Tables B1-B8 of the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, subject to the provisos stipulated in paragraph 28 of the said policy document.
12 (3x4h)
total 27,5
The allocated time per week may be utilised only for the minimum required NCS subjects as specified above, and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wish to offer additional subjects, additional time must be allocated for the offering of these subjects
MATHEMATICS GRADES 10-12
8 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
SeCTIoN 2
introduction
In Chapter 2, the Further Education and Training (FET) Phase Mathematics CAPS provides teachers with a definition of mathematics, specific aims, specific skills, focus of content areas and the weighting of content areas.
2.1 What is mathematics?
mathematics is a language that makes use of symbols and notations for describing numerical, geometric and graphical relationships. It is a human activity that involves observing, representing and investigating patterns and qualitative relationships in physical and social phenomena and between mathematical objects themselves. It helps to develop mental processes that enhance logical and critical thinking, accuracy and problem solving that will contribute in decision-making.Mathematical problem solving enables us to understand the world (physical, social and economic) around us, and, most of all, to teach us to think creatively.
2.2 SpecificAims
1. To develop fluency in computation skills without relying on the usage of calculators.
2. Mathematical modeling is an important focal point of the curriculum. Real life problems should be incorporated into all sections whenever appropriate. examples used should be realistic and not contrived. Contextual problems should include issues relating to health, social, economic, cultural, scientific, political and environmental issues whenever possible.
3. To provide the opportunity to develop in learners the ability to be methodical, to generalize, make conjectures and try to justify or prove them.
4. To be able to understand and work with number system.
5. To show Mathematics as a human creation by including the history of Mathematics.
6. To promote accessibility of Mathematical content to all learners. It could be achieved by catering for learners with different needs.
7. To develop problem-solving and cognitive skills. Teaching should not be limited to “how”but should rather feature the “when” and “why” of problem types. Learning procedures and proofs without a good understanding of why they are important will leave learners ill-equipped to use their knowledge in later life.
8. To prepare the learners for further education and training as well as the world of work.
2.3 SpecificSkills
To develop essential mathematical skills the learner should:
• develop the correct use of the language of Mathematics;
• collect, analyse and organise quantitative data to evaluate and critique conclusions;
MATHEMATICS GRADES 10-12
9CAPS
• use mathematical process skills to identify, investigate and solve problems creatively and critically;
• use spatial skills and properties of shapes and objects to identify, pose and solve problems creatively and critically;
• participate as responsible citizens in the life of local, national and global communities; and
• communicate appropriately by using descriptions in words, graphs, symbols, tables and diagrams.
2.4 Focus of Content areas
Mathematics in the FeT Phase covers ten main content areas. each content area contributes towards the acquisition of the specific skills. The table below shows the main topics in the FET Phase.
the main topics in the Fet mathematics Curriculum
1. Functions
2. number Patterns, sequences, series
3. Finance, growth and decay
4. algebra
5. differential Calculus
6. Probability
7. euclidean Geometry and measurement
8. analytical Geometry
9. trigonometry
10. statistics
2.5 Weighting of Content areas
The weighting of mathematics content areas serves two primary purposes: firstly the weighting gives guidance on the amount of time needed to address adequately the content within each content area; secondly the weighting gives guidance on the spread of content in the examination (especially end of the year summative assessment).
MATHEMATICS GRADES 10-12
10 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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.
MATHEMATICS GRADES 10-12
11CAPS
SeCTIoN 3
introduction
Chapter 3 provides teachers with:
• specification of content to show progression;
• clarification of content with teaching guidelines; and
• allocation of time.
3.1 SpecificationofContenttoshowProgression
The specification of content shows progression in terms of concepts and skills from Grade 10 to 12 for each content area. However, in certain topics the concepts and skills are similar in two or three successive grades. The clarification of content gives guidelines on how progression should be addressed in these cases. The specification of content should therefore be read in conjunction with the clarification of content.
MATHEMATICS GRADES 10-12
12 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
3.1.
1 o
verv
iew
of t
opic
s
1. F
un
Cti
on
s
Gra
de 1
0G
rade
11
Gra
de 1
2
Wor
k w
ith re
latio
nshi
ps b
etw
een
varia
bles
in
term
s of
num
eric
al,
gra
phic
al, v
erba
l and
sy
mbo
lic re
pres
enta
tions
of f
unct
ions
and
co
nver
t flex
ibly
bet
wee
n th
ese
repr
esen
tatio
ns
(tabl
es, g
raph
s, w
ords
and
form
ulae
). In
clud
e lin
ear a
nd s
ome
quad
ratic
pol
ynom
ial f
unct
ions
, ex
pone
ntia
l fun
ctio
ns, s
ome
ratio
nal f
unct
ions
and
tri
gono
met
ric fu
nctio
ns.
ext
end
Gra
de 1
0 w
ork
on th
e re
latio
nshi
ps
betw
een
varia
bles
in te
rms
of
num
eric
al,
gr
aphi
cal,
verb
al a
nd s
ymbo
lic re
pres
enta
tions
of
func
tions
and
con
vert
flexi
bly
betw
een
thes
e re
pres
enta
tions
(tab
les,
gra
phs,
wor
ds a
nd
form
ulae
). In
clud
e lin
ear a
nd q
uadr
atic
pol
ynom
ial
func
tions
, exp
onen
tial f
unct
ions
, som
e ra
tiona
l fu
nctio
ns a
nd tr
igon
omet
ric fu
nctio
ns.
Intro
duce
a m
ore
form
al d
efini
tion
of a
func
tion
and
exte
nd G
rade
11
wor
k on
the
rela
tions
hips
be
twee
n va
riabl
es in
term
s of
num
eric
al,
grap
hica
l, ve
rbal
and
sym
bolic
repr
esen
tatio
ns
of fu
nctio
ns a
nd c
onve
rt fle
xibl
y be
twee
n th
ese
repr
esen
tatio
ns (t
able
s, g
raph
s, w
ords
and
fo
rmul
ae).
Incl
ude
linea
r, qu
adra
tic a
nd s
ome
cubi
c po
lyno
mia
l fun
ctio
ns, e
xpon
entia
l and
lo
garit
hmic
func
tions
, and
som
e ra
tiona
l fun
ctio
ns.
Gen
erat
e as
man
y gr
aphs
as
nece
ssar
y, in
itial
ly
by m
eans
of p
oint
-by-
poin
t plo
tting
, sup
porte
d by
av
aila
ble
tech
nolo
gy, t
o m
ake
and
test
con
ject
ures
an
d he
nce
gene
ralis
e th
e ef
fect
of t
he p
aram
eter
w
hich
resu
lts in
a v
ertic
al s
hift
and
that
whi
ch
resu
lts in
a v
ertic
al s
tretc
h an
d /o
r a re
flect
ion
abou
t the
x a
xis.
Gen
erat
e as
man
y gr
aphs
as
nece
ssar
y, in
itial
ly
by m
eans
of p
oint
-by-
poin
t plo
tting
, sup
porte
d by
av
aila
ble
tech
nolo
gy, t
o m
ake
and
test
con
ject
ures
an
d he
nce
gene
ralis
e th
e ef
fect
s of
the
para
met
er
whi
ch re
sults
in
a h
oriz
onta
l shi
ft an
d th
at w
hich
re
sults
in a
hor
izon
tal s
tretc
h an
d/or
refle
ctio
n ab
out t
he y
axi
s.
The
inve
rses
of p
resc
ribed
func
tions
and
be
awar
e of
the
fact
that
, in
the
case
of m
any-
to-o
ne
func
tions
, the
dom
ain
has
to b
e re
stric
ted
if th
e in
vers
e is
to b
e a
func
tion.
Pro
blem
sol
ving
and
gra
ph w
ork
invo
lvin
g th
e pr
escr
ibed
func
tions
.P
robl
em s
olvi
ng a
nd g
raph
wor
k in
volv
ing
the
pres
crib
ed fu
nctio
ns. A
vera
ge g
radi
ent b
etw
een
two
poin
ts.
Pro
blem
sol
ving
and
gra
ph w
ork
invo
lvin
g
the
pres
crib
ed fu
nctio
ns (i
nclu
ding
the
loga
rithm
ic fu
nctio
n).
2. n
um
Ber
Pat
ter
ns,
seQ
uen
Ces
an
d s
erie
s
Inve
stig
ate
num
ber p
atte
rns
lead
ing
to th
ose
whe
re th
ere
is c
onst
ant
diffe
renc
e be
twee
n co
nsec
utiv
e te
rms,
and
the
gene
ral t
erm
is
ther
efor
e lin
ear.
Inve
stig
ate
num
ber p
atte
rns
lead
ing
to th
ose
whe
re th
ere
is a
con
stan
t sec
ond
diffe
renc
e be
twee
n co
nsec
utiv
e te
rms,
and
the
gene
ral t
erm
is
ther
efor
e qu
adra
tic.
Iden
tify
and
solv
e pr
oble
ms
invo
lvin
g nu
mbe
r pa
ttern
s th
at le
ad to
arit
hmet
ic a
nd g
eom
etric
se
quen
ces
and
serie
s, in
clud
ing
infin
ite g
eom
etric
se
ries.
3. F
ina
nC
e, G
ro
WtH
an
d d
eCay
Use
sim
ple
and
com
poun
d gr
owth
form
ulae
and
A =
P(1
+ i)
n to
sol
ve p
robl
ems
(incl
udin
g in
tere
st, h
ire p
urch
ase,
infla
tion,
po
pula
tion
grow
th a
nd o
ther
real
life
pro
blem
s).
Use
sim
ple
and
com
poun
d de
cay
form
ulae
A
= P
(1 +
in) a
nd A
= P
(1- i
)n to s
olve
pro
blem
s (in
clud
ing
stra
ight
line
dep
reci
atio
n an
d de
prec
iatio
n on
a re
duci
ng b
alan
ce).
Link
to w
ork
on fu
nctio
ns.
(a) C
alcu
late
the
valu
e of
n in
the
form
ulae
A
= P
(1 +
i)n an
d A
= P
(1- i
)n
(b)
App
ly k
now
ledg
e of
geo
met
ric s
erie
s to
sol
ve
annu
ity a
nd b
ond
repa
ymen
t pro
blem
s.
The
impl
icat
ions
of fl
uctu
atin
g fo
reig
n ex
chan
ge
rate
s.Th
e ef
fect
of d
iffer
ent p
erio
ds o
f com
poun
ding
gr
owth
and
dec
ay (i
nclu
ding
effe
ctiv
e an
d no
min
al
inte
rest
rate
s).
Crit
ical
ly a
naly
se d
iffer
ent l
oan
optio
ns.
MATHEMATICS GRADES 10-12
13CAPS
4. a
lGeB
ra (a
) U
nder
stan
d th
at re
al n
umbe
rs c
an b
e irr
atio
nal
or ra
tiona
l.Ta
ke n
ote
that
ther
e ex
ist n
umbe
rs o
ther
than
th
ose
on th
e re
al n
umbe
r lin
e, th
e so
-cal
led
non-
real
num
bers
. It
is p
ossi
ble
to s
quar
e ce
rtain
non
-re
al n
umbe
rs a
nd o
btai
n ne
gativ
e re
al n
umbe
rs a
s an
swer
s.
Nat
ure
of ro
ots.
(a)
Sim
plify
exp
ress
ions
usi
ng th
e la
ws
of
expo
nent
s fo
r rat
iona
l exp
onen
ts.
(b)
est
ablis
h be
twee
n w
hich
two
inte
gers
a g
iven
si
mpl
e su
rd li
es.
(c) R
ound
real
num
bers
to a
n ap
prop
riate
deg
ree
of a
ccur
acy
(to a
giv
en n
umbe
r of d
ecim
al
digi
ts).
(a) A
pply
the
law
s of
exp
onen
ts to
exp
ress
ions
in
volv
ing
ratio
nal e
xpon
ents
.
(b) A
dd, s
ubtra
ct, m
ultip
ly a
nd d
ivid
e si
mpl
e su
rds.
Dem
onst
rate
an
unde
rsta
ndin
g of
the
defin
ition
of
a lo
garit
hm a
nd a
ny la
ws
need
ed to
sol
ve re
al li
fe
prob
lem
s.
Man
ipul
ate
alge
brai
c ex
pres
sion
s by
:
•m
ultip
lyin
g a
bino
mia
l by
a tri
nom
ial;
•fa
ctor
isin
g tri
nom
ials
;
•fa
ctor
isin
g th
e di
ffere
nce
and
sum
s of
two
cube
s;
•fa
ctor
isin
g by
gro
upin
g in
pai
rs; a
nd
•si
mpl
ifyin
g, a
ddin
g an
d su
btra
ctin
g al
gebr
aic
fract
ions
with
den
omin
ator
s of
cub
es (l
imite
d to
sum
and
diff
eren
ce o
f cub
es).
Rev
ise
fact
oris
atio
n.•
Take
not
e an
d un
ders
tand
, the
Rem
aind
er a
nd
Fact
or T
heor
ems
for p
olyn
omia
ls u
p to
the
third
deg
ree.
•Fa
ctor
ise
third
-deg
ree
poly
nom
ials
(inc
ludi
ng
exam
ples
whi
ch re
quire
the
Fact
or T
heor
em).
Sol
ve:
•lin
ear e
quat
ions
;
•qu
adra
tic e
quat
ions
;
•lit
eral
equ
atio
ns (c
hang
ing
the
subj
ect o
f a
form
ula)
;
•ex
pone
ntia
l equ
atio
ns;
•lin
ear i
nequ
aliti
es;
•sy
stem
of l
inea
r equ
atio
ns; a
nd
•w
ord
prob
lem
s.
Sol
ve:
•qu
adra
tic e
quat
ions
;
•qu
adra
tic in
equa
litie
s in
one
var
iabl
e an
d in
terp
ret t
he s
olut
ion
grap
hica
lly; a
nd
•eq
uatio
ns in
two
unkn
owns
, one
of w
hich
is
linea
r the
oth
er q
uadr
atic
, al
gebr
aica
lly o
r gr
aphi
cally
.
MATHEMATICS GRADES 10-12
14 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
5. d
iFFe
ren
tia
l C
alC
ulu
s
(a)
An
intu
itive
und
erst
andi
ng o
f the
con
cept
of a
lim
it.
(b)
Diff
eren
tiatio
n of
spe
cifie
d fu
nctio
ns fr
om fi
rst
prin
cipl
es.
(c)
Use
of t
he s
peci
fied
rule
s of
diff
eren
tiatio
n.
(d)
The
equa
tions
of t
ange
nts
to g
raph
s.
(e)
The
abili
ty to
ske
tch
grap
hs o
f cub
ic fu
nctio
ns.
(f) P
ract
ical
pro
blem
s in
volv
ing
optim
izat
ion
and
rate
s of
cha
nge
(incl
udin
g th
e ca
lcul
us o
f m
otio
n).
6. P
ro
Ba
Bil
ity
(a) C
ompa
re th
e re
lativ
e fre
quen
cy o
f an
expe
rimen
tal o
utco
me
with
the
theo
retic
al
prob
abili
ty o
f the
out
com
e.
(b)
Venn
dia
gram
s as
an
aid
to s
olvi
ng p
roba
bilit
y pr
oble
ms.
(c) M
utua
lly e
xclu
sive
eve
nts
and
com
plem
enta
ry
even
ts.
(d)
The
iden
tity
for a
ny tw
o ev
ents
A a
nd B
:P
(A o
r B) =
P(A
) + (B
) - P
(A a
nd B
)
(a) D
epen
dent
and
inde
pend
ent e
vent
s.
(b) V
enn
diag
ram
s or
con
tinge
ncy
tabl
es a
nd
tree
diag
ram
s as
aid
s to
sol
ving
pro
babi
lity
prob
lem
s (w
here
eve
nts
are
not n
eces
saril
y in
depe
nden
t).
(a) G
ener
alis
atio
n of
the
fund
amen
tal c
ount
ing
prin
cipl
e.
(b) P
roba
bilit
y pr
oble
ms
usin
g th
e fu
ndam
enta
l co
untin
g pr
inci
ple.
7. e
uC
lid
ean
Geo
met
ry a
nd
mea
sur
emen
t
(a) R
evis
e ba
sic
resu
lts e
stab
lishe
d in
ear
lier
grad
es.
(b) I
nves
tigat
e lin
e se
gmen
ts jo
inin
g th
e m
id-
poin
ts o
f tw
o si
des
of a
tria
ngle
.
(c) P
rope
rties
of s
peci
al q
uadr
ilate
rals
.
(a) I
nves
tigat
e an
d pr
ove
theo
rem
s of
the
geom
etry
of c
ircle
s as
sum
ing
resu
lts fr
om
earli
er g
rade
s, to
geth
er w
ith o
ne o
ther
resu
lt co
ncer
ning
tang
ents
and
radi
i of c
ircle
s.
(b) S
olve
circ
le g
eom
etry
pro
blem
s, p
rovi
ding
re
ason
s fo
r sta
tem
ents
whe
n re
quire
d.
(c) P
rove
ride
rs.
(a) R
evis
e ea
rlier
(Gra
de 9
) wor
k on
the
nece
ssar
y an
d su
ffici
ent c
ondi
tions
for
poly
gons
to b
e si
mila
r.
