TECHNICAL MATHEMATICS
National Curriculum Statement (NCS)
Curriculum Assessment
Policy Statement
GRADES 10 – 12
CURRICULUM AND ASSESSMENT POLICY
STATEMENT (CAPS)
GRADES 10 – 12
TECHNICAL MATHEMATICS
CAPS
TECHNICAL MATHEMATICS
1
DISCLAIMER
In view of the stringent time requirements encountered by the Department of Basic Education to effect the necessary
editorial changes and layout adjustments to the Curriculum and Assessment Policy Statements and the supplementary
policy documents, possible errors may have occurred in the said documents placed on the official departmental website.
If any editorial, layout, content, terminology or formulae inconsistencies are detected, the user is kindly requested to
bring this to the attention of the Department of Basic Education.
E-mail: capscomments@dbe.gov.za or fax (012) 328 9828
Department of Basic Education
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Private Bag X895
Pretoria 0001
South Africa
Tel: +27 12 357 3000
Fax: +27 12 323 0601
120 Plein Street Private Bag X9023
Cape Town 8000
South Africa
Tel: +27 21 465 1701
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© 2014 Department of Basic Education
ISBN: 978- 4315-0573-9
Design and Layout by:
Printed by: Government Printing Works
2
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
FOREWORD BY THE MINISTER
Our national curriculum is the culmination of our efforts over a period of seventeen
years to transform the curriculum bequeathed to us by apartheid. From the start of
democracy we have built our curriculum on the values that inspired our Constitution
(Act 108 of 1996). The Preamble to the Constitution states that the aims of the
Constitution are to:
•
heal the divisions of the past and establish a society based on democratic
values, social justice and fundamental human rights;
•
improve the quality of life of all citizens and free the potential of each person;
•
lay the foundations for a democratic and open society in which government is
based on the will of the people and every citizen is equally protected by law; and
•
build a united and democratic South Africa able to take its rightful place as a
sovereign state in the family of nations.
Education and the curriculum have an important role to play in realising these aims.
In 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience
of implementation prompted a review in 2000. This led to the first curriculum revision: the Revised National Curriculum
Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).
Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National Curriculum
Statement (2002) to produce this document.
From 2012 the two 2002 curricula, for Grades R-9 and Grades 10-12 respectively, are combined in a single document
and will simply be known as the National Curriculum Statement Grades R-12. The National Curriculum Statement for
Grades R-12 builds on the previous curriculum but also updates it and aims to provide clearer specification of what is 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
CAPS
TECHNICAL MATHEMATICS
3
CONTENTS
SECTION 1:
INTRODUCTION TO THE CURRICULUM AND ASSESSMENT POLICY STATEMENTS
FOR TECHNICAL MATHEMATICS GRADE 10 - 12 TECHNICAL MATHEMATICS
6
1.1
Background
6
1.2
Overview
6
1.3
General Aims of the South African Curriculum
7
1.4
Time Allocation
8
1.4.1
Foundation Phase
8
1.4.2
Intermediate Phase
8
1.4.3
Senior Phase
9
1.4.4
Grades 10 – 12
9
FET TECHNICAL MATHEMATICS INTRODUCTION
10
SECTION 2:
2.1
What is Technical Mathematics?
10
2.2
Specific Aims of Technical Mathematics
10
2.3
Specific Skills
11
2.4
Focus of Content Areas
11
2.5
Weighting of Content Areas
11
SECTION 3:
3.1
3.2
FET TECHNICAL MATHEMATICS CONTENT SPECIFICATION AND CLARIFICATION
13
Specification of Content to show Progression
13
3.1.1
14
Overview of topics
Content Clarification with teaching guidelines
19
3.2.1
Allocation of Teaching Time
20
3.2.2
Sequencing and Pacing of Topics
22
3.2.3
Topic allocation per term and clarification
24
FET TECHNICAL MATHEMATICS ASSESSMENT GUIDELINES
46
SECTION 4:
4.1
Introduction
46
4.2
Informal or Daily Assessment
47
4.3
Formal Assessment
47
4
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
4.4
Programme of Assessment
48
4.5
Recording and Reporting
50
4.6
Moderation of Assessment
51
4.7
General
51
4.7.1
National policy pertaining to the programme and promotion requirements of the National
Curriculum Statement Grades R – 12; and
51
4.7.2
The policy document, National Protocol for Assessment Grades R – 12.
51
CAPS
TECHNICAL MATHEMATICS
5
SECTION 1
INTRODUCTION TO THE CURRICULUM AND ASSESSMENT POLICY STATEMENTS FOR TECHNICAL
MATHEMATICS GRADE 10 - 12
TECHNICAL MATHEMATICS
1.1Background
The National Curriculum Statement Grades R – 12 (NCS) stipulates policy on curriculum and assessment in the
schooling sector. To improve its implementation, the National Curriculum Statement was amended, with the amendments
coming into effect in January 2012. A single comprehensive National Curriculum and Assessment Policy Statement
was developed for each subject to replace the old Subject Statements, Learning Programme Guidelines and Subject
Assessment Guidelines in Grades R – 12.
The amended National Curriculum and Assessment Policy Statements (January 2012) replace the National Curriculum
Statements Grades R – 9 (2002) and the National Curriculum Statements Grades 10 – 12 (2004).
1.2Overview
(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:
National Curriculum and Assessment Policy statements for each approved school subject as listed in the policy document,
and the National policy pertaining to the programme and promotion requirements of the National Curriculum Statement
Grades R – 12, which replaces the following policy documents:
(i)
National Senior Certificate: A qualification at Level 4 on the National Qualifications Framework (NQF); and
(ii)
An addendum to the policy document, the National Senior Certificate: A qualification at Level 4 on the National
Qualifications Framework (NQF), for learners with special needs, published in the Government Gazette, No.29466 of
11 December 2006.
(b)
The National Curriculum Statement Grades R – 12 (January 2012) should be read in conjunction with the
National Protocol for Assessment Grade R – 12, which replaces the policy document, An addendum to the policy
document, the National Senior Certificate: A qualification at Level 4 on the National Qualifications Framework
(NQF), for the National Protocol for Assessment Grade R – 12, published in the Government Gazette, No. 29467
of 11 December 2006.
(c)
The Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines for Grades R
– 9 and Grades 10 – 12 have been repealed and replaced by the National Curriculum and Assessment Policy
Statements for Grades R – 12 (January 2012).
(d)
The sections on the Curriculum and Assessment Policy as discussed in Chapters 2, 3 and 4 of this document
constitute the norms and standards of the National Curriculum Statement Grades R – 12. Therefore, in terms of
section 6A of the South African Schools Act, 1996 (Act No. 84 of 1996,) this forms the basis on which the Minister
of Basic Education will determine minimum outcomes and standards, as well as the processes and procedures
for the assessment of learner achievement, that will apply in public and independent schools.
6
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
1.3
General Aims of the South African Curriculum
(a)
The National Curriculum Statement Grades R – 12 spells out what is regarded as knowledge, skills and values
worth learning. It will ensure that children acquire and apply knowledge and skills in ways that are meaningful to
their own lives. In this regard, the curriculum promotes the idea of grounding 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 competencies.
(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 our 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: specifying the minimum standards of knowledge and skills to be achieved at each
grade setting high, achievable standards in all subjects;
•
progression: showing progression from simple to complex in the content and context of each grade;
•
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 10 – 12 (General) is sensitive to issues of diversity such as poverty,
inequality, race, gender, language, age, disability and other factors.)
•
value of 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 efficiently;
•
collect, analyse, organise and evaluate information critically;
•
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.
CAPS
TECHNICAL MATHEMATICS
7
(e)
Inclusivity should be a central part of the organisation, planning and teaching at each school. This can only occur
if all teachers have the capacity to recognise and address barriers to learning, and to plan for diversity. The key to
managing inclusivity is to ensure 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 employ
various curriculum differentiation strategies such as those contained in the Department of Basic Education’s
Guidelines for Inclusive Teaching and Learning (2010).
1.4
Time Allocation
1.4.1 Foundation Phase
(a)
The instructional time for each subject in the Foundation Phase is indicated in the table below:
Subject
i.
ii.
iii.
Time allocation per week (hours)
Languages (FAL and HL)
Mathematics
Life Skills
•
Beginning Knowledge
•
Creative Arts
•
Physical Education
•
Personal and Social Well-being
10 (11)
7
6 (7)
1 (2)
2
2
1
(b)
Total instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.
(c)
To Languages 10 hours are allocated in Grades R – 2 and 11 hours in Grade 3. A maximum of 8 hours and a
minimum of 7 hours are allocated to Home Language and a minimum of 2 hours and a maximum of 3 hours to
First Additional Language in Grades R – 2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are
allocated to Home Language and a minimum of 3 hours and a maximum of 4 hours to First Additional Language.
(d)
To Life Skills Beginning Knowledge 1 hour is allocated in Grades R – 2 and 2 hours are allocated for Grade 3 as
indicated by the hours in brackets.
1.4.2 Intermediate Phase
(a)
The table below shows the subjects and instructional times allocated to each in the Intermediate Phase.
Subject
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
Time allocation per week (hours)
Home Language
First Additional Language
Mathematics
Science and Technology
Social Sciences
Life Skills
Creative Arts
Physical Education
Religious Studies
8
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
6
5
6
3.5
3
4
1.5
1.5
1
1.4.3 Senior Phase
(a)
The instructional time for each subject in the Senior Phase is allocated as follows:
Subject
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
Time allocation per week (hours)
Home Language
First Additional Language
Mathematics
Natural Sciences
Social Sciences
Technology
Economic Management Sciences
Life Orientation
Arts and Culture
5
4
4.5
3
3
2
2
2
2
1.4.4 Grades 10 – 12
(a)
The instructional time for each subject in Grades 10 – 12 is allocated as follows:
Subject
i.
ii.
iii.
iv.
v.
vi.
vii.
Home Language
First Additional Language
Mathematics
Technical Mathematics
Mathematical Literacy
Life Orientation
Three Electives
Time allocation per week (hours)
4.5
4.5
4.5
4.5
4.5
2
12 (3x4h)
The allocated time per week may be utilised only for the minimum number of 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 has to be allocated in order to offer these subjects.
CAPS
TECHNICAL MATHEMATICS
9
Section 2
Curriculum and Assessment Policy Statement (CAPS)
FET TECHNICAL MATHEMATICS
Introduction
In Section 2, the Further Education and Training (FET) Phase Technical Mathematics CAPS provides teachers with a
definition of Technical Mathematics, specific aims, specific skills focus of content areas, and the weighting of content
areas.
2.1 What is Technical Mathematics?
Mathematics is a universal science 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, teaches us to think creatively. The aim of Technical Mathematics is to apply the Science of Mathematics to the
Technical field where the emphasis is on APPLICATION andnot on abstract ideas.
2.2 Specific Aims of Technical Mathematics
1.
To apply mathematical principles.
2.
To develop fluency in computation skills with the usage of calculators.
3.
Mathematical modelling is an important focal point of the curriculum. Real life technical 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.
4.
To provide the opportunity to develop in learners the ability to be methodical, to generalize and to be skilful users
of the Science of Mathematics.
5.
To be able to understand and work with the number system.
6.
To promote accessibility of Mathematical content to all learners. This could be achieved by catering for learners
with different needs, e.g. TECHNICAL 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.
8.
To provide learners at Technical schools an alternative and value adding substitute to Mathematical Literacy.
9.
To support and sustain technical subjects at Technical schools.
10.
Technical Mathematics can only be taken by learners offering a Technical subject (mechanical, civil and electrical
engineering).
11.
To provide a vocational route aligned with the expectations of labour in order to ensure direct access to learnership/
apprenticeship.
10
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
12.
To create the opportunity for learners to further their studies at FET Colleges at an entrance level of N-4 and thus
creating an alternative route to access other HEIs.
2.3
Specific Skills
To develop essential mathematical skills the learner should:
•
develop the correct use of the language of Mathematics;
•
use mathematical process skills to identify and solve problems.
•
use spatial skills and properties of shapes and objects to identify, pose and solve problems creatively and critically;
•
participate as responsible citizens in the technical environment locally, as well as in national and global
communities; and
•
communicate appropriately by using descriptions in words, graphs, symbols, tables and diagrams.
2.4
Focus of Content Areas
Technical 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.
1.
Number system
2.
Functions and graphs
3.
Finance, growth and decay
4.
Algebra
5.
Differential Calculus
6.
Euclidean Geometry
7.
Mensuration
8.
Circles, angles and angular movement
9.
Analytical Geometry
10.
Trigonometry
Main topics for Technical Mathematics:
2.5 Weighting of Content Areas
The weighting of Technical 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).
CAPS
TECHNICAL MATHEMATICS
11
Weighting of Content Areas
Description
Grade 10
Grade 11
Grade 12
Algebra ( Expressions, equations and
inequalities including nature of roots in Grades 11 & 12)
60 ± 3
90 ± 3
50 ± 3
Functions & Graphs (excluding trig. functions)
25 ± 3
45 ± 3
35 ± 3
Finance, growth and decay
15 ± 3
15 ± 3
15 ± 3
PAPER 1
Differential Calculus and Integration
TOTAL
50 ± 3
100
150
150
Grade 10
Grade 11
Grade 12
Analytical Geometry
15 ± 3
25 ± 3
25 ± 3
Trigonometry (including trig. functions)
40 ± 3
50 ± 3
50 ± 3
Euclidean Geometry
30 ± 3
40 ± 3
40 ± 3
Mensuration, circles, angles and angular movement
15 ± 3
35 ± 3
35 ± 3
100
150
150
PAPER 2 :
Description
TOTAL
2.6 Technical Mathematics in the FET
The subject Technical Mathematics in the Further Education and Training Phase forms the link between the Senior
Phase and the Higher Education band. All learners passing through this phase acquire a functioning knowledge of
Technical Mathematics that empowers them to make sense of their Technical field of study and their place in society.
It ensures access to an extended study of the technical mathematical sciences and a variety of technical career paths.
In the FET Phase, learners should be exposed to technical mathematical experiences that give them many opportunities
to develop their mathematical reasoning and creative skills in preparation for more applied mathematics in HEIs or in-job
training.
12
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Section 3
Curriculum and Assessment Policy Statement (CAPS)
FET TECHNICAL MATHEMATICS Content Specification and Clarification
Introduction
Section 3 provides teachers with:
•
Specification of content to show progression
•
Clarification of content with teaching guidelines
•
Allocation of time
3.1
Specification of Content to show Progression
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.
CAPS
TECHNICAL MATHEMATICS
13
3.1.1 Overview of topics
3.1.1
3.1.1
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CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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andsymbolic
symbolic
representations (tables, graphs, words and formulae).
representations of functions and convert
representations
representations
representations
(tables,
graphs,
words
and
representations
of
functions
and
convert
representations(tables,
(tables,graphs,
graphs,words
wordsand
and
representationsof
offunctions
functionsand
andconvert
convert
flexibly between these representations
formulae).
flexibly
between
these
representations
Include
linear
and
quadratic
polynomial
functions,
formulae).
flexibly
formulae).
flexiblybetween
betweenthese
theserepresentations
representations
(tables, graphs, words and formulae).
(tables,
exponential functions andsome rational functions.
(tables,
graphs,
words
and
formulae).
(tables,graphs,
graphs,words
wordsand
andformulae).
formulae).
Include
linear
and
quadratic
polynomial
Include
linear,
quadratic and some cubic
Include
Includelinear
linearand
andquadratic
quadraticpolynomial
polynomial
polynomial
functions,
exponential
and
functions,
Include
and
cubic
functions,
exponential
functions
and
Include
linear,
quadratic
and
some
cubic
functions,exponential
exponentialfunctions
functionsand
and
Includelinear,
linear,quadratic
quadratic
andsome
some
cubic
some
rational
functions.
some
rational
functions.
polynomial
functions,
exponential
and
some
some
polynomial
somerational
rationalfunctions.
functions.
polynomialfunctions,
functions,exponential
exponentialand
andsome
some
rational
functions.
rational
functions.
• functions.
Revise
work studied in earlier grades.
Generate as many graphs as necessary, initially by rational
Generate
as
many
necessary,
Revise

Generate
as
many
graphs
as
necessary,
initially
Revise
work
studied
in
earlier
grades.
Generate
aspoint-by-point
manygraphs
graphsas
as
necessary,
initially
Revisework
workstudied
studiedin
inearlier
earliergrades.
grades.
means of
plotting,
to initially
make
and test
by
means
plotting,
make
by
means
of
point-by-point
plotting,
to
make
by
meansof
ofpoint-by-point
point-by-point
plotting,to
tothe
make
conjectures
and hence generalise
effects of the
and
test
and
and
test
conjectures
and
hence
generalise
the
parameter
which results
in ageneralise
horizontal
shift and that
and
testconjectures
conjectures
andhence
hence
generalisethe
the
effects
which
aaa
effects
of
the
parameter
which
results
in
whichof
results
in a horizontal
stretch
and/or
reflection
effects
ofthe
theparameter
parameter
whichresults
resultsin
in
horizontal
and
about theshift
y-axis.
horizontal
shift
and
that
which
results
in
horizontal
shift
andthat
thatwhich
whichresults
resultsin
inaaa
horizontal
horizontal
stretch
and/or
reflection
about
the
yhorizontalstretch
stretchand/or
and/orreflection
reflectionabout
aboutthe
theyyaxis.
axis.
axis.
Problem solving and graph work involving the prescribed • Problem solving and graph work involving
functions. Average
gradient
between twothe
points.
the prescribed
functions.
Problem
Problem
Problem
solving
and
graph
work
involving
Problem
solving
and
graph
work
involving
the
Problemsolving
solvingand
andgraph
graphwork
workinvolving
involving the
the 
Problemsolving
solvingand
andgraph
graphwork
workinvolving
involvingthe
the
prescribed
functions.
Average
gradient
between
prescribed
functions.
prescribed
functions.
Average
gradient
between
prescribed
functions.
prescribed functions. Average gradient between
prescribed functions.
two
two
points.
twopoints.
points.
Extend Grade 10 work on the relationships
Take
note
that
numbers
exist
other
than
those
numbers
those
studied
Take
note
that
numbers
exist
other
than
those on the There
• are
There
are other
numbers
those
Take
note
that
numbers
exist
other
than
those
There
are
numbers
other
than
those
studied
Take
note
that
numbers
exist
other
than
those
There
are
numbers
otherthan
thanother
thosethan
studied
on
the
real
number
line,
the
so-called
non-real
in
earlier
grades
called
imaginary
numbers
real
number
line,
the
so-called
non-real
numbers.
It
studied
in
earlier
grades
called
on
the
real
number
line,
the
so-called
non-real
in
earlier
grades
called
imaginary
numbers
on the real number line, the so-called non-real
in earlier grades called imaginary numbersimaginary
is
possible
to
square
certain
non-real
numbers
and
numbers
and complex numbers.
numbers.
It
is
possible
to
square
certain
nonand
numbers.
numbers.
and
complex
numbers.
numbers.ItItisispossible
possibleto
tosquare
squarecertain
certainnonnonandcomplex
complex
numbers.
obtain
negative
real
numbers
as
answers.
real
numbers
and
obtain
negative
real
numbers
real
realnumbers
numbersand
andobtain
obtainnegative
negativereal
realnumbers
numbers
Add, subtract, divide, multiply and simplify
as
Add,
as
answers.
Add,
subtract,
divide,
multiply
and
simplify
asanswers.
answers.
Add,subtract,
subtract,divide,
divide,multiply
multiplyand
andsimplify
simplify
imaginary
numbers
and
complex numbers.
imaginary
numbers
and
complex
imaginary
numbers.
imaginarynumbers
numbersand
andcomplex
complexnumbers.
numbers.
Binary
numbers
should
be
known.
Binary
numbers
should
be
Binary
numbers
should
be
known.
Binary
numbers
should
beknown.
known.
Solve equations involving complex
Solve
involving
Solve
equations
involving
complex
numbers.
Solveequations
equations
involvingcomplex
complexnumbers.
numbers.
numbers.
Grade
11
Grade
11
GradeGrade
11 11
•

The effect of different periods of compounding
Critically analyse different loan options.

The implications
of fluctuating
foreign
The effect of different periods of compounding
 growth and decay

(including
effective
and
•
The effect of different periods of compounding growth
• Critically analyse different loan options.
exchange
rates.
growth and decay (including effective and
nominal
interest
rates). effective and nominal interest
and decay
(including
nominal interest rates).
rates).
TECHNICAL MATHEMATICS
Page 18 of 59
4. ALGEBRA
4. ALGEBRA
(a) Apply the laws of exponents to expressions involving • Apply any law of logarithm to solve real
•
(a)Simplify expressions using the laws of •4. ALGEBRA
exponents
for integral
exponents.
exponents.
lifeofproblems.
(a) Simplify
expressions
using
the laws of
(a)rational
Apply the
laws of exponents to expressions
Apply any law
logarithm to solve real life



(a)
Simplify
expressions using the laws of
(a) Apply the laws of exponents to expressions


exponents
for
integral
exponents.
involving
rational
exponents.
problems.
(b)
Establish between which two integers a
(b) Add, subtract,
multiplyintegral
and divide
simple surds.
exponents
exponents.
involving rational exponents.
(b) Establish
between
(b) Add, subtract,
multiply for
and divide simple
given simple
surdwhich
lies. two integers a
(b)
Establish
between
which
two
integers
a
(b)
Add,
subtract, multiply and divide simple
(c)
Demonstrate an understanding of the definition
given simple surd lies.
surds.
(c)Round
real
numbers
to
an
appropriate
given
simple
surd
lies.
surds.
a logarithman
and
any laws needed
(c) Round real numbers to an appropriate
(c)of
Demonstrate
understanding
of the to solve real life
degreeofofaccuracy
accuracy
a given
number
of
real numbers
an appropriate
(c) Demonstrate an understanding of the
problems.
degree
(to a(to
given
number
of
definition(c)ofRound
a logarithm
and anyto
laws
decimal digits).
degree
of
accuracy
(to
a
given
number
of
definition of a logarithm and any laws
decimal digits).
needed to solve real life problems.
decimal
digits).
needed to solve real life problems.
(d)Revise
scientific
notation.
(d)
Revise scientific
notation.
(d) Revise scientific notation.
• •
Take note and understand the
•
Revise factorisation from Grade 10.
•
Manipulate algebraic expressions by:
Manipulate algebraic expressions by:
Revise factorisation from Grade 10.