(b) P
rove
(acc
eptin
g re
sults
est
ablis
hed
in e
arlie
r gr
ades
):
•th
at a
line
dra
wn
para
llel t
o on
e si
de o
f a
trian
gle
divi
des
the
othe
r tw
o si
des
prop
ortio
nally
(and
the
Mid
-poi
nt T
heor
em
as a
spe
cial
cas
e of
this
theo
rem
);
•th
at e
quia
ngul
ar tr
iang
les
are
sim
ilar;
•th
at tr
iang
les
with
sid
es in
pro
porti
on a
re
sim
ilar;
•th
e P
ytha
gore
an T
heor
em b
y si
mila
r tri
angl
es; a
nd
•rid
ers.
MATHEMATICS GRADES 10-12
15CAPS
Sol
ve p
robl
ems
invo
lvin
g vo
lum
e an
d su
rface
ar
ea o
f sol
ids
stud
ied
in e
arlie
r gra
des
as w
ell a
s sp
here
s, p
yram
ids
and
cone
s an
d co
mbi
natio
ns o
f th
ose
obje
cts.
R
evis
e G
rade
10
wor
k.
8. t
riG
on
om
etry
(a)
Defi
nitio
ns o
f th
e tri
gono
met
ric r
atio
s si
n θ,
cos θ
and
tan θ
in a
righ
t-ang
led
trian
gles
.
(b) E
xten
d th
e de
finiti
ons
of s
in θ
, cos
θ a
nd
tan θ
to 0
o ≤ θ≤360
o .
(c)
Der
ive
and
use
valu
es o
f th
e tri
gono
met
ric
ratio
s (w
ithou
t usi
ng a
cal
cula
tor f
or th
e
spec
ial a
ngle
s θ
∈ {0
o ;30o ;4
5o ;60o ;9
0o }
(d)
Defi
ne th
e re
cipr
ocal
s of
trig
onom
etric
ratio
s.
(a)
Der
ive
and
use
the
iden
titie
s:
sin θ
cos θ
tan θ=
and
sin
2 θ+s
in2 θ=1.
(b) D
eriv
e th
e re
duct
ion
form
ulae
. (c
) Det
erm
ine
the
gene
ral s
olut
ion
and
/ or s
peci
fic
solu
tions
of t
rigon
omet
ric e
quat
ions
.(d
) est
ablis
h th
e si
ne, c
osin
e an
d ar
ea ru
les.
Pro
of a
nd u
se o
f the
com
poun
d an
gle
and
doub
le a
ngle
iden
titie
s
So
Sol
ve p
robl
ems
in tw
o di
men
sion
s.S
olve
pro
blem
s in
2-d
imen
sion
s.
Sol
ve p
robl
ems
in tw
o an
d th
ree
dim
ensi
ons.
9. a
na
lyti
Ca
l G
eom
etry
Rep
rese
nt g
eom
etric
figu
res
in a
Car
tesi
an c
o-or
dina
te s
yste
m, a
nd d
eriv
e an
d ap
ply,
for a
ny
two
poin
ts (x
1 ; y
1) an
d (x
2 ; y
2), a
form
ula
for
calc
ulat
ing:
•th
e di
stan
ce b
etw
een
the
two
poin
ts;
•th
e gr
adie
nt o
f the
line
seg
men
t joi
ning
the
poin
ts;
•co
nditi
ons
for p
aral
lel a
nd p
erpe
ndic
ular
line
s;
and
•th
e co
-ord
inat
es o
f the
mid
-poi
nt o
f the
line
se
gmen
t joi
ning
the
poin
ts.
Use
a C
arte
sian
co-
ordi
nate
sys
tem
to d
eriv
e an
d ap
ply
:•
the
equa
tion
of a
line
thro
ugh
two
give
n po
ints
;•
the
equa
tion
of a
line
thro
ugh
one
poin
t and
pa
ralle
l or p
erpe
ndic
ular
to a
giv
en li
ne; a
nd•
the
incl
inat
ion
of a
line
.
Use
a tw
o-di
men
sion
al C
arte
sian
co-
ordi
nate
sy
stem
to d
eriv
e an
d ap
ply:
•th
e eq
uatio
n of
a c
ircle
(any
cen
tre);
and
•th
e eq
uatio
n of
a ta
ngen
t to
a ci
rcle
at a
giv
en
poin
t on
the
circ
le.
10. s
tati
stiC
s
(a)
Col
lect
, org
anis
e an
d in
terp
ret u
niva
riate
nu
mer
ical
dat
a in
ord
er to
det
erm
ine:
•m
easu
res
of c
entra
l ten
denc
y;
•fiv
e nu
mbe
r sum
mar
y;•
box
and
whi
sker
dia
gram
s; a
nd•
mea
sure
s of
dis
pers
ion.
(a)
Rep
rese
nt m
easu
res
of c
entra
l ten
denc
y an
d
disp
ersi
on in
uni
varia
te n
umer
ical
dat
a by
:•
usin
g og
ives
; and
•ca
lcul
atin
g th
e va
rianc
e an
d st
anda
rd
devi
atio
n of
set
s of
dat
a m
anua
lly (f
or
smal
l set
s of
dat
a) a
nd u
sing
cal
cula
tors
(fo
r lar
ger s
ets
of d
ata)
and
repr
esen
ting
resu
lts g
raph
ical
ly.(b
) Rep
rese
nt S
kew
ed d
ata
in b
ox a
nd w
hisk
er
diag
ram
s, a
nd fr
eque
ncy
poly
gons
. Ide
ntify
ou
tlier
s.
(a) R
epre
sent
biv
aria
te n
umer
ical
dat
a as
a
scat
ter p
lot a
nd s
ugge
st in
tuiti
vely
and
by
sim
ple
inve
stig
atio
n w
heth
er a
line
ar, q
uadr
atic
or
exp
onen
tial f
unct
ion
wou
ld b
est fi
t the
dat
a.
(b) U
se a
cal
cula
tor t
o ca
lcul
ate
the
linea
r re
gres
sion
line
whi
ch b
est fi
ts a
giv
en s
et o
f bi
varia
te n
umer
ical
dat
a.
(c) U
se a
cal
cula
tor t
o ca
lcul
ate
the
corr
elat
ion
co-e
ffici
ent o
f a s
et o
f biv
aria
te n
umer
ical
dat
a an
d m
ake
rele
vant
ded
uctio
ns.
MATHEMATICS GRADES 10-12
16 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
3.2 ContentClarificationwithteachingguidelines
In Chapter 3, content clarification includes:
• teaching guidelines;
• sequencing of topics per term; and
• pacing of topics over the year.
• each content area has been broken down into topics. The sequencing of topics within terms gives an idea of how content areas can be spread and re-visited throughout the year.
• The examples discussed in the Clarification Column in the annual teaching plan which follows are by no means a complete representation of all the material to be covered in the curriculum. They only serve as an indication of some questions on the topic at different cognitive levels. Text books and other resources should be consulted for a complete treatment of all the material.
• The order of topics is not prescriptive, but ensure that part of trigonometry is taught in the first term and more than six topics are covered / taught in the first two terms so that assessment is balanced between paper 1 and 2.
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 five-minutes periods, per week in grades 10, 11 and 12.
terms Grade 10 Grade 11 Grade 12
no. ofweeks
no. of weeks
no. of weeks
term 1Algebraic expressions
exponents
Number patterns
equations and inequalities
Trigonometry
3
2
1
2
3
exponents and surds
equations and inequalities
Number patterns
Analytical Geometry
3
3
2
3
Patterns, sequences and
series
Functions and inverse
functions
exponential and
logarithmic functions
Finance, growth and decay
Trigonometry - compound
angles
3
3
1
2
2
term 2Functions
Trigonometric functions
euclidean Geometry
MID-YeAR eXAMS
4
1
3
3
Functions
Trigonometry (reduction
formulae, graphs,
equations)
MID-YeAR eXAMS
4
4
3
Trigonometry 2D and 3D
Polynomial functions
Differential calculus
Analytical Geometry
MID-YeAR eXAMS
2
1
3
2
3
term 3Analytical Geometry
Finance and growth
Statistics
Trigonometry
euclidean Geometry
Measurement
2
2
2
2
1
1
Measurement
euclidean Geometry
Trigonometry (sine, area,
cosine rules)
Probability
Finance, growth and decay
1
3
2
2
2
Geometry
Statistics (regression and
correlation)
Counting and Probability
Revision
TRIAL eXAMS
2
2
2
1
3
term 4 Probability
Revision
eXAMS
2
4
3
Statistics
Revision
eXAMS
3
3
3
Revision
eXAMS
3
6
The detail which follows includes examples and numerical references to the overview.
MATHEMATICS GRADES 10-12
18 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
3.2.
2 se
quen
cing
and
Pac
ing
of t
opic
s
mat
Hem
atiC
s: G
ra
de
10 P
aC
e se
tter
1te
rm
1
Wee
ksW
eek
1W
eek
2W
eek
3W
eek
4W
eek
5W
eek
6W
eek
7W
eek
8W
eek
9W
eek
10
Wee
k
11
topi
csA
lgeb
raic
exp
ress
ions
exp
onen
tsN
umbe
r pa
ttern
se
quat
ions
and
ineq
ualit
ies
Trig
onom
etry
ass
essm
ent
Inve
stig
atio
n or
pro
ject
Test
dat
e co
mpl
eted
2te
rm
2
Wee
ksW
eek
1W
eek
2W
eek
3W
eek
4W
eek
5W
eek
6W
eek
7W
eek
8W
eek
9W
eek
10
Wee
k
11
topi
csFu
nctio
nsTr
igon
omet
ric
func
tions
euc
lidea
n G
eom
etry
ass
essm
ent
Ass
ignm
ent /
Tes
tM
ID-Y
eA
R e
XA
MIN
ATIo
Nd
ate
com
plet
ed3
ter
m 3
Wee
ksW
eek
1W
eek
2W
eek
3W
eek
4W
eek
5W
eek
6W
eek
7W
eek
8W
eek
9W
eek
10
topi
csA
naly
tical
Geo
met
ryFi
nanc
e an
d gr
owth
Sta
tistic
sTr
igon
omet
rye
uclid
ean
Geo
met
ryM
easu
rem
ent
ass
essm
ent
Test
Test
dat
e co
mpl
eted
4te
rm
4P
aper
1: 2
hou
rsP
aper
2: 2
hou
rs
Wee
ksW
eek
1
Wee
k
2W
eek
3
Wee
k
4W
eek
5
Wee
k
6W
eek
7
Wee
k 8
Wee
k 9
Wee
k
10A
lgeb
raic
ex
pres
sion
s an
d eq
uatio
ns (a
nd
ineq
ualit
ies)
expo
nent
sN
umbe
r Pat
tern
s Fu
nctio
ns a
nd g
raph
sFi
nanc
e an
d gr
owth
P
roba
bilit
y
30 10 30 15 15
euc
lidea
n ge
omet
ry
and
mea
sure
men
t
Ana
lytic
al g
eom
etry
Trig
onom
etry
Sta
tistic
s
20 15 50 15
topi
csP
roba
bilit
yR
evis
ion
Adm
in
ass
essm
ent
Test
exa
min
atio
ns
dat
e co
mpl
eted
Tota
l mar
ks10
0To
tal m
arks
100
MATHEMATICS GRADES 10-12
19CAPS
mat
Hem
atiC
s: G
ra
de
11 P
aC
e se
tter
1te
rm
1
Wee
ksW
eek
1W
eek
2W
eek
3W
eek
4W
eek
5W
eek
6W
eek
7W
eek
8W
eek
9W
eek
10
Wee
k
11to
pics
exp
onen
ts a
nd s
urds
equ
atio
ns a
nd in
equa
litie
sN
umbe
r pat
tern
sA
naly
tical
Geo
met
rya
sses
smen
tIn
vest
igat
ion
or p
roje
ctTe
std
ate
com
plet
ed2
ter
m 2
Wee
ksW
eek
1W
eek
2W
eek
3W
eek
4W
eek
5W
eek
6W
eek
7W
eek
8W
eek
9W
eek
10
Wee
k
11to
pics
Func
tions
Trig
onom
etry
(red
uctio
n fo
rmul
ae, g
raph
s, e
quat
ions
)a
sses
smen
tA
ssig
nmen
t / T
est
MID
-Ye
AR
eX
AM
INAT
IoN
dat
e co
mpl
eted
3te
rm
3W
eeks
Wee
k 1
Wee
k 2
Wee
k 3
Wee
k 4
Wee
k 5
Wee
k 6
Wee
k 7
Wee
k 8
Wee
k 9
Wee
k 1
0to
pics
Mea
sure
men
te
uclid
ean
Geo
met
ryTr
igon
omet
ry (s
ine,
cos
ine
and
area
rule
s)Fi
nanc
e, g
row
th a
nd d
ecay
Pro
babi
lity
ass
essm
ent
Test
Test
dat
e co
mpl
eted
4te
rm
4P
aper
1: 3
hou
rsP
aper
2: 3
hou
rs
Wee
ksW
eek
1
Wee
k
2W
eek
3
Wee
k
4W
eek
5
Wee
k
6W
eek
7
Wee
k
8W
eek
9W
eek
10
Alg
ebra
ic e
xpre
ssio
ns
and
equa
tions
(and
in
equa
litie
s)N
umbe
r pat
tern
sFu
nctio
ns a
nd g
raph
s Fi
nanc
e, g
row
th a
nd d
ecay
Pro
babi
lity
45 25 45 15 20
euc
lidea
n G
eom
etry
and
mea
sure
men
tA
naly
tical
geo
met
ryTr
igon
omet
ry
Sta
tistic
s
40 30 60 20
topi
csS
tatis
tics
Rev
isio
nFI
NA
L e
XA
MIN
ATIo
NA
dmin
ass
essm
ent
Test
dat
e co
mpl
eted
Tota
l mar
ks15
0To
tal m
arks
150
MATHEMATICS GRADES 10-12
20 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
mat
Hem
atiC
s: G
ra
de
12 P
aC
e se
tter
1te
rm
1W
eeks
Wee
k 1
Wee
k 2
Wee
k 3
Wee
k 4
Wee
k 5
Wee
k 6
Wee
k 7
Wee
k 8
Wee
k 9
Wee
k 1
0W
eek
11
topi
csN
umbe
r pat
tern
s, s
eque
nces
and
ser
ies
Func
tions
: For
mal
defi
nitio
n; in
vers
esFu
nctio
ns:
expo
nent
ial
and
loga
rithm
ic
Fina
nce,
gro
wth
and
dec
ayTr
igon
omet
ry
ass
essm
ent
Test
Inve
stig
atio
n or
pro
ject
Ass
ignm
ent
dat
e co
mpl
eted
2te
rm
2W
eeks
Wee
k 1
Wee
k 2
Wee
k 3
Wee
k 4
Wee
k 5
Wee
k 6
Wee
k 7
Wee
k 8
Wee
k 9
Wee
k 1
0W
eek
11
topi
csTr
igon
omet
ryFu
nctio
ns:
poly
nom
ials
Diff
eren
tial C
alcu
lus
Ana
lytic
al G
eom
etry
ass
essm
ent
Test
MID
-Ye
AR
eX
AM
INAT
IoN
dat
e co
mpl
eted
3te
rm
3W
eeks
Wee
k 1
Wee
k 2
Wee
k 3
Wee
k 4
Wee
k 5
Wee
k 6
Wee
k 7
Wee
k 8
Wee
k 9
Wee
k 1
0to
pics
Geo
met
ryS
tatis
tics
Cou
ntin
g an
d P
roba
bilit
yR
evis
ion
tria
l eX
am
inat
ion
ass
essm
ent
Test
dat
e co
mpl
eted
4te
rm
4P
aper
1: 3
hou
rsP
aper
2: 3
hou
rs
Wee
ksW
eek
1
Wee
k
2W
eek
3
Wee
k
4W
eek
5
Wee
k
6W
eek
7
Wee
k
8W
eek
9W
eek
10
Alg
ebra
ic e
xpre
ssio
ns
and
equa
tions
(and
ineq
ualit
ies)
Num
ber p
atte
rns
Func
tions
and
gra
phs
Fina
nce,
gro
wth
and
dec
ay
Diff
eren
tial C
alcu
lus
Cou
ntin
g an
d pr
obab
ility
25 25 35 15 35 15
euc
lidea
n G
eom
etry
and
mea
sure
men
t
Ana
lytic
al G
eom
etry
Trig
onom
etry
Sta
tistic
s
50 40 40 20
topi
csR
evis
ion
FIN
AL
eX
AM
INAT
IoN
Adm
ina
sses
smen
t
dat
e co
mpl
eted
Tota
l mar
ks15
0To
tal m
arks
150
MATHEMATICS GRADES 10-12
21CAPS
3.2.
3 to
pic
allo
catio
n pe
r ter
m
Gr
ad
e 10
: ter
m 1
no
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
Whe
re a
n ex
ampl
e is
giv
en, t
he c
ogni
tive
dem
and
is s
ugge
sted
: kno
wle
dge
(k),
rout
ine
proc
edur
e (r
), co
mpl
ex p
roce
dure
(C) o
r pro
blem
-sol
ving
(P)
3a
lgeb
raic
ex
pres
sion
s
1.
Und
erst
and
that
real
num
bers
can
be
ratio
nal o
r irr
atio
nal.
2.
est
ablis
h be
twee
n w
hich
two
inte
gers
a g
iven
sim
ple
surd
lies
.3.
R
ound
real
num
bers
to a
n ap
prop
riate
deg
ree
of
accu
racy
. 4.
M
ultip
licat
ion
of a
bin
omia
l by
a tri
nom
ial.
5.
Fact
oris
atio
n to
incl
ude
type
s ta
ught
in g
rade
9 a
nd:
•tri
nom
ials
•gr
oupi
ng in
pai
rs•
sum
and
diff
eren
ce o
f tw
o cu
bes
6.
Sim
plifi
catio
n of
alg
ebra
ic fr
actio
ns u
sing
fact
oriz
atio
n w
ith d
enom
inat
ors
of c
ubes
(lim
ited
to s
um a
nd
diffe
renc
e of
cub
es).
exam
ples
to il
lust
rate
the
diffe
rent
cog
nitiv
e le
vels
invo
lved
in fa
ctor
isat
ion:
1.
Fact
oris
e fu
lly:
1.1.
m
2 - 2
m +
1 (r
evis
ion)
Le
arne
rs m
ust b
e ab
le to
reco
gnis
e th
e si
mpl
est
p
erfe
ct s
quar
es.
(R
)1.
2.
2x2 -
x -
3
This
type
is ro
utin
e an
d ap
pear
s in
all
text
s.
(R)
1.3.
13
y 2+
18-
y2 2
Le
arne
rs a
re re
quire
d to
wor
k w
ith fr
actio
ns a
nd
ide
ntify
w
hen
an e
xpre
ssio
n ha
s be
en “f
ully
fact
oris
ed”.
(R
)
2.
Sim
plify
(C
)
2ex
pone
nts
1.
Rev
ise
law
s of
exp
onen
ts le
arnt
in G
rade
9 w
here
€
x,y
>0
and
€
m,
€
n ∈ Z:
•
€
xm×xn
=xm
+n
•
€
xm÷xn
=xm
−n
•
€
(xm)n
=xm
n
•
€
xm×ym
=(xy)
m
Als
o by
defi
nitio
n:
•,
€
x≠0 ,
and
•
€
x0=1 ,
€
x≠0
2.
Use
the
law
s of
exp
onen
ts to
sim
plify
exp
ress
ions
and
so
lve
equa
tions
, acc
eptin
g th
at th
e ru
les
also
hol
d fo
r
€
m,
€
n ∈
Q.
exam
ples
:1.
Sim
plify
: (3
x 52 )3 -
75
A si
mpl
e tw
o-st
ep p
roce
dure
is in
volv
ed.
(R
)
2. S
impl
ify
Ass
umin
g th
is ty
pe o
f que
stio
n ha
s no
t bee
n ta
ught
,
sp
ottin
g th
at th
e nu
mer
ator
can
be
fact
oris
ed a
s a
diffe
renc
e of
squ
ares
requ
ires
insi
ght.
(P
)3.
S
olve
for
x :
3.1
12
5,0
2=
x
(R
)
3.2
€
2x3 2
=54
(R
)
3.3
(C
)
3.4
(C
)
MATHEMATICS GRADES 10-12
22 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 10
: ter
m 1
no
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
1n
umbe
rs a
nd
patte
rns
Pat
tern
s: In
vest
igat
e nu
mbe
r pat
tern
s le
adin
g to
thos
e w
here
ther
e is
a c
onst
ant d
iffer
ence
bet
wee
n co
nsec
utiv
e te
rms,
and
the
gene
ral t
erm
(with
out u
sing
a fo
rmul
a-se
e co
nten
t ove
rvie
w) i
s th
eref
ore
linea
r.
Com
men
t:
• A
rithm
etic
seq
uenc
e is
don
e in
Gra
de 1
2, h
ence
is
not u
sed
in
Gra
de 1
0.
exam
ples
:1.
D
eter
min
e th
e 5th
and
the
nth te
rms
of th
e nu
mbe
r pat
tern
10;
7; 4
; 1; …
. The
re is
an
alg
orith
mic
app
roac
h to
ans
wer
ing
such
que
stio
ns.
(R
)
2.
If th
e pa
ttern
MAT
HS
MAT
HS
MAT
HS
… is
con
tinue
d in
this
way
, wha
t will
the
267th
le
tter b
e? It
is n
ot im
med
iate
ly o
bvio
us h
ow o
ne s
houl
d pr
ocee
d, u
nles
s si
mila
r qu
estio
ns h
ave
been
tack
led.
(P
)
2eq
uatio
ns a
nd
ineq
ualit
ies
1.
Rev
ise
the
solu
tion
of li
near
equ
atio
ns.
2.
Sol
ve q
uadr
atic
equ
atio
ns (b
y fa
ctor
isat
ion)
.
3.
Sol
ve s
imul
tane
ous
linea
r equ
atio
ns in
two
unkn
owns
.
4.
Sol
ve w
ord
prob
lem
s in
volv
ing
linea
r, qu
adra
tic o
r si
mul
tane
ous
linea
r equ
atio
ns.
5.
Sol
ve li
tera
l equ
atio
ns (c
hang
ing
the
subj
ect o
f a
form
ula)
.
6.
Sol
ve li
near
ineq
ualit
ies
(and
sho
w s
olut
ion
grap
hica
lly).
Inte
rval
not
atio
n m
ust b
e kn
own.
exam
ples
:
1.
Sol
ve fo
r x:
(R
)
2.
Sol
ve fo
r m:
2m2 -
m =
1
(R)
3.
Sol
ve fo
r x a
nd y
: x +
2y
= 1;
1
23
=+
yx
(C
)
4.
Sol
ve fo
r r in
term
s of
V, ∏
and
h: V
=∏
r2 h
(R
)
5.
Sol
ve fo
r x:
-1 ≤
2 -
3x ≤
8
(
C)
MATHEMATICS GRADES 10-12
23CAPS
Gr
ad
e 10
: ter
m 1
no
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3tr
igon
omet
ry
1.
Defi
ne th
e tri
gono
met
ric ra
tios
sin
θ, c
os θ
and
tan θ,
us
ing
right
-ang
led
trian
gles
.
2.
Ext
end
the
defin
ition
s of
sin
θ, c
os θ
and
tan θ
for
00 ≤ θ
≤ 3
600 .
3.
Defi
ne th
e re
cipr
ocal
s of
the
trigo
nom
etric
ratio
s
cose
c θ,
sec
θ a
nd c
ot θ
, usi
ng ri
ght-a
ngle
d tri
angl
es
(thes
e th
ree
reci
proc
als
shou
ld b
e ex
amin
ed in
gra
de
10 o
nly)
.
4.
Der
ive
valu
es o
f the
trig
onom
etric
ratio
s fo
r the
spe
cial
ca
ses
(with
out u
sing
a c
alcu
lato
r)
θ∈
{00 ;
300 ;
450 ;
600 ;
900 }.
5.
Sol
ve tw
o-di
men
sion
al p
robl
ems
invo
lvin
g rig
ht-a
ngle
d tri
angl
es.
6.
Sol
ve s
impl
e tri
gono
met
ric e
quat
ions
for a
ngle
s be
twee
n 00 a
nd 9
00 .
7.
Use
dia
gram
s to
det
erm
ine
the
num
eric
al v
alue
s of
ra
tios
for a
ngle
s fro
m 0
0 to
3600 .
Com
men
t: It
is im
porta
nt to
stre
ss th
at:
• si
mila
rity
of tr
iang
les
is fu
ndam
enta
l to
the
trigo
nom
etric
ratio
s si
n θ,
cos
θ a
nd ta
n θ;
• tri
gono
met
ric ra
tios
are
inde
pend
ent o
f the
leng
ths
of th
e si
des
of a
sim
ilar
right
-ang
led
tria
ngle
and
dep
end
(uni
quel
y) o
nly
on th
e an
gles
, hen
ce w
e co
nsid
er
them
as
func
tions
of t
he a
ngle
s;
• do
ublin
g a
ratio
has
a d
iffer
ent e
ffect
from
dou
blin
g an
ang
le, f
or e
xam
ple,
gen
eral
ly
2sin
θ≠
sin
2θ;a
nd
• S
olve
equ
atio
n of
the
form
c
x=
sin
, or
cx=
cos
2, o
r c
x=
2ta
n, w
here
c is
a
cons
tant
.
exam
ples
:
1.
If 5s
in θ+4=0
and
00 ≤
θ ≤
270
0 , c
alcu
late
the
valu
e of
sin
2 θ+c
os2 θw
ithou
t us
ing
a ca
lcul
ator
.
(R
)
2.
Let A
BC
D b
e a
rect
angl
e, w
ith A
B =
2cm
. Let
E b
e on
AD
suc
h th
at A
EB
ˆˆ= E =
450
and
BÊ
C =
750 .
Det
erm
ine
the
area
of t
he re
ctan
gle.
(P
)
3.
Det
erm
ine
the
leng
th o
f the
hyp
oten
use
of a
righ
t-ang
led
trian
gle
AB
C, w
here
EB
ˆˆ= =
900 ,
DA
ˆˆ= =
300 a
nd A
B =
10c
m
(K
)
4.
Sol
ve fo
r x:
for
(C)
ass
essm
ent t
erm
1:
1. I
nves
tigat
ion
or p
roje
ct (o
nly
one
proj
ect p
er y
ear)
(at l
east
50
mar
ks)
e
xam
ple
of a
n in
vest
igat
ion:
Im
agin
e a
cube
of w
hite
woo
d w
hich
is d
ippe
d in
to re
d pa
int s
o th
at th
e su
rface
is re
d, b
ut th
e in
side
stil
l whi
te. I
f one
cut
is m
ade,
par
alle
l to
each
face
of t
he c
ube
(and
thro
ugh
the
cent
re o
f the
cub
e), t
hen
ther
e w
ill b
e 8
smal
ler c
ubes
. eac
h of
the
smal
ler c
ubes
will
hav
e 3
red
face
s an
d 3
whi
te fa
ces.
Inve
stig
ate
the
num
ber o
f sm
alle
r cub
es w
hich
will
hav
e 3,
2,
1 a
nd 0
red
face
s if
2/3/
4/…
/n e
qual
ly s
pace
d cu
ts a
re m
ade
para
llel t
o ea
ch fa
ce. T
his
task
pro
vide
s th
e op
portu
nity
to in
vest
igat
e, ta
bula
te re
sults
, mak
e co
njec
ture
s an
d ju
stify
or
pro
ve th
em.
2.
Test
(at l
east
50
mar
ks a
nd 1
hou
r). M
ake
sure
all
topi
cs a
re te
sted
.
C
are
need
s to
be
take
n to
set
que
stio
ns o
n al
l fou
r cog
nitiv
e le
vels
: ap
prox
imat
ely
20%
kno
wle
dge,
app
roxi
mat
ely
35%
rout
ine
proc
edur
es, 3
0% c
ompl
ex p
roce
dure
s an
d 15
%
prob
lem
-sol
ving
.
MATHEMATICS GRADES 10-12
24 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 10
: ter
m 2
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
(4 +
1)
5Fu
nctio
ns
1.
The
conc
ept o
f a fu
nctio
n, w
here
a
certa
in q
uant
ity (o
utpu
t val
ue) u
niqu
ely
depe
nds
on a
noth
er q
uant
ity (i
nput
va
lue)
. Wor
k w
ith re
latio
nshi
ps b
etw
een
varia
bles
usi
ng ta
bles
, gra
phs,
wor
ds a
nd
form
ulae
. Con
vert
flexi
bly
betw
een
thes
e re
pres
enta
tions
.
Not
e: th
at th
e gr
aph
defin
ed b
yy
x=
shou
ld b
e kn
own
from
Gra
de 9
.
2.
Poi
nt b
y po
int p
lotti
ng o
f bas
ic g
raph
s
defin
ed b
y 2 x
y=
, x
y1
=an
d x
by=
;
0>
b a
nd
to d
isco
ver s
hape
, dom
ain
(inpu
t val
ues)
, ran
ge (o
utpu
t val
ues)
, as
ympt
otes
, axe
s of
sym
met
ry, t
urni
ng
poin
ts a
nd in
terc
epts
on
the
axes
(whe
re
appl
icab
le).
3.
Inve
stig
ate
the
effe
ct o
f q
xf
ay
+=
)(
. and
qx
fa
y+
=)
(.
on
the
grap
hs d
efine
d by
q
xf
ay
+=
)(
.,
whe
re
xx
f=
)(
, ,
)(
2 xx
f=
xx
f1
)(
=
and
,)
(x
bx
f=
,0
>b
4.
Poi
nt b
y po
int p
lotti
ng o
f bas
ic g
raph
s
defin
ed b
y ,
and
fo
r
5. S
tudy
the
effe
ct o
f a
and
qx
fa
y+
=)
(.
on
the
grap
hs
defin
ed b
y:
; ; a
nd w
here
q
xf
ay
+=
)(
. , q
xf
ay
+=
)(
. ∈
Q fo
r .
6.
Ske
tch
grap
hs, fi
nd th
e eq
uatio
ns o
f giv
en
grap
hs a
nd in
terp
ret g
raph
s.
not
e: S
ketc
hing
of t
he g
raph
s m
ust b
e ba
sed
on
the
obse
rvat
ion
of n
umbe
r 3 a
nd 5
.
Com
men
ts:
• A
mor
e fo
rmal
defi
nitio
n of
a fu
nctio
n fo
llow
s in
Gra
de 1
2. A
t thi
s le
vel i
t is
enou
gh to
inve
stig
ate
the
way
(uni
que)
out
put v
alue
s de
pend
on
how
inpu
t val
ues
vary
. The
term
s in
depe
nden
t (in
put)
and
depe
nden
t (ou
tput
) var
iabl
es m
ight
be
usef
ul.
• A
fter s
umm
arie
s ha
ve b
een
com
pile
d ab
out b
asic
feat
ures
of p
resc
ribed
gra
phs
and
the
effe
cts
of p
aram
eter
s a
and
q ha
ve b
een
inve
stig
ated
: a: a
ver
tical
stre
tch
(and
/or a
refle
ctio
n ab
out t
he
x-ax
is) a
nd q
a v
ertic
al s
hift.
The
follo
win
g ex
ampl
es m
ight
be
appr
opria
te:
• R
emem
ber t
hat g
raph
s in
som
e pr
actic
al a
pplic
atio
ns m
ay b
e ei
ther
dis
cret
e or
con
tinuo
us.
exam
ples
:
1.
Ske
tche
d be
low
are
gra
phs
of
qxa
xf
+=
)(
and
.
The
horiz
onta
l asy
mpt
ote
of b
oth
grap
hs is
the
line
y =
1.
Det
erm
ine
the
valu
es o
f a
, b
, n
, q
and
t.
(C)
Ox
y
(1;
-1)
(2;
0)
2.
Ske
tch
the
grap
h de
fined
by
fo
r
(R)
MATHEMATICS GRADES 10-12
25CAPS
Gr
ad
e 10
: ter
m 2
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3eu
clid
ean
Geo
met
ry
1.
Rev
ise
basi
c re
sults
est
ablis
hed
in e
arlie
r gr
ades
rega
rdin
g lin
es, a
ngle
s an
d tri
angl
es, e
spec
ially
the
sim
ilarit
y an
d co
ngru
ence
of t
riang
les.
2.
Inve
stig
ate
line
segm
ents
join
ing
the
mid
-po
ints
of t
wo
side
s of
a tr
iang
le.
3.
Defi
ne th
e fo
llow
ing
spec
ial q
uadr
ilate
rals
: th
e ki
te, p
aral
lelo
gram
, rec
tang
le, r
hom
bus,
sq
uare
and
trap
eziu
m. I
nves
tigat
e an
d m
ake
conj
ectu
res
abou
t the
pro
perti
es o
f th
e si
des,
ang
les,
dia
gona
ls a
nd a
reas
of
thes
e qu
adril
ater
als.
Pro
ve th
ese
conj
ectu
res.
Com
men
ts:
•Tr
iang
les
are
sim
ilar i
f the
ir co
rres
pond
ing
angl
es a
re e
qual
, or i
f the
ratio
s of
thei
r sid
es a
re
equa
l: Tr
iang
les
AB
Can
d D
EF
are
sim
ilar i
fD
Aˆ
ˆ=
,
EB
ˆˆ=
and
FC
ˆˆ=
. The
y ar
e al
so
sim
ilar i
f .
•W
e co
uld
defin
e a
para
llelo
gram
as
a qu
adril
ater
al w
ith tw
o pa
irs o
f opp
osite
sid
es p
aral
lel.
Then
we
inve
stig
ate
and
prov
e th
at th
e op
posi
te s
ides
of t
he p
aral
lelo
gram
are
equ
al, o
ppos
ite
angl
es o
f a p
aral
lelo
gram
are
equ
al, a
nd d
iago
nals
of a
par
alle
logr
am b
isec
t eac
h ot
her.
•It
mus
t be
expl
aine
d th
at a
sin
gle
coun
ter e
xam
ple
can
disp
rove
a C
onje
ctur
e, b
ut n
umer
ous
spec
ific
exam
ples
sup
porti
ng a
con
ject
ure
do n
ot c
onst
itute
a g
ener
al p
roof
.
exam
ple:
In q
uadr
ilate
ral K
ITe
, KI =
Ke
and
IT =
eT.
The
dia
gona
ls in
ters
ect a
t M. P
rove
that
:
1.
IM =
Me
and
(R)
2.
KT
is p
erpe
ndic
ular
to Ie
.
(
P)
As
it is
not
obv
ious
, firs
t pro
ve th
at
.