Take
note
and
understand
Remainder
Remainderthe
and
Factor Theorems
•
multiplying a binomial by a trinomial;
Manipulate algebraic expressions by:
Revise
factorisation
from Gradeup
10.

and Factor
 multiplying a binomial by a trinomial;
Theorems
for polynomials
for polynomials
up to the third
•
factorising common factor (revision);

multiplying
a
binomial
by
a
trinomial;
to the third degree
(proofs
of the
 factorising common factor (revision);
degree
(proofs
of the Remainder
 factorising common factor (revision);
factorising
by grouping
in pairs;
Remainder andand
Factor
theorems
will not
Factor
theorems
will not be
• factorising
by grouping
in pairs;
 factorising by grouping in pairs;
be examined). examined).
factorising
trinomials;
• factorising
trinomials;
 factorising trinomials;
 Factorise•third-degree
polynomials
• factorising
difference
of twoofsquares
factorising
difference
two squares
Factorise
third-degree
 factorising difference of two squares
(including examples
which
require
the examples
(revision);
(revision);
polynomials
(including
(revision);
Factor
Theorem).
• factorising
the difference
and sums
two of
which require the Factor
factorising
the difference
and of
sums
 factorising the difference and sums of two
cubes;
Theorem).
twoand
cubes; and
cubes; and
• simplifying,
adding,
subtracting,
simplifying, adding, subtracting,
 simplifying, adding, subtracting,
multiplying
and division
of algebraic
multiplying
and division
of algebraic
multiplying and division of algebraic
fractions
with with
numerators
and and
fractions
numerators
fractions with numerators and
denominators
limited
to thetopolynomials
denominators
limited
the polynomials
denominators limited to the polynomials
covered
in factorisation.
covered
in factorisation.
covered in factorisation.

The implications of fluctuating foreign
exchange
rates. of fluctuating foreign
The implications
exchange rates.
3. FINANCE, GROWTH AND DECAY
3. FINANCE, GROWTH AND DECAY
3. FINANCE, GROWTH AND DECAY
Use
and
compound
growth
formulae
simple
and and
compound
growth/decay
Strengthen
Grade 11the
work.
 •

• the
Strengthen
Grade 11 work.
Usesimple
simple
and
compound
growth
formulae  • Use
Use
simple
compound
growth/decay
simple and compound growth formulae
Use simple and compound growth/decay
 formulae A Use

A  P(1  in) and
and A  P(1  i)n to solve
 P(1  in) and A  P(1  i)n to solve
solve problems
A  P(1  in) and
andhire
formulae A  P(1  in) and A  P(1  i)n to solve
A  P(1  i)n to solve
formulae
(including(including
interest,interest,
hire purchase,
inflation,
problems
hire purchase,
problems
(including
interest,
purchase, solve problems
(including
interest,
hire purchase,
inflation,
population
problems
(including
hire
problems (including interest, hire purchase,
population
growth and
other
lifereal life
inflation,
population
growth
andreal
other
inflation,
population
growth
and interest,
other real
lifepurchase,
growth
and
other
real
life
problems).
inflation,
population
growth
and
other
real
life
inflation, population growth and other real life
problems).
problems).
problems).
problems).
problems).
CAPS
15




CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)

(a) Revise basic results established in earlier
grades.
(b) Investigate and form conjectures about the
properties of special triangles (scalene,
isosceles, equilateral and right-angled
triangle) and quadrilaterals.
6. EUCLIDEAN GEOMETRY
•

4. ALGEBRA
Solve:

•
Solve:
 linear equations;
linear
equations;
 •
quadratic
equations
by factorisation;
quadratic(changing
equationsthe
bysubject
factorisation;
 •
literal equations
of
formula);
•
literal equations (changing the subject
of formula);
 exponential
equations (accepting that the
laws ofexponential
exponents hold
for real (accepting
exponents
•
equations
and solutions
notof
necessarily
integral
that theare
laws
exponents
hold for
or evenreal
rational);
exponents and solutions are not
 linear inequalities
one variable
andrational);
necessarilyinintegral
or even
illustrate
the
solution
graphically;
and
•
linear inequalities in one variable
and
 linear equations
in
two
variables
illustrate the solution graphically; and
simultaneously (algebraically and
•
linear equations in two variables
graphically).
simultaneously (algebraically and
graphically).
5. DIFFERENTIAL CALCULUS AND INTEGRATION
5. DIFFERENTIAL CALCULUS AND INTEGRATION

16
•
(a) Investigate theorems of the geometry of
circles assuming results from earlier
grades, together with one other result
concerning tangents and radii of circles.
(b) Solve circle geometry problems, providing
reasons for statements when required.


Page 19 of 59
(a) Revise the concept of similarity and
proportionality.
(b) Apply proportionality in triangles.
(c) Apply mid-point theorem.
(g)Basic integration.
• (a)
An intuitive understanding
(a) An intuitive
understanding
of the concept of the
concept
of
a
limit.
of a limit.
(b) Differentiation
specified functions
(b)Dof
ifferentiation
of specified functions
from first principles.
from first principles.
(c) Use of the specified rules of
(c)Use of the specified rules of
differentiation.
differentiation.
(d) The equations of tangents to graphs.
The equations
tangents to graphs.
(e) The ability(d)
to sketch
graphs of of
cubic
functions. (e)The ability to sketch graphs of cubic
(f) Practical problems
involving optimisation
functions.
and rates of change (including the
Practical problems involving
calculus of(f)
motion).
optimisation and rates of change
(g) Basic integration.
(including the calculus of motion).
Solve:

 Determine the nature of roots and the
•
Solve:
• •
Determine the nature of roots
 quadratic equations (by factorisation and by
conditions for which
are real,
and the
the roots
conditions
for which the
• thequadratic
using
quadratic equations
formula); (by factorisation and by using
non-real,
equal,
unequal,
rational
and
roots
are
real,
non-real,
equal,
the
formula);
 equations
in quadratic
two unknowns,
one of which is
unequal,
rational
and
irrational.
irrational.
• theequations
in two algebraically
unknowns, one
linear
other quadratic,
or of which is linear
the other quadratic, algebraically or graphically.
graphically.
 Explore
the
naturethe
of roots
thethrough the value of
•
Explore
naturethrough
of roots
value of b2  4ac ..
6. EUCLIDEAN GEOMETRY
•
(b)Solve circle geometry problems, providing
reasons for statements when required.
(a)Investigate theorems of the geometry of circles
assuming results from earlier grades, together
with one other result concerning tangents and
radii of circles.
•
(c)Apply mid-point theorem.
(b)Apply proportionality in triangles.
(a)Revise the concept of similarity and
proportionality.
TECHNICAL MATHEMATICS

•
Represent
geometric
figures
in
coRepresent
geometric
figuresfigures
in aa Cartesian
Cartesian
coRepresent
geometric
in a Cartesian
co
ordinate
system,
and
and
any
ordinate
system,
and derive
and for
apply,
ordinate
system,
and derive
derive
and apply,
apply,
for
anyfor any two
two
points
and
twopoints
points ((( xx11;; yy11))) and
and (((xx22;; yy22 ))) aaa formula
formula
for
formulafor
for calculating:
calculating:
calculating:
•
the distance between the two points;
 •the
between
the distance
distance
between
the
two
points;
the gradient
of the
the two
linepoints;
segment joining the
 the
of
the
line
segment
joining
the gradient
gradient
of
the
line
segment
joining the
the
points;
points;
points;
•
the co-ordinates of the mid-point of the line
 the
the co-ordinates
co-ordinates of
of the
the mid-point
mid-point of
of the
the
segment joining the points; and
line
line segment
segment joining
joining the
the points;
points; and
and
the equation
of a straight
linethe
joining the two
 •the
of
line
the equation
equation
of aa straight
straight
line joining
joining
the
points.
two
two points.
points.
9.
9. ANALYTICAL
ANALYTICAL GEOMETRY
GEOMETRY
9. ANALYTICAL GEOMETRY
Sectors and segments
Angular and circumferential velocity.
Page
Page 20
20 of
of 59
59
Use
aa Cartesian
system
Use
Cartesian
Use •
Cartesian
co-ordinate
system to
to system todetermine:
Use aa two-dimensional
two-dimensional
Cartesian co-ordinate
co-ordinate
•
Use a two-dimensional
Cartesian coUse aco-ordinate
Cartesian co-ordinate
determine:
system
to
determine:
ordinate
system
to
determine:
determine:
system
to
determine:
•
the equation of a line through two given
 the
of
 the
circle
with
the equation
equation
of aa line
line through
through two
two given
given
the equation
equation
of aathe
circle
with centre
centre
at
• of
equation
of a at
circle
with
points;
points;
the
origin
(centre
is
(0;0));
points;
the
origin
(centre
is
(0;0));
centre
at
the
origin
(centre
is
•
the equation of a line through one point and
 the
of
a
line
through
one
point

the
equation
of
a
tangent
to
a
circle
at
a
the equation
equation
of
a
line
through
one
point

the
equation
of
a
tangent
to
a
circle
at
a
(0;0));
parallel or perpendicular to a given line; and
and
given
circle;
and
and parallel
parallel or
or perpendicular
perpendicular to
to aa given
given
given point
point
on the
the
circle;
and of a tangent to a
• on
the
equation
•
the angle of inclination of a line.
line;
line; and
and
 point/s
of
a
aa on the
point/s of
of intersection
intersection
of
circle
and
circle at aacircle
givenand
point
 the
straight
the angle
angle of
of inclination
inclination of
of aa line.
line.
straight line.
line.
circle; and
•
point/s of intersection of a circle
and a straight line.
•
•

Solve
Revise
Solve problems
problems involving
involving volume
volume and
and
Revise work
work studied
studied in
in earlier
earlier Grades.
Grades.
surface
surface area
area of
of solids
solids studied
studied in
in earlier
earlier
grades
grades and
and combinations
combinations of
of those
those objects
objects
to
form
more
complex
shaped
solids.
to
form
more
complex
shaped
solids.
•
Revise work studied in earlier Grades.
•
Conversion of units, square units and cubic units.
• (a)Solve problems involving volume and surface
(b)
the
of
irregular
figure
(b) Determine
Determine
theofarea
area
of an
an
irregular
figure grades and
area
solids
studied
in earlier
using
Rule.
using Mid-ordinate
Mid-ordinate
Rule.
combinations
of those objects to form more
complex shaped solids.
8.
8. CIRCLES,
CIRCLES, ANGLES
ANGLES AND
AND ANGULAR
ANGULAR MOVEMENT
MOVEMENT
(b)Determine the area of an irregular figure using
Mid-ordinate Rule.


 Define

 Angles
Define aa radian.
radian.
Angles and
and arcs
arcs
8. CIRCLES,
ANGLES
AND
ANGULAR
MOVEMENT
 Converting
 Degrees
Converting degrees
degrees to
to radians
radians and
and vice
vice
Degrees and
and radians
radians
•
•
•versa.
• and
and arcs
versa.Define a radian.
 •Sectors
segments
Sectors
andAngles
segments
circumferential
velocity.
Angular
and
circumferential
velocity.
•
Converting degrees to radians and vice versa. Angular
• and
Degrees
and radians
•
(a)Revise basic results established in earlier grades.
(c)
(c) Investigate
Investigate alternative
alternative (but
(but equivalent)
equivalent)
(b)Investigate and form conjectures about the
definitions
definitions of
of various
various polygons
polygons (including
(including
properties of special triangles (scalene, isosceles,
the
scalene,
equilateral
and
theequilateral
scalene, isosceles,
isosceles,
equilateral
and rightright-and
and right-angled triangle)
angled
triangle,
the
kite,
parallelogram,
angled
triangle,
the
kite,
parallelogram,
quadrilaterals.
rectangle,
rectangle, rhombus,
rhombus, square
square and
and trapezium).
trapezium).
(c)Investigate
alternative
(but
equivalent) definitions
(d)
theorem
Pythagoras.
(d) Application
Application of
of the
the
theorem of
of
Pythagoras.
of various polygons (including the scalene,
isosceles, equilateral and right-angled triangle,
7.
7. MENSURATION
MENSURATION
the kite, parallelogram, rectangle, rhombus,
square and trapezium).

Conversion
(a)
Conversion of
of units,
units, square
square units
units and
and cubic
cubic
(a)

(d)Application of the theorem of Pythagoras.
units.
units.
7. MENSURATION
CAPS
17
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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10. TRIGONOMETRY
10.
10.
TRIGONOMETRY
10. TRIGONOMETRY
10. TRIGONOMETRY
TRIGONOMETRY
10.
(a)TRIGONOMETRY
Definitions
of
the trigonometric
functions

 the trigonometric

 Applysin
trigonometric
identities
studied
in trigonometric i
10. TRIGONOMETRY
10.
TRIGONOMETRY
10.
TRIGONOMETRY
(a) Definitions of
functions tan   sin  ,(a) Use the identities:
10.
TRIGONOMETRY


 Apply
 ,
(a) Use the identities:
10. TRIGONOMETRY
10. TRIGONOMETRY
TRIGONOMETRY
10.
  grades
tanearlier
cos

cos

,
and
to
prove
that
left
hand
sin

tan

in
right

angled
cos

(a)
Definitions
of
the
trigonometric
functions




trigonome
(a)
Definitions
of
the
trigonometric
functions
sin

cos

,
and
earlier
grades
to prov
sin
trigonometric
in right  angled


Apply
trigonometric
id
sin
(a) Definitions of the trigonometric
functions

 oftan

  tan
Apply
identities
(a)Definitions
the(a)


 studied
 inApply
Apply
trigonome
 ,,
sin
 trigonometric
(a)
Use
the

tan
(a),22 
Use
the
identities:
, toApply
22 the
22functions
 22 sin
tan
Use
identities:
. TRIGONOMETRY (a)10.
tancos
(a)
Use
the2identities:
identities:
(a)
Definitions
of
the
trigonometric
functions




trigonometric
identities
studied
in
2
2
2

sin
10.
TRIGONOMETRY
side
equals
right
hand
side.
,
,
sin

cos


1
1

tan

sec
cos


TRIGONOMETRY
triangles.
Definitions
of
the
trigonometric
functions
10.
TRIGONOMETRY
(a)
Definitions
of
the
trigonometric
functions
cos

,
and
earlier
grades
to
sin

tan

in
right

angled
(a)
Definitions
of
the
trigonometric
functions




Apply
trigonometric
identities
studied
in
side
equals
to
right
h
(a)
Definitions
of
the
trigonometric
functions
,
,
sin


cos


1
1

tan


sec





Apply
trigonometric
identities
st
sin

cos

,
and
earlier
grades
to
prove
sin

tan

in
right

angled
cos


sin


tan




Apply
trigonometric
identities
studied
in
(a)
Use
the
identities:
,



Apply
trigonometric
identities
studied
in

sin

sin
cos

cos

,
and
earlier
grades
to
prove
that
left
hand
sin

tan

in
right

angled
(a)
Definitions
of
the
trigonometric
functions
triangles.




Apply
trigonometric
identities
studied
in
cos

,
and
earlier
grades
to
sin

tan

in
right

angled

sin
 identities:
tan
(a) 
the
identities:
(a) Definitions
Definitions of
of the
thesin
trigonometric
functions
  2Apply
(a)
trigonometric
functions
Use
, trigonometric
 

tan
(a)
tan,
(a)
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the
identities:
Apply
trigonometric
identities
studied
inthat left hand
(a)
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the
identities:
Use
 tan
identities
studied
in
 ,,,, the ,identities:
sin
sin

tan
(a) the
Use
the
cos
22
22  2cos
22  2
22 grades
cos
special
, in
and
earlier
to
prove
angled
tan
 in
right
angled

tan
2 sin
2tan
(a)
Use
the
identities:
(a)
Use
identities:
10. TRIGONOMETRY
cos
for
10.
TRIGONOMETRY
2 22cos
2tan
2
2sin
10.
TRIGONOMETRY
2prove
cos

cot

1

cos
ec

and
.
cos
cos

Take
note
that
there
are
names
for
10.
2earlier
10. TRIGONOMETRY
TRIGONOMETRY
side
equals
to
rig
10.
TRIGONOMETRY
,
,

1
1
sec
cos

,
and
earlier
grades
to
that
left
hand
sin

tan

in
right

cos

,
and
earlier
grades
to
prove
that
left
h
sin

tan

in
right

angled
side
equals
to
right
ha
,
,

cos

1
1

tan

sec

cos
,
and
grades
to
prove
that
left
hand
sin

cos

,
and
earlier
grades
to
prove
that
left
hand
tan
right

angled
sin

tan
in
right

angled
cos
triangles.
side
equals
to
right
hand
side.
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,
sin

1
1

tan

sec

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

1

cos
ec

and
.
Take
note
that
there
are
special
names
triangles.
cos

,
and
earlier
grades
to
prove
that
left
hand
sin

tan

in
right

angled
side
equals
to
rig
,
,
sin

cos


1
1

tan


sec

cos

cos

TRIGONOMETRY
10. 10.
TRIGONOMETRY
cos  and
and
earlier
grades
to prove
prove
that left
left
handhand side.
sin,, triangles.
tan in
inright
right angled
angled(a) Definitions
cos
earlier
grades
to
that
hand
sin
tan
triangles.
2   cos
2  sec 2  ,
(a) Definitions
of the trigonometric
functions
22sin
Apply
identities
studied
inequals
sin
2tan
side
toside
right
sin
2122)22,and
1,,cos
2
2 22
2 2
2 (2180
2 trigonometric
2 hand
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of
the
trigonometric
functions
trigonometric
sec
side.
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trigonometric
22 2
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and
triangles.
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2equals
reciprocals
of
the
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2
2tan
(b)
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formulae,

(a) the
Definitions
of
the
trigonometric
functions
tan

(a)
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the
identities:
,
side
equals
to
right
side.
triangles.


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trigonometric
identities
studied
in
,
sin


cos

1
1


sec
(a)
Definitions
of
the
trigonometric
functions
equals
right
hand
side.
sin
,
1

tan


sec
2
side
to
right
hand
side.
side
equals
to
right
hand
side.
,
sin


cos

1
1

tan




Apply
trigonometri
,
sin




1
1

tan


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sin

2
2
2
2
2
2
1

cos
ec

and
.
Take
note
that
there
are
special
names
for
tan


(a)
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the
identities:
,
the
reciprocals
of
the
trigonometric
cot

1

cos
ec

and
.
triangles.
Take
note
that
there
are
special
names
for
side
equals
to
right
hand
,
,
sin


cos


1
1

tan


sec

triangles.
(b)
Reduction
formulae,
triangles.
(
180



)
cot
.sec
and
Take
note
that there are special names for
tan
(a) Use
the
side
equals
to
right
hand side.
side. identities
ecleft
equals
right
hand
sin
cos
cos
 
1
1names
tan
sec  ,, (a)
Use
thecot
identities:
, trigonometric
•side
1  tan
cos
to
and
. hand
triangles.
,,111cos

cos
tan
 
Take note•thatsin
there
are
special
for
 identities:
triangles.
2 ec
2earlier
triangles.
•
Apply
cos
 and
grades
totrigonometric
prove
that
sin
tan
Definitions
in
right
the
angled
cos

and
earlier
sin
the
(cot
in
right
(b)
(a) Definitions
trigonometric
functions
cot
21and
cos
cos
ec
(b)
and
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2  tan
2 
Take
note
there
are
special
names
for
• ,(a)
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cos
trigonometric
identities
studied
in in
(a)
of
the
trigonometric
functions
(a)
Definitions
of
the
trigonometric
functions
22right
22 . sin
cos
functions
2cot
Apply
Apply
trigonometric
identities
studied
formulae,
  (180
Apply
trigonometric
identities
studied
in
of
the
functions
sin
cot
sin
of
,of
and
earlier
grades
to
prove
that
hand
sin
trigonometric
tan
that
inTake
right
functions
angled
(a)
Definitions
of
the
trigonometric
functions
(a)
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of
the
trigonometric
functions

that
2,Reduction
Apply
identities
studied
inin left
sin
cos
cos
and
earlier
gradestotopro
pr
sin
,(a)
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ofcos
the
trigonometric
functions
tan
cot
intrigonometric
angled
functions
 ec
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trigonometric
studied
 Definitions
special
2 . formulae,
Apply
trigonometric
identities
studied
in grades
sin
sin
reciprocals
of
the

1

cos
and
note
that
there
are
special
names
for
note
there
are
names
for
the
reciprocals
of
the
trigonometric
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((180
identities
)) 2and
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
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
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ec
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360
ec
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identities:
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and
.ec
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note
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note
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
(a)
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the
identities:
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

)
2the
2tan
2the
2
tan




(a)
Use
,
(a)
Use
,
the
reciprocals
oftrigonometric
the
trigonometric
2
2
tan

(a)
Definitions
the
Use
the
identities:


1


(b)
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formulae,
and
and
.
(
180



)
Take
note
that
there
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names
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

(a)
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the
identities:
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

Take



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trigonometric
identities
studied
in
(a)
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the
identities:
the
reciprocals
of
trigonometric
sin

.
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formulae,
and
(
360



)
180
2
2
2
cot

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ec

and
.
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note
that
there
are
special
names
for
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
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
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
and
.
studied
in
earlier
grades
to
prove
Take
note
that
there
are
special
names
for
side
equals
to
right
hand
side.
,
,
sin


cos


1
1

tan

sec

2
2
2
2
tan


(a)
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identities:
,
(a)
Use
the
identities:
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2
2
2
cos

triangles.
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
side
equals
totoright
cos

,
,
sin


cos


1
1

tan


sec

the
reciprocals
of
the
trigonometric
cos

cos

,
and
earlier
grades
to
prove
that
left
hand
sin

tan

in
right

angled
cos

(b)
Reduction
formulae,
and
cos

(
180



)
cos

,
and
earlier
grades
to
prove
that
left
hand

cos

,
and
earlier
grades
to
prove
that
left
hand
tan

in
right

angled
sin

tan

in
right

angled
1
1
side
equals
to
right
hand
side.
,
,
sin


cos


1
1

tan


sec

and
earlier
grades
to
prove
that
left
hand
, , cos
triangles.
tan

in
right

angled
and
side
equals
right
cos
sin
and
earlier
grades
to
prove
that
left
hand
sin
tan

in
right

angled
cos

,
,
,
and
earlier
grades
to
prove
that
left
hand
sin


cos


1
1

tan


sec

sin

tan

in
right

angled
functions
thesin
reciprocals
of
the
trigonometric
triangles.
the
reciprocals
of
the
trigonometric
functions
the
reciprocals
of
the
trigonometric
(b)
Reduction
formulae,
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the
reciprocals
of
the
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(
180



)
triangles.
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formulae,
and
1 formulae,
(b)
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formulae,
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cos
 (c)
(b)
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formulae,
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
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1802(

cos
 of
sec
in right
;oftrigonometric
and
functions
(c)
the
solutions
of
trigonometric
the
reciprocals
the
, cos
and
grades
tohand
prove
thatequals
left hand
sin
ec
tantrigonometric
 angled
functions
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triangles
.Take
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Reduction
180

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)2.(180
2 112(b)
2
that
left
side
to right
cos ec
note
sec
22Determine
; cos
and
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and
Take note
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



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equals
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right
hand
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
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note
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equals
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2
2. 
2
triangles.
triangles.
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
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triangles.
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1
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
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that
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side
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
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functions
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note
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ec
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the
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and
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note
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equations
for
.
(d)
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rules
0



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
(c)
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the
solutions
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trigonometric
(c)
Determine
the
of
trigonometric
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cos
ec


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
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cos
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;
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.
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
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(c)
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equations
for
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



360
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cos
ec
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ec
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;
and
tan
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functions
(c)
Determine
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solutions
of
trigonometric
(c)
Determine
the
solutions
of
trigonometric
sin

cos
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the
reciprocals
of
the
trigonometric
sin
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cos

.
(
360



)
1
sin
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cos
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sin
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cos

(b)
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and
the
reciprocals
of
the
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the
reciprocals
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(
180



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1
functions
(b)
Reduction
formulae,
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(b)
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(
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180
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thereciprocals
reciprocals
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the
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180
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these
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360


)
.
.
cot
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cot
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.
.
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360
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
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.
(
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

)
1
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
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(c)
Determine
the
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these
rules
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be
examined).
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Apply
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and
rules
(proofs
(d)
Apply
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(proofs
of
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.
these
rules
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examined).
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Determine
the
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tan
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(d)
Apply
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(d)
Apply
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and
area
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(proofs
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

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to
and
calculate
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


360

these
rules
will
not
be
examined).
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.
.
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360
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.
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(c)
Extend
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definitions
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and
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the
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these
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equations
for00360
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Determine
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Extend
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rules
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Determine
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
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to
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equations
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360
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and
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and
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
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
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(d)
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Apply
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these
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Simplification
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
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(c)
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the
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(c)
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sin
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to
and
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of
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and
expressions/equations
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use
of
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
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the
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Simplification
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time
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.
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)
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
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parameter
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given
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vectors
(sine
and
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parameter
should
be
tested
at
a
given
Rotating
vectors
(sine
and
cosine
curves
only).
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vectors
(sine
and
cosine
curves
only).
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
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vectors
(sine
and
cosine
curves
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

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
.
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) only).
(sine
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 horizontal
Rotating
vectors
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curves
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and
curves
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time if examining
shift.
time
ififexamining
horizontal
shift.
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atshift.
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be
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at
aagiven
One
parameter
should
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tested
atat
given
time
ifparameter
examining
horizontal
One
should
be
tested
at
a
given
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parameter
should
be
tested
at
a
given
time
examining
horizontal
shift.
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should
be
tested
a
given
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parameter
should
be tested at a given
Rotating vectors
and
cosine
curves
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time
ifRotating
examining
horizontal
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 
 curves
time
ififhorizontal
examining
horizontal
shift.
time
examining
horizontal
shift.
time
examining
shift.
vectors
(sine
and
only). vectors
timeifif(sine
examining
horizontal
shift.
time
examining
horizontal
shift.