3m
id-y
ear
exam
inat
ions
ass
essm
ent t
erm
2:
1. A
ssig
nmen
t / te
st (a
t lea
st 5
0 m
arks
)
2. M
id-y
ear e
xam
inat
ion
(at l
east
100
mar
ks)
o
ne p
aper
of
2 h
ours
(100
mar
ks) o
r Tw
o pa
pers
- on
e, 1
hou
r (50
mar
ks) a
nd th
e ot
her,
1 ho
ur (5
0 m
arks
)
MATHEMATICS GRADES 10-12
26 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 10
: ter
m 3
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2a
naly
tical
G
eom
etry
Rep
rese
nt g
eom
etric
figu
res
on a
Car
tesi
an
co-o
rdin
ate
syst
em.
Der
ive
and
appl
y fo
r any
two
poin
ts
);
(1
1y
xan
d )
;(
22
yx
the
form
ulae
for
calc
ulat
ing
the:
1.
dist
ance
bet
wee
n th
e tw
o po
ints
;
2.
grad
ient
of t
he li
ne s
egm
ent c
onne
ctin
g th
e tw
o po
ints
(and
from
that
iden
tify
para
llel
and
perp
endi
cula
r lin
es);
and
3.
coor
dina
tes
of th
e m
id-p
oint
of t
he li
ne
segm
ent j
oini
ng th
e tw
o po
ints
.
exam
ple:
Con
side
r the
poi
nts
)5;2(P
and
in th
e C
arte
sian
pla
ne.
1.1.
Cal
cula
te th
e di
stan
ce P
Q.
(K)
1.2
Fin
d th
e co
ordi
nate
s of
R if
M
is th
e m
id-p
oint
of P
R.
(R
)
1.3
Det
erm
ine
the
coor
dina
tes
of S
if P
QR
S is
a p
aral
lelo
gram
. (C
)
1.4
Is
PQ
RS
a re
ctan
gle?
Why
or w
hy n
ot?
(R
)
2Fi
nanc
e an
d gr
owth
Use
the
sim
ple
and
com
poun
d
grow
th fo
rmul
ae
and
ni
PA
)1(+
=] to
sol
ve p
robl
ems,
incl
udin
g an
nual
inte
rest
, hire
pur
chas
e,
infla
tion,
pop
ulat
ion
grow
th a
nd o
ther
real
-lif
e pr
oble
ms.
Und
erst
and
the
impl
icat
ion
of
fluct
uatin
g fo
reig
n ex
chan
ge ra
tes
(e.g
. on
the
petro
l pric
e, im
ports
, exp
orts
, ove
rsea
s tra
vel).
MATHEMATICS GRADES 10-12
27CAPS
Gr
ad
e 10
: ter
m 3
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2st
atis
tics
1. R
evis
e m
easu
res
of c
entra
l ten
denc
y in
un
grou
ped
data
.
2. M
easu
res
of c
entra
l ten
denc
y in
gro
uped
da
ta:
ca
lcul
atio
n of
mea
n es
timat
e of
gro
uped
an
d un
grou
ped
data
and
iden
tifica
tion
of
mod
al in
terv
al a
nd in
terv
al in
whi
ch th
e m
edia
n lie
s.
3.
Rev
isio
n of
rang
e as
a m
easu
re o
f di
sper
sion
and
ext
ensi
on to
incl
ude
perc
entil
es, q
uarti
les,
inte
rqua
rtile
and
sem
i in
terq
uarti
le ra
nge.
4.
Five
num
ber s
umm
ary
(max
imum
, min
imum
an
d qu
artil
es) a
nd b
ox a
nd w
hisk
er
diag
ram
.
5.
Use
the
stat
istic
al s
umm
arie
s (m
easu
res
of c
entra
l ten
denc
y an
d di
sper
sion
), an
d gr
aphs
to a
naly
se a
nd m
ake
mea
ning
ful
com
men
ts o
n th
e co
ntex
t ass
ocia
ted
with
th
e gi
ven
data
.
Com
men
t:In
gra
de 1
0, th
e in
terv
als
of g
roup
ed d
ata
shou
ld b
e gi
ven
usin
g in
equa
litie
s, th
at is
, in
the
form
0≤
x<20
rath
er th
an in
the
form
0-1
9, 2
0-29
, …
exam
ple:
The
mat
hem
atic
s m
arks
of 2
00 g
rade
10
lear
ners
at a
sch
ool c
an b
e su
mm
aris
ed a
s fo
llow
s:
Perc
enta
ge o
btai
ned
num
ber o
f can
dida
tes
0≤x<
204
20≤x
<30
10
30≤x
<40
37
40≤x
<50
43
50≤x
<60
36
60≤x
<70
26
70≤x
<80
24
80≤x
<100
20
1.
Cal
cula
te th
e ap
prox
imat
e m
ean
mar
k fo
r the
exa
min
atio
n.
(R
)
2.
Iden
tify
the
inte
rval
in w
hich
eac
h of
the
follo
win
g da
ta it
ems
lies:
2.1.
th
e m
edia
n;
(R
)
2.2.
th
e lo
wer
qua
rtile
;
(R
)
2.3.
th
e up
per q
uarti
le; a
nd
(R)
2.4.
the
thirt
ieth
per
cent
ile.
(R)
MATHEMATICS GRADES 10-12
28 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 10
: ter
m 3
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2tr
igon
omet
ry
Pro
blem
s in
two
dim
ensi
ons.
exam
ple:
Two
flagp
oles
are
30
m a
part.
The
one
has
hei
ght 1
0 m
, whi
le th
e ot
her h
as h
eigh
t 15
m. T
wo
tig
ht ro
pes
conn
ect t
he to
p of
eac
h po
le to
the
foot
of t
he o
ther
. At w
hat h
eigh
t abo
ve th
e
grou
nd d
o th
e tw
o ro
pes
inte
rsec
t? W
hat i
f the
pol
es w
ere
at d
iffer
ent d
ista
nce
apar
t?
(P)
1eu
clid
ean
Geo
met
ry
Sol
ve p
robl
ems
and
prov
e rid
ers
usin
g th
e pr
oper
ties
of p
aral
lel l
ines
, tria
ngle
s an
d qu
adril
ater
als.
Com
men
t:U
se c
ongr
uenc
y an
d pr
oper
ties
of q
uads
, esp
. par
alle
logr
ams.
exam
ple:
eFG
H is
a p
aral
lelo
gram
. Pro
ve th
at M
FNH
is a
par
alle
logr
am.
N
M
HE
FG
(C)
2m
easu
rem
ent
1.
Rev
ise
the
volu
me
and
surfa
ce a
reas
of
right
-pris
ms
and
cylin
ders
.
2.
Stu
dy th
e ef
fect
on
volu
me
and
surfa
ce
area
whe
n m
ultip
lyin
g an
y di
men
sion
by
a co
nsta
nt fa
ctor
k.
3.
Cal
cula
te th
e vo
lum
e an
d su
rface
are
as o
f sp
here
s, ri
ght p
yram
ids
and
right
con
es.
exam
ple:
The
heig
ht o
f a c
ylin
der i
s 10
cm
, and
the
radi
us o
f the
circ
ular
bas
e is
2 c
m. A
hem
isph
ere
is
atta
ched
to o
ne e
nd o
f the
cyl
inde
r and
a c
one
of h
eigh
t 2 c
m to
the
othe
r end
. Cal
cula
te th
e vo
lum
e an
d su
rface
are
a of
the
solid
, cor
rect
to th
e ne
ares
t cm
3 and
cm
2 , res
pect
ivel
y.
(R
)
Com
men
ts:
• In
cas
e of
pyr
amid
s, b
ases
mus
t eith
er b
e an
equ
ilate
ral t
riang
le o
r a s
quar
e.
• P
robl
em ty
pes
mus
t inc
lude
com
posi
te fi
gure
.
ass
essm
ent t
erm
3: T
wo
(2) T
ests
(at l
east
50
mar
ks a
nd 1
hou
r) c
over
ing
all t
opic
s in
app
roxi
mat
ely
the
ratio
of t
he a
lloca
ted
teac
hing
tim
e.
MATHEMATICS GRADES 10-12
29CAPS
Gr
ad
e 10
: ter
m 4
no
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2Pr
obab
ility
1. T
he u
se o
f pro
babi
lity
mod
els
to
com
pare
the
rela
tive
frequ
ency
of
even
ts w
ith th
e th
eore
tical
prob
abili
ty.
2. T
he u
se o
f Ven
n di
agra
ms
to s
olve
prob
abili
ty p
robl
ems,
der
ivin
g an
d
a
pply
ing
the
follo
win
g fo
r any
two
e
vent
s A
and
B in
a s
ampl
e sp
ace
S:
AP
(or
a
nd);
B
A
and
B a
re m
utua
lly e
xclu
sive
if
AP
(an
d;0
)=
B
A an
d B
are
com
plem
enta
ry if
they
are
mut
ually
exc
lusi
ve ;
and
.1)
()
(=
+B
PA
P
Then
()
(P
BP
=no
t .
Com
men
t: •
It ge
nera
lly ta
kes
a ve
ry la
rge
num
ber o
f tria
ls b
efor
e th
e re
lativ
e fre
quen
cy o
f a c
oin
falli
ng
head
s up
whe
n to
ssed
app
roac
hes
0,5.
exam
ple:
In a
sur
vey
80 p
eopl
e w
ere
ques
tione
d to
find
out
how
man
y re
ad n
ewsp
aper
S o
r D o
r bot
h. T
he s
urve
y re
veal
ed th
at 4
5 re
ad D
, 30
read
S a
nd 1
0 re
ad n
eith
er.
Use
a V
enn
diag
ram
to fi
nd h
ow m
any
read
1.
S o
nly;
(C)
2.
D o
nly;
and
(C)
3.
both
D a
nd S
.
(C
)
4r
evis
ion
Com
men
t:Th
e va
lue
of w
orki
ng th
roug
h pa
st p
aper
s ca
nnot
be
over
em
phas
ised
.
3ex
amin
atio
ns
ass
essm
ent t
erm
41.
Tes
t (at
leas
t 50
mar
ks)
2. e
xam
inat
ion
Pap
er 1
: 2 h
ours
(100
mar
ks m
ade
up a
s fo
llow
s: 1
5±3
on n
umbe
r pat
tern
s, 3
0±3
on a
lgeb
raic
exp
ress
ions
, equ
atio
ns a
nd in
equa
litie
s , 3
0±3
on fu
nctio
ns, 1
0±3
on fi
nanc
e an
d
gro
wth
and
15±
3 on
pro
babi
lity.
Pap
er 2
: 2 h
ours
(100
mar
ks m
ade
up a
s fo
llow
s: 4
0±3
on tr
igon
omet
ry, 1
5±3
on A
naly
tical
Geo
met
ry, 3
0±3
on e
uclid
ean
Geo
met
ry a
nd M
easu
rem
ent,
and
15±3
on
Sta
tistic
s
MATHEMATICS GRADES 10-12
30 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 11
: ter
m 1
no
fWee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
Whe
re a
n ex
ampl
e is
giv
en, t
he c
ogni
tive
dem
and
is s
ugge
sted
: kno
wle
dge
(k),
rout
ine
proc
edur
e (r
), co
mpl
ex p
roce
dure
(C) o
r pro
blem
sol
ving
(P)
3ex
pone
nts
and
surd
s
1.
Sim
plify
exp
ress
ions
and
sol
ve e
quat
ions
us
ing
the
law
s of
exp
onen
ts fo
r ra
tiona
l ex
pone
nts
whe
re
;
qp
qp
xx
=0
;0>
>q
x.
2.
Add
, sub
tract
, mul
tiply
and
div
ide
sim
ple
surd
s.
3.
Sol
ve s
impl
e eq
uatio
ns in
volv
ing
surd
s.
exam
ple:
1.
Det
erm
ine
the
valu
e of
23
9.
(R)
2.
Sim
plify
:
(R)
3.
Sol
ve fo
r x
: .
(P
)
3eq
uatio
ns a
nd
ineq
ualit
ies
1.
Com
plet
e th
e sq
uare
.
2.
Qua
drat
ic e
quat
ions
(by
fact
oris
atio
n an
d by
usi
ng th
e qu
adra
tic fo
rmul
a).
3.
Qua
drat
ic in
equa
litie
s in
one
unk
now
n (In
terp
ret s
olut
ions
gra
phic
ally
).
NB
: It i
s re
com
men
ded
that
the
solv
ing
of
equa
tions
in tw
o un
know
ns is
impo
rtant
to
be u
sed
in o
ther
equ
atio
ns li
ke h
yper
bola
- st
raig
ht li
ne a
s th
is is
nor
mal
in th
e ca
se o
f gr
aphs
.
4.
equ
atio
ns in
two
unkn
owns
, one
of w
hich
is
linea
r and
the
othe
r qua
drat
ic.
5.
Nat
ure
of ro
ots.
exam
ple:
1.
I hav
e 12
met
res
of fe
ncin
g. W
hat a
re th
e di
men
sion
s of
the
larg
est r
ecta
ngul
ar a
rea
I can
en
clos
e w
ith th
is fe
ncin
g by
usi
ng a
n ex
istin
g w
all a
s on
e si
de?H
int:
let t
he le
ngth
of t
he e
qual
si
des
of th
e re
ctan
gle
be x
met
res
and
form
ulat
e an
exp
ress
ion
for t
he a
rea
of th
e re
ctan
gle.
(C)
(
With
out t
he h
int t
his
wou
ld p
roba
bly
be p
robl
em s
olvi
ng.)
2.1.
Sho
w th
at th
e ro
ots
of
are
irrat
iona
l.
(R)
2.2.
Sho
w th
at
01
2=
++
xx
has
no
real
root
s.
(R
)
3.
Sol
ve fo
r x
: .
(R
)
4.
Sol
ve fo
r x
:
.
(
R)
5.
Two
mac
hine
s, w
orki
ng to
geth
er, t
ake
2 ho
urs
24 m
inut
es to
com
plet
e a
job.
Wor
king
on
its
own,
one
mac
hine
take
s 2
hour
s lo
nger
than
the
othe
r to
com
plet
e th
e jo
b. H
ow lo
ng d
oes
th
e sl
ower
mac
hine
take
on
its o
wn?
(
P)
2n
umbe
r pa
ttern
s
Pat
tern
s: In
vest
igat
e nu
mbe
r pat
tern
s le
adin
g to
thos
e w
here
ther
e is
a c
onst
ant s
econ
d di
ffere
nce
betw
een
cons
ecut
ive
term
s, a
nd th
e ge
nera
l ter
m is
ther
efor
e qu
adra
tic.
exam
ple:
In th
e fir
st s
tage
of t
he W
orld
Cup
Soc
cer F
inal
s th
ere
are
team
s fro
m fo
ur d
iffer
ent c
ount
ries
in e
ach
grou
p. e
ach
coun
try in
a g
roup
pla
ys e
very
oth
er c
ount
ry in
the
grou
p on
ce. H
ow m
any
mat
ches
are
ther
e fo
r eac
h gr
oup
in th
e fir
st s
tage
of t
he fi
nals
? H
ow m
any
gam
es w
ould
ther
e
be if
ther
e w
ere
five
team
s in
eac
h gr
oup?
Six
team
s? n
team
s?
(
P)
MATHEMATICS GRADES 10-12
31CAPS
Gr
ad
e 11
: ter
m 1
no
fWee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3a
naly
tical
G
eom
etry
Der
ive
and
appl
y:1.
th
e eq
uatio
n of
a li
ne th
ough
two
give
n po
ints
;2.
th
e eq
uatio
n of
a li
ne th
roug
h on
e po
int a
nd
para
llel o
r per
pend
icul
ar to
a g
iven
line
; and
3.
the
incl
inat
ion
(θ) o
f a li
ne, w
here
is th
e gr
adie
nt o
f the
line
exam
ple:
G
iven
the
poin
ts A
(2;5
) ; B
(-3;
-4) a
nd C
(4;-2
) det
erm
ine:
1.
the
equa
tion
of th
e lin
e A
B;
and
(R
)
2.
the
size
of
CA
Bˆ
.
(
C)
ass
essm
ent t
erm
1:
1.
A
n In
vest
igat
ion
or a
pro
ject
(a
max
imum
of o
ne p
roje
ct in
a y
ear)
(at l
east
50
mar
ks)
Not
ice
that
an
assi
gnm
ent i
s ge
nera
lly a
n ex
tend
ed p
iece
of w
ork
unde
rtake
n at
hom
e. L
inea
r pro
gram
min
g qu
estio
ns c
an b
e us
ed a
s pr
ojec
ts.
exam
ple
of a
n as
sign
men
t: r
atio
s an
d eq
uatio
ns in
two
varia
bles
.(T
his
assi
gnm
ent b
rings
in a
n el
emen
t of h
isto
ry w
hich
cou
ld b
e ex
tend
ed to
incl
ude
one
or tw
o an
cien
t pai
ntin
gs a
nd e
xam
ples
of a
rchi
tect
ure
whi
ch a
re in
the
shap
e of
a re
ctan
gle
with
the
ratio
of s
ides
equ
al to
the
gold
en ra
tio.)
Task
1
If 2x
2 - 3
xy +
y2 =
0 th
en (2
x - y
)(x-
y) =
0 s
o 2y
x=
or
yx=
. Hen
ce th
e ra
tio
21=
yx o
r 11
=yx
. In
the
sam
e w
ay fi
nd th
e po
ssib
le v
alue
s of
the
ratio
yx
if it
is g
iven
that
2x2 -
5xy
+ y
2 = 0
Task
M
ost p
aper
is c
ut to
inte
rnat
iona
lly a
gree
d si
zes:
A0,
A1,
A2,
…, A
7 w
ith th
e pr
oper
ty th
at th
e A
1 sh
eet i
s ha
lf th
e si
ze o
f the
A0
shee
t and
sim
ilar t
o th
e A
0
shee
t, th
e A
2 sh
eet i
s ha
lf th
e si
ze o
f the
A1
shee
t and
sim
ilar t
o th
e A
1 sh
eet,
etc.