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(sineand
andcosine
cosinecurves
curvesonly).
only).
time
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horizontal
shift.
Rotating
vectors
(sine
and
cosine
curves
only).
  

Rotating
vectors
(sine
and
cosine
curves
only).
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vectors
(sine
and
cosine
curves
only).


Rotating
vectors
(sine
and
cosine
curves
only).
Rotating
vectors
(sine
and
cosine
curves
only).
Rotating
vectors
(sine
and
cosine
curves
only).



Rotating vectors (sine and cosine curves only).


18
3.2
Content Clarification with teaching guidelines
In Section 3, content clarification includes:
◦◦ Teaching guidelines
◦◦ Sequencing of topics per term
◦◦ 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 ensures that in the first two terms, more than six topics are covered/
taught so that assessment is balanced between paper 1 and 2.
CAPS
TECHNICAL MATHEMATICS
19
3.2.1 Allocation of Teaching Time
Time allocation for Technical Mathematics: 4 hours and 30 minutes, e.g. six forty-five-minute periods per week in Grades
10, 11 and 12.
Terms
Grade 10
Grade 11
No. of
weeks
Term 1
Term 2
Term 3
Term 4
20
Introduction
Number systems
Exponents
Mensuration
Algebraic Expressions
2
3
2
1
3
Grade 12
No. of
weeks
Exponents and surds
Logarithms
Equations and
inequalities
(including nature of
roots)
Analytical Geometry
3
2
4
Functions and graphs
Euclidean Geometry
MID-YEAR EXAMS
Complex numbers
Polynomials
Differential Calculus
3
2
6
4
4
3
Integration
Analytical Geometry
Euclidean Geometry
MID-YEAR EXAMS
3
2
3
3
Euclidean Geometry
Trigonometry
Revision
TRIAL EXAMS
2
3
1
4
Revision
EXAMS
3
5
2
Algebraic Expressions
Equations and
inequalities
Trigonometry
MID-YEAR EXAMS
2
3
Trigonometry
Functions and graphs
Euclidean Geometry
Analytical Geometry
2
3
4
1
Circles, angles and
angular movement
Trigonometry
Finance, growth and
decay
4
Analytical Geometry
Circles, angles and
angular movement
Finance and growth
Revision
EXAMS
1
1
Mensuration
Revision
EXAMS
3
3
3
3
3
2
2
3
No. of
weeks
4
2
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
CAPS
TECHNICAL MATHEMATICS
21
WEEK 2
Analytical
Geometry
Topics
Date
completed
Assessment
WEEK 1
Weeks
Circles,
angles
and
angular
movement
Test
WEEK
3
4
Finance and
growth
Functions and graphs
WEEK 4
5
WEEK 5
WEEK
8
WEEK 6
WEE
K9
WEEK 7
Mensuration
WEEK
10
Admin
Algebraic
expressions
and equations
(including
inequalities and
exponents )
Finance and
growth
Functions and
graphs (excluding
trig. functions)
Total marks
WEEK 10
WEEK
11
100
25
15
60
Total marks
100
40
15
15
30
Paper 2: 2 hours
Analytical
Geometry
WEEK 10
Euclidean
Geometry
Analytical
Geometry
Trigonometry
Mensuration,
circles, angles
and angular
movement
Test
WEEK 9
MID-YEAR EXAMINATION
WEEK
9
WEEK 8
WEEK
8
Test
WEEK
WEEK 11
10
Algebraic Expressions
WEEK 9
Paper 1: 2 hours
WEEK 7
Trigonometry
Euclidean Geometry
TERM 3
TERM 2
WEEK 6
Exponents
Examinations
WEEK
7
WEEK 5
WEEK
6
Revision
WEEK
TERM 4
WEEK
WEEK 3
Assignment / Test
Date
completed
Term 4
WEEK 2
WEEK 4
Equations and Inequalities
WEEK 3
Investigation or project
Number systems
WEEK 4
Test
WEEK WEEK 2
1
Trigonometry
Algebraic
Expressions
WEEK 1
WEEK 3
MATHEMATICS: GRADE 10 PACE SETTER
TERM 1
WEEK 5
WEEK 6
WEEK 7
WEEK 8
Assessment
Topics
Date
completed
Term 3
Weeks
Assessment
Topics
Date
completed
Term 2
Weeks
Assessment
Introduction
Topics
WEEK 2
WEEK 1
Term 1
Weeks
The detail3.2.2
whichSequencing
follows includes
numerical references to the Overview.
and examples
Pacing ofand
Topics
22
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Date
completed
Assessment
Topics
Weeks
Date
completed
Term 4
Assessment
Date
completed
Term 3
Weeks
Topics
Assessment
Topics
Date
completed
Term 2
Weeks
Assessment
Topics
Term 1
Weeks
1
WEEK
Equations and inequalities
Test
WEEK
2
3
Mensuration
WEEK
WEEK
4
5
Revision
WEEK
6
TERM 4
WEEK
Test
Test
WEEK 8
Algebraic
expressions,
equations,
inequalities
and nature of roots
Functions and
graphs
(excluding trig.
functions)
Finance, growth and
decay
Total marks
WEEK 11
WEEK 10
WEEK 11
Analytical Geometry
WEEK 10
150
15
45
90
Total marks
Euclidean
Geometry
Analytical
Geometry
Trigonometry
and
Mensuration,
circles,
angles
and angular
movement
150
35
50
25
40
Paper 2: 3 hours
WEEK 9
WEEK 10
Finance, growth and
decay
MID-YEAR EXAMINATION
WEEK 9
Nature of
roots
Test
WEEK 9
Paper 1: 3 hours
WEEK 8
WEEK 7
WEEK
10
Admin
TERM 3
WEEK 6
Trigonometry
WEEK
WEEK
WEEK
7
8
9
FINAL EXAMINATION
WEEK 5
TERM 2
WEEK
WEEK 3
WEEK 4
WEEK 5
WEEK 6
WEEK 7
2
Functions and graphs
Euclidean Geometry Trigonometry
Assignment / Test
WEEK 1 WEEK 2 WEEK 3 WEEK 4
Circles, angles and angular movement
WEEK
1
Logarithms
WEEK 4
MATHEMATICS: GRADE 11 PACE SETTER
TERM 1
WEEK 5
WEEK 6
WEEK 7
WEEK 8
Investigation or project
WEEK WEEK 2 WEEK 3
1
Exponents and surds
3.2.2 Sequencing and Pacing of Topics
CAPS
TECHNICAL MATHEMATICS
23
WEEK 2
Integration
WEEK 2
Date
completed
1
2
Revision
3
WEEK
4
WEEK
WEEK
WEEK
WEEK 5
5
6
7
FINAL EXAMINATION
WEEK
TERM 4
WEEK
WEEK 4
Trigonometry
Test
8
WEEK
9
WEEK
TERM 3
WEEK 6
Revision
WEEK 7
10
Admin
WEEK
WEEK 9
Total marks
WEEK
10
WEEK 11
WEEK 11
WEEK 9
WEEK 10
150
50
15
35
50
Total marks
150
Paper 2: 3 hours
Euclidean
40
Geometry
Analytical
25
Geometry
Trigonometry
50
and
Mensuration,
35
circles, angles
and angular
movement
TRIAL EXAMINATION
WEEK 8
MID-YEAR EXAMINATION
WEEK 9
Paper 1: 3 hours
Algebraic expressions
and equations (and
inequalities, logs and
complex numbers)
Functions and graphs
(excluding trig.
functions)
Finance, growth and
decay
Differential Calculus
and integration
WEEK 7
WEEK 8
WEEK 10
Assignment / Test
Differential Calculus
Euclidean Geometry
TERM 2
WEEK 6
Investigation or project
WEEK 5
Analytical Geometry
WEEK 4
Date
completed
Term 4
WEEK 3
WEEK 3
Test
Functions:
Polynomials
WEEK 4
Test
WEEK 1
WEEK 2
Euclidean Geometry
WEEK
WEEK 3
Complex numbers
WEEK 1
WEEK
1
MATHEMATICS: GRADE 12 PACE SETTER
TERM 1
WEEK 5 WEEK 6
WEEK 7
WEEK 8
Assessment
Date
completed
Term 3
Weeks
Topics
Assessment
Topics
Date
completed
Term 2
Weeks
Assessment
Topics
Term 1
Weeks
3.2.3 allocation
Topic allocation
allocation
perand
term
and clarification
clarification
3.2.3
Topic
per
term
and
3.2.3
Topic
perterm
term
clarification
2.3 Topic
allocation
per
and
clarification
3.2.3
Topic allocation
per
term
and clarification
3.2.3 Topic allocation per term and clarification GRADE 10: TERM 1
Weeks
Weeks
Weeks
Weeks
eeks Weeks
Topic
Topic Topic
Topic
Topic
2
22
33
22
Topic
Curriculum statement
Clarification
GRADE10:
10:TERM
TERM11
GRADE
GRADE
10:
TERM
1
Where
an example
is given, the cognitive demand
GRADE 10:GRADE
TERM
1 TERM
10:
1
is
suggested:
knowledge
(K), routine
procedure (R),
Curriculum
statement
Clarification
Curriculum
statement
Clarification
Curriculum
statement
Clarification
Curriculum
statement
Clarification
complex
procedure
(C)
or
problem-solving
(P). demand is suggeste
Curriculum
statement
Clarification
Where an example is given, the cognitive
Where an example is given, the cognitive demand is suggested
Introduction
Wherean
anexample
exampleisisgiven,
given,the
thecognitive
cognitivedemand
demandisissuggested:
suggested:
Where
Where
example
is given,
the cognitive
demand
is suggest
Mathematical language and
All basic
algebraan
must
revised.
knowledge
(K),be
routine
procedure
(R),complex
complex
procedure
(C)
knowledge
(K),
routine
procedure
(R),
procedure
knowledge
(K),
routine
procedure
(R),
complex
procedure
(C)oror (C)
(K), routine
procedure
(R), complex
procedure
(C)
concepts used in previous years knowledge
knowledge
(K),
routine
procedure
(R),
complex
procedure
(C
problem-solving
(P).
problem-solving
problem-solving
(P). (P).
problem-solving
(P).
are revised.
problem-solving
(P).
•
Use
real numbers
as thebeset
of points and explain
•
Understand
that and
real concepts
Mathematical
language
Allalgebra
basic
algebra
must
revised.
Mathematical
language
and concepts
All
basic
algebra
must
be revised.
Mathematical
language
and
concepts
Allbasic
basic
must
be
revised.
each
set
of
numbers
on
a
line.
(Natural, whole,
numbers
can
be
natural,
Mathematical
language
and
concepts
All
algebra
must
be
revised.
2
Mathematical
language
and
concepts
All
basic
algebra
must
be
revised.
Introduction
used
inprevious
previous
years
arerevised.
revised.
2 Introduction
Introduction
in
years
are
usedininused
previous
yearsare
are
revised.
integers,
rational,
irrational).
whole,
integers,
rational,
2Introduction
used
previous
years
revised.
Introduction
used in previous years are revised.
irrational.
•
Deal
with real
imaginary,
binary
and
numbers
Understandthat
thatreal
realnumbers
numberscan
can
Use
numbers
asthe
the
setcomplex
ofpoints
points
andexplain
explaineach
eachset
set
 • Understand
 real
Use
real numbers
as
set
of
and

Understand
that
real
numbers
can

Use
numbers
as
the
set
of
points
and
explain
each
setof
of set
Introduce
binary
and
 Understand
that real
numbers
can rational,
can
real
numbers
as– athe
setoperations
ofthe
points
and
explain
each
set
• UseBinary
numbers
basic
including
 be
Understand
that
real
numbers

Use
real
numbers
as
set
of
points
and
explain
each
be
natural,
whole,
integers,
numbers
on
line.
(Natural,
whole,
integers,
rational,
irrat
integers,
rational, numbers
numbers
on (Natural,
a line.
(Natural,
whole,
integers,
rational,
irrati
benatural,
natural,natural,
whole,whole,
integers,
rational,
onsubtraction,
aline.
line.
whole,integers,
integers,
rational,
irrational).
complex
numbers.
addition,
multiplication
and division
of rational,
be
rational,
numbers
on
awith
(Natural,
whole,
rational,
irrational).
bewhole,
natural,integers,
whole, integers,
rational,
numbers
on
a line.
(Natural,
whole,
integers,
irra
irrational.
 Deal
Deal
imaginary,
binaryand
and
complex
numbers
irrational.

with
imaginary,
binary
complex
numbers
irrational.
whole
numbers)
Deal
with
imaginary,
binaryand
and
complex
numbersnumbers
• irrational.
Round real numbers off to  Deal
irrational.
with
imaginary,
binary
complex
numbers

Deal
with
imaginary,
binary
and
complex
Introduce
imaginary,
binaryand
and
Binarynumbers
numbers
basicoperations
operations
including
addition,
 Introduce
imaginary,
binary
Binary
––operations
basic
including
addition,
Introduce
imaginary,
binaryand
and
Binary
numbers
basic
including
addition,
a significant/appropriate
• Binary
Complex
numbers
– define
only
 Introduce
imaginary,
binary
numbers
––basic
operations
including
addition,
 complex
Introduce
imaginary,
binary
and
Binary
numbers
–
basic
operations
including
addition,
complex
numbers.
subtraction,
multiplication
and
division
of
whole
numbers)
numbers.
subtraction,
multiplication
and division
of whole
numbers)
degree
of accuracy.
complexnumbers.
numbers.
subtraction,
multiplication
and
division
ofwhole
whole
numbers)
Numbercomplex
•
Learners
must
be
able
to
round
off
to
one,
two
or
subtraction,
multiplication
and
division
of
numbers)
3
complex
numbers.
subtraction,
multiplication
and
division
of
whole
numbers
Complexnumbers
numbers––define
defineonly
only
Round
realnumbers
numbers
offto
toaa
Complex
systems
 • Round
real
off
Convert
rational
numbers
Complex
numbersnumbers
–define
defineonly
only
 Round
Round
real
numbers
off
to
a
three
decimals.
Complex
numbers
–

real
numbers
off
to
a
Complex
–
define
only
 significant/appropriate
Round
numbers
off
to a of
Number
significant/appropriate
degree
 Learners
Learners
must
be
able
tooff
round
offto
to
one,
twoor
ordecimals.
threede
de
into real
decimal
numbers
Number
degree
numbers
must
be
able
to
round
off
one,
two
three
Number
significant/appropriate
degreeof
ofand of
 Learners
Learners
must
be
able
toround
round
toone,
one,
two
orthree
three
Binary
system
consists
of to
two
numbers,
significant/appropriate
degree

must
be
able
to
off
to
two
or
decimals.
33 Number
Number
significant/appropriate
degree
of

Learners
must
be
able
round
off
to
one,
two
or
three
d
systems
accuracy.
vice versa.
systems
accuracy.
3 systems
systems
accuracy.
namely 0 and 1.
systems accuracy.
accuracy.
Binarynumbers
numbers
system
consists
oftwo
twonumbers,
numbers,
namely
and
Convert
rational
numbers
into Binary Binary
Determine
between
system
consists
of
00and
 • Convert
rational
numbers
into
numbers
systemconsists
consists
oftwo
twonumbers,
numbers,
namelynamely
0and
and1.1.
Convert
rational
numbers
into which
Examples:
Binary
numbers
system
of
namely
0
 Convert
rational
numbers
into
Binary
numbers
system
consists
of
two
numbers,
namely
0
an
 decimal
Convert
rational
numbers
into
Examples:
decimal
numbers
and
vice
versa.
two numbers
integers
aand
given
Examples:
vice versa.Examples:
decimalnumbers
numbers
andvice
vice
versa.
Examples:
decimal
and
versa.
2
1
Examples:
decimal
numbers
and
vice
versa.
1
1
1
simple between
surd
lies. which
1.1111
(R)111 2.
2. 1(R)
(R)
111211222 111221(R)
Determine
between
whichtwo
two 1. 111 1.
11
(R)
1177 (R)
 Determine
2.
22  112122 11771(R)
Determine
between
whichtwo
two
101
101
11101
1(R)2.
1.1.111  11.
2111
2.72. (R)
(R)
 Determine
between
which
111
(R)
 1  2   1  2 (R)
1

• integers
Determine
between
which
two
integers
a
given
simple
surd
lies.
Set
builder
notation,
 101
asimple
given simple
surd lies.

101
integers
a
given
surd
lies.
1100
integers
aintegers
given
simple
surd
lies.
a given
simple
surd lies.
interval
notation
and
1100 1100
 Set
Set
builder
notation,
interval
builder
notation,
interval
1100
1100
Setbuilder
builder
notation,
interval
 Set
notation,
interval
number
lines.
 notation
Set builder
interval
notation
andnotation,
number
lines.
and
number
lines.
notation
and
number
lines.
notation
and number
lines.
notation
number lines.
Revise Revise
prime
numbers
and prime
Revise
lawsand
ofexponents
exponents
studied
1.1.Revise
Revise
laws
of
exponents
studiedComment:
in
Comment:
Revisebase
prime
basenumbers
numbers
andprime
primefactorisation
factorisation
1.
laws
of
in
Comment:
prime
base
and
1.
Revise
laws
of
exponents
studiedstudied
in
Comment:
Reviseprime
prime
base
numbers
andprime
prime
factorisation
1. Revise1.laws
of
exponents
studied
in
Comment:
Revise
base
numbers
and
factorisation
in
Grade
9
where
factorisation
Revise
laws
of
exponents
studied
in
Comment:
Revise
prime
base
numbers
and
prime
factorisatio
where
99where
Grade9Grade
9Grade
where
Grade
where
where
09,and
and
Examples:
ZZ ...
and
xxGrade
,,and
yy 0m
Examples:
Examples:
nZm
Zm.,.,nn 
Examples:
xx, ,yy00xand
Examples:
m
,
n
2
, y m
0
and
.
m
,
n

Z
m
1.Examples:
(K)
2233 (K)
3 22 
mxxnnnn xxmmmn+nn
m
m
 xn nxx
33 2
1. 22222×1.
(K)
2

x
x
2
1.
(K)
m•
m× nxn = xm n
x
1.
(K)
2
m
x11 23
1.
(K)
2

x  x xmxmxxxnn xmxmnn
x
9
2. 9 xx(R)
(R)
m
mxn  x
  xn nxm
9x x112.
(R)
11


x
x
m
m

n
2.
2
Exponents
9
−
n
m

n
x

1
3
9
2 Exponents
Exponents 
x • x 
2. 93x x1+1 2. 3 (R)
÷n x 
=mnx
xxm )n
(R)
m n ((xxmmn
2 Exponents
Exponents 
)  xxmnmn
2. 3 x −1 (R) 3x 1
m n

(x(xm•)n) x(xmn
3
x ) ymm x (xy)mm
m
m
 mxxm (xy
y m)mm (xy) m
Solve
for xx::
Solve
Solve
for
 xxm•yym xm(xy
)
Solvefor
for
xx: ::xfor
 y  (xy)
Page2
Solve
x
Page
Solve
Also
by
definition:
x : (K)
by definition:
3.2733x for
27
x 3.
Alsoby
byAlso
definition:
Also
by definition:
2
Exponents
(K)
27
3.
(K)
3

x
Also
definition:
Also by
definition:
3.3. 3  4.
27
0
xx (K)
3. 3(K)
(K)
27
and
x  00x,,0and
(K)
36
36
1xn−,nnx1101n ,,xand

n
x 4. 66x 
xx0 011,,4.
(K)

,

1
x
(K)
4.
(K)
6

36
0
 n  1xnx
,
x
n
1
x
n
x (K)
, xx 
,and
≠x 0
0
=x0 ,nand

1 , x  14., 6  36
x  xn x, x 
,
,
and
4.
(K)
6

36
• x x0 = 1 ,xxn
x ≠ 0.
2. Use the laws of exponents
to simplify expressions and
Comment: Make sure to do examples of very big and
solve easy exponential
very small
equations (the exponents
numbers.
may only be whole numbers).
3. Revise scientific notation.
1
Mensuration
24
1. Conversion of units and
square units and cubic
units.
All conversions should be
done both ways.
2. Applications in technical
fields.
•
•
•
•
Units of length: (mm, cm, m, km)
e.g. 1000m = 1km
Units of area: (mm2, cm2, m2)
e.g. 1 m2 = 1 000 000 mm2
Units of volume: (ml = cm3, m3, dm3 = 1l).
Typical practical examples on the learners’ level
should be introduced.
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
111
Comment:Make
Makesure
suretotodo
doexamples
examplesofofvery
verybig
bigand
andvery
verysmall
small
exponentialequations
equations(the
(the
Comment:
exponential
numbers.
exponents
may
only
be
whole
numbers.
exponentsmay
mayonly
onlybe
bewhole
whole
numbers.
exponents
numbers).
numbers).
numbers).
3.
Revise
scientific
notation.
3.Revise
Revisescientific
scientificnotation.
notation.
3.
1.
Conversion
of
units
and
square
units
Units
of
length:
(mm,
cm,
m,
km)
e.g.
1000m
1km
1.Conversion
Conversionof
ofunits
unitsand
andsquare
squareunits
units  Units
Unitsof
oflength:
length:(mm,
(mm,cm,
cm,m,
m,km)
km)e.g.
e.g.1000m
1000m===1km
1km
1.
22
22
22
22
2
2
2
2
2
and
cubic
units.
andcubic
cubicunits.
units.
Units
of
area:
(mm
cm
m
e.g.
m
000
000
mm
GRADE 10:TERM
1of
and
Units
ofarea:
area:(mm
(mm,,,cm
cm,,, m
m)))e.g.
e.g.111m
m ===111000
000000
000mm
mm2 2
Units
3
3
3
All
conversions
should
be
done
Allconversions
conversions
shouldbe
be
done
All
should
done
Units
of
volume:
(m
cm
m
dm
1l).
Unitsof
ofvolume:
volume:(m
(m
cm3,3,,m
m3,3,,dm
dm3 3===1l).
1l).
Weeks
Topic
Curriculum
statement
Clarification
 Units
lll===cm
both
ways.
both
ways.
both
ways.
Mensuration
Mensuration
Typical
practical
examples
on
the
learners’
level
should
be
Mensuration
Typical
practicalexamples
examples
onthe
the
learners’
levelshould
shouldbe
be
Where
Typical
learners’
level
an practical
example
is
given, on
the
cognitive
demand
2.
Applications
technical
fields.
2.Applications
Applicationsinin
intechnical
technicalfields.
fields.
2.
introduced.
introduced.
is suggested:
knowledge
(K),
routine
procedure
(R),
introduced.
complex procedure (C) or problem-solving (P).
333
1.
Revise
notation
(interval,
set
1.
Revise(interval,
notation
set
1. Revise
Revise
notation
(interval,(interval,
set
1.
notation
set
Examples
builder,
number
line,
sets).
builder,
number
line,
sets).
Examples
builder,number
numberline,
line,sets).
sets).
Examples
builder,
Examples
2.
Adding
and
subtracting
of
2.
Adding
and
subtracting
of
algebraic
2. Adding
Addingand
andsubtracting
subtractingof
ofalgebraic
algebraic 1.
10
1.
Subtract
from
(K)
10bbb (K)
1.
Subtract
from
2.
1.Subtract
Subtract444
from555
(K)
a4aaa+888b8bbbfrom
aaa10
algebraic terms.
terms.
terms.
terms.
3. Multiplication of a binomial by Remove brackets
3.
Multiplication
of
binomial
by
3. Multiplication
Multiplicationof
ofaaabinomial
binomialby
byaaa
Remove
brackets
Removebrackets
brackets
3.
Remove
a binomial.
binomial.
binomial.
binomial.


2.
(K)
+222
2.
(K)
xxxx−2222
(K)
)=
2)(
2.x(xxx
(K)
4. Multiplication of a binomial by 2.
4.
Multiplication
of
a
binomial
by
a
4.
Multiplication
of
a
binomial
by
a
4. Multiplication
of a binomial by a
2222
a trinomial.
3.
(K)
((444xxxx−5555yyy)y))) =
3.
(K)(K)
3.
(K)
3.((4
trinomial.
trinomial.
trinomial.
5. Determine the HCF and
22xxx333yyy
4.
(K)
4.x(xxyyy2
(K)
(K)
5.
Determine
the
HCF
and
LCM
of
not
5. Determine
Determine
theof
HCF
and
LCM
ofthree
not 4.
LCM
notand
more
than
5.
the
HCF
LCM
of
not
x − 3y) =
4. x − y )(2
(K)
2
2
2
numerical
or
monomial
more
than
three
numerical
or
more
than
three
numerical
or
3
Algebraic
more than three numerical or


2
a

3
a

2
a

1

5.
(R)


2
a

3
a

2
a

1

5.
(R)
5. 2a  3 a 2 2a  1  (R)
algebraic
expressions
by
5. (2a + 3) a − 2a − 1 = (R)
monomial
algebraic
expressions
by
monomial
algebraic
expressions
by
Algebraic
monomial
algebraic
expressions
by
Algebraic expressions
Algebraic
making
use
of
factorisation.
making
use
of
factorisation.
makinguse
useof
offactorisation.
factorisation.
expressions
making
expressions
expressions
Factorise
Factorise
Factorise
(
6. Factorisation of the following
types:
6.
Factorisation
of
the
following
types:
6. Factorisation
Factorisationof
ofthe
thefollowing
followingtypes:
types:
6.
•
common factors

common
factors

common
factors
 common factors
•  grouping
in
pairs
grouping
in
pairs
groupingin
inpairs
pairs
 grouping
•  difference
of
difference
of
two
difference
of
twosquares
 difference of two
two
•
addition/subtraction
of two
squares
squares
squares
cubes
addition/subtraction
of
addition/subtractionof
of
 addition/subtraction
•
trinomials
two
cubes
twocubes
cubes
two
Assessment Term 1:
trinomials
trinomials
 trinomials
Factorise
22
)
22
2
xy
xy
6.
(K)
444xy
xy2 666xy
xy (K)
6.
(K)
6.
6. 222xxx yyy
(K)
ab
ac
7.
(R)
ab
ac222bbb222ccc (R)
7.
(R)
7.
(R)
7. ab
aac
222
222
8.
(K)
8.
(K)
8.
(K)
8. 2
(K)
222aaaa2 −8888bbbb2
33 is not
3a
333 restricted to  in grade 11.
8y
9.
(R)
8y3
9. xxx38y
(R)
9.
(R)
9.
x 2 − 8y
10.
44
10.xxx
x2 22 777xxx
44
10.
44
8
10. 7x
(R)
(R)
(R)
(R)
(R)
cosec  1
sin 
1. Investigation or project (only one project or one investigation a year) (at least 50 marks)
Example of an investigation:
Page
Page22
Page
Imagine a cube of white wood which is dipped into red paint so that
surface
is red,
but the
inside
still white.
a the
 for
parabola
graphs
only
in grade
10 If
one cut is made, parallel to each face of the cube (and through the centre of the cube), then there will be 8 smaller
2
cubes. Each of the smaller cubes will have 3 red faces and 3 white
cotfaces.
  1Investigate
 cosec2 the number of smaller cubes
which will have 3, 2, 1 and 0 red faces if 2/3/4/…/n equally spaced cuts are made parallel to each face. This task
provides the opportunity to investigate, tabulate results, make conjectures and justify or prove them.
2. Test (at least 50 marks and 1 hour). Make sure all topics are tested.
Care needs to be taken to set questions on all four cognitive levels: approximately 20% knowledge, approximately
35% routine procedures, 30% complex procedures and 15% problem-solving.
CAPS
TECHNICAL MATHEMATICS
25
ks
ks
eks
2
22
Topic
Topic
Topic
Weeks
Algebraic
Algebraic
Expressions
Algebraic
2
Expressions
(continue)
Expressions
(continue)
(continue)
3
33
Equations
Equations
and
Equations
and
Inequalities
and
3
Inequalities
Inequalities
3
33
Trigonometry
Trigonometry
Trigonometry
26
Topic
GRADE 10: TERM 2
GRADE
10: TERM 2
Curriculum statement GRADE 10: TERM 2
Clarification
GRADE 10: TERM 2
Curriculum
statement
Clarification
Where an example is given, the
cognitive demand is suggested:
Curriculum statement
Clarification
Where
an
example
is
given,
the
cognitive
demand
isissuggested:
knowledge
(K),
routine
procedure
(R), complex
procedure
(C) or
Curriculum statement
Clarification
Where an example is given,
the cognitive
demand
suggested:
7. Do addition, subtraction,
7.
subtraction,
multiplication
and
division
of
7. Do
addition,
subtraction,
7. Do
Doaddition,
addition,
subtraction,
multiplication
and
of
algebraic
fractions
using
multiplication
and
multiplication
anddivision
division
of division
algebraic
fractions
using
factorisation
(numerators
and
of
algebraic
fractions
algebraic fractions using
Algebraic
using
factorisation
factorisation
(numerators
and
denominators
should
be limited
factorisation
(numerators
and to
Expressions
(numerators
and
denominators
should
be
limited
to
the
polynomials
covered
in
(continue)
denominators
should be limited
to
denominators
should be
the
polynomials
covered
in
factorisation).
the polynomials
covered
in
limited to the polynomials
factorisation).
factorisation).
covered in factorisation).
1.1 Revise notation (interval, set builder,
1.1 Revise notation (interval,
1.1
(interval, set
number
line, sets).
1.1Revise
Revisenotation
notation
setbuilder,
builder,
set (interval,
builder, number
line,
number
line,
sets).
1.2 Solve
linear
equations.
number line,sets).
sets).
1.2
1.3
equation
withlinear
fractions.
1.2equations.
Solve
equations.
1.2Solve
Solvelinear
linear
equations.
1.3
Solve
equation
with
fractions.
1.3
Solve
equation
with
1.3 Solve equation with fractions.
2. Solve quadratic
equations by
fractions.
2. Solve
quadratic
2.
equations
by
factorisation
2. Solve
Solvequadratic
quadratic
equations
by
equations
by
3. factorisation
Solve
simultaneous
linear
equations
factorisation
factorisation
3.
simultaneous
linear
with
variables
3. Solve
Solvetwo
simultaneous
linearequations
equations
3. Solve simultaneous
two
variables
4.1with
Do
basic
Grade
8
&
9 word
with two variables
linear equations with two
Equations
4.1
Do
88&&99word
4.1problems.
Dobasic
basicGrade
Grade
word
variables
and
problems.
4.2
Solve
word
problems
problems.4.1 Do basicinvolving
Grade 8 & 9
Inequalities
4.2
Solve
involving
quadratic
or problems.
simultaneous
word
4.2linear,
Solveword
wordproblems
problems
involving
linear,
quadratic
or
linear
4.2 Solve
word
linear,equations.
quadratic
orsimultaneous
simultaneous
problems
involving
equations.
5. linear
Solve
simple
linear
inequalities
(and
linear equations.
linear,
quadratic
or
5.
Solve
simple
linear
inequalities
(and
graphically).
5. show
Solve solution
simple linear
inequalities (and
simultaneous
linear
solution
graphically).
6. show
Manipulation
of
formulae
show solutionequations.
graphically).(technical
6.
of
(technical
related).
6. Manipulation
Manipulation
offormulae
formulae
5. Solve
simple(technical
linear
related).
related).
inequalities (and show
1. Know definitions
of the
solution
graphically).
1.
Know
definitions
of
 and
trigonometric
ratios
sin  , ofcos
6. Manipulation
formulae
1. Know definitions
ofthe
the
trigonometric
ratios
,, cos
(technical
cos and
trigonometric
ratiossin
sinrelated).
and
knowledge
(K),
procedure
(R),
procedure
problem-solving
(P).is given,
knowledge
(K),routine
routine
procedure
(R),complex
complex
procedure(C)
(C)or
or
Where
an example
the cognitive
demand
problem-solving
(P).
is
suggested:
knowledge
(K),
routine
procedure
(R),
problem-solving (P).
complex procedure (C) or problem-solving (P).
Simplify
Simplify
Simplify
Simplify
11.
11.
11.
11.
12.
12.
12.
12.
x 2 y  xy 2 x 2  xy  bx  by
 2
2
xx2bx
xy
bx
2yyby
xy 2  xx 2 xy
xyxy
bxby
by

bx

by
xy
a

3
4
5
bxa−by
xy


3
4
5
a 22 aa3a33 2 + aa44+ 11 − a 2255 4
 a2 − 4
a2 + 3a + 2 
aa 2 33aa22 aa11 aa 2 44
(R)
(R)
(R)
(R)
(R)
(R)
(R)
(R)
Examples
Examples
Examples
Solve
for x :
Examples
Solve
for x :
Solve
for
3
x

4 xx:8:
1.
(K)
Solve
for
8
1. 3x + 4 =
(K)
1.
(K)
1. 33xxx344
(K)
828
2.
(R)
3xxx−331
 =
2
2.
(R)
2.
2.
(R)(R)
+
141x22  0
3. 3x3x2x
(K)

2
2
3. xx 2for
− 4x +22 = 00y :
(K)
3.
(K)
Solve
3. x 44xxxand
(K)
20
Solve
3x for
fory xx 4and
4.
andyy2:x:  y  6 (R)
Solve
and
Solve
4.
4. 33xx + yy =44 and
(R)
 yy =
66 (R)
4.
and22xx+
(R)
5. v  u  at (Change the subject of the formula to a ) (R)
5.
(R)
at
(Changethe
thesubject
subjectof
ofthe
theformula
formulato
to
5.
5. vEvuu1mv
(Change
the
subject
of
the
formula
at2 (Change
6.
to aav))) (R)
(R)
2 2
1
1
2 (Change
E

mv
6.
the
subject
of
the
formula
to
(R)
v
6.
(Change
the
subject
of
the
formula
)
(R)
6. E  2 mv (Change the subject of the formula to v ) (R)
2
1. Determine the values of cos  and tan  if sin   3 and
35
1.
cosand
tanififsin
sin 53 and
1. Determine
Determinethe
thevalues
valuesof
ofcos
andtan
and
5
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Page 30
Page
Page30
30
3
GRADE 10: TERM 2
Weeks
Topic
Curriculum statement
Clarification
Where an example is given, the cognitive demand
is suggested: knowledge (K), routine procedure (R),
complex procedure (C) or problem-solving (P).
1. Know definitions of the
trigonometric ratios sin θ ,
2.
1. Determine the values of cos θ and tan θ if sin θ = 3 and
5
    360 .
tan  , using cos
right-angled
(C)(C)
θ triangles
θ , using 90   90
and tantriangles
 360 .
tan  , using right-angled
(C)
y
360 .
for 0    right-angled
triangles for
y
for 0    360 . a
2. Introduce the
0° ≤reciprocals
θ ≤of360
° . of the
Introduce the reciprocals
the
3basic trigonometric
ratios,
sin  ,
2. Introduce
the
5
a is
not restricted
3basic trigonometric
ratios,
sin  , to  in grade 11.
53
reciprocals of the 3basic
1
3
cos  and tan  : cosec
,
1  , sin sin
cos  and tan  : cosec
trigonometric
x2 7
x sin8  ratios,
x
x
1: .
0
θ
and
tan
sec1  1θ , cos
andθcot


0
sec  
and
coscot
   1 1 . tan 
cos 
cosec tan

3. Trigonometric ratios insin
each
 of the
Trigonometric ratios in each of the ,
quadrants are calculated
where one
1 one
quadrants are calculated
θ =where
andby
ratio in the sec
quadrant
is
given
cos
ratio in the quadrant is given
byθ
Making
use
of Pythagoras’
theorem.
Making
use of
Pythagoras’
theorem.
making use of diagrams.
use of
a θ=for 1parabola
graphs Making
only in grade
10Pythagoras’ theorem.
making use of diagrams.
cot
.
θ
4. Practise the use of atan
calculator
for
2.
360°by
2. Draw
Drawthe
thegraph
graphofof yy=33sin
for00°≤θ≤360
by making the
sinθ for
Practise the use3.
of Trigonometric
acot
calculator
ratios
2
2 in
  1to
 for
cosec
2. Draw
0 by
 point
360plotting
the
graphthe
of use
by making
the
y of
3 sin
 forpoint
questions applicable
making
a
table,
and
each
questions applicable
to of the quadrants
use
of
a
table,
point
by
point
plotting
and
identify
the
following:
trigonometry.
table, point
by point plotting and identify the following:
the following:
are calculated where oneuse of aidentify
trigonometry.
- asymptotes
- •
asymptotes
ratio
in the quadrant is
5. Solve simple
trigonometric
-asymptotes
axes of symmetry
Solve simple trigonometric
0of
axes
of
symmetry
given
by
making
use
•
axes
of
symmetry
equations for angles between
0 and
0
the
domain
and range.
(C)
Trigonometry
equations 0for angles
between 0 and
diagrams.
the
domain
and
(C)
90 .
•
the domainrange.
and range.
(C)
0
90 .
4. Practise the use of a
Note:
6. Solve two-dimensional
calculator forproblems
questions
Note: Note:
Solve two-dimensional problems
- It is very important to be able to read off values from the graph.
applicable to
trigonometry.
involving right-angled
triangles.
- It is •
very important
to be able toberead
off values
from
the from
graph.
involving right-angled
triangles.
It is very important
read
off
values
5. Solve simple
- Investigate
the effectto
of a able
and to
the
graph.
q on
Investigate
the
effect
of
and
on
the
graph.
a
q
the graph.
7. Trigonometry
graphs equations
trigonometric
Trigonometry graphs
0
 y  a sin
,
and
y

a
cos


between 0 and •
Investigate the effect of a and q on the graph.
 y  a sin  , yfor
 aangles
cos  and
900. for 0    360 .
y  a tan
0  two-dimensional
 360 .
forSolve
y  a tan  6.
 y  a sin
and