Fin
d th
e ra
tio o
f the
leng
th
yx= to
the
brea
dth
yx=
of A
0, A
1, A
2, …
, A7
pape
r (in
sim
ples
t sur
d fo
rm).
Task
3Th
e go
lden
rect
angl
e ha
s be
en re
cogn
ised
thro
ugh
the
ages
as
bein
g ae
sthe
tical
ly p
leas
ing.
It c
an b
e se
en in
the
arch
itect
ure
of th
e G
reek
s, in
scu
lptu
res
and
in R
enai
ssan
ce
pain
tings
. Any
gol
den
rect
angl
e w
ith le
ngth
x a
nd b
read
th y
has
the
prop
erty
that
whe
n a
squa
re th
e le
ngth
of t
he s
horte
r sid
e (y
) is
cut f
rom
it, a
noth
er re
ctan
gle
sim
ilar t
o it
is le
ft. T
he
proc
ess
can
be c
ontin
ued
inde
finite
ly, p
rodu
cing
sm
alle
r and
sm
alle
r rec
tang
les.
Usi
ng th
is in
form
atio
n, c
alcu
late
the
ratio
x:yin
sur
d fo
rm.
exa
mpl
e of
pro
ject
: Col
lect
the
heig
hts
of a
t lea
st 5
0 si
xtee
n-ye
ar-o
ld g
irls
and
at le
ast 5
0 si
xtee
n-ye
ar-o
ld b
oys.
Gro
up y
our d
ata
appr
opria
tely
and
use
thes
e tw
o se
ts o
f gro
uped
dat
a to
dra
w fr
eque
ncy
poly
gons
of t
he re
lativ
e he
ight
s of
boy
s an
d of
girl
s, in
diff
eren
t col
ours
, on
the
sam
e sh
eet o
f gra
ph p
aper
. Ide
ntify
the
mod
al in
terv
als,
the
inte
rval
s in
whi
ch th
e m
edia
ns li
e an
d th
e ap
prox
imat
e m
eans
as
calc
ulat
ed fr
om th
e fre
quen
cies
of t
he g
roup
ed d
ata.
By
how
muc
h do
es th
e ap
prox
imat
e m
ean
heig
ht o
f you
r sam
ple
of s
ixte
en-y
ear-
old
girls
diff
er fr
om th
e ac
tual
mea
n? C
omm
ent o
n th
e sy
mm
etry
of t
he tw
o fre
quen
cy p
olyg
ons
and
any
othe
r asp
ects
of t
he d
ata
whi
ch a
re il
lust
rate
d by
the
frequ
ency
pol
ygon
s.2.
Te
st (
at le
ast 5
0 m
arks
and
1 h
our)
. Mak
e su
re a
ll to
pics
are
test
ed.
Car
e ne
eds
to b
e ta
ken
to a
sk q
uest
ions
on
all f
our c
ogni
tive
leve
ls: a
ppro
xim
atel
y 20
% k
now
ledg
e, a
ppro
xim
atel
y 35
% ro
utin
e pr
oced
ures
, 30%
com
plex
pro
cedu
res
and
15
% p
robl
em-s
olvi
ng.
MATHEMATICS GRADES 10-12
32 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 11
: ter
m 2
no
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
4Fu
nctio
ns
1.
Rev
ise
the
effe
ct o
f the
par
amet
ers
a an
d q
and
inve
stig
ate
the
effe
ct o
f p o
n th
e gr
aphs
of
the
func
tions
defi
ned
by:
1.1.
q
px
ax
fy
++
==
2 )(
)(
1.2.
q
px
ax
fy
++
==
)(
1.3.
q
ba
xf
yp
x+
==
+.
)(
whe
re
b>0,b≠1
2.
Inve
stig
ate
num
eric
ally
the
aver
age
grad
ient
bet
wee
n tw
o po
ints
on
a cu
rve
and
deve
lop
an in
tuiti
ve u
nder
stan
ding
of t
he
conc
ept o
f the
gra
dien
t of a
cur
ve a
t a p
oint
.
3.
Poi
nt b
y po
int p
lotti
ng o
f bas
ic g
raph
s
defin
ed b
y ,
and
fo
r
€
θ∈[−360°;360
°]
4.
Inve
stig
ate
the
effe
ct o
f the
par
amet
er k
on th
e gr
aphs
of t
he fu
nctio
ns d
efine
d by
€
y=sin(kx)
, an
d
.
5.
Inve
stig
ate
the
effe
ct o
f the
par
amet
er
p on
the
grap
hs o
f the
func
tions
defi
ned
by
),si
n(p
xy
+=
,),
cos(
px
y+
= a
nd
),ta
n(p
xy
+=
.
6.
Dra
w s
ketc
h gr
aphs
defi
ned
by:
𝑦=
𝑎 𝑠𝑖
𝑛 𝑘
(𝑥+
𝑝),
𝑦=𝑎
𝑐𝑜𝑠
𝑘 (𝑥
+𝑝)
and
𝑦=𝑎
𝑡𝑎 𝑛
𝑘 (𝑥
+𝑝)
at m
ost t
wo
para
met
ers
at a
tim
e.
Com
men
t: •
onc
e th
e ef
fect
s of
the
para
met
ers
have
bee
n es
tabl
ishe
d, v
ario
us p
robl
ems
need
to b
e se
t: dr
awin
g sk
etch
gra
phs,
det
erm
inin
g th
e de
finin
g eq
uatio
ns o
f fun
ctio
ns fr
om s
uffic
ient
dat
a,
mak
ing
dedu
ctio
ns fr
om g
raph
s. R
eal l
ife a
pplic
atio
ns o
f the
pre
scrib
ed fu
nctio
ns s
houl
d be
st
udie
d.
• Tw
o pa
ram
eter
s at
a ti
me
can
be v
arie
d in
test
s or
exa
min
atio
ns.
exam
ple:
Ske
tch
the
grap
hs d
efine
d by
a
nd
€
f(x)
=cos(2x
−120°)
on th
e sa
me
set o
f axe
s, w
here
.
(C
)
MATHEMATICS GRADES 10-12
33CAPS
Gr
ad
e 11
: ter
m 2
no
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
4tr
igon
omet
ry
1.
Der
ive
and
use
the
iden
titie
s
kan
odd
inte
ger;
and
.2.
D
eriv
e an
d us
e re
duct
ion
form
ulae
to
sim
plify
the
follo
win
g ex
pres
sion
s:
2.1.
;
2.2.
2.3.
an
d
2.4.
.
3.
Det
erm
ine
for w
hich
val
ues
of a
var
iabl
e an
id
entit
y ho
lds.
4.
Det
erm
ine
the
gene
ral s
olut
ions
of
trigo
nom
etric
equ
atio
ns. A
lso,
det
erm
ine
solu
tions
in s
peci
fic in
terv
als.
Com
men
t:•
Teac
hers
sho
uld
expl
ain
whe
re re
duct
ion
form
ulae
com
e fro
m.
exam
ples
:
1.
Pro
ve th
at
. (R
)
2.
For w
hich
val
ues
of
is
und
efine
d?
(R)
3.
Sim
plify
€
cos180°−x
() sin
x−90
°(
) −1
tan2540°
+x
() sin90
°+x
() cos
−x
()
(R)
4.
Det
erm
ine
the
gene
ral s
olut
ions
of
. (C
)
3m
id-y
ear
exam
inat
ions
ass
essm
ent t
erm
2:
1.
Ass
ignm
ent
( at l
east
50
mar
ks)
2.
Mid
-yea
r exa
min
atio
n:
Pap
er 1
: 2 h
ours
(100
mar
ks m
ade
up a
s fo
llow
s: g
ener
al a
lgeb
ra (2
5±3)
equ
atio
ns a
nd in
equa
litie
s (3
5±3)
; num
ber p
atte
rns
(15±
3); f
unct
ions
(25±
3)
Pap
er 2
: 2 h
ours
(100
mar
ks m
ade
up a
s fo
llow
s: a
naly
tical
geo
met
ry (3
0±3)
and
trig
onom
etry
(70
±3))
.
MATHEMATICS GRADES 10-12
34 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 11
: ter
m 3
no.
of
wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
1m
easu
rem
ent
1.
Rev
ise
the
Gra
de 1
0 w
ork.
3eu
clid
ean
Geo
met
ry
Acc
ept r
esul
ts e
stab
lishe
d in
ear
lier g
rade
s
as a
xiom
s an
d al
so th
at a
tang
ent t
o a
circ
le
is p
erpe
ndic
ular
to th
e ra
dius
, dra
wn
to th
e
poin
t of c
onta
ct.
Then
inve
stig
ate
and
prov
e th
e th
eore
ms
of
the
geom
etry
of c
ircle
s:
•Th
e lin
e dr
awn
from
the
cent
re o
f a c
ircle
pe
rpen
dicu
lar t
o a
chor
d bi
sect
s th
e ch
ord;
•Th
e pe
rpen
dicu
lar b
isec
tor o
f a c
hord
pa
sses
thro
ugh
the
cent
re o
f the
circ
le;
•Th
e an
gle
subt
ende
d by
an
arc
at th
e ce
ntre
of a
circ
le is
dou
ble
the
size
of t
he
angl
e su
bten
ded
by th
e sa
me
arc
at th
e ci
rcle
(on
the
sam
e si
de o
f the
cho
rd a
s th
e ce
ntre
);
•A
ngle
s su
bten
ded
by a
cho
rd o
f the
circ
le,
on th
e sa
me
side
of t
he c
hord
, are
equ
al;
•Th
e op
posi
te a
ngle
s of
a c
yclic
qua
drila
tera
l ar
e su
pple
men
tary
;
•Tw
o ta
ngen
ts d
raw
n to
a c
ircle
from
the
sam
e po
int o
utsi
de th
e ci
rcle
are
equ
al in
le
ngth
;
•Th
e an
gle
betw
een
the
tang
ent t
o a
circ
le
and
the
chor
d dr
awn
from
the
poin
t of
cont
act i
s eq
ual t
o th
e an
gle
in th
e al
tern
ate
segm
ent.
Use
the
abov
e th
eore
ms
and
thei
r
conv
erse
s, w
here
they
exi
st, t
o so
lve
rider
s.
Com
men
ts:
Pro
ofs
of th
eore
ms
can
be a
sked
in e
xam
inat
ions
, but
thei
r con
vers
es
(whe
reve
r the
y ho
ld) c
anno
t be
aske
d.
exam
ple:
1.
AB
and
CD
are
two
chor
ds o
f a c
ircle
with
cen
tre o
. M i
s on
AB
and
N is
on
CD
suc
h th
at
OM
⊥ A
B a
nd O
N ⊥
CD
. Als
o, A
B =
50m
m, O
M =
40m
m a
nd O
N =
20m
m. D
eter
min
e th
e
radi
us o
f the
circ
le a
nd th
e le
ngth
of C
D.
(
C)
2.
O is
the
cent
re o
f the
circ
le b
elow
and
x
O2
ˆ 1=
.
2.1.
D
eter
min
e 2
O a
nd M
in te
rms
of x
.
(R
)
2.2.
D
eter
min
e 1
K a
nd
2K
in te
rms
of x
.
(R
)
2.3.
D
eter
min
eM
Kˆ
ˆ 1+
. Wha
t do
you
notic
e?
(R)
2.4.
Writ
e do
wn
your
obs
erva
tion
rega
rdin
g th
e m
easu
res
of
2K
and
M.
(R)
MATHEMATICS GRADES 10-12
35CAPS
Gr
ad
e 11
: ter
m 3
no.
of
wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3.
O is
the
cent
re o
f the
circ
le a
bove
and
MP
T is
a ta
ngen
t. A
lso,
.
Det
erm
ine,
with
reas
ons,
y
x, a
nd z
.
(C)
2
y
3 z
O
B
T M
A
P x
4. G
iven
: ,
and
2
2ˆ
ˆB
A=
. .
Pro
ve th
at:
4.1
PA
L is
a ta
ngen
t to
circ
le A
BC
;
(P
)
4.2
AB
is a
tang
ent t
o ci
rcle
AD
P.
(P)
MATHEMATICS GRADES 10-12
36 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 11
: ter
m 3
no.
of
wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
5.
In th
e ac
com
pany
ing
figur
e, tw
o ci
rcle
s in
ters
ect a
t F a
nd D
.
BFT
is a
tang
ent t
o th
e sm
alle
r circ
le a
t F. S
traig
ht li
ne A
FE is
dra
wn
such
that
FD
= F
E. C
DE
is a
stra
ight
line
and
cho
rd A
C a
nd B
F cu
t at K
.
Pro
ve th
at:
5.1
BT
// C
E
(C)
5.2
BC
EF
is a
par
alle
logr
am
(
P)
5.3
AC
= B
F
(
P)
MATHEMATICS GRADES 10-12
37CAPS
Gr
ad
e 11
: ter
m 3
no.
of
wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2tr
igon
omet
ry
1.
Pro
ve a
nd a
pply
the
sine
, cos
ine
and
area
ru
les.
2.
Sol
ve p
robl
ems
in tw
o di
men
sion
s us
ing
the
sine
, cos
ine
and
area
rule
s.
Com
men
t:•
The
proo
fs o
f the
sin
e, c
osin
e an
d ar
ea ru
les
are
exam
inab
le.
exam
ple:
In
D is
on
BC
, AD
C =
θ, D
A =
DC
= r,
BD
= 2
r, AC=k
, and
.
Sho
w th
at
.
(P)
2Fi
nanc
e, g
row
th
and
deca
y
1.
Use
sim
ple
and
com
poun
d de
cay
form
ulae
:
A =
P(1
- in
) and
A =
P(1
- i)n
to s
olve
pro
blem
s (in
clud
ing
stra
ight
line
de
prec
iatio
n an
d de
prec
iatio
n on
a re
duci
ng
bala
nce)
.
2.
The
effe
ct o
f diff
eren
t per
iods
of c
ompo
und
grow
th a
nd d
ecay
, inc
ludi
ng n
omin
al a
nd
effe
ctiv
e in
tere
st ra
tes.
exam
ples
:
1.
The
valu
e of
a p
iece
of e
quip
men
t dep
reci
ates
from
R10
000
to R
5 00
0 in
four
yea
rs.
Wha
t is
the
rate
of d
epre
ciat
ion
if ca
lcul
ated
on
the:
1.1
stra
ight
line
met
hod;
and
(R)
1.2
redu
cing
bal
ance
?
(C)
2.
Whi
ch is
the
bette
r inv
estm
ent o
ver a
yea
r or l
onge
r: 10
,5%
p.a
. com
poun
ded
daily
or
10,5
5% p
.a. c
ompo
unde
d m
onth
ly?
(R)
3.
R50
000
is in
vest
ed in
an
acco
unt w
hich
offe
rs 8
% p
.a. i
nter
est c
ompo
unde
d qu
arte
rly fo
r th
e fir
st 1
8 m
onth
s. T
he in
tere
st th
en c
hang
es to
6%
p.a
. com
poun
ded
mon
thly.
Tw
o ye
ars
af
ter t
he m
oney
is in
vest
ed, R
10 0
00 is
with
draw
n. H
ow m
uch
will
be
in th
e ac
coun
t afte
r 4
year
s?
(
C)
Com
men
t:•
The
use
of a
tim
elin
e to
sol
ve p
robl
ems
is a
use
ful t
echn
ique
.
• S
tress
the
impo
rtanc
e of
not
wor
king
with
roun
ded
answ
ers,
but
of u
sing
the
max
imum
acc
urac
y af
ford
ed b
y th
e ca
lcul
ator
righ
t to
the
final
ans
wer
whe
n ro
undi
ng m
ight
be
appr
opria
te.
MATHEMATICS GRADES 10-12
38 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 11
: ter
m 3
no.
of
wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2Pr
obab
ility
1.
Rev
ise
the
addi
tion
rule
for m
utua
lly
excl
usiv
e ev
ents
:
𝑃
(𝐴 𝑜𝑟
𝐵)=
𝑃𝐴 +
𝑃(𝐵)
,
the
com
plem
enta
ry ru
le:
𝑃
(𝑛 𝑜𝑡
𝐴 )=
1−𝑃(
𝐴 )an
d th
e id
entit
y
P
(A o
r B) =
P(A
) + P
(B) -
P(A
and
B)
2.
Iden
tify
depe
nden
t and
inde
pend
ent e
vent
s an
d th
e pr
oduc
t rul
e fo
r ind
epen
dent
ev
ents
:
𝑃
(𝐴 𝑎 𝑛
𝑑 𝐵)
=𝑃(
𝐴 )×
𝑃(𝐵)
.
3.
The
use
of V
enn
diag
ram
s to
sol
ve
prob
abili
ty p
robl
ems,
der
ivin
g an
d
appl
ying
form
ulae
for a
ny th
ree
even
ts A
, B a
nd C
in a
sam
ple
spac
e S
.
4.
Use
tree
dia
gram
s fo
r the
pro
babi
lity
of
cons
ecut
ive
or s
imul
tane
ous
even
ts w
hich
ar
e no
t nec
essa
rily
inde
pend
ent.