q
involving right y  a sin   q problems
and
for
y  a cos
  qtriangles.
angled
y  a cos   q for
Trigonometry
graphs
0 7. 
360 .
0    360 .
 16   4   1
 16   4   1
3.
4.
3
5.
6.
7.
Mid-year
Mid-year
examinations
examinations
•
y = a sin θ ,
y = a cos θ and
essment Term 2:
t Term 2:
y = a tan θ for
Assignment / test (at least 50 marks). Note that the weight of a test is equal to the weight of an assignment.
ent / test (at least 50 marks). Note that the weight
test° .is equal to the weight of an assignment.
0° ≤ θof≤a360
Mid-year examination (at least 100 marks)
r examination (at least 100 marks)
One paper of 2 hours (100 marks) or Two papers
(50 marks) and the other, 1 hour (50 marks)
y =- aone,
sin θ1+hour
q and
• - one, 1 hour (50 marks) and the other, 1 hour (50 marks)
er of 2 hours (100 marks) or Two papers
y = a cos θ + q for
0° ≤ θ ≤ 360° .
3
Page 31
Page 31 of 59
Mid-year
examinations
Assessment Term 2:
1. Assignment / test (at least 50 marks). Note that the weight of a test is equal to the weight of an assignment.
2. Mid-year examination (at least 100 marks)
One paper of 2 hours (100 marks) or Two papers - one, 1 hour (50 marks) and the other, 1 hour (50 marks)
CAPS
TECHNICAL MATHEMATICS
27
al
y
WeeksWeeks
Weeks
Topic
Topic
Topic
GRADE 10:
TERM
GRADE
10:3TERM 3
GRADE 10: TERM 3
Curriculum
statement
Clarification
Curriculum
statement
Clarification
Curriculum statementWhere an example is given, the cognitive
Clarification
demand
Where an example is given, the cognitive
demand is sugges
Where
an example
is given,procedure
the cognitive
is sug
is suggested:
knowledge
(K),
routine
(R), demand
knowledge (K), routine procedure (R), complex
procedure (C
knowledge
routine procedure
(R), complex procedu
complex problem-solving
procedure
(C) (K),
or(P).
problem-solving
(P).
Represent
GRADE 10:geometric
TERM 3 figures on Example: problem-solving (P).
a Cartesiangeometric
co-ordinate
system.
the points P(2 ; 5) and Q(-3 ; 1) in the
figures
on a Consider
Example:
Curriculum statement Represent
Clarification
Represent geometric figures onCartesian
a
Example:
plane.
(R)
Cartesian
co-ordinate
the
points P(2
; 5) and Q(-3 ; 1) in the Cartesian plan
( x1; y1) is given, theConsider
Apply
for any
two points
an system.
example
cognitive
demand
is
suggested:
CartesianWhere
co-ordinate
system. 1.1
Consider
the
points
P(2
;
5)
and
Q(-3
;
1)
in the Cartesian
Calculate
the 3distance
10:
(R)TERM
(x1routine
; y1) andGRADE
Apply for any
two points(K),
knowledge
procedure
(R),
complex
procedure
(C)
or
(R)
( x2; y2for
) formulae
and Apply
PQ.
any two for
points (x1; y1) and
1.1 Calculate the distance PQ. Clarification
Weeks
Topic
Curriculum
statement
problem-solving
(P). the:
(x2; y2 ) formulae
for determining
determining
the:
1.2 Find the1.1
gradient of PQ.the distance PQ.
(x2; y2 ) formulae for determining the: 1.2 FindCalculate
the
gradient
of
Where
anthe
example
is PQ.
given,
1.
distance
between
the
two
1.3
Find
the
mid-point
of PQ.
1.2
Find
gradient
of PQ.the cognitive demand is sug
1. distance between the two points;
1.3
Find
the
mid-point
of PQ.
1.
distance
between
the
two
points;
points; Example:
Analytical
1.4
Determine
the
equation
of
PQ.
knowledge
(K),
routine
(R), complex procedur
Represent geometric
figures on2.
a gradient
1.3 Find the mid-point procedure
of PQ.
of the line segment
Analytical
1.4
Determine
the
equation
of
PQ.
2.
gradient
of
the
line
segment
2.
gradient
of
the
line
segment
1
Geometry
problem-solving
(P).
Analytical
Cartesian co-ordinate
system.
Consider
points
P(2from
; 5) and Q(-3
in the Cartesian
plane. of PQ.
1.4; 1) Determine
the equation
connecting
the twothe
points
(and
1
Geometry
connecting
the two
points
connecting
the two
points (and from
1 any two points
Geometry
(R)
(x1; y1) and
Apply for
that
identify
and
(andthat
from
thatparallel
identify
parallel
identify
parallel
anddistance
Represent
geometric
figures
on a PQ. Example:
1.1
Calculate
the
perpendicular
lines);
(x2; y2 ) formulae for determining the:
andperpendicular
perpendicular lines);
lines);
Cartesian1.2
co-ordinate
system.
Consider the points P(2 ; 5) and Q(-3 ; 1) in the Cartesian p
the
gradient
3. coordinates
coordinates
ofFind
themid-point
mid-point
of of
thePQ.
3.
of
the
1. distance between the two points;
3. coordinates
of the
mid-point
of
the
(R)
1.3
Find
the
mid-point
of
PQ.
(
x
;
y
)
Apply
for
any
two
points
and
of the
line segment
segment
joiningjoining
the two1 points;
1
2. gradient of the line segment line
line
segment
joining
the
two
points;
1.1 Calculate the distance PQ.
1.4 Determine
the equation
the
two
andfor determining
(x2;and
y2 ) points;
formulae
the: of PQ.
connecting the two points (and and
from
1.2 Find the gradient of PQ.
4.
equation
of
line
4. the
the
equationbetween
ofaastraight
straight
line points;
passing
1.
the two
that identify parallel and
4. distance
the equation
of apoints.
straight
line passing 1.3 Find the mid-point of PQ.
passing
through
two
through two points.
3.
4.
1.
2.
s
3.
2. gradient
of the line segment
perpendicular lines);
Analytical
1.4 Determine the equation of PQ.
y through
mx  c two points.
connecting
coordinates
of the
mid-point of the y  mx  c the two points (and from
1
Geometry
1. Functional
notation
Investigate
the way (unique)
values
depend
Functional
notation
Investigate
the wayoutput
(unique)
output
values depend on how t
identify
parallel and
line segment joining the two1.
points;
1. that
Functional
notation
Investigate
the way
(unique)
output values depend on ho
2.
Generate
graphs
by
means
on
how
the
input
values
vary.
The
terms
independent
2.
Generate
graphs
by
means
of
pointvalues
vary.
The
terms
independent
(input)
and dependent (o
perpendicular
lines);
and
2.point-by-point
Generate graphs
by means(input)
of pointvalues vary.
The terms
independent
of
plotting
and
dependent
(output)
variables
might be (input) and depende
by-point
plotting
supported
by
variables
might
be
useful.
3. coordinates
of the supported
mid-pointuseful.
of
the equation of a straight line passing
by-point
plotting
bythe
variables 2might be useful.
supported
by available
available
technology.
y  ax  q . Draw the parabola for a  1 only. Use t
7.1.1.1
line
segment
joining
the
two
points;
through two points.
technology.
available technology.
only. Usefor
thea  1 only. U
a =the
±1 parabola
7.1.1.1 Draw the parabola y  ax2  q .for
Draw
y  mx  c
and of the following
method only.
3. Drawing
table method only.
Functions
method only.
Functions
functions:
4. the equation
of athe
straight
line
passing
Identify
the characteristics:
following
Functional notation
Investigate
way (unique)
output
values
depend
oncharacteristics:
how the input
Identify
the
following
Identify
the following characteristics:
3Generate graphs
andby means •
through
two
points.
Linear
function:
*
y-intercept
of
pointvalues
vary.
The
terms
independent
(input)
and
dependent
(output)
3
and
* y-intercept
◦◦ y-intercept
y

mx

c
*
x-intercepts
Graphs
by-point plotting supported by
variables(revise)
might be useful.
* x-intercepts
Graphs
1.
Functional
notation
Investigate
output
values depend on ho
* (unique)
the
turning
points
available technology.
x-intercepts
•
Quadratic:
y

ax2  q . Draw the◦◦parabola
7.1.1.1
for a the
only.
theturning
table
1 way
*Usethe
points
2. Generate graphs
by
means
of
pointvalues
vary.
The
terms
independent
(input)
and dependen
*
axes
of
symmetry
method
only.
* axes of symmetry
3. Drawing
of the
following
functions:
◦
◦
the
turning
points
by-point
plotting
supported
by
variables
might
be
useful.
*
the
roots
of
the
parabola
(x-intercep
afollowing
Drawing
ofythe
functions:
• 3.
=the
Identify
following
characteristics:
* the roots of the parabola (x-inter
y

mx

c
 Hyperbola:
Linear
function:
Functions
2
x
available
the domain
(input for
values)
and
range
y  ax  q*. Draw
7.1.1.1
thedomain
parabola

1 only.
y  mx
c ◦◦ axes of symmetry
 Lineartechnology.
function:
* y-intercept
* the
(input avalues)
and raU
3
and
(revise) y = a.b x
•
Exponential:
values)
method only.
(revise)
* x-intercepts
values)
Graphs
Functions
◦◦ the roots of the parabola (x-intercepts)
where b ≠ 1 and b > 0 * the turning
Identify
points the following characteristics:
3
and
* and
y-intercept
◦ symmetry
the domain (input values)
range (output
* axes◦of
Drawing of the following
Note: a, b, c, m, p, q ℝ
*
x-intercepts
Graphs functions:
* the roots
of the parabola (x-intercepts)
values)
 Linear function: y  mx  c
* the(output
turning points
* the domain (input values) and range
◦◦ Very important to be able
readofoffsymmetry
values
(revise)
* toaxes
a = ±1 for parabola graphs only.
values)
3. Drawing of the following functions: from the graphs.
* the roots
parabola (x-interc
Pageof32the
of 59
 Linear function: y  mx  c
◦◦ Investigate the effect of *q onthe
thedomain
graph. (input values) and ran
(revise)
values)
◦◦ asymptotes where applicable
NOTE: Use this approach to engage with all the
other graphs.
28
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
GRADE 10: TERM 3
Weeks
Topic
Curriculum statement
Clarification
Where an example is given, the cognitive demand
is suggested: knowledge (K), routine procedure (R),
complex procedure (C) or problem-solving (P).
4
Euclidean
Geometry
1. Revise basic geometry done
in Grades 8 and 9.
Lines and parallel lines,
angles, triangles congruency
and similarity.
2. Apply the properties of
line segments joining the
mid-points of two sides
of a triangle. Do practical
problems.
3. Know the features of
the following special
quadrilaterals: the kite,
parallelogram, rectangle,
rhombus, square and
trapezium (apply to practical
problems).
4. Pythagoras’ theorem
•
Calculate the unknown
side of a right-angled
triangle.
No formal proves are required, only calculation of
unknowns.
Know the properties of the following kinds of triangles
•
scalene
•
isosceles triangle
•
equiangular triangle
Congruency:
Investigate the conditions for two triangles to be
congruent:
•
•
•
•
3 sides
side, angle side
angle, angle, corresponding side
right angle, hypotenuse and side
Similarity:
Investigate the condition for two triangles to be similar:
•
Give drawings of similar triangles, write down the
corresponding angles and calculate the ratio of
the corresponding sides.
Investigate: line segment joining the mid-points of two
sides of a triangle is parallel to the third side and half of
the length of the third side.
Investigate and make conjectures about the
properties of the sides, angles and diagonals of these
quadrilaterals.
Calculation of one unknown side of a right-angled
triangle, using Pythagoras’ theorem.
Assessment Term 3: Two (2) tests (at least 50 marks and 1 hour) covering all topics in approximately the ratio of
the allocated teaching time.
CAPS
TECHNICAL MATHEMATICS
29
GRADE 10: TERM 4
GRADE 10: TERM 4
GRADE 10: TERM 4
Weeksstatement
Topic
Curriculum statement
Clarification
Curriculum
Clarification
Where
an
example
is
given, the cognitive demand
Curriculum statement
Clarification
Where an example is given, the cognitive demand is suggested:
is
suggested:
knowledge
procedure (R),
Where(K),
an example
is given, the
is(K),
suggested:
knowledge
routine procedure
(R),cognitive
complexdemand
procedure
(C) routine
or
complex
procedure
(C)
or
problem-solving
(P).
knowledge (K), routine procedure (R), complex procedure (C) or
Analytical
Geometry
1
problem-solving (P).
problem-solving
GRADE
10: TERM 4
Continuation
from term
3. (P).
Continuation
from term 3.
s
Topic
Continuation from term 3.
Curriculum
statement
Clarification
1. Define
a radian
Example: (K)
Where
example
is given,
the cognitive
2. Indicate the relationship
• an Revise
circle
terminology:
chord,demand
secant, is suggested:
Example: (K)
between
degrees
and
knowledge
(K),
routine
procedure
(R),
complex
(C) or
segment, sector, diameter, radius, arc, procedure
etc.
Example:
1. Define a radian
 Revise
circle(K)
terminology: chord, secant,
segment, sector,
radians,
convert
radians
problem-solving
(P).
• chord,
Rediscover
ratiosector,
between circumference
1. Define a radian
 Revise
circle arc,
terminology:
secant,unique
segment,
diameter,
radius,
to degrees
or degrees
to etc.
diameter represented
by π .
diameter,
radius,
etc. and
 Rediscover
unique
ratioarc,
between
circumference
and diameter
radians,
convert
degrees
Analytical
 3.Rediscover
unique
Continuation from
andterm
minutes
to radians
represented
by 
.and ratio
360°diameter
= 2π radians and
• between
Showcircumference
that any circle and
Geometry

represented
by
.
radians
to
degrees
and
  2 radians
 Show that any circle 360
and consequently
consequently
that 360° =that
6,283 radians and that
Example:
(K) radians
minutes.
3601radian
  Show
that
any circle
2. Indicate the relationship between
radians
and that
360
 6,283
 57,3and
 . consequently that
12radian
1. Define a radian
 and
Revise
circle
terminology:
secant, segment, sector,
2. Indicate
the relationship
radians
that
1 radian
  6,283
 57,3minutes
 . chord,and
degrees
and radians,
convert between Revise360
degrees,
minutes
and
seconds.
•
Revise
degrees,
seconds.
diameter,
radius,
arc,
etc.
degrees
and radians,
convert
radians
to degrees
or degrees
to
 Revise
degrees,
and
seconds.
 Learners
should
knowminutes
to
convert
radians
to
degrees
and
to
Learners
should
to convert
radians toand diameter
 •
Rediscover
unique
ratioknow
between
circumference
radians
to degrees
degrees to
radians,
convert
degreesorand
 Learners
should
know to convert
radians
to convert
degreesdegrees
and to to radians.
degrees
and
to
convert
degrees
to radians.
represented by  .
radians,
convert
minutes
to radians
anddegrees
radiansand
to
convert
degrees
to radians.
 Examples
should
include
the
following:
•
Examples
should
360include
  2 the

Show
that
any circle
radians and consequently that
minutes
to radians and radians to
degrees
and minutes.

Examples
should
include
the
following:
following:
convert
degrees
to radians:
convert degrees
to radians: 360
etc.
213
; 133
,
3

;
300
,
12
'
;
110
,
24
'
6
"
2.
Indicate
the
relationship
between
6,283 radians and that 1 radian  57,3 .
degrees and minutes.
convert
degrees
to
radians:
213

;
133
,
3

;
300
,
12
'
;
110
,
24
" etc.
etc.
convert
radians to degrees:
1,5 rad;
65,98 rad;
16,25and
rad;seconds.
etc.' 6(K)
degrees and radians,
convert
 Revise
degrees,
minutes
• and1,5
convert
to degrees:
rad;(K)65,98 rad;
radians
to degrees:
rad; radians
65,98 rad;
16,25 rad;1,5
etc.
(answers
in degrees,
minutes
seconds).
radians to degrees
orconvert
degrees
to
 Learners
should
know
to convert
radians
to degrees
and to
16,25
rad;
etc.
(K)
(answers
in
degrees,
minutes
(answers
seconds).
 Practical
application
in theminutes
technicaland
field:
radians, convert
degrees
and in degrees,
convert
degrees
to
radians.
and seconds).
 and
ininthe
technical
field:which a pulley with
- Practical
Calculate
radians
through
minutes to radians
radiansapplication
tothe angle
Circles,
 •
Examples
should
include the
Practical
application
in following:
thea technical
field:
Calculate
the
angle
in
radians
through
which
pulley with
will rotate
if a length
of belt
of 120m
anglesdegrees
and and minutes. a diameter of 0,6mconvert
degrees
to
radians:
213
; 133,3; 300,12' ; 110,24' 6" etc.
Circles,1
a diameter
of 0,6m will
rotate if athe
length
ofinbelt
of 120m
angular
passes
over the pulley.
◦◦ radians
Calculate
angle
radians
through
whichrad; etc. (K)
angles and
convert
to degrees:
1,5 rad;
65,98
rad; 16,25
passes
over
the
pulley.
movement
- A road wheel with a diameter
of
560mm
turns
through
an
ainpulley
withminutes
a diameter
of
0,6m will rotate if a
angular
(answers
degrees,
andthrough
seconds).
- Aofroad
wheel
with athe
diameter
of moved
560mmby
turns
an
150

angle
. Calculate
distance
a point
length
of
belt
of
120m
passes
over the pulley.
movement

Practical
application
in
the
technical
field:
150of
 . the
angle
Calculate
a point
on the
tyreof
tread
wheel.the distance moved by (C)
- ◦the
Calculate
the
angle
in
radians
through
which
a pulley with
on
the
tyre
tread
of
wheel.
(C)560mm
◦ A road
wheel with a diameter
turns
 Also ensure the following are covered
:
(R) of
a diameter
of 0,6m will rotate if(R)
a length of belt of 120m
 Also ensure the
following are covered
through: an angle of 150° . Calculate
the
- Add     2 radians and
covert
to the
degrees.
passes
over
pulley.

2

4
3
distance
moved
by a point on the tyre tread of
- Add   
radians
andwheel
covert
to degrees.
with
a diameter of 560mm turns through an
4 3 - A road

cos

sin

- Simplify: sin 90  cos 0 angle
the wheel.
(C)by a point
150
. Calculate
the distance moved
  sin
2of
90  cos
0


cos

- Simplify: sin •
Also
following
covered :
(R)
on ensure
the tyre2the
tread
of the are
wheel.
(C)
Page
35
of
59
 Also ensure
theπ following
are covered
:
(R)
◦◦ Add
+ π + 2π radians
and covert
toof 59
Page 35
4 23

 
- Add
radians and covert to degrees.
degrees.
4 3
Simplify: sin 90  cos 0  cos   sin 
- ◦◦ Simplify:
2
◦◦ Calculate sin π + cos π
2
4
Page 35 o
◦◦ Determine the value of the following:
sin −1 0,5 + cos−1 0,866 + tan −1 0,577 (answer in
radians).
30
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
GRADE 10: TERM 4
- Calculate sin-  Calculate
cos  sin  cos 
Weeks
Topic
Curriculum statement
Clarification
2

sin4  cos2
4



- sinCalculate
- - Calculate
Calculate
sin  cos
 cos
sin  cos
4value of the
2the
4 of
2 value
4 2thethe
Determine
following:
Determine
2
4
Where an example is- -given,
the
cognitive
demand

Calculate
sin
1 cos
-0,5the
Determine
value
followi
- - Determine
value
of1the
the
following:
value
following:
1 of
Determine
the
1 the
2procedure
4of
e the value of the following:
(K),1routine
(R),
3. FINANCE, GROWTH AND DECAY is suggested: knowledge
(answer
sin
 cos
0sin
,866
tan
0,577
0,5the

cos
0,866
 tan

1
1

1
problem-solving
1 1
1 value
10,following:
10
866
1577
sin
,5,866
(P).
cos
(answer
tan
0,577
Determine
the
of
the
complex
procedure
(C)
or
in ri
sin
0
,
5

cos
0
,
866
tan
0
,
(answer
sin
0
,
5

cos
0

tan
0
,
577
cos1 0,866  tan1 0,577 (answer in radians).Use the simple and
Usecompound
the simple and compound

1

1

1
Use
simple
and
compound
growth
formulae
Use
simple
and
compound
growth/deca
Use
the
simple
and
compound
 Use

(answer
in
sin
0
,
5

cos
0
,
866

tan
0
,
577
Use
the
simple
and
compound
Use
the
simple
and
compound
the
simple
and
compound
A  P(formulae
1  in) andA  P(1  in) and
growth formulaegrowth
n
n
growth
formulae
and
A

P
(
1

in
)
and
to
solve
formulae
and
A

P
(
1

i
)
A

P
(
1

i
)
A

P
(
1

in
)
growth
formulae
and
A

P
(
1

in
)
A Acompound
P(1P(1in)ninand
growth
formulae
) and
Use
the
simple
and
growth
formulae
A  P(1  i)nproblems
to solve
problems,
A  nP(including
(1  i) tointerest,
solve problems,
hire purchase,
problems (including interest, hire purch
A
(to
1 solve
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growth
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population
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and growth
inflation,
population
growth
and otherthe
inflation,
population
growth
and
other
including
interest,
hire
purchase,
inflation,
population
growth
and
other
real
life
problems.
Understand
the
real
life
problems.
Understand
2
growth
Finance
and
growth
and other realreal
life problems.
growth
2
problems.
Understand
the
real
lifelife
problems.
Understand
the
population
growth
and
other foreign
real
problems.
Understand
the
The
implications
of
fluctuating
The effect of different periods of compo
inflation,

implication
oflife
fluctuating
implication
of
fluctuating
foreign
growth
Understand
the implication
of foreign
implication
of
fluctuating
foreign
exchange
rates.
growth and decay (including effective a
implication
of
fluctuating
foreign
real
life
problems.
Understand
the
implication
of
fluctuating
foreign
exchange
rates
(e.g.
on therates
petrol
price,
exchange
(e.g.
on the petrol price,
fluctuating
foreign
exchange
nominal interest rates).
exchange
rates
(e.g.
on
the
petrol
price,
exchange
rates
on
thethe
petrol
price,
implication
of (e.g.
fluctuating
foreign
exchange
rates
(e.g.
on
petrol
price, travel).
imports,
exports,
overseas
travel).
rates
(e.g. on
the
petrol
price,
imports,
exports,
overseas
imports,
exports,
overseas
travel).
imports,
exports,
overseas
travel).
exchange
rates
(e.g.
on the
petrol
imports,
exports,
overseas
travel).price,
imports,
exports,
overseas
2
Revision
2
Revision
2
Revision
travel).
2
Revision
imports,
exports,
overseas
travel).
2
Revision
Assessment Term
4:
Assessment
Term
4:
4. ALGEBRA
Assessment
Term
4: 4: Term 4:
2 2 Assessment
Revision
Assessment
Term
Revision
Assessment Term
4:
Assessment
Term 4:
Assessment
Term
(a) Simplify expressions using the laws of
(a) Apply the laws of exponents to expr

Assessment
Term
Assessment
Term 4: 
Assessment
Term
4:4:4: 4:
Assessment
Term
1.1.Test
(at(atleast
5050
marks)
1.
Test
(at least 50 marks)
exponents
for
integral
exponents.
involving rational exponents.
Test
least
marks)
Term
4:marks)
1.least
Test
(at
least 50 marks)
1.Assessment
Test
(at(at
least
502.
marks)
1.
50
2.
Examination
(b) Establish between which two integers a
(b) Add, subtract, multiply and divide si
Examination
2.Test
Examination
2.1.2.
Examination
Test
(at1:2.
least
50 marks)
Examination
given
lies. 60 
surds.
Paper
1:
hours
(100marks)
marks
made
up marks
as
on
algebraic
expressions,
equations,
inequalities
exponents, and
60
3surd
25 exp
3
Paper
1: 2 hours
(100
madesimple
up as
follows:
expressions,
equations,
expressions,
equations,
inequalities
andinequalities
Paper
22Examination
hours
(100
as follows:
follows:
3 on algebraic
1:
2functions
hours
(100
marks
made
up
as
follows:
on
algebraic
expressions,
equations,
inequalities
and
exponents
60

3
1: 1:
2 hours
marks
made
up
as
follows:
on
algebraic
expressions,
equations,
inequalities
and
exponents,
60

3
25

3
(c)
Round
real
numbers
to
an
appropriate
(c)
Demonstrate
an
understanding
of
th
2.Paper
Examination
Paper
2Paper
hours
(100
marks
made
up
as
follows:
on
algebraic
expressions,
equations,
inequalities
and
exponents,
60

3
25

3
equalities and
exponents,
on functions
graphs
(trig.
functions
will
be
examined
in
paper
2)
and
on
finance
and
growth.
on
functions
and
graphs
(trig.
functions
will
be
examined
in
paper
2)
and
on
finance
and
25and
(100
3on
15

3
and graphs (trig. functions will
15  3 on finance and growth.
on
functions
and
graphs
(trig.
functions
will
be
examined
in
paper
2)
and
on
finance
and
growth.
15

3
degree
of
accuracy
(to
a
given
number
of
definition
of
a
logarithm
and
any
law
on
functions
and
graphs
(trig.
functions
will
be
examined
in
paper
2)
and
on
finance
and
growth.
15

3
Paper
1:
2
hours
(100
marks
made
up
as
follows:
on
algebraic
expressions,
equations,
inequalities
and
exponents,
on
functions
and
graphs
(trig.
functions
will
be
examined
in
paper
2)
and
on
finance
and
growth.
15

3
60

3
25

3
growth.
growth.
Paper 2: 2 hoursPaper
(100 marks
made
up marks
as follows:
trigonometry,
3 on
 3 on Analytical
30 Geometry,
3 on Euclidean
2: 2 hours
(100
made40
upas
follows:
trigonometry,
40  3 on15
15  Geometry,
3 on Analytical
30  3 o
decimal
digits).
needed30
to30
solve
lifeproblems.
2:
2marks
hours
(100
marks
made
upexamined
as40
follows:
on
trigonometry,
onGeometry,
Analytical
Geometry,
40

3 2)
15
 3 and
30
3 on Eucl
2:Euclidean
2 hours
(100
made
upup
as
follows:
on
trigonometry,
Analytical
Euclidean
Paper
2:
22Paper
hours
(100
marks)
made
up
as
follows:
trigonometry,
Analytical
Geometry,
on
40

3and
15
33on

3on
functions
and
graphs
(trig.
functions
will
be
in
paper
and
on
finance
growth.
Paper
2:
hours
(100
marks
made
as
follows:
on
trigonometry,
Analytical
Geometry,
on
Euclidean
15
3circles,
15
3onon
3real
Geometry, 30Paper
on
3 on
Geometry
and
mensuration,
circles,
angles
angular
movement.
15
3 on
Geometry
and
mensuration,
angles
and
angular
movement.
15
3 on
(d) angles
Revise
notation.
Geometry
mensuration,
circles,
angles
and
angular
15

3 on
Euclidean
Geometry
and
onup
mensuration,
circles,
angles
and
angular
movement.
Geometry
mensuration,
circles,
and
movement.
1515
(100
3on
Paper
2: 2and
hours
marks
made
ascircles,
follows:
on
trigonometry,
Geometry
and
on
mensuration,
angles
angular
movement.
15movement.
 3 on Analytical Geometry, 30  3 on Euclidean
40scientific
and
3angular
3and
Geometry and 15  3 on mensuration, circles, angles and angular movement.

Page 36 of 59
CAPS
Manipulate algebraic expressions by:
 multiplying a binomial by a trinomial;
 factorising common factor (revision);
 factorising by grouping in pairs;
 factorising trinomials;
 factorising difference of two squares
(revision);
 factorising the difference and sums of two
cubes; and
 simplifying, adding, subtracting,
multiplying and division of algebraic
fractions with numerators and
denominators limited to the polynomials
covered in factorisation.

Revise factorisation from Grade 10.
TECHNICAL MATHEMATICS
31
eeks
Topic
Weeks
TopicTopic
eeks Weeks Weeks
Topic
s
Topic
Weeks
Topic
GRADE 11: TERM 1
GRADE
GRADE 11:
TERM11:
1 TERM 1
GRADE 11: TERM 1
Curriculum statement
Clarification
GRADE 11: TERM 1
Curriculum
statement GRADE 11: TERM 1
Clarification
Curriculum
statement
Curriculum
statement
Where an example is Clarification
given, Clarification
the cognitive demand is suggested:
Curriculum statement
Clarification
Where
an
example
is
given,
the
cognitive
demand
is(C)suggeste
Where
an
example
is
given,
the
cognitive
demand
is suggested:
Where an example
is given,
the cognitive
demand
knowledge
(K), routine
procedure
(R),
complex
procedure
or
Curriculum statement
Clarification
knowledge
(K), procedure
routine
procedure
(R), complex
Where
an example
is given,
the(K),
cognitive
demand
is suggested:
knowledge
(K), routine
(R), complex
procedure
(C) or (C)
is suggested:
knowledge
routine
procedure
(R), procedure
problem-solving
(P).
Where
an
example
is given,
the cognitive
demand
knowledge
(K),
routine
procedure
(R), complex
procedure
(C) is
orsuggeste
problem-solving
problem-solving
(P).
complex
procedure
(C)(P).
or problem-solving
(P).
knowledge
problem-solving
(P). (K), routine procedure (R), complex procedure (C)
1. S
implify expressions
1. Simplify
expressions
and solveand
problem-solving
(P).
1. expressions
Simplify
expressions
and solve Example: Without the use
1. Simplify
solve
equations
using
of aa calculator,
calculator,
equations
using
the and
lawssolve
of the
Example: Without the use of
1. Simplify
expressions
and
solve
equations
using
the
laws
of Example:Example:
Without
the
use of a calculator,
laws
ofthe
exponents
for
rational
equations
using
laws
of
Without
the
use
of
3a3 calculator,
exponents
for rational
exponents
1. using
Simplify
expressions
and
solve
23 2.(K)
1. Determine
ofofa99
3 (K)
exponents
where
1.
Determine
the
value
.
equations
laws
of
Example:
Withoutthe
thevalue
use of
calculator,
exponents
for
rational
exponents
exponents
forthe
rational
exponents
where equations
2 . use
1.
Determine
the
value
of of
. calculator,
(K)
9 2a(K)
1.
Determine
the
value
of
9
using
the
laws
of
Example:
Without
the
3
p
exponents
for rational
exponents
where
where
p
(
3

2
)(
3

2
)
2.
Simplify:
.
(R)
q
2
3
q
1. 2.Determine
the
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3the
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x >rational
0; q > 0exponents
2. Simplify:
Simplify:
where
xqp q q xp pxqp; x=
1. Grade
Determine
.
(K)
q 0;pq  0 .
.
3.
Revise
10
exponential
equations.
where
; q  0 . and 2. 3.Simplify:
x subtract,
0x; q;x0. 0multiply
x xA
; dd,
p x  2.
(3Revise
 210
)(Grade
3exponential
exponential
210
) . exponential
(R) equations.
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Grade
10
equations.
3.
Grade
equations.
q
4.
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10.
p
(3  laws
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Simplify:
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(R)
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4.Revise
Revise
all
exponential
laws
Grade
10.
qq
3. 4.
Revise
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10
exponential
equations.
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all exponential
laws
from
Grade 10.
exponential
laws
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Grade
10.
q
2.subtract,
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and
divide
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
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;
q
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0
x

x
;
simple
3. surds.
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3.exponential
Revise Grade
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exponential
equations.
4. Revise all
laws
Grade 10.
2. Add,
subtract,
multiply
simple
surds.and divide.
surds.
Examples
should
include
but
not
be
limited
to
3. simple
Solve
exponential
equations.
Examples
should
include
but
not
be
limited
to
4.
Revise
all
exponential
laws
from
Grade
Add,
multiply
and divide
Examples
shouldbut
include
butlimited
not beto
limited10.
to
Examples
should
include
not be
surds.
3.
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exponential
equations.
3.simple
Solve2.
exponential
equations.
3
6
8
x
simple
surds.
3
3should
6 but
Examples
be limited to
5.
(R) not(R)
3. Solve exponential equations.
82x6 include
2 8x
should
5.
(R)but not be limited to
(R) include
3. Solve exponential equations. 5.5. 3 166xExamples

9
x
2 2
8x 2  9x16
9x 2
16
Exponents and
3x 6(R)
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3
625
Exponents
and
Exponents
andExponents
(R)
16535x332×35.
x23
39625
3 surds
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3
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2
3
3
55 16
−29
x323625
5 

and surds
Exponents
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2 x (C)
6.
8
6.
(C)
+
8
5
3 2
625
Exponents and
3125
6.×555  3 82 (C)
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8
6.
125
53  125
3surds
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3125
5

5
3 2
5
3
5

surds
6. Solve:  8 5 (C) 3 2
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(C)
Solve: 6. 125 5  8
Solve: 525 Solve:
7. 4x = 128
(R)
7. 4x5 2  1285
(R)
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2
2
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7.128
(R)
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(R)
 5x3
8.
(R)
8. 225
(R)
2x 128x 3 25x (R)x 3

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25 2  5 (R)
8.
(R)

5
9.
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C included
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9. Practical
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Q
V isCgiven
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 10
The formula
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Q
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The formula
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9. Practical
the
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must
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V
Q
QV
4
V

200
volt
.
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with
Theformula
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with Q  6  10 CCand
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V  200The
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C
Determine
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V a calculator. (R)
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volt
.
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200 volt
C using
Determine
without
using a calculator.
(R)
C. without
a calculator.
(R)
V
 200 volt
. a calculator. (R)
C
Determine
without
using
Determine C without using a calculator. (R)
Laws of logarithms
1. Explain relationship
between
logs and
exponents and
Cbetween
Determine
without
using
a calculator.
(R) show
Explain
relationship
logsand
andlogs
exponents
Laws
logarithms
Laws
of of
logarithms
1. relationship
Explain
relationship
between
and exponents
and show
Laws of logarithms
1.1. Explain
between
logs
exponents
and
show
conversion from log-form to exponential form and vice
versa.
 loga xy  loga x  loga y
and
show
conversion
from
log-form
to
exponential
2
Logarithms
Laws of logarithms
1.
Explain
relationship
between
logs
and
exponents
and
show
conversion
from
log-form
to exponential
vice ver
from
log-form
to exponential
form form
vice and
versa.
logaa yx  loga y 2. conversion
log
loga axyx  log
•a xy log
Application
of versa.
laws
of logarithms:
2
Logarithms
2
Logarithms
Laws
of
logarithms
Explain
relationship
between
logs
and
exponents
and show
log
xylog
 log
 log
form1.
and
vice
2.
Application
of
laws
of
logarithms:
conversion
from
log-form
to
exponential
form
and
vice
versa.
a
a x
a y
2.
Application
of
laws
of
logarithms:
xy
x

log
y
 loglog
a
a xy
a
log
x  loga y
log
x 
Logarithms
a axy
a
aa y
conversion
from
log-form to exponential form and vice ver
2. Application
of laws of
logarithms:
log
 log
log
xy log
a
a x  loga y 2. Application of laws of logarithms:
2
Logarithms  log •
Page 3
xy

log
x

log
y
a
a
a
2.
Application
of
laws
of logarithms:
Page 3
 loga xy  loga x  loga y
x = log x − log y -- Simplify
- Simplify
without
theof
aidaa of
a calculator:
without
the
aid
calculator:
xx  loglog
without
the
aid
of
 log
log
Page 37 o
--Simplify
Simplify
without
the
aid
of
aacalculator:
calculator:
a
a
a
a yx
a x
a y

log
x

log
y
Simplify
without
the
aid
of
calculator:
Simplify
without
the
aid
of
a
calculator:
y
x
x
  log
log

log
x

log
y
a
a
a
log
343
aa y
aa x 
aa y y
log
log
log
log
x log
 log
•ya  
log
343
a
a
log
343
2.1
(R)
y y log x n = n log x
2.1
(R)
log
343
log
343
2.1
(R)
n
2.1
(R)
49
2.1
(R)(R)
nn n log ax
2.1log
 log
a
log
49
log
49
•
a x
a xx
x
n 
n nnlog
log
x
log
  log
log
49
log
49
a
a
log
xa x nSimplify
log
aa •
aa x x applying the law:
log
n log
a
log
4

log
25
log
44log
25
 Simplify
applying
the
law:
log
log
25
2.2
applying
the
law:
log
4
log
2525
log
 log
2.2
  Simplify
Simplify
applying
the
law:
2.2
040,,01
Simplify
applying
the
law:
Simplify
applying
the
law:
2.2
2.2 log
2.2
log
01
log
b
log
0
,
01
c
log
b
log
0
,
01
log
0
,
01
cc b
 log
 log
log
bc b b = logc b
log
2.3
(R)
log
 log
ab
  log
log
log
2.3
(R)
log666222log
log20
20
log333333log
log222 (R)
aabb
2.3
2.3
20

log
log
logcc caalog
a
log
2.3
(R)(R)
log
6
2log
log
2020
 log
log
3 3 3log
log
2 2 (R)
a ba b
a
2.3log
log
6
2 log
 log
3 log
log
a
c
log
a
log
a
c
2
Logarithms
c c
log
64

log
4

log
8
x 64
x 44log
x 88 1
log

log
 Solving
of
logarithmic
equations.
log
64

log
log
xx 6464
xx 4 
xx 88 11
- Prove:
2.4
(C)
logarithmic
equations.
log
 log
log
 log
 log
  Solving
Solving
of
logarithmic
2.4
(C)
• of
x x 4 log
x x21 1 (C)
Prove:
2.4
(C)
Solving
ofof
logarithmic
equations.
Solving
logarithmic
equations. ---Prove:
Solving
of equations.
logarithmic
-- Prove:
22
Prove:
2.42.4 x xlog
(C)(C)
Prove: 2.4
x 1024
log
1024
log
1024
x
xx 1024
log
2
log
1024
2
equations.
x
-- Simplify:
2.5
32 64
log
64
2.5 log
64
--Simplify:
Simplify:
32
32
log
6464
Simplify:
2.5
log
Simplify:2.5
2.5log
-- Simplify:
2.5
32 32
3.
Show
application
of
logs
to
solve
55xxxx 33
3.
Show
application
of
logs
to
solve
3.
Show
application
of
logs
to
solve
55 5x 53
3.3.Solving
Show
application
ofof
logs
toto
solve
3x 3= 3
Show
application
logs
solve
3.
Show
application
of
logs
to
solve
4.
of
log
equations
limited
to
the
following:
4.
Solving
of
log
equations
limited
to
the
following:
4.
Solving
of
log
equations
limited
to
the
following:
Solving
of
log
limited
tothe
the
following:
4.4.4.
Solving
ofof
log
equations
limited
toto
the
following:
Solving
log
equations
limited
following:
11equations
log

x
4.1
(K)
1
2
log

x
4.1
(K)
1
1 
xx x
4.1
(K)
228
log
4.1
(K)(K)
log
4.1log
1
288
2
8
8
4.1
log
=
x
(K)
4.2
(K)
2
log
x

2

log
900
2
4.2
(K)
8
2
log
x

2

log
900
4.2
(K)
log
xx 
22

log
900
4.2
(K)
log


log
900
4.2224.2
(K)
2 log
x

2

log
900
+ 2 (=x log
(K)
log
x 2log
3) xlog
 44)900
4.3
2 (((
2
log
) 3333 (K)
4.3
(K)

log
4.3
22 (xx
log
333)))
log
log222(((xxx2
x 44
4.3
(K)(K)
log
(
))4
)  3 (K)
4.3log
2 x
2 (x  3)  log
1.
Solve
quadratic
equations
by
means
4.3 log2 ( x + 3) + log2 ( x − 4) = 3
(K)
1.
Solve
quadratic
equations
by
means
1.
Solve
quadratic
equations
by
means
1.1.of:
Solve
quadratic
equations
byby
means
Solve
quadratic
equations
means - When explaining the quadratic formula it is important to show
of:
-- When
explaining
the
quadratic
formula
ititisisimportant
to
show
of:
When
explaining
the
quadratic
formula
important
to
show
of:of:
- where
When
explaining
the
quadratic
formula
it it
isnot
important
to
show
- When
explaining
the
quadratic
formula
is
important
to
show
1.1
Factorisation
itit
comes
from
although
learners
do
need
to
know
the
1.1
Factorisation
where
comes
from
although
learners
do
not
need
to
know
the
1.1
Factorisation
where
itit comes
from
although
learners
do
not
need
to
know
the
1.1
Factorisation
where
comes
from
although
learners
do
not
need
to
know
the
1.1
Factorisation
where
it
comes
from
although
learners
do
not
need
to
know
the
1.2
Quadratic
formula.
proof.
1.2
Quadratic
formula.
proof.
1.2
Quadratic
formula.
proof.
1.2
formula.
proof.
1.2Quadratic
Quadratic
formula.
proof.
-- Use
the
formula
to
introduce
the
discriminant
and
how
itit
the
formula
to
introduce
the
discriminant
and
how
-- Use
Use
the
formula
to
introduce
the
discriminant
and
how
itit it
Use
the
formula
toto
introduce
the
discriminant
and
how
Use
the
formula
introduce
the
discriminant
and
how
2.
Quadratic
inequalities
(interpret
determines
the
nature
of
the
roots.
32
CURRICULUM
AND
ASSESSMENT
POLICY
STATEMENT
(CAPS)
2.
Quadratic
inequalities
(interpret
determines
the
nature
of
the
roots.
2.
Quadratic
inequalities
(interpret
determines
the
nature
of
the
roots.
2.2.solutions
Quadratic
inequalities
(interpret
determines
the
nature
ofof
the
roots.
Quadratic
inequalities
(interpret
determines
the
nature
the
roots.
graphically).
-- Show
by
means
of
sketches
how
the
discriminant
affects
the
solutions
graphically).
Show
by
means
of
sketches
how
the
discriminant
affects
the
solutions
graphically).
Show
by
means
of
sketches
how
the
discriminant
affects
the
solutions
graphically).
Show
by
means
of
sketches
how
the
discriminant
affects
the
solutions
graphically).
Show
by
means
of
sketches
how
the
discriminant
affects
the
3.
Determine
the
nature
of
roots
and
parabola.
3.
Determine
the
nature
of
roots
and
parabola.
3.
Determine
the
nature
of
roots
and
parabola.
3.3.the
Determine
the
nature
of
roots
and
parabola.
Determine
the
nature
of
roots
and
parabola.
conditions for
which the
roots
-- Learners
should only
be able
to apply
the quadratic
formula and
to
the
theconditions
conditionsfor
forwhich
whichthe
theroots
roots
- Learners
Learnersshould
shouldonly
onlybe
beable
ableto
toapply
applythe
thequadratic
quadraticformula
formulaand
andto
to
GRADE 11: TERM 1
Weeks
Topic
Curriculum statement
Clarification
Where an example is given, the cognitive demand
is suggested: knowledge (K), routine procedure (R),
complex procedure (C) or problem-solving (P).
4
Equations
1. Solve quadratic equations by
means of:
1.1Factorisation
1.2Quadratic formula.
2. Quadratic inequalities
(interpret solutions
graphically).
3. Determine the nature of roots
and the conditions for which
the roots are real, non-real,
equal, unequal, rational and
irrational.
4. Equations in two unknowns,
one of which is linear and the
other quadratic.
5. Word problems.
6. Manipulating formulae (Make
a variable the subject of the
formula).
•
•
•
•
•
•
•
2
Analytical
Geometry
1. Revise to find the equation
of a line through two given
points;
Determine:
2. the equation of a line through
one point and parallel or
perpendicular to a given line;
and
3. the inclination (θ) of a
line, where m = tan θ is
the gradient of the line and
0° ≤ θ ≤ 180°
When explaining the quadratic formula it is
important to show where it comes from although
learners do not need to know the proof.
Use the formula to introduce the discriminant and
how it determines the nature of the roots.
Show by means of sketches how the discriminant
affects the parabola.
Learners should only be able to apply the
quadratic formula and to derive from b2 − 4a
c the
nature of the roots.
Word problems should focus and be related to
the technical field and should include examples
similar to the following: e.g. The length of
a rectangle is 4m longer than the breadth.
Determine the measurements of the rectangle if
the area equals 621m2.
With manipulation of formulae the fundamentals
of changing of the subject should be emphasized
and consolidated.
All related formulae from the technical fields
should be covered.
1. Revision of linear equation from Grade 10.
2. Showing the influence of the gradient and
consequently the relationship when lines are parallel
and perpendicular.
3. Example: Given A(−2;4) , B(2; 6) and C(3; − 2)
Determine:
3.1 Equation of line passing through point C and
parallel to line AC.
(R)
3.2 Equation of line passing through point B and
perpendicular to line AC.
(R)
4. Example:
A ladder leans against a straight line wall defined by
y = 2 x + 4.
4.1
4.2
Determine the length of a ladder. (P)
How far it reaches up the wall and the
ladder’s inclination with the floor. (C)
Assessment Term 1:
1. An investigation or a project (a maximum of one project in a year) (at least 50 marks)
2. Test (at least 50 marks). Make sure all topics are tested.
Care needs to be taken to ask questions on all four cognitive levels: approximately 20% knowledge, approximately
35% routine procedures, 30% complex procedures and 15% problem-solving.
CAPS
TECHNICAL MATHEMATICS
33
GRADE 11: TERM 2
Weeks
Weeks
Curriculum statement
Clarification
GRADE 11: TERM 2
Where an example is given, the cognitive
Curriculum statement
Clarification
demand is suggested: knowledge
(K), routine
procedure
(R),
complex
procedure
(C) or demand is suggeste
Where an example is given, the cognitive
problem-solving
(P).
knowledge (K), routine procedure (R), complex procedure (C)
Topic
4
4
Topic
a
1. Revise
the effect of the
Comment:
problem-solving (P).
parameters and q on the graphs.
a isthe
noteffect
restricted
 in1 grade a11.
• Comment:
Learners should gain confidence and get
1. Revise
of thetoparameters
a grasp of graphs from tabling and dotting
and q2 on the graphs.
Investigate
the
effect of p on the
joining points
to gain
drawconfidence
the graphs.and get a grasp of gra
x

7
x

8
Investigate
the
effect ofdefined
p on the
andLearners
should
graphs
of the
functions
by:
They
should
understand
the influence
of points to draw th
graphs of the functions defined by: •
from
tabling
and dotting
and joining
2
variables
on
the
form
and
calculate
critical
1
2+ q y
=
f
(
x
)
=
a
(
x
+
p
)
1.1.
graphs.
y  f(x)  a(x  p)  q
1.1.cosec
points to draw graphs.
sin 2
 They should understand the influence of variables on
1.2. y  f (x)  ax  bx  c
•
The concept of asymptotes should be clear.
1.2.
form and calculate critical points to draw graphs.
•
They
should
be able
to deduce the
a q

The
concept
of asymptotes
should be clear.
y

Functions
1.3.
a
Functions
equations
when
critical
points are given.
x
1.3. y = x + q
and
 They should be able to deduce the equations when cr
10
andgraphs
the information from graphs
. f (parabola
x)  a..bx graphs
 q , b only
 0 in•gradeAnalyse
1.4.a yafor
points
are given.
x
y
=
a
.
f
(
x
)
=
a
.
b
+
q
1.4.
,
(graphs given).
graphs
b