Com
men
t:
• Ve
nn D
iagr
ams
or C
ontin
genc
y ta
bles
can
be
used
to s
tudy
dep
ende
nt a
nd in
depe
nden
t ev
ents
.
exam
ples
:
1. P
(A) =
0,4
5, P
(B) =
0,3
and
P(A
or B
) = 0
,615
. Are
the
even
ts A
and
B m
utua
lly e
xclu
sive
, in
depe
nden
t or n
eith
er m
utua
lly e
xclu
sive
nor
inde
pend
ent?
(R)
2. W
hat i
s th
e pr
obab
ility
of t
hrow
ing
at le
ast o
ne s
ix in
four
rolls
of a
regu
lar s
ix s
ided
die
?
(C
)
3. I
n a
grou
p of
50
lear
ners
, 35
take
Mat
hem
atic
s an
d 30
take
His
tory
, whi
le 1
2 ta
ke n
eith
er
of th
e tw
o. If
a le
arne
r is
chos
en a
t ran
dom
from
this
gro
up, w
hat i
s th
e pr
obab
ility
that
he
/she
take
s bo
th M
athe
mat
ics
and
His
tory
?
(C)
4. A
stu
dy w
as d
one
to te
st h
ow e
ffect
ive
thre
e di
ffere
nt d
rugs
, A, B
and
C w
ere
in re
lievi
ng
head
ache
s. o
ver t
he p
erio
d co
vere
d by
the
stud
y, 8
0 pa
tient
s w
ere
give
n th
e op
portu
nity
to
use
all
two
drug
s. T
he fo
llow
ing
resu
lts w
ere
obta
ined
:from
at l
east
one
of t
he d
rugs
?
(R
)
40 re
porte
d re
lief f
rom
dru
g A
35 re
porte
d re
lief f
rom
dru
g B
40 re
porte
d re
lief f
rom
dru
g C
21 re
porte
d re
lief f
rom
bot
h dr
ugs
A an
d C
18 re
porte
d re
lief f
rom
dru
gs B
and
C
68 re
porte
d re
lief f
rom
at l
east
one
of t
he d
rugs
7 re
porte
d re
lief f
rom
all
thre
e dr
ugs.
4.1
Rec
ord
this
info
rmat
ion
in a
Ven
n di
agra
m.
(
C)
4.2
How
man
y su
bjec
ts g
ot n
o re
lief f
rom
any
of t
he d
rugs
?
(K)
4.3
How
man
y su
bjec
ts g
ot re
lief f
rom
dru
gs A
and
B,
but n
ot C
?
(R
)
4.4
Wha
t is
the
prob
abili
ty th
at a
rand
omly
cho
sen
subj
ect g
ot re
lief f
rom
at l
east
one
of t
he
drug
s?
(R
)
MATHEMATICS GRADES 10-12
39CAPS
Gr
ad
e 11
: ter
m 4
no.
of
wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3st
atis
tics
1.
His
togr
ams
2.
Freq
uenc
y po
lygo
ns
3.
ogi
ves
(cum
ulat
ive
frequ
ency
cur
ves)
4.
Varia
nce
and
stan
dard
dev
iatio
n of
un
grou
ped
data
5.
Sym
met
ric a
nd s
kew
ed d
ata
6.
Iden
tifica
tion
of o
utlie
rs
Com
men
ts:
•Va
rianc
e an
d st
anda
rd d
evia
tion
may
be
calc
ulat
ed u
sing
cal
cula
tors
.
•P
robl
ems
shou
ld c
over
topi
cs re
late
d to
hea
lth, s
ocia
l, ec
onom
ic, c
ultu
ral,
polit
ical
and
en
viro
nmen
tal i
ssue
s.
•Id
entifi
catio
n of
out
liers
sho
uld
be d
one
in th
e co
ntex
t of a
sca
tter p
lot a
s w
ell a
s th
e bo
x an
d w
hisk
er d
iagr
ams.
3r
evis
ion
3ex
amin
atio
ns
ass
essm
ent t
erm
4:
1.
Test
(at l
east
50
mar
ks)
2.
exa
min
atio
n (3
00 m
arks
)
Pap
er 1
: 3 h
ours
(150
mar
ks m
ade
up a
s fo
llow
s: (2
5±3)
on
num
ber p
atte
rns,
on
(45±
3) e
xpon
ents
and
sur
ds, e
quat
ions
and
ineq
ualit
ies,
(45±
3) o
n fu
nctio
ns, (
15±3
) on
finan
ce
grow
th a
nd d
ecay
, (20
±3) o
n pr
obab
ility
).
Pap
er 2
: 3 h
ours
(150
mar
ks m
ade
up a
s fo
llow
s: (5
0±3)
on
trigo
nom
etry
, (30
±3) o
n A
naly
tical
Geo
met
ry, (
50±3
) on
euc
lidea
n G
eom
etry
and
Mea
sure
men
t, (2
0±3)
on
Sta
tistic
s.
MATHEMATICS GRADES 10-12
40 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 12
: ter
m 1
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3Pa
ttern
s,
sequ
ence
s,
serie
s
1.
Num
ber p
atte
rns,
incl
udin
g ar
ithm
etic
and
ge
omet
ric s
eque
nces
and
ser
ies
2.
Sig
ma
nota
tion
3.
Der
ivat
ion
and
appl
icat
ion
of th
e fo
rmul
ae
for t
he s
um o
f arit
hmet
ic a
nd g
eom
etric
se
ries:
3.1
;
;
3.2
; a
nd
3.3
,
Com
men
t:D
eriv
atio
n of
the
form
ulae
is e
xam
inab
le.
exam
ples
:1.
Writ
e do
wn
the
first
five
term
s of
the
sequ
ence
with
gen
eral
term
.
(K)
2. C
alcu
late
.
(R)
3. D
eter
min
e th
e 5th
term
of t
he g
eom
etric
seq
uenc
e of
whi
ch th
e 8th
term
is 6
and
the
12th
term
is 1
4.
(
C)
4. D
eter
min
e th
e la
rges
t val
ue o
f n
suc
h th
at
.
(R
)
5. S
how
that
1
999
9,0
.
=.
(P
)
3Fu
nctio
ns
1.
Defi
nitio
n of
a fu
nctio
n.
2.
Gen
eral
con
cept
of t
he in
vers
e of
a fu
nctio
n an
d ho
w th
e do
mai
n of
the
func
tion
may
ne
ed to
be
rest
ricte
d (in
ord
er to
obt
ain
a on
e-to
-one
func
tion)
to e
nsur
e th
at th
e in
vers
e is
a fu
nctio
n.3.
D
eter
min
e an
d sk
etch
gra
phs
of th
e in
vers
es o
f the
func
tions
defi
ned
by
Focu
s on
the
follo
win
g ch
arac
teris
tics:
do
mai
n an
d ra
nge,
inte
rcep
ts w
ith th
e ax
es,
turn
ing
poin
ts, m
inim
a, m
axim
a,as
ympt
otes
(hor
izon
tal a
nd v
ertic
al),
shap
e an
d sy
mm
etry
, ave
rage
gra
dien
t (av
erag
e ra
te o
f cha
nge)
, int
erva
ls o
n w
hich
the
func
tion
incr
ease
s /d
ecre
ases
.
exam
ples
:
1.
Con
side
r the
func
tion
fw
here
.
1.1
W
rite
dow
n th
e do
mai
n an
d ra
nge
of f
.
(K
)
1.2
S
how
that
f is
a o
ne-to
-one
rela
tion.
(R)
1.3
D
eter
min
e th
e in
vers
e fu
nctio
n .
(
R)
1.4
S
ketc
h th
e gr
aphs
of t
he fu
nctio
ns
f,
and
x
y=
line
on th
e sa
me
set o
f axe
s.
W
hat d
o yo
u no
tice?
(R
)
2.
Rep
eat Q
uest
ion
1 fo
r the
func
tion
and
.
(C)
Cau
tion:
1. D
o no
t con
fuse
the
inve
rse
func
tion
with
the
reci
proc
al
)(1 x
f. F
or e
xam
ple,
for t
he fu
nctio
n w
here
x
xf
=)
(, t
he re
cipr
ocal
is
x1, w
hile
fo
r
€
x≥0 .
2.
Not
e th
at th
e no
tatio
n is
use
d on
ly fo
r one
-to-o
ne re
latio
n an
d m
ust n
ot b
e
used
for i
nver
ses
of m
any-
to-o
ne re
latio
ns, s
ince
in th
ese
case
s th
e in
vers
es a
re n
ot fu
nctio
ns.
MATHEMATICS GRADES 10-12
41CAPS
Gr
ad
e 12
: ter
m 1
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3Pa
ttern
s,
sequ
ence
s,
serie
s
1.
Num
ber p
atte
rns,
incl
udin
g ar
ithm
etic
and
ge
omet
ric s
eque
nces
and
ser
ies
2.
Sig
ma
nota
tion
3.
Der
ivat
ion
and
appl
icat
ion
of th
e fo
rmul
ae
for t
he s
um o
f arit
hmet
ic a
nd g
eom
etric
se
ries:
3.1
;
;
3.2
; a
nd
3.3
,
Com
men
t:D
eriv
atio
n of
the
form
ulae
is e
xam
inab
le.
exam
ples
:1.
Writ
e do
wn
the
first
five
term
s of
the
sequ
ence
with
gen
eral
term
.
(K)
2. C
alcu
late
.
(R)
3. D
eter
min
e th
e 5th
term
of t
he g
eom
etric
seq
uenc
e of
whi
ch th
e 8th
term
is 6
and
the
12th
term
is 1
4.
(
C)
4. D
eter
min
e th
e la
rges
t val
ue o
f n
suc
h th
at
.
(R
)
5. S
how
that
1
999
9,0
.
=.
(P
)
3Fu
nctio
ns
1.
Defi
nitio
n of
a fu
nctio
n.
2.
Gen
eral
con
cept
of t
he in
vers
e of
a fu
nctio
n an
d ho
w th
e do
mai
n of
the
func
tion
may
ne
ed to
be
rest
ricte
d (in
ord
er to
obt
ain
a on
e-to
-one
func
tion)
to e
nsur
e th
at th
e in
vers
e is
a fu
nctio
n.3.
D
eter
min
e an
d sk
etch
gra
phs
of th
e in
vers
es o
f the
func
tions
defi
ned
by
Focu
s on
the
follo
win
g ch
arac
teris
tics:
do
mai
n an
d ra
nge,
inte
rcep
ts w
ith th
e ax
es,
turn
ing
poin
ts, m
inim
a, m
axim
a,as
ympt
otes
(hor
izon
tal a
nd v
ertic
al),
shap
e an
d sy
mm
etry
, ave
rage
gra
dien
t (av
erag
e ra
te o
f cha
nge)
, int
erva
ls o
n w
hich
the
func
tion
incr
ease
s /d
ecre
ases
.
exam
ples
:
1.
Con
side
r the
func
tion
fw
here
.
1.1
W
rite
dow
n th
e do
mai
n an
d ra
nge
of f
.
(K
)
1.2
S
how
that
f is
a o
ne-to
-one
rela
tion.
(R)
1.3
D
eter
min
e th
e in
vers
e fu
nctio
n .
(
R)
1.4
S
ketc
h th
e gr
aphs
of t
he fu
nctio
ns
f,
and
x
y=
line
on th
e sa
me
set o
f axe
s.
W
hat d
o yo
u no
tice?
(R
)
2.
Rep
eat Q
uest
ion
1 fo
r the
func
tion
and
.
(C)
Cau
tion:
1. D
o no
t con
fuse
the
inve
rse
func
tion
with
the
reci
proc
al
)(1 x
f. F
or e
xam
ple,
for t
he fu
nctio
n w
here
x
xf
=)
(, t
he re
cipr
ocal
is
x1, w
hile
fo
r
€
x≥0 .
2.
Not
e th
at th
e no
tatio
n is
use
d on
ly fo
r one
-to-o
ne re
latio
n an
d m
ust n
ot b
e
used
for i
nver
ses
of m
any-
to-o
ne re
latio
ns, s
ince
in th
ese
case
s th
e in
vers
es a
re n
ot fu
nctio
ns.
Gr
ad
e 12
: ter
m 1
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
1
Func
tions
:
expo
nent
ial a
nd
loga
rithm
ic
1.
Rev
isio
n of
the
expo
nent
ial f
unct
ion
and
the
expo
nent
ial l
aws
and
grap
h of
the
func
tion
defin
ed b
y w
here
a
nd
2.
Und
erst
and
the
defin
ition
of a
loga
rithm
: ,
whe
re
and
.
3.
The
grap
h of
the
func
tion
defin
ex
yb
log
=
for b
oth
the
case
s 1
0<
<b
and
1
>b
.
Com
men
t:
The
four
loga
rithm
ic la
ws
that
will
be
appl
ied,
onl
y in
the
cont
ext o
f rea
l-life
pro
blem
s
rela
ted
to fi
nanc
e, g
row
th a
nd d
ecay
, are
:
;
;
; a
nd
BA
AB
log
log
log
=.
They
follo
w fr
om th
e ba
sic
expo
nent
ial l
aws
(term
1 o
f gra
de 1
0).
• M
anip
ulat
ion
invo
lvin
g th
e lo
garit
hmic
law
s w
ill n
ot b
e ex
amin
ed.
Cau
tion:
1.
Mak
e su
re le
arne
rs k
now
the
diffe
renc
e be
twee
n th
e tw
o fu
nctio
ns d
efine
d by
x
yb
= a
nd
by
x=
whe
re b
is a
pos
itive
(con
stan
t) re
al n
umbe
r.
2. M
anip
ulat
ion
invo
lvin
g th
e lo
garit
hmic
law
s w
ill n
ot b
e ex
amin
ed.
exam
ples
:
1.
Sol
ve f
orx
:
(R)
2.
Let
x ax
f=)
(,
.0
>a
2.1
Det
erm
ine
aif
the
grap
h of
fgo
es th
roug
h th
e po
int
(R
)
2.2
Det
erm
ine
the
func
tion
.
(R
)
2.3
For
whi
ch v
alue
s of
xis
?
(C)
2.4
Det
erm
ine
the
func
tion
h if
the
grap
h of
h
is th
e re
flect
ion
of th
e gr
aph
of f
thro
ugh
the
y-a
xis.
(C
)
2.5
Det
erm
ine
the
func
tion
kif
the
grap
h of
kis
the
refle
ctio
n of
the
grap
h of
f
thro
ugh
the
x-a
xis.
(C
)
2.6
Det
erm
ine
the
func
tion
p if
the
grap
h of
p
is o
btai
ned
by s
hifti
ng th
e gr
aph
of f
two
units
to th
e le
ft.
(C)
2.7
Writ
e do
wn
the
dom
ain
and
rang
e fo
r eac
h of
the
func
tions
,k
and
p.
(R
)
2.8
Rep
rese
nt a
ll th
ese
func
tions
gra
phic
ally.
(R)
MATHEMATICS GRADES 10-12
42 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 12
: ter
m 1
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2
Fina
nce,
gr
owth
and
de
cay
1.
Sol
ve p
robl
ems
invo
lvin
g pr
esen
t val
ue a
nd
futu
re v
alue
ann
uitie
s.
2.
Mak
e us
e of
loga
rithm
s to
cal
cula
te
the
valu
e of
n, t
he ti
me
perio
d, in
the
equa
tions
ni
PA
)1(+
= o
r.
3.
Crit
ical
ly a
naly
se in
vest
men
t and
loan
op
tions
and
mak
e in
form
ed d
ecis
ions
as
to
best
opt
ion(
s) (i
nclu
ding
pyr
amid
).
Com
men
t:D
eriv
atio
n of
the
form
ulae
for p
rese
nt a
nd fu
ture
val
ues
usin
g th
e ge
omet
ric s
erie
s
form
ula,
sh
ould
be
part
of th
e te
achi
ng p
roce
ss to
ens
ure
that
the
lear
ners
und
erst
and
whe
re th
e fo
rmul
ae c
ome
from
.
The
two
annu
ity fo
rmul
ae:
€
F=x[(1
+i)
n−1]
i a
nd
hol
d on
ly w
hen
paym
ent c
omm
ence
s on
e pe
riod
from
the
pres
ent a
nd e
nds
afte
r n
perio
ds.
Com
men
t: Th
e us
e of
a ti
mel
ine
to a
naly
se p
robl
ems
is a
use
ful t
echn
ique
.
exam
ples
:
Giv
en th
at a
pop
ulat
ion
incr
ease
d fro
m 1
20 0
00 to
214
000
in 1
0 ye
ars,
at w
hat a
nnua
l (c
ompo
und)
rate
did
the
popu
latio
n gr
ow?
(R)
1.
In
orde
r to
buy
a ca
r, Jo
hn ta
kes
out a
loan
of R
25 0
00 fr
om th
e ba
nk. T
he b
ank
char
ges
an
ann
ual i
nter
est r
ate
of 1
1%, c
ompo
unde
d m
onth
ly. T
he in
stal
men
ts s
tart
a m
onth
afte
r he
has
rece
ived
the
mon
ey fr
om th
e ba
nk.
1.1
Cal
cula
te h
is m
onth
ly in
stal
men
ts if
he
has
to p
ay b
ack
the
loan
ove
r a p
erio
d of
5 y
ears
. (
R)
1.2
Cal
cula
te th
e ou
tsta
ndin
g ba
lanc
e of
his
loan
afte
r tw
o ye
ars
(imm
edia
tely
afte
r the
24th
in
stal
men
t).
(C
)
2tr
igon
omet
ry
Com
poun
d an
gle
iden
titie
s:
; ;
;
;
; and
.