1
and

Analyse
the information from graphs (graphs given).
2
cotb2 > 0 1and
 cosec
b ≠1 
2.
x2  y22  r 22
x +2 y 2= r 2
2.
y r x
y = ± r 2 − x2
y   r 2  x2
y = + r 2 − x2
y   r 2  x2
y = − r 2 − x2
4
Euclidean
Geometry
34
Accept results established in earlier
grades as axioms and also that a tangent
to a circle is perpendicular to the radius,
drawn to the point of contact.
Then investigate and apply the theorems
of the geometry of circles:
 The line drawn from the centre of a
circle perpendicular to a chord
bisects the chord;
 The perpendicular bisector of a
Comments:
Proofs of theorems and their converses will not be examined.
But proofs of theorems and their converses will applied in solv
riders.
The focus of all questions will be on applications and calculatio
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
GRADE 11: TERM 2
Weeks
Topic
Curriculum statement
Clarification
Where an example is given, the cognitive
demand is suggested: knowledge (K), routine
procedure (R), complex procedure (C) or
problem-solving (P).
Euclidean
Geometry
4 fields.
n from the technical
Accept results established in earlier Comments:
Proofs of theorems and their converses will not be
grades as axioms and also that a
examined.
tangent to a circle is perpendicular
But proofs of theorems and their converses will
to the radius, drawn to the point of
applied in solving
contact.
riders.
Then investigate and apply the
theorems of the geometry of circles:
The focus of all questions will be on applications
•
The line drawn from
and calculations.
the centre of a circle
perpendicular to a chord
bisects the chord;
Make use of problems taken from the technical
•
The perpendicular bisector of fields.
a chord passes through the
centre of the circle;
•
The angle subtended by an
chord
chord
passes
passes
through
through
the
centre
centre
of
chord
passes through the centre of
chord
passes
through
the
centre
of
arc at
the centre
of athe
circle
is of
the
the
circle;
circle;
double
the circle;
the
circle;the size of the angle
subtended
by the same
arc
atat
 The
The
angle
angle
subtended
by
by
an
arc
arc
at
the
The
angle
The
anglesubtended
subtended
byan
an
arc
atthe
thesubtended by an arc at the
the
circle
(on
the
same
side
centre
centre
of
circle
double
the
size
size
of
of
centre
centreof
ofaaacircle
circleisisisdouble
doublethe
theof
sizeof
ofa circle is double the size of
Make
Make
use
of
problems
taken
from
from
the
the
technical
technical
fields.
fields.
Make
problems
taken fr
Makeuse
useof
ofproblems
problemstaken
taken
fromuse
theof
technical
fields.
the
chord
as the centre);
the
the
angle
angle
subtended
subtended
by
by
the
the
same
same
arc
arc
the
angle
the angle subtended by the same arcsubtended by the same arc
• at
subtended
by
a chord
at
the
the
circle
(on
(on
the
same
side
side
of
of
the
at the
circle
atAngles
thecircle
circle
(onthe
thesame
same
side
ofthe
the (on the same side of the
of
the
circle,
on
the
same
side
chord
chord
as
the
centre);
chord
as the centre);
chordas
asthe
thecentre);
centre);
of the chord, are equal;
 Angles
Angles
subtended
by
chord
of
of
the
chord
Angles
subtended by a chord of the
Anglessubtended
subtendedby
byaaachord
ofthe
the
•
The opposite angles of
circle,
circle,
on
the
same
side
of
the
chord,
chord,
circle,
on the same side of the chord,
circle,on
onthe
thesame
sameside
sideof
ofthe
the
chord,
a cyclic quadrilateral are
are
are
equal;
equal;
are equal;
are
equal;
supplementary;
 The
The
opposite
angles
of
cyclic
The opposite angles of a cyclic
Theopposite
oppositeangles
anglesof
ofaaacyclic
cyclic
•
Exterior angle of cyclic quad.
quadrilateral
quadrilateral
are
are
supplementary;
supplementary;
quadrilateral are supplementary;
quadrilateral
are
supplementary;
is equal to opposite interior
 Exterior
Exterior
angle
of
cyclic
quad.
isisisequal
equal
 Exterior
angle of cyclic quad. is equal
Exterior
angleof
ofcyclic
cyclicquad.
quad.
equal
angle;angle
to
to
opposite
opposite
interior
interior
angle;
angle;
to
opposite
interior angle;
to
opposite
interior
angle;
•
Two tangents drawn to a
 Two
Two
tangents
tangents
drawn
drawn
to
to
aaacircle
circle
from
Twofrom
tangents drawn to a circle from
Two
tangents
drawn
topoint
circle
from
circle
from the
same
the
the
same
same
point
outside
outside
the
circle
are
are
the
the
samepoint
point
outside
thecircle
circle
arepoint outside the circle are
outside
the
circle
are the
equal
insame
length;
equal
equal
in
in
length;
equal in length;
equal
inlength;
length;
 Radius
Radius
isisisperpendicular
perpendicular
to
the
the
•
Radius
is
perpendicular
the is perpendicular to the
to
Radius
Radius
perpendicular
toto
the
tangent;
and
tangent;
tangent;
and
and
tangent; and
tangent;
and
•
The
angle
between
the
 The
The
angle
angle
between
between
the
the
tangent
tangent
to
tangent
The to
angle
The
angle
between
the
toaaa between the tangent to a
tangent
to
a
circle
and
thefrom
circle
circle
and
the
chord
drawn
from
the
circle
and
circleand
andthe
thechord
chorddrawn
drawn
fromthe
the the chord drawn from the
chord
drawn
from
the point
ofangle
point
point
of
of
contact
isisisequal
equal
to
to
the
angle
point
of contact is equal to the angle
point
ofcontact
contact
equal
tothe
the
angle
is equal
to the angle
in
in
the
the
alternate
segment.
segment.
in the alternate segment.
incontact
thealternate
alternate
segment.
in the alternate segment.
Mid-year
Mid-year
Mid-year
Mid-year
3
Mid-year
examinations
examinations
examinations
examinations
3
examinations
Assessment
Assessment
Term
2:
Assessment Term 2:
AssessmentTerm
Term2:
2:
333
Assessment Term 2:
1.
1.
Assignment
///test
test
(at
(at
least
50
50
marks)
1.
Assignment
1. Assignment
Assignment
test
(atleast
least
50marks)
marks)
1.
Assignment
/ test
(at
least
50
marks)/ test (at least 50 marks)
2.
2.
Mid-year
examination
examination
(at
(at
least
least
200
200
marks)
marks)
2.(at
Mid-year
examination
(at least 200 marks)
2. Mid-year
Mid-year
examination
(at
least
200
marks)
2.
Mid-year
examination
least
200
marks)
Paper
Paper
1:
hours
(100
marks
made
made
up
as
follows:
General
algebra
algebra
((35
equations,
inequalities
inequalities
and
nature
of
roots
(((40
),),),fu
fu
333),),),equations,
40
inequalities
and
nature
Paper1:
made
asfollows:
follows:
algebra
(35
Paper
1:up
2 as
hours
(100General
marks
made
up (as
follows:
General algebra
( 35 and
), nature
equations,
inequalities
3and
1:222hours
hours(100
(100marks
marks
made
up
as
follows:
General
algebra
equations,
inequalities
natureof
ofroots
roots
fu
35
40333and
function
and
roots
and nature of roots
(( 40
function
andgraphs ( 25  3 ).

graphs
graphs
(((25
).).
25
graphs
253),333).
Paper2:
made
asfollows:
follows:
Geometry
and
Euclidean
Paper
Paper
2:
hours
(100
marks
made
made
up
as
follows:
Analytical
Geometry
Geometry
((((40
Geometry
Geometry
40
33Euclidean
Paper
2:up
2 as
hours
(100Analytical
marks
made
up as follows:
Geometry
( 40  3(((60
)60
and
Geometr
2:222hours
hours(100
(100marks
marks
made
up
as
follows:
Analytical
Geometry
andEuclidean
Euclidean
Geometry
4033Analytical
3)))and
60
3).).).).
metry ( 60  3 ).
CAPS
Page 41 of 59
TECHNICAL MATHEMATICS
35
GRADE 11: TERM 3
Weeks
Topic
Curriculum statement
Clarification
Where an example is given, the cognitive demand
is suggested: knowledge (K), routine procedure
(R), complex procedure (C) or problem-solving (P).
1. Circle
1.1
x2 + y 2 = r 2 ,
with centre (0;0 ) only
1.2 Angles and arcs
1.3 Degrees and radians
Pay attention to the following: diameter, radius, chord,
segment, arc,secant, tangent.
1.1 If a point on a circumference is given, how to
determine r and the equation of the circle?
1.2 What is an arc, central angle, inscribed angle?
1.3 A radian is the angle at the centre of a circle
subtended by an arc of the same length as the
radius.
Complete revolution: 3600 = 2π radians; 1800 = π
radians
•
If an arc of length s is intercepted by a central
angle (in radians) the angle subtended will be
equal to the arc divided by the radius.
•
•
θ= s.
r
If s = r then = 1 radian.
Convert degrees to radians and vice versa.
Convert 2 radians to degrees
π rad = 180°
Circles, angles
and
angular
movement
4
180°
π
180°
2 rad = 2 ×
π
1 rad =
1.4 Sectors and segments
= 114,590
Convert 52,60 to radians
1° = π rad
1800°

52,6
0
52,6
= =5252
,6,6 
52,60 =
180
180
 
0, 918
= =0, 918
radrad
= 0,
918 bounded
rad
1.3
A
sector
of
a
circle
is
a
plane
figure
by
and
tw
1.3 AAsector
of
aacircle
isisaaplane
figure
bounded
by
anan
arcarc
and
two
1.3
sector
of
circle
plane
figure
bounded
by
radii.
radii.
an arc and two radii.
2. Angular and
circumferential/peripheral
velocity
2
  r = radius; s = arc length and
r r 
area of
a sector rs
= rs
area

r ==radius;
radius;s = arc length and
Areaof
of aasector
sector== 2
2
2
2
2
s = arc length and
centralangle
angle
radians.
ininradians.
 θ= =central
 = central angle in radians.
Angular
and
•
2. 2.
Angular
and
circumferential/peripheral
velocity
circumferential/peripheral velocity
A segment of a circle is the area bounded by an
- segment
A and
segment
a circle
is the
area
bounded
and
a cho
a chord.
- Aarc
of of
a circle
is the
area
bounded
byby
anan
arcarc
and
a chord
The
relation
between
thethe
diameter
of aofcircle,
a a chord and th
The
relation
between
diameter
a circle,
The
relation
between
the
diameter
offormed
a circle,
a chord and the
chord
and
the
height
of
the
segment
by
height
of
the
segment
formed
by
the
chord,
in
height
of the
formed
the chord, cancan
bebe
setset
outout
in th
the chord,
cansegment
be set out
in theby
formula
formula
formula
2
2
= height
segment;
= diameter
4dh
of of
segment;
d =ddiameter
of of
cir
h2 h 4dh
 x2 x 0;0 h; =hheight
= length
chord.
of of
chord.
h =h length
 can
Angular
velocity
(omega)
determined
multiplying
 can
2. 2.Angular
velocity
(omega)
bebe
determined
byby
multiplying
th
2

radians
in
one
revolution
(
)
with
the
revolutions
per
seco
radians in one revolution
( 2 ) with the revolutions per second
0
 n=360360
0

 22n=
n n
Circumferential
velocity
is the
linear
velocity
a point
Circumferential
velocity
is the
linear
velocity
of of
a point
onon
thethe
circumference
circumference
36
v   D n with D the diameter, n is the rotation frequency
with D the diameter, n is the rotation frequency
v   D n (CAPS)
CURRICULUM AND ASSESSMENT POLICY STATEMENT
Revise
ratios
in the
solving
Comment:
1. 1.Revise
thethe
trigtrig
ratios
in the
solving
of of Comment:
right-angle
triangle
in
all
4
quadrants
right-angle triangle in all 4 quadrants
(Grade 10).
No proofs of the sine, cosine and area rules are required.
== 0,
0,918
918rad
rad
2circleis
1.3
1.3 AAsector
sector
of
of
a
a
circle
is
a
a
plane
plane
figure
figure
bounded
bounded
by
byan
anarc
arca
rs r 
area of a sector
radii.
radii.= 2  2  r = radius; s = arc length and
radii.
22
rs
rr   rr ==radius;
area
area
ofcentral
aasector
sector
== rs
radius;ss==arc
arclengt
lengt
angle
in
radians.
 =of
Weeks
22
GRADE 11: TERM 3
2. Angular and
22
centralangle
anglein
inradians.
radians.
 ==central
Clarification
- A segment of a circle
is the area bounded by an arc and a chord.
Topic
Curriculum statement
circumferential/peripheral
velocity
2.
2. Angular
Angularand
and
Where
an example
is given,
the cognitive
demand
The relation
between
the diameter
of a circle,
a chord and the
--AAknowledge
segment
segmentof
of(K),
aacircle
circle
isisthe
the
area
areabounded
boundedby
byan
anarc
arcand
an
is suggested:
routine
procedure
circumferential/peripheral
circumferential/peripheralvelocity
velocity
height of the segment formed by the chord, can be set out in the
(R), complex procedure (C) or problem-solving (P).
The
Therelation
relationbetween
betweenthe
thediameter
diameterof
ofaacircle,
circle,aachord
chord
2
height
height
of
of
the
the
segment
segment
formed
formed
by
by
the
the
chord,
chord,
can
can
be
beset
se
height of segment; d = diameter of circle;
h  4dh  x  0 ; h == height
formula
formula
of of
chord.
hd = length
diameter
circle; h = length of chord.
22
; hbe
h==determined
height
heightof
ofsegment;
segment;dd==diamet
diame
h
h

4(omega)
4dh
dh xx22 can
can
00;be
ω
Angular velocity
2. 2.Angular
velocity (omega)
determined byby
multiplying the
length
lengthof
ofchord.
chord.
hh ==radians
multiplying
the
( 2π ) with per second (n)
2 ) revolution
radians
in one
revolutionin( one
with the revolutions
the revolutions
second
(n)
0 per velocity


2.
2.
Angular
Angular
velocity
(omega)
(omega)
can
can
be
bedetermined
determinedby
bymult
mult
  2 n= 360 n
0
ωCircumferential
= 2π n= 360
nvelocity
radians
radians
in
inone
one
revolution
revolution
((22))with
with
the
revolutions
revolutions
pe
is the
linear velocity
of athe
point
on the pe
0linear
0
Circumferential
velocity
is
the
velocity
of
a
point

 22n=
n= 360
360 nn
circumference
on the circumference
Circumferential
Circumferentialvelocity
velocityisisthe
thelinear
linearvelocity
velocityof
ofaapoint
point
v =v π D
D the
diameter,
n is nthe
rotation
circumference
circumference
D the
diameter,
is the
rotation frequency
 nD with
n with
formula
2
frequency
Comment:
Revise
trig solving
ratios inof Comment:
withDDthe
thediameter,
diameter,nnisisthe
therotation
rotationfrequ
frequ
vv  D
Dnn with
1. Revise the1.trig
ratiosthe
in the
the solving of right-angle
right-angle triangle in all 4 quadrants
No proofs of the sine, cosine and area rules are
triangle in all 4 quadrants
1.
1. Revise
Revisethe
thetrig
trigratios
ratiosin
inthe
thesolving
solving
of
of Comment:
Comment:
(Grade 10).
No proofs
of
the sine, cosine and area rules are required.
required.
(Grade 10).
right-angle
right-angle
triangle
triangle
in
in
all
all
4
4
quadrants
quadrants
2. Apply the2.
sine,
cosine
and
area
rules.
Apply
only
with
actualnumbers,
numbers,no
novariables.
variables.
Apply the sine, cosine and Apply only with actual
(Grade
(Grade
10).
10).
No
No
proofs
proofs
of
of
the
the
sine,
sine,
cosine
cosine
and
andarea
arearules
rulesare
arerequired
required
3. Solve problems
in
two
dimensions
(Acuteand
obtuse-angled
triangles)
(Acute- and obtuse-angled triangles)
area rules.
2.
2.
Apply
Apply
the
the
sine,
sine,
cosine
cosine
and
and
area
area
rules.
rules.
Apply
Apply
only
only
with
with
actual
actual
numbers,
numbers,
no
no
variables.
variables.
using the 3.
sine,
cosine
and area
rules
Solve
problems
in two
Trigonometry
3.
Solve
Solve
problems
in
intwo
twosine,
dimensions
dimensions
(Acute(Acuteand
obtuse-angled
triangles)
dimensions
using
the
4. Draw the3.
graphs
ofproblems
the functions
•
Learners
mustand
be obtuse-angled
able to draw alltriangles)
mentioned
cosine
and
area
rules
using
using
the
the
sine,
sine,
cosine
cosine
and
and
area
area
rules
rules
defined
by
Learners
must
be
able
to
draw
all
mentioned
graphs and also be able
graphs and also be able to deduct important
44
Trigonometry
Trigonometry
4.
Draw
the
graphs
of
the
4.
4.
Draw
Draw
the
the
graphs
graphs
of
of
the
the
functions
functions
information
from
given sketches.
to deduct
important
information
from given sketches.
y  k sin x , y  k cos x ,
functions
defined by
defined
defined
by
by
Learners
Learners
must
must
be
be
able
able
to
todraw
draw
all
mentioned
mentioned
graphs
graphsand
and
•
One
parameter
should
be
tested
at a all
given
time
y  sin ( kx ) , y  cos (kx )
=
sin
,, yyy 
=
k
cos
x
, - One parameter
,
,
to
to
deduct
deduct
important
important
information
information
from
from
given
given
sketches.
sketches.
y
y


k
k
sin
sin
x
x

k
k
cos
cos
x
x
when
examining
horizontal
shifts
should
be
tested
at
a
given
time
when
examining
and y  tan x .
Rotating vectors should be done on graph paper.
yysin
sin((kx
kx)),, yycos
cos((kx
kx)) •
Page 4
-- One
Oneparameter
parameter
should
should
be
betested
tested
ataagiven
giventime
timewhen
whenex
ex
•
Determine
the solutions
of equations
forat
tanxxx...
and
and yyy=tan
tan
5. Draw the graphs of the
4
Trigonometry
θ ∈ [0° ; 360°]
functions defined by
y = sin( x + p) and
ay = cos(x + p)
•
Limited to routine procedures.
•
•
Reduction formulae, (180° ± θ) and (360° ± θ) .
Examples related to the use of identities limited
to routine procedures.
6. Rotating
vectorsto  in grade 11.
a is not restricted
Developing the sine and
cosine
x2  7xcurve.
8
7. Trigonometric equations.
8. Introduce identities
and
1
cosec 
sin 
sin θ ,
cos θ
sin 2 θ + cos2 θ = 1 ,
a   for parabola graphs only in grade 10
1 + tan 2 θ = sec2 θ and
cot2   1  cosec2  .
apply tan θ =
CAPS
TECHNICAL MATHEMATICS
37
GRADE 11: TERM 3
Weeks
Topic
Curriculum statement
Clarification
Where an example is given, the cognitive demand
is suggested: knowledge (K), routine procedure
(R), complex procedure (C) or problem-solving (P).
Finance,
growth
and decay
2
3. FINANCE, GROWTH AND DECAY
1. Use simple and
Examples:
compound
decay
1. The
valueformulae
of a piece of equipment
depreciates
from growth/deca
Use simple and compound
growth
Use simple
and compound

R10n 000 to R5 000 in four years. What is the rate of
formulae: A  P(1  in) and A  P(1  i) to solve
formulae A  P(1  in) and A  P(1  i)n
depreciation if calculated on the:
problems (including interest, hire purchase,
problems (including interest, hire purch
1.1 straight line method?; and (R)
and A = P(1 − i)n to solve
inflation, population growth and other real life
inflation, population growth and other r
problems (including straight 1.2 reducing balance? (C)
problems).
2. Which is the better investmentproblems).
over a year or
line depreciation and
longer: 10,5% p.a. compounded daily or 10,55%
depreciation on a reducing
foreign
The effect of different periods of compo
 balance). The implications of fluctuating

p.a. compounded
monthly?
(R)
exchange
rates.
growth and decay (including effective an
2. The effect of different
nominal interest rates).
Comments:
periods of compound
The use of a timeline to solve problems is a useful
growth and decay,
technique.
including nominal and
4. ALGEBRA
effective interest rates.
3. R50 000 is invested in an account which offers
(a) Simplify expressions using the laws of
(a) Apply the laws of exponents to expre


8% p.a. interest compounded
quarterly for the first
exponents for integral18
exponents.
involving
rational
months. The interest then changes
to 6%
p.a. exponents.
(b) Establish between which
two
integers
a
(b)
Add,
subtract,
multiply
compounded monthly. Two years after the money
is and divide sim
given simple surd lies.invested, R10 000 is withdrawn. How
surds.much will be
(c) Round real numbers toinan
appropriate
(c) Demonstrate an understanding of th
the
account after 4 years? (C)
degree of accuracy (to a given number of
definition of a logarithm and any law
decimal digits). Comment:
needed to solve real life problems.
(d) Revise scientific notation.
Stress the importance of not working with rounded
answers, but of using the maximum accuracy afforded
Manipulate algebraic by
expressions
by: right to the
from Grade 10.
 final Revise
the calculator
answerfactorisation
when
 multiplying a binomial
by a trinomial;
rounding
might be appropriate.

factorising
common
factor
(revision);
Mid-year
3
 factorising by grouping in pairs;
examinations
 factorising trinomials;
Assessment Term 3:
 factorising difference of two squares
Two (2) tests (at least 50 marks per test and 1 hour) covering all topics in approximately the ratio of the allocated
(revision);
teaching time.
 factorising the difference and sums of two
cubes; and
 simplifying, adding, subtracting,
multiplying and division of algebraic
fractions with numerators and
denominators limited to the polynomials
covered in factorisation.