2. A
ccep
ting
, der
ive
the
othe
r com
poun
d an
gle
id
entit
ies.
(C
)
3. D
eter
min
e th
e ge
nera
l sol
utio
n of
0co
s2
sin
=+
xx
.
(R
)
4.
Pro
ve th
at
.
(C
)
MATHEMATICS GRADES 10-12
43CAPS
Gr
ad
e 12
: ter
m 1
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
ass
essm
ent t
erm
1:
1.
Inve
stig
atio
n or
pro
ject
. (a
t lea
st 5
0 m
arks
)
onl
y on
e in
vest
igat
ion
or p
roje
ct p
er y
ear i
s re
quire
d.
• e
xam
ple
of a
n in
vest
igat
ion
whi
ch re
vise
s th
e si
ne, c
osin
e an
d ar
ea ru
les:
Gra
de 1
2 In
vest
igat
ion:
Pol
ygon
s w
ith 1
2 M
atch
es
• H
ow m
any
diffe
rent
tria
ngle
s ca
n be
mad
e w
ith a
per
imet
er o
f 12
mat
ches
?
• W
hich
of t
hese
tria
ngle
s ha
s th
e gr
eate
st a
rea?
• W
hat r
egul
ar p
olyg
ons
can
be m
ade
usin
g al
l 12
mat
ches
?
• In
vest
igat
e th
e ar
eas
of p
olyg
ons
with
a p
erim
eter
of 1
2 m
atch
es in
an
effo
rt to
est
ablis
h th
e m
axim
um a
rea
that
can
be
encl
osed
by
the
mat
ches
.
Any
ext
ensi
ons
or g
ener
alis
atio
ns th
at c
an b
e m
ade,
bas
ed o
n th
is ta
sk, w
ill e
nhan
ce y
our i
nves
tigat
ion.
But
you
nee
d to
stri
ve fo
r qua
lity,
rath
er th
an s
impl
y
prod
ucin
g a
larg
e nu
mbe
r of t
rivia
l obs
erva
tions
.
ass
essm
ent:
The
focu
s of
this
task
is o
n m
athe
mat
ical
pro
cess
es. S
ome
of th
ese
proc
esse
s ar
e: s
peci
alis
ing,
cla
ssify
ing,
com
parin
g, in
ferr
ing,
est
imat
ing,
gen
eral
isin
g, m
akin
g
conj
ectu
res,
val
idat
ing,
pro
ving
and
com
mun
icat
ing
mat
hem
atic
al id
eas.
2.
Ass
ignm
ent
or T
est.
(at l
east
50
mar
ks)
3.
Test
. (at
leas
t 50
mar
ks)
MATHEMATICS GRADES 10-12
44 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 12
: ter
m 2
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2tr
igon
omet
ryco
ntin
ued
1.
Sol
ve p
robl
ems
in tw
o an
d th
ree
dim
ensi
ons.
exam
ples
:
a
150°
yx
PQ
R
T
1.
is a
tow
er. I
ts fo
ot,
P, a
nd th
e po
ints
Q a
ndR
are
on
the
sam
e ho
rizon
tal p
lane
.
From
Q th
e an
gle
of e
leva
tion
to th
e to
p of
the
build
ing
is x
. Fur
ther
mor
e,
,
y an
d th
e di
stan
ce b
etw
een
Pan
d R
is a
met
res.
Pro
ve th
at
(C
)
2.
In
, . P
rove
that
:
2.1
Bc
Cb
aco
sco
s+
=w
here
and
.
(R)
2.2
(on
cond
ition
that
).
(P)
2.3
(on
cond
ition
that
).
(P)
2.4
Cb
aB
ac
Ac
bc
ba
cos
)(
cos
)(
cos
)(
++
++
+=
++
.
( P
)
1Fu
nctio
ns:
poly
nom
ials
Fact
oris
e th
ird-d
egre
e po
lyno
mia
ls. A
pply
th
e R
emai
nder
and
Fac
tor T
heor
ems
to
poly
nom
ials
of d
egre
e at
mos
t 3 (n
o pr
oofs
re
quire
d).
Any
met
hod
may
be
used
to fa
ctor
ise
third
deg
ree
poly
nom
ials
but
it s
houl
d in
clud
e ex
ampl
es
whi
ch re
quire
the
Fact
or T
heor
em.
exam
ples
:
1. S
olve
for
:x
(
R)
2. If
is
div
ided
by
, the
rem
aind
er is
.
D
eter
min
e th
e va
lue
of p
.
(P)
MATHEMATICS GRADES 10-12
45CAPS
Gr
ad
e 12
: ter
m 2
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
3d
iffer
entia
lC
alcu
lus
1.
An
intu
itive
und
erst
andi
ng o
f the
lim
it co
ncep
t, i
n th
e co
ntex
t of a
ppro
xim
atin
g th
e ra
te o
f cha
nge
or g
radi
ent o
f a fu
nctio
n at
a p
oint
.
2.
Use
lim
its to
defi
ne th
e de
rivat
ive
of a
func
tion
fat
any
x:
.
Gen
eral
ise
to fi
nd th
e de
rivat
ive
of f
at
any
poin
t x
in th
e do
mai
n of
f, i
.e.,
defin
e
the
deriv
ativ
e fu
nctio
n )
('x
fof
the
func
tion
)(xf
. Und
erst
and
intu
itive
ly th
at
)('af
is
the
grad
ient
of t
he ta
ngen
t to
the
grap
h of
fat
the
poin
t with
x-c
oord
inat
ea
.
3.
Usi
ng th
e de
finiti
on (fi
rst p
rinci
ple)
, fin
d th
e
deriv
ativ
e,
)('x
f fo
r a, b
and
cco
nsta
nts:
3.1
3.2
;
3.3
xax
f=
)(
; an
d
3.3
cx
f=)
(.
Com
men
t: D
iffer
entia
tion
from
firs
t prin
cipl
es w
ill b
e ex
amin
ed o
n an
y of
the
type
s
desc
ribed
in 3
.1, 3
.2 a
nd 3
.3.
exam
ples
:
1.
In e
ach
of th
e fo
llow
ing
case
s, fi
nd th
e de
rivat
ive
of
)(xf
at th
e po
int w
here
, u
sing
th
e de
finiti
on o
f the
der
ivat
ive:
1.1
2)
(2+
=x
xf
(R)
1.2
(R)
1.3
(R)
1.4
(C
)
Cau
tion:
Car
e sh
ould
be
take
n no
t to
appl
y th
e su
m ru
le fo
r diff
eren
tiatio
n 4.
1 in
a s
imila
r way
to p
rodu
cts.
• D
eter
min
e .
• D
eter
min
e .
• W
rite
dow
n yo
ur o
bser
vatio
n.
2. U
se d
iffer
entia
tion
rule
s to
do
the
follo
win
g:
2.1
Det
erm
ine
)('x
f if
(R
)
2.2
Det
erm
ine
)('x
f if
x
xx
f3 )2
()
(+
=
(C
)
(P
)
MATHEMATICS GRADES 10-12
46 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 12
: ter
m 2
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
4.
Use
the
form
ula
(fo
r
a
ny re
al n
umbe
r n) t
oget
her w
ith th
e ru
les
4.1
an
d
4.2
(k a
con
stan
t)
5.
Find
equ
atio
ns o
f tan
gent
s to
gra
phs
of
func
tions
.
6.
Intro
duce
the
seco
nd d
eriv
ativ
e
of
)(xf
and
how
it
dete
rmin
es th
e co
ncav
ity o
f a fu
nctio
n.
7. S
ketc
h gr
aphs
of c
ubic
pol
ynom
ial f
unct
ions
us
ing
diffe
rent
iatio
n to
det
erm
ine
the
co-
ordi
nate
of s
tatio
nary
poi
nts,
and
poi
nts
of in
flect
ion
(whe
re c
onca
vity
cha
nges
). A
lso,
det
erm
ine
the
x-in
terc
epts
of t
he
grap
h us
ing
the
fact
or th
eore
m a
nd o
ther
te
chni
ques
.
8. S
olve
pra
ctic
al p
robl
ems
conc
erni
ng
optim
isat
ion
and
rate
of c
hang
e, in
clud
ing
calc
ulus
of m
otio
n.
2.3
Det
erm
ine
if
(R)
2.4
Det
erm
ine
if
(C
)
3.
Det
erm
ine
the
equa
tion
of th
e ta
ngen
t to
the
grap
h de
fined
by
)2(
)12(
2+
+=
xx
y
whe
re43
=x
.
(C)
4.
Ske
tch
the
grap
h de
fined
by
by:
4.1
findi
ng th
e in
terc
epts
with
the
axes
;
(C
)
4.2
findi
ng m
axim
a, m
inim
a an
d th
e co
-ord
inat
e of
the
poin
t of i
nflec
tion;
(R
)
4.3
look
ing
at th
e be
havi
our o
f y a
s an
d as
.
(P
)
(Rem
embe
r: To
und
erst
and
poin
ts o
f infl
ectio
n, a
n un
ders
tand
ing
of c
onca
vity
is n
eces
sary
. Th
is is
whe
re th
e se
cond
der
ivat
ive
play
s a
role
.)
5.
The
radi
us o
f the
bas
e of
a c
ircul
ar c
ylin
dric
al c
an is
xcm
, and
its
volu
me
is 4
30 c
m3 .
5.1
Det
erm
ine
the
heig
ht o
f the
can
in te
rms
of x
.
(R
)
5.2
Det
erm
ine
the
area
of t
he m
ater
ial n
eede
d to
man
ufac
ture
the
can
(that
is, d
eter
min
e
the
tota
l sur
face
are
a of
the
can)
in te
rms
of x
.
(C)
5.3
Det
erm
ine
the
valu
e of
x fo
r whi
ch th
e le
ast a
mou
nt o
f mat
eria
l is
need
ed to
m
anuf
actu
re s
uch
a ca
n.
(C
)
5.4
If th
e co
st o
f the
mat
eria
l is
R50
0 pe
r m2
, wha
t is
the
cost
of t
he c
heap
est c
an
(labo
ur e
xclu
ded)
?
(P)
MATHEMATICS GRADES 10-12
47CAPS
Gr
ad
e 12
: ter
m 2
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2a
naly
tical
Geo
met
ry1.
Th
e eq
uatio
n d
efine
s
a ci
rcle
with
radi
us r
and
cent
re)
;(
ba
.
2.
Det
erm
inat
ion
of th
e eq
uatio
n of
a ta
ngen
t to
a g
iven
circ
le.
exam
ples
:
1.
Det
erm
ine
the
equa
tion
of th
e ci
rcle
with
cen
tre
and
radi
us6
(K)
2.
Det
erm
ine
the
equa
tion
of th
e ci
rcle
whi
ch h
as th
e lin
e se
gmen
t with
end
poin
ts
)3;5(
and
as d
iam
eter
.
(R
)
3.
Det
erm
ine
the
equa
tion
of a
circ
le w
ith a
radi
us o
f 6
units
, whi
ch in
ters
ects
the
x-a
xis
at
and
the
y-a
xis
at
)3;0(. H
ow m
any
such
circ
les
are
ther
e?
(P
)
4.
Det
erm
ine
the
equa
tion
of th
e ta
ngen
t tha
t tou
ches
the
circ
le d
efine
d by
at
the
poin
t .
(C)
5.
The
line
with
the
equa
tion
2+
=x
yin
ters
ects
the
circ
le d
efine
d by
at
Aan
d B
.
5.1
Det
erm
ine
the
co-o
rdin
ates
of
Aan
d B
.
(R
)
5.2
Det
erm
ine
the
leng
th o
f cho
rd
.
(K
)
5.3
Det
erm
ine
the
co-o
rdin
ates
of
,M
the
mid
poin
t of
.
(K
)
5.4
Sho
w th
at
, whe
re O
is th
e or
igin
.
(
C)
5.5
Det
erm
ine
the
equa
tions
of t
he ta
ngen
ts to
the
circ
le a
t the
poi
nts
A
and
B.
(C
)
5.6
Det
erm
ine
the
co-o
rdin
ates
of t
he p
oint
Cw
here
the
two
tang
ents
in 5
.5 in
ters
ect.
(C
)
5.7
Ver
ify th
at
.
(R)
5.8
Det
erm
ine
the
equa
tions
of t
he tw
o ta
ngen
ts to
the
circ
le, b
oth
para
llel t
o th
e lin
e
with
the
equa
tion
.
(P)
3m
id-y
ear
exam
inat
ions
ass
essm
ent t
erm
2:
1. A
ssig
nmen
t (at
leas
t 50
mar
ks)
2. e
xam
inat
ion
(300
mar
ks)
MATHEMATICS GRADES 10-12
48 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 12
ter
m 3
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2eu
clid
ean
Geo
met
ry
1. R
evis
e ea
rlier
wor
k on
the
nece
ssar
y an
d su
ffici
ent c
ondi
tions
for p
olyg
ons
to b
e si
mila
r. 2.
Pro
ve (a
ccep
ting
resu
lts e
stab
lishe
d in
ea
rlier
gra
des)
:•
that
a li
ne d
raw
n pa
ralle
l to
one
side
of
a tr
iang
le d
ivid
es th
e ot
her t
wo
side
s pr
opor
tiona
lly (a
nd th
e M
id-p
oint
Th
eore
m a
s a
spec
ial c
ase
of th
is
theo
rem
) ;•
that
equ
iang
ular
tria
ngle
s ar
e si
mila
r;•
that
tria
ngle
s w
ith s
ides
in p
ropo
rtion
are
si
mila
r; an
d •
the
Pyt
hago
rean
The
orem
by
sim
ilar
trian
gles
.
exam
ple:
Con
side
r a ri
ght t
riang
le A
BC
with
. L
et
and
.
Let
Dbe
on
suc
h th
at
. Det
erm
ine
the
leng
th o
f in
term
s of
aan
d c
.
(P)
1st
atis
tics
(reg
ress
ion
and
corr
elat
ion)
1. R
evis
e sy
mm
etric
and
ske
wed
dat
a.2.
U
se s
tatis
tical
sum
mar
ies,
sca
tterp
lots
, re
gres
sion
(in
parti
cula
r the
leas
t squ
ares
re
gres
sion
line
) and
cor
rela
tion
to a
naly
se
and
mak
e m
eani
ngfu
l com
men
ts o
n th
e co
ntex
t ass
ocia
ted
with
giv
en b
ivar
iate
da
ta, i
nclu
ding
inte
rpol
atio
n, e
xtra
pola
tion
and
disc
ussi
ons
on s
kew
ness
.
exam
ple:
The
follo
win
g ta
ble
sum
mar
ises
the
num
ber o
f rev
olut
ions
x (p
er m
inut
e) a
nd th
e co
rres
pond
ing
pow
er o
utpu
t y (h
orse
pow
er) o
f a D
iese
l eng
ine:
x40
050
060
070
075
0
y58
010
3014
2018
8021
00
1. F
ind
the
leas
t squ
ares
regr
essi
on li
ne
(K)
2. U
se th
is li
ne to
est
imat
e th
e po
wer
out
put w
hen
the
engi
ne ru
ns a
t 800
m.
(R
)3.
Rou
ghly
how
fast
is th
e en
gine
runn
ing
whe
n it
has
an o
utpu
t of 1
200
hors
e po
wer
?
(R
)
MATHEMATICS GRADES 10-12
49CAPS
Gr
ad
e 12
ter
m 3
no.
of
Wee
ksto
pic
Cur
ricul
um s
tate
men
tClarifi
catio
n
2C
ount
ing
and
prob
abili
ty
1. R
evis
e:•
depe
nden
t and
inde
pend
ent e
vent
s;•
the
prod
uct r
ule
for i
ndep
ende
nt e
vent
s:
P(A
and
B) =
P(A
) × P
(B).
•th
e su
m ru
le fo
r mut
ually
exc
lusi
ve
even
ts A
and
B:
AP
(or
)
()
()
BP
AP
B+
=
•th
e id
entit
y:
AP
(or
an
d)
B
•th
e co
mpl
emen
tary
rule
:
(P
not
2. p
roba
bilit
y pr
oble
ms
usin
g Ve
nn d
iagr
ams,
tre
es, t
wo-
way
con
tinge
ncy
tabl
es a
nd
othe
r tec
hniq
ues
(like
the
fund
amen
tal
coun
ting
prin
cipl
e) to
sol
ve p
roba
bilit
y pr
oble
ms
(whe
re e
vent
s ar
e no
t nec
essa
rily
inde
pend
ent).
3. A
pply
the
fund
amen
tal c
ount
ing
prin
cipl
e to
so
lve
prob
abili
ty p
robl
ems.
exam
ples
:1.
How
man
y th
ree-
char
acte
r cod
es c
an b
e fo
rmed
if th
e fir
st c
hara
cter
mus
t be
a le
tter a
nd
the
seco
nd tw
o ch
arac
ters
mus
t be
digi
ts?
(K
) 2.
Wha
t is
the
prob
abili
ty th
at a
rand
om a
rran
gem
ent o
f the
lette
rs B
AFA
NA
star
ts a
nd e
nds
w
ith a
n ‘A
’?
(R
)3.
A d
raw
er c
onta
ins
twen
ty e
nvel
opes
. Eig
ht o
f the
env
elop
es e
ach
cont
ain
five
blue
and
th
ree
red
shee
ts o
f pap
er. T
he o
ther
twel
ve e
nvel
opes
eac
h co
ntai
n si
x bl
ue a
nd tw
o re
d
shee
ts o
f pap
er. o
ne e
nvel
ope
is c
hose
n at
rand
om. A
she
et o
f pap
er is
cho
sen
at ra
ndom
fro
m it
. Wha
t is
the
prob
abili
ty th
at th
is s
heet
of p
aper
is re
d?
(C)
4. A
ssum
ing
that
it is
equ
ally
like
ly to
be
born
in a
ny o
f the
12
mon
ths
of th
e ye
ar, w
hat i
s th
e pr
obab
ility
that
in a
gro
up o
f six
, at l
east
two
peop
le h
ave
birth
days
in th
e sa
me
mon
th?
(P
)
3ex
amin
atio
ns /
r
evis
ion
ass
essm
ent t
erm
3:
1. T
est (
at l
east
50
mar
ks)
2. P
relim
inar
y ex
amin
atio
ns (
300
mar
ks)
impo
rtan
t:Ta
ke n
ote
that
at l
east
one
of t
he e
xam
inat
ions
in te
rms
2 an
d 3
mus
t con
sist
of t
wo
thre
e-ho
ur p
aper
s w
ith th
e sa
me
or v
ery
sim
ilar s
truct
ure
to th
e fin
al N
SC
pap
ers.
The
oth
er
exam
inat
ion
can
be re
plac
ed b
y te
sts
on re
leva
nt s
ectio
ns.
MATHEMATICS GRADES 10-12
50 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 12
: ter
m 4
no
ofW
eeks
topi
cC
urric
ulum
sta
tem
ent
Clarifi
catio
n
3r
evis
ion
6ex
amin
atio
ns
ass
essm
ent t
erm
4:
Fina
l exa
min
atio
n:Pa
per 1
: 150
mar
ks: 3
hou
rs
P
aper
2: 1
50 m
arks
: 3 h
ours
Pat
tern
s an
d se
quen
ces
(2
5±3)
e
uclid
ean
Geo
met
ry a
nd M
easu
rem
ent
(50
±3)
Fina
nce,
gro
wth
and
dec
ay
(15
±3)
A
naly
tical
Geo
met
ry
(40±
3)
Func
tions
and
gra
phs
(35±
3)
Sta
tistic
s an
d re
gres
sion
(2
0±3)
Alg
ebra
and
equ
atio
ns
(2
5±3)
T
rigon
omet
ry
(40±
3)
Cal
culu
s
(35±
3)
Pro
babi
lity
(15±
3)
MATHEMATICS GRADES 10-12
51CAPS
SeCTIoN 4
4.1 introduction
assessment is a continuous planned process of identifying, gathering and interpreting information about the performance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence of achievement; evaluating this evidence; recording the findings and using this information to understand and assist in the learner’s development to improve the process of learning and teaching.
Assessment should be both informal (Assessment for Learning) and formal (Assessment of Learning). In both cases regular feedback should be provided to learners to enhance the learning experience.
Although assessment guidelines are included in the Annual Teaching Plan at the end of each term, the following general principles apply:
1. Tests and examinations are assessed using a marking memorandum.
2. Assignments are generally extended pieces of work completed at home. They can be collections of past examination questions, but should focus on the more demanding aspects as any resource material can be used, which is not the case when a task is done in class under strict supervision.
3. At most one project or assignment should be set in a year. The assessment criteria need to be clearly indicated on the project specification. The focus should be on the mathematics involved and not on duplicated pictures and regurgitation of facts from reference material. The collection and display of real data, followed by deductions that can be substantiated from the data, constitute good projects.
4. Investigations are set to develop the skills of systematic investigation into special cases with a view to observing general trends, making conjecures and proving them. To avoid having to assess work which is copied without understanding, it is recommended that while the initial investigation can be done at home, the final write up should be done in class, under supervision, without access to any notes. Investigations are marked using rubrics which can be specific to the task, or generic, listing the number of marks awarded for each skill:
• 40% for communicating individual ideas and discoveries, assuming the reader has not come across the text before. The appropriate use of diagrams and tables will enhance the investigation.
• 35% for the effective consideration of special cases;
• 20% for generalising, making conjectures and proving or disproving these conjectures; and
• 5% for presentation: neatness and visual impact.
4.2 informal or daily assessment
the aim of assessment for learning is to collect continually information on a learner’s achievement that can be used to improve individual] learning.
Informal assessment involves daily monitoring of a learner’s progress. This can be done through observations, discussions, practical demonstrations, learner-teacher conferences, informal classroom interactions, etc. Although informal assessment may be as simple as stopping during the lesson to observe learners or to discuss with learners
MATHEMATICS GRADES 10-12
52 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
how learning is progressing. Informal assessment should be used to provide feedback to the learners and to inform planning for teaching, it need not be recorded. This should not be seen as separate from learning activities taking place in the classroom. Learners or teachers can evaluate these tasks.
Self assessment and peer assessment actively involve learners in assessment. Both are important as these allow learners to learn from and reflect on their own performance. Results of the informal daily assessment activities are not formally recorded, unless the teacher wishes to do so. The results of daily assessment tasks are not taken into account for promotion and/or certification purposes.
4.3 Formal assessment
All assessment tasks that make up a formal programme of assessment for the year are regarded as Formal Assessment. Formal assessment tasks are marked and formally recorded by the teacher for progress and certification purposes. All Formal Assessment tasks are subject to moderation for the purpose of quality assurance.
Formal assessments provide teachers with a systematic way of evaluating how well learners are progressing in a grade and/or in a particular subject. examples of formal assessments include tests, examinations, practical tasks, projects, oral presentations, demonstrations, performances, etc. Formal assessment tasks form part of a year-long formal Programme of Assessment in each grade and subject.Formal assessments in Mathematics include tests, a June examination, a trial examination(for Grade 12), a project or an investigation.
The forms of assessment used should be age- and developmental- level appropriate. The design of these tasks should cover the content of the subject and include a variety of activities designed to achieve the objectives of the subject.
Formal assessments need to accommodate a range of cognitive levels and abilities of learners as shown below:
MATHEMATICS GRADES 10-12
53CAPS
4.4
Prog
ram
me
of a
sses
smen
t
The
four
cog
nitiv
e le
vels
use
d to
gui
de a
ll as
sess
men
t tas
ks a
re b
ased
on
thos
e su
gges
ted
in th
e TI
MS
S s
tudy
of 1
999.
Des
crip
tors
for e
ach
leve
l and
the
appr
oxim
ate
perc
enta
ges
of ta
sks,
test
s an
d ex
amin
atio
ns w
hich
sho
uld
be a
t eac
h le
vel a
re g
iven
bel
ow:
Cog
nitiv
e le
vels
des
crip
tion
of s
kills
to b
e de
mon
stra
ted
exam
ples
kno
wle
dge 20
%
•S
traig
ht re
call
•Id
entifi
catio
n of
cor
rect
form
ula
on th
e in
form
atio
n sh
eet (
no c
hang
ing
of th
e su
bjec
t)
Use
of m
athe
mat
ical
fact
s
•A
ppro
pria
te u
se o
f mat
hem
atic
al v
ocab
ular
y
1. W
rite
dow
n th
e do
mai
n of
the
func
tion
(Gra
de 1
0)
2. T
he a
ngle
ˆ
AO
Bsu
bten
ded
by a
rc A
Bat
the
cent
re o
of a
circ
le
......
.
rou
tine
Proc
edur
es
35%
•e
stim
atio
n an
d ap
prop
riate
roun
ding
of n
umbe
rs
•P
roof
s of
pre
scrib
ed t
heor
ems
and
deriv
atio
n of
form
ulae
•Id
entifi
catio
n an
d d
irect
use
of c
orre
ct fo
rmul
a on
the
info
rmat
ion
shee
t (no
cha
ngin
g of
the
subj
ect)
•P
erfo
rm w
ell k
now
n pr
oced
ures
•S
impl
e ap
plic
atio
ns a
nd c
alcu
latio
ns w
hich
mig
ht in
volv
e fe
w s
teps
•D
eriv
atio
n fro
m g
iven
info
rmat
ion
may
be
invo
lved
•Id
entifi
catio
n an
d u
se (a
fter c
hang
ing
the
subj
ect)
of c
orre
ct fo
rmul
a
•G
ener
ally
sim
ilar t
o th
ose
enco
unte
red
in c
lass
1.
Sol
ve fo
r
(Gra
de 1
0)
2.
Det
erm
ine
the
gene
ral s
olut
ion
of th
e eq
uatio
n
(
Gra
de 1
1)
2.
Pro
ve th
at th
e an
gle
ˆA
OB
subt
ende
d by
arc
AB
at th
e ce
ntre
o
of a
circ
le is
dou
ble
the
size
of t
he a
ngle
ˆA
CB
whi
ch th
e sa
me
arc
subt
ends
at t
he c
ircle
.
(G
rade
11)
Com
plex
Pro
cedu
res
30%
•P
robl
ems
invo
lve
com
plex
cal
cula
tions
and
/or h
ighe
r ord
er re
ason
ing
•Th
ere
is o
ften
not a
n ob
viou
s ro
ute
to th
e so
lutio
n
•P
robl
ems
need
not
be
base
d on
a re
al w
orld
con
text
•C
ould
invo
lve
mak
ing
sign
ifica
nt c
onne
ctio
ns b
etw
een
diffe
rent
re
pres
enta
tions
•R
equi
re c
once
ptua
l und
erst
andi
ng
1.
Wha
t is
the
aver
age
spee
d co
vere
d on
a ro
und
trip
to a
nd fr
om
a de
stin
atio
n if
the
aver
age
spee
d go
ing
to th
e de
stin
atio
n is
a
nd th
e av
erag
e sp
eed
for t
he re
turn
jour
ney
is
(G
rade
11)
2.
Diff
eren
tiate
x
x2 )2
(+
with
resp
ect t
o x.
(Gra
de 1
2)
Prob
lem
sol
ving
15%
•N
on-r
outin
e pr
oble
ms
(whi
ch a
re n
ot n
eces
saril
y di
fficu
lt)
•H
ighe
r ord
er re
ason
ing
and
proc
esse
s ar
e in
volv
ed
•M
ight
requ
ire th
e ab
ility
to b
reak
the
prob
lem
dow
n in
to it
s co
nstit
uent
pa
rts
Sup
pose
a p
iece
of w
ire c
ould
be
tied
tight
ly a
roun
d th
e ea
rth a
t the
eq
uato
r. Im
agin
e th
at th
is w
ire is
then
leng
then
ed b
y ex
actly
one
met
re
and
held
so
that
it is
stil
l aro
und
the
earth
at t
he e
quat
or. W
ould
a m
ouse
be
abl
e to
cra
wl b
etw
een
the
wire
and
the
earth
? W
hy o
r why
not
?
(A
ny g
rade
)
The
Pro
gram
me
of A
sses
smen
t is
desi
gned
to s
et fo
rmal
ass
essm
ent t
asks
in a
ll su
bjec
ts in
a s
choo
l thr
ough
out t
he y
ear.
MATHEMATICS GRADES 10-12
54 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
a)
num
ber o
f ass
essm
ent t
asks
and
Wei
ghtin
g:
Lear
ners
are
exp
ecte
d to
hav
e se
ven
(7) f
orm
al a
sses
smen
t tas
ks fo
r the
ir sc
hool
-bas
ed a
sses
smen
t. Th
e nu
mbe
r of t
asks
and
thei
r wei
ghtin
g ar
e lis
ted
belo
w:
Gr
ad
e 10
Gr
ad
e 11
Gr
ad
e 12
task
sW
eiG
Ht
(%)
task
sW
eiG
Ht
(%)
task
sW
eiG
Ht
(%)
school-based assessment
term
1
Proj
ect /
inve
stig
atio
nte
st20 10
Proj
ect /
inve
stig
atio
nte
st20 10
test
Proj
ect /
inve
stig
atio
na
ssig
nmen
t
10 20 10
term
2a
ssig
nmen
t/tes
tm
id-y
ear e
xam
inat
ion
10 30a
ssig
nmen
t/tes
tm
id-y
ear e
xam
inat
ion
10 30te
stm
id-y
ear e
xam
inat
ion
10 15
term
3te
stte
st10 10
test
test
10 10te
sttr
ial e
xam
inat
ion
10 25
term
4te
st10
test
10
scho
ol-b
ased
a
sses
smen
t mar
k 10
010
010
0
scho
ol-b
ased
a
sses
smen
t m
ark
(as
% o
f pr
omot
ion
mar
k)
25%
25%
25%
end-
of-y
ear
exam
inat
ions
75%
75%
Prom
otio
n m
ark
100%
100%
not
e:•
Alth
ough
the
proj
ect/i
nves
tigat
ion
is in
dica
ted
in th
e fir
st te
rm, i
t cou
ld b
e sc
hedu
led
in te
rm 2
. Onl
y o
ne
proj
ect/i
nves
tigat
ion
shou
ld b
e se
t per
yea
r.•
Test
s sh
ould
be
at le
ast o
Ne
hou
r lon
g an
d co
unt a
t lea
st 5
0 m
arks
.•
Pro
ject
or i
nves
tigat
ion
mus
t con
tribu
te 2
5% o
f ter
m 1
mar
ks w
hile
the
test
mar
ks c
ontri
bute
75%
of t
he te
rm 1
mar
ks.
The
com
bina
tion
(25%
and
75%
) of t
he m
arks
mus
t app
ear i
n th
e le
arne
r’s re
port.
•N
one
grap
hic
and
none
pro
gram
mab
le c
alcu
lato
rs a
re a
llow
ed (f
or e
xam
ple,
to fa
ctor
ise
, or t
o fin
d ro
ots
of e
quat
ions
) will
be
allo
wed
. Cal
cula
tors
sho
uld
only
be
use
d to
per
form
sta
ndar
d nu
mer
ical
com
puta
tions
and
to v
erify
cal
cula
tions
by
hand
.•
Form
ulasheetm
ustn
otbeprovidedfo
rtestsand
forfi
nalexaminationsinGrades10and
11.
MATHEMATICS GRADES 10-12
55CAPS
b) examinations:
In Grades 10, 11 and 12, 25% of the final promotion mark is a year mark and 75% is an examination mark.
All assessments in Grade 10 and 11 are internal while in Grade 12 the 25% year mark assessment is internally set and marked but externally moderated and the 75% examination is externally set, marked and moderated.
Mark distribution for Mathematics NCS end-of-year papers: Grades 10-12
PAPeR 1: Grades 12: bookwork: maximum 6 marks
description Grade 10 Grade 11 Grade. 12
Algebra and equations (and inequalities) 30 ± 3 45 ± 3 25 ± 3
Patterns and sequences 15 ± 3 25 ± 3 25 ± 3
Finance and growth 10 ± 3
Finance, growth and decay 15 ± 3 15 ± 3
Functions and graphs 30 ± 3 45 ± 3 35 ± 3
Differential Calculus 35 ± 3
Probability 15 ± 3 20 ± 3 15 ± 3
total 100 150 150
PaPer 2: Grades 11 and 12: theorems and/or trigonometric proofs: maximum 12 marks
description Grade 10 Grade 11 Grade 12
Statistics 15 ± 3 20 ± 3 20 ± 3
Analytical Geometry 15 ± 3 30 ± 3 40 ± 3
Trigonometry 40 ± 3 50 ± 3 40 ± 3
euclidean Geometry and Measurement 30 ± 3 50 ± 3 50 ± 3
total 100 150 150
note: • Modelling as a process should be included in all papers, thus contextual questions can be set on any topic.
• Questions will not necessarily be compartmentalised in sections, as this table indicates. Various topics can be integrated in the same question.
• FormulasheetmustnotbeprovidedfortestsandforfinalexaminationsinGrades10and11.
4.5 recording and reporting
• Recording is a process in which the teacher is able to document the level of a learner’s performance in a specific assessment task.
- It indicates learner progress towards the achievement of the knowledge as prescribed in the Curriculum and Assessment Policy Statements.
- Records of learner performance should provide evidence of the learner’s conceptual progression within a grade and her / his readiness to progress or to be promoted to the next grade.
- Records of learner performance should also be used to monitor the progress made by teachers and learners in the teaching and learning process.
• Reporting is a process of communicating learner performance to learners, parents, schools and other stakeholders. Learner performance can be reported in a number of ways.
MATHEMATICS GRADES 10-12
56 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
- These include report cards, parents’ meetings, school visitation days, parent-teacher conferences, phone calls, letters, class or school newsletters, etc.
- Teachers in all grades report percentages for the subject. Seven levels of competence have been described for each subject listed for Grades R-12. The individual achievement levels and their corresponding percentage bands are shown in the Table below.
Codes and PerCentaGes For reCordinG and rePortinG
ratinG Code desCriPtion oF ComPetenCe PerCentaGe
7 outstanding achievement 80 – 100
6 Meritorious achievement 70 – 79
5 Substantial achievement 60 – 69
4 Adequate achievement 50 – 59
3 Moderate achievement 40 – 49
2 elementary achievement 30 – 39
1 Not achieved 0 - 29
note: the seven-point scale should have clear descriptors that give detailed information for each level.
teachers will record actual marks for the task on a record sheet; and indicate percentages for each subject on the learners’ report cards.
4.6 moderation of assessment
Moderation refers to the process that ensures that the assessment tasks are fair, valid and reliable. Moderation should be implemented at school, district, provincial and national levels. Comprehensive and appropriate moderation practices must be in place to ensure quality assurance for all subject assessments.
4.7 General
This document should be read in conjunction with:
4.7.1 National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R – 12; and
4.7.2 The policy document, National Protocol for Assessment Grades R – 12.
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