38
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Weeks
WeeksWeeks
Weeks
Topic
Topic Topic
Weeks
Topic
Weeks
Clarification
GRADE
11:4TERM
TERM44
11:
GRADEGRADE
11:
TERM
GRADE 11:
11: TERM
TERM 44
GRADE
11:
TERM
4
GRADE
Curriculum
statement
Clarification
Curriculum
statement
Clarification
Curriculum
statement
Clarification
Topic
Curriculum statement
statement
Curriculum
statement
Clarification
Topic
Curriculum
C
Where
an
example
is
given,
the
cognitivedema
dema
Where an example is given, the cognitive
GRADE 11: TERM 4
given, the cognitive demand is suggested:
Weeks
Topic
ne procedure (R),
complex procedure
(C) or Curriculum statement
Where an
an example
example is
is given,
the cognitive
cognitive
demand
is su
st
Where
an
example
given,
Where
the
demand
is
Where
an
example
isiscomplex
given,
th
knowledge
(K),given,
routine
procedure
(R),
complex
knowledge
(K),
routine
procedure
(R),
knowledge
(K),
routine
procedure
(R),
complex
proced
knowledge
(K),
routineproced
proce
knowledge
(K), routine (P).
procedure
(R),
complex
knowledge
(K),
routine
proce
problem-solving
(P).
problem-solving
problem-solving
(P).
problem-solving
(P).
problem-solving
(P).
Clarification
problem-solving (P).
Where an example is given, the cognitive demand
is
suggested:
(K), routine
(R),
Surface
area
andvolume
volume
rightknowledge
Surface
Area
2ofarea
area
base++circumferen
circumfere
1.1. Surface
area
and
ofofright
1.1. Surface
Area
==2procedure
ofof
base
1.
Surface
area
and
volume
of
right
1.
Surface
Area
=
2
area
base
+
circumference
of

complex
procedure
(C)
or
problem-solving
(P).
1.
Surface
area
and
volume
of
right
1.
Surface
Area
=
2
areaof
ofb
1. Surfaceprisms,
area and
volume
of
right
1.
Surface
Area
=
2
area
of
base
+
circumference

1.
Surface
area
and
volume
of
right
1.
Surface
Area
=
2
of
 area
cylinders, pyramids, cones
(for closed right-angled prism)
cylinders,
pyramids,
cones (for closed
(for closed
right-angled
prism)
prisms,prisms,
cylinders,
pyramids,
conescylinders,
right-angled
prism)
prisms,
pyramids,
cones
(for
closed
right-angled
prio
prisms,
cylinders,
pyramids,
cones
(for
right-angled
prism)
Surface
area
and
volume
prisms,
cylinders,
pyramids,
cones
(for
closed
right-angled
pris
area of base + circumference of base 1.
height
1.
Surface
Area
=
2 ×closed
area
of base
+==circumference
and
spheres,
and
combinations
of
Surface
Area
area
of
base
circumference
and
spheres,
and
combinations
of
Surface
Area
area
of
base
++circumference
and
spheres,
and combinations
combinations
of
Surface
Area ==of
area of
of base
base
+ circumference
circumference
of
base
of
right
prisms,
cylinders,
and
spheres,
and
combinations
Surface
Area
=
area
of
base
and
spheres,
and
of
Surface
Area
area
+
of
base
and of
spheres,
combinations
ofright
Surface
Area = area of base
base ×and
height(for
closed
right-angled
prism)
ngled prism)
thesegeometric
geometric
objects.
(forright
open
rightangled
angled
prism)
these
objects.
(for
open
prism)
thesecones
geometric
objects.
(for
open
angled
prism)
and objects.
these
geometric
objects.
(for
open
right angled
angled prism
prism
these
geometric
(for
open
right
angled
prism)
Surface
Areaobjects.
=
area
of
base
+
circumference
of
these
geometric
(for
open
right
a of base + circumference of base  height pyramids,
Volume
=area
area
base
height
Volume
=of
height
Volume
= area
area
baseofof
height
base
spheres, and combinations
base
height
(for
open
right
angled
prism)
×
Volume
=
area
of
base
h
Volume
=
of
base
height

Volume
=
area
of
base
 he
led prism)
of these geometric objects.
Mensuration
Volume
=
area
of
base
height
×
Mensuration
Mensuration2. The effect
ase  height
33 Mensuration
2.effect
The
effect
onvolume
volume
andsurface
surface2. What
What
theeffect
some
ofthe
themeasuremen
measureme
The
effect
on
and
2.2.is
What
isisthe
ififof
some
Mensuration
on
volume
Mensuration
2. The
The2.
on
volume
andThe
surface
the
effect
ifeffect
some
theisof
measurements
are
33
33 2.
2.
effect
on
volume
and
surface
2.
What
the
effect
some
effect
on
volume
and
surface
2.
What
is
the
effect
if
some
of
the
measurements
are
2.
The
effect
on
volume
and
surface
2.
What
is
the
effect
ifif some
o
area
when
multiplying
any is the effect
factor
k? measurements are
area
when
any
factor
and surface
areamultiplying
whenmultiplying
2. What
if some
of k?
the
area
when
any
factor
k?
Mensuration
area
when
multiplying
any
factor
k?
area
when
multiplying
any
factor
k?
area
when
multiplying
any
factor
k?
3
if some of the measurements are multiplied multiplying
by a
dimension
byfactor
any
dimension
dimension
by
k.k.multiplied by a factor k?
dimension
by factor
factor
k.factor
dimension
by mid-ordinate
factor k.
k.
dimension
by
k.
dimension
by
factor
by factor
k.
Using
themid-ordinate
mid-ordinate
rule:
3.3.the
Using
the
rule:
3.
Using
the
rule:
3.
Using
mid-ordinate
rule:
3.
Determine
the
area
of
an
irregular
3.
Determine
the
area
of
an
irregular
3.
Using
the mid-ordinate
mid-ordinate rule
rul
3.
Using
the
mid-ordinate
rule:
3.
Determine
the
area
of
an
irregular
3.
Using
the
3. Determine
the
area
of
an
3.
Determine
the area
area of
of an
an irregular
irregular
3. Determine
theusing
areamid-ordinate
of
anDetermine
irregular
3.
the
figure
using
mid-ordinate
rule.
o

figure
rule.
a
(
m

m

m

.
..

m
)
A
=
where
m
a
(
m
+
m
+
m
+
.
.
+
m
)
A
=
where
a
(
m

m

m

.
..

m
)
1
A
=
where
m
irregular
figure
using
midT
figure
using
mid-ordinate
rule.
o

oo
2 ... 
nate rule:
1
n1 m 2
3 3 m ) where
n n m  1 1 1
m
m
m2 1
AT2 == aa3((Tm
figure
using mid-ordinate
mid-ordinate
rule.
figure using mid-ordinatefigure
rule.T using
rule.
1
3
n
1
a
(
m

m

m

.
..

m

.
..

m
)
A
=
A
where
m

a
(
m

m

m

.
..
A
=
T
2 
TT
1
2
3
n
ordinate rule.
11
22 1
33 2
o1  o2
n
etc.
and
=
number
of
ordinates
n
etc.
and
=
number
of
ordinates
o + o etc. and n = number of ordinates
m3  ...  mn ) where m1 
etc. and
and nn == number
number of
of ord
ord
etc.
m1 = 1 2 etc. and n = number of ordinates
2
2
etc. and n = number of ordinates
er of ordinates
Revision
33
Revision
33
Revision
Revision
Revision
Revision
33
Revision
Examinations
33Examinations
Examinations
3
Examinations
Examinations
3 Assessment
Examinations
Examinations
Term4:4: 33
Assessment
Term
Assessment
Term 4:
Assessment Term
Term 4:
4:
Assessment
AssessmentTerm
Term4:4: Assessment
Test
(at
least
50marks)
marks)
1.1.
Test
(at
least
50
Test
(at(at
least
50
marks)
1.
Test
least
50
marks)
1. marks)
Test
(at least
least 50
50 marks)
marks)
1. Test
least 50 marks)
1.
Test
(at
Examination
(300
marks)
2.2. (atExamination
(300
2. Examination
(300
marks)
Examination
(300
marks)
2. marks
Examination
(300
marks) (90
2. Examination
(300
marks)
2.
Examination
(300
marks)
Paper
hours
(150
marks
made
up
follows:
onalgebraic
algebraic
expressions,
equations,
inequalities
andnature
nature
ro
(90
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nature of
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algebraic
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trigonometric
functions)
and
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and
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and graphs
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(excluding
trigonometric
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and
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functions)
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2:
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functions),
onAA
(
50

3
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2: 3 hours
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functions),
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3) on trigonometry
()25
Analytic
33
) )on
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2:
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(including
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3
(
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(including trigonometric
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angular
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ovement.
Page 46 of 59
CAPS
TECHNICAL MATHEMATICS
39
Weeks
Weeks
eeks
eeks
Topic
Topic
Topic
Topic
Topic
Weeks
Weeks
Weeks
Weeks
3
333
omplex
umbers
3
2
222
ynomials
2
GRADE
12:
TERM
GRADE12:
12:TERM
TERM111
GRADE
GRADE
12: TERM
1
GRADE 12: TERM
GRADE112: TERM 1
Curriculum
statement
Clarification
Curriculum
statement
Clarification
Curriculum
statement
Clarification
GRADE
12: TERM 1
Curriculum
statement
Clarification
Topic
Curriculum
statement
Clarification
Topic
Curriculum statement
Clarification
Where
an
example
isisgiven,
given,
the
cognitive
demand
suggested:
Where
an
example
given,
the
cognitivedemand
demandis
suggested:
Where
an
example
is
the
cognitive
demand
isisissuggested:
suggested:
Where an example is given, the cognitive
Curriculum statement
Clarification
Where
an
example
iscognitive
given,
thedemand
cognitive
demand
is sugg
knowledge
(K),
routine
procedure
(R),
complex
procedure
(C)or
or
knowledge
(K),
routine
procedure
(R),
complex
procedure
(C)
or
Where
an
example
is
given,
the
knowledge
(K),
routine
(R), complex procedure (C)
GRADE
12:
TERM
1 procedure
Where an example
is
given,
the
cognitive
demand
is
suggested:
knowledge
(K),
routine
procedure
(R),
complex
procedur
problem-solving
(P).
is
suggested:
knowledge
(K),
routine
procedure
(R),
problem-solving(P).
(P).
problem-solving
(P).
problem-solving
procedure
(C)complex
or problem-solving
knowledge
(K), complex
routine procedure
(R),
(C)(P).
or
problem-solving
(P).procedureClarification
Defineaacomplex
complexnumber,
number,
 Define
ℂℂ,, statement
Topic
Curriculum

Define a complex number,
ℂ,
problem-solving
Simplify
::
bi...Define
Defineaacomplex
complex
number,Simplify
ℂ(P).
,
Simplify
number,
z  a•bi
bi
Where an example is given, the cognitive demand is sug
Simplify ::
zzzaaabi
.
Simplify
:
GRADE
12:
TERM
1
 Define a complex
number,
ℂ
,
a  bi .
, z know:

Learners
should
know:
knowledge
(K), routine procedure (R), complex procedu

Learners
should
 Learners should know: Simplify :
z  a  bi . --- the

Learners
should
know:
z

a

bi
the
conjugate
of
.
•
Learners
should
know:
z

a

bi
the
conjugatestatement
of zz 
(P).
16
4  1
1.
(R)
 aa  bi
bi .. .
conjugate
of
16 problem-solving
1. 16
(R)Clarification
16
1.
(R)
1.
Topic
Curriculum
- the
conjugate
of
444 111 (R)
1.
(R)
222  of
 Learners should--know:
z

a

bi
- Define
the
conjugate
of
.

16


4

1
1.
(R) demand is suggested:
◦
◦
the
conjugate
imaginary
numbers,
.

a
complex
number,
ℂ
,
i

1
imaginary
numbers,
.
imaginary numbers,
numbers, ii2i 111..
Where
anexample
is given,
the cognitive
16
2. 16
(K)
16
555
2.
(K)
-- of
imaginary
2.
(K)
22.


(K)
z

a

bi
- the conjugate
.
.

16


4


1
1.
(R)
Simplify
:
imaginary
numbers,
.
i


1
--- how
how
to
add,
subtract,
divide
and
z subtract,
subtract,
a  bi . divide
howto
toadd,
add,
divideand
and knowledge (K),
to
add,
and
2.  16   5
(K)
(R), complex
procedure (C) or
- how
subtract,
divide
12
12 routine procedure
and
444.... 12
12
Complex
- imaginary numbers,
3.
(R)
-complex
to
add,
subtract,
divide
i2 ◦◦complex

1 .how numbers.
imaginary
numbers,

4
Complex
3.
(R)
Learners
should
know:
multiply
numbers.
multiply
Complex
3.
(R)

16


5
2.
(K) (P).
Complex
3.problem-solving
multiply complex numbers.
 4.  12(R)
2 multiply
- howComplex
to add,--Define
subtract,
divide
and
complex
numbers.
represent
complex
numbers
in
3. bi . 666 3.1.  16  (R)
numbers
z

a
the
conjugate
of
numbers
represent
complex
numbers
in
 4   1 (R)
(R)
represent
complex
numbers
in
.
i
=
−
1
a
complex
number,
ℂ
,
3
numbers
- represent complex numbers
 4.in 12 4.

6
2

3
i

i

1

5
i
4.
(K)
2

3
i

i

1

5
i
4.
(K)
2
2

3
i

i

1

5
i
(K)
numbers
3.
(R)
multiply
complex
numbers.
represent
complex
numbers
in
the
Argand
diagram.
the
Argand
diagram.
2
−
3
i
+
i
−
1
−
5
i
2

3
i

i

1

5
i
4.
(K)
4.
(K)
the
Argand
diagram.
imaginary
numbers,
.
i


1
Simplify : 4.2. 2 316
z the
a Argand
bi .◦◦ how
add, subtract,
(K)
diagram.
6
i i  1(K)
5 5i
(K)
5. ((3(33222ii)(
(K)
i)()(iii11)1))
5.
zz..to
- represent complex
numbers
in
the
diagram.
argument
of
- argument
argument
ofknow:
(K)
-of
to add,
subtract,5.
divide and
argument
of
5.
(K)
divide
and
multiply
zzhow
. . Argand
 ---Learners
should
2  3zof
i.  i  1  5i
4.form
(K)
5. (3 24i)(
(K)
i  1)
the Complex
Argand
- complex
argument
of
trigonometric
(polar)
- trigonometric
trigonometric
(polar)
form
of
Complex
numbers.
3.4   1.  12
(R)
multiply
complex
numbers.
---diagram.
trigonometric
(polar)
form
of
3
z

a

bi
the
conjugate
of
.

16


1.
(R)
(polar)
form
of
5. (3  (polar)
(K)
2i)(i  1form
)Solve
3 - argument
numbers
x
Solve
for
and
y
:

6
x
Solve
for
and
y
:
of z.complex
trigonometric
of
x
for
and
y
:
complex
numbers.
numbers.
numbers
2
represent
complex
numbers
in
and yy: :
Solvefor
for xx and
◦◦numbers.
represent complex
Solve
- complex
imaginary
numbers,
i  1 .
16
iiSolve
334.5
2.
for
2yiyi
 3i x iand
(K)
1
y5:i
(K)
- trigonometric
(polar)
formnumbers
of
complex
 Solve
Solve
equations
with
complex
6. 222xxx
(R)
15
15
6.
(R)
15
555
(R)
innumbers.
thediagram.
Argand 6.
Solve
equations
with
complex
the
Argand

equations
with
complex
(R)
i

3

yi
- how
to add,with
subtract,
divide
and
 Solve
equations
complex
x
Solve
for
and
y
:
5.
(K)
(
3

2
i
)(
i

1
)
6.
(R)
2
x

15
i

3

5
yi
complex numbers.
with
Solve
equations
z. complex
diagram.
numbers
with
two
variables.
numbers
with
twoargument
variables.
-two
ofwith
numbers
two
variables.
Complex
3.  4.  12
(R)
multiply
complex
numbers.
numbers
with
variables.
6.
(R) notation.
2
x

15
i

3

5yi offunctional
 Solve equations
with
complex
numbers
with
two
variables.
z
.
◦
◦
argument
of
Factorise
third-degree
polynomials.
Revise

6
trigonometric
(polar)
form
Factorise
third-degree
polynomials.
Revise
functional
notation.
Factorise
third-degree
polynomials.
Revise
functional
notation.
numbers
- represent
complex
numbers in
Factorise
third-degree
polynomials.
Revise functional notation.
numbers with
twothe
variables.
x to
Solve
and
y:
Factorise
third-degree
polynomials.
Revise
functional
notation.
Apply
the
Remainder
and
Factor
 3i  i may
1  5be
i for
4.
(K)
◦◦ trigonometric
(polar)
Apply
the
Remainder
and
Factor
complex
numbers.
Any
method
may
be
used
to
factorise
third
degree
polynomials
but
Apply
Remainder
and
Factor
Any2method
method
may
be
used
to
factorise
thirddegree
degreepolynomials
polynomialsbut
butitititit
Any
method
used
factorise
third
degree
polynomials
but
the
Argand
diagram.
Apply
the
Remainder
and
Factor
Any
may
be
used
to
factorise
third
Factorise
third-degree
polynomials.
Revise
functional
notation.
Apply
the
Remainder
and
Factor
form
of
complex
6.
(R)
2
x

15
i

3

5
yi
5.
(K)
(
3

2
i
)(
i

1
)
Theorems
to
polynomials
of
the
third
Any
method
may
be
used
to
factorise
third
degree
polyno
Theorems
to
polynomials
of
the
third
 Solve
with complex
Polynomials
should
include
examples
which
require
the
Factor
Theorem.
Polynomials
shouldinclude
includeexamples
exampleswhich
whichrequire
requirethe
theFactor
FactorTheorem.
Theorem.
- argument
of z.equations
Theorems
to polynomials
of the third
Polynomials
should
include
examples
which
require
the
Factor
Theorem.
Polynomials
should
numbers.
Apply the Remainder
and
Factor
Theorems
to polynomials
ofmay
the
third
degree
(no
proofs
are
required).
degree
(no
proofs
are
required).
Any
method
be
used
to
factorise
third
degree
polynomials
but
it
numbers
with
two
variables.
degree
(no
proofs
are
required).
Polynomials
should
include
examples
which
require
the Factor Theore
- (no
trigonometric
(polar) form of
2
degree
proofs are required).
Example:
Example:
Example:
Theorems to polynomials
the
third
(no
proofs
are
required).
•of degree
Solve
equations
with
Long
division
method
can
also
be
used.
Long
division
method
can
also
be
used.
Long
division
method
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degree
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concept,
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the
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approximating
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to
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Page
approximating
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rate
of
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or
Page44
Examples:
Page
3. Determine the gradient of a tangent
described indx
3.1.
to a graph,
gradient
Page
f (xat
which
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 f is(xalso
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h
Page 47 of 59
2. Determine the average gradient
of a
Examples:
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d
curve between two points.
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, f ' (x)
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to a graph, which is also the gradient
f (x  h)  f (x)
m
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Examples:
3. Determine the gradient of a tangent
to a graph, which is also the gradient
Page
40
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
-
trigonometric (polar) form of
Solve for x and y :
complex numbers.
6. 2x  15i  3  5yi
(R)
 Solve equations with complex
numbers with two variables.
Factorise third-degree polynomials.
Revise functional notation.
TERM
1
Apply the Remainder and FactorGRADE 12:Any
method
may be used to factorise third degree polynomials but it
Theorems
to
polynomials
of
the
third
Polynomials
should include examples
which require the Factor Theorem.
2
Weeks
Topic
Curriculum statement
Clarification
degree (no proofs are required).
Example:
Where an example is given, the cognitive demand
Long division method can also be used.
is suggested:
procedure (R),
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Page
d
n the gradient
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+2
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2
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1 , using
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4.7.BySketch
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On word problems
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thebediagram
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Guide
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)  ax the
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f (x)  k , f (x)  ax and
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fstationary
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displacement formulae
formulae like s  u  1 at2 .
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2
d
n
n 1
fthe
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the factor
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5. Use
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for n  ℝ Very
problems.
techniques.
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to practical
application in the technical field.
ndx
ℝ
the technical
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n  ℝ 6. Find equations of tangents Refer to practical application in 2.
2
defined by y  x
y  x3 the
 4xgraph
 x by:
2.
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defined by Sketch
6.
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equations
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tangents
graphs
8. Solve practical
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6. Find
equations
of
tangents
to
graphs
to graphs of functions
3
2
2.1
xthe
finding
4axes;
x  xtheby:
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by y 
2.1 graph
findingdefined
the intercepts
with
intercepts with the
of and
functions
of functions
optimisation
rates
of of
change,
7. Sketch
graphs
cubic
6. Find
equations
of tangents
to
graphs
2.2
finding
maxima,
minima.
(C)
finding maxima, minima.
polynomial
functions using
of motion.
2.1 finding the intercepts with the2.2
axes;
ofincluding
functionscalculus
7. Sketch
graphs oftocubic
differentiation
determine
7. polynomial
Sketch graphs
of
cubic
polynomial
2.2 finding maxima, minima.
(C)
functions
using differentiation
to using On
word problems
with
allproblems
the measurements
mustwith
be all
the co-ordinate
of stationary
functions
differentiation
tothe diagram
ssessment Term 1:
On
word
the diagram
7. Sketch graphs
of
cubic
polynomial
determine
the co-ordinate
of
given.
Guide
the
learners
through
the
question
with
subsections.
points. Also,
determine
the
determine
the co-ordinate
of diagram with
given.
Guide
the learners through
functions using
tograph
On word
problems the
all the
measurements
must be the q
stationary
points.
Also,
determine
Test (at least 50 marks).
intercepts
of the
x - differentiation
1 at2 .
Refer
to
displacement
formulae
like
s

u

stationary
points.
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determine
determine the
co-ordinate
ofoftheorem
the
the graph using
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given. Guide the learners throughRefer
the question
with
subsections.
2
Investigation or project.
using
the factor
to displacement
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the
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using
x
the
factor
theorem
and
other
stationary
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and other
techniques.
1
2
Test (at least 50 marks) or Assignment (at least
50 marks).
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toVery
displacement
formulae like s  u  at .
the factor
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and
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simple
problems.
the x - intercepts
the graph
using
8. techniques.
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practical
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2
problems.
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in thesimple
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concerning
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8.
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Refer to practical application in the tech
techniques. rates of change, including Very simple problems.
optimisation
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calculus of motion.
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8. ofSolve
practical
problems
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Refer to practical application in the technical field.
Page 4
including calculus of motion.
6
Calculus
optimisation and rates of change,
8. Solve practical problems concerning
Assessment Term
1:
optimisation
and rates of change,including calculus of motion.
Assessment
1. Test (atTerm
least1:50 marks).
including calculus of motion.
Investigation
or project. Term 1:
1. 2.Test
(at least 50 marks).
Assessment
Test (at least
50 marks) or Assignment (at least 50 marks).
2. 3.Investigation
or project.
essment Term
1: (at least 50 marks)
1. Testor(at
least 50 marks).
3. Test
Assignment
(at least 50 marks).
2. Investigation or project.
Test (at least 50 marks).
3. Test (at least 50 marks) or Assignment (at least 50 marks).
nvestigation or project.
Test (at least 50 marks) or Assignment (at least 50 marks).
Page 48
Page 48
CAPS
TECHNICAL MATHEMATICS
41
GRADE12:
12:TERM
TERM 22
GRADE
Weeks
Topic
Weeks
GRADE 12: TERM 2
Curriculum
statement
Topic
Curriculum
statement
Curriculum statement
Clarification
Clarification
Where
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example
the cognitive
cognitive demand
GRADE
12: TERM
2given, the
Topic
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Where
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isisgiven,
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procedure
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Where
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Weeks
Topic
Curriculum
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Clarification
GRADE
12: TERM
2 or problem-solving (P).
problem-solving
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Introduce
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Introduce integration.
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problem-solving
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knowledge (K), routine procedure (R), complex proced
1. Understand
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Calculate the
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Page 49 of 59
1.1 Determine
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Page 50
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Page 50
Page 50 of 59
CAPS
TECHNICAL MATHEMATICS
43
GRADE 12: TERM 3
GRADE 12: TERM 3
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the distance between P and R is 28m. Find the height
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2. Trial examination
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Assessment
Term 3:
Assessment
Term
3:
Assessment
Term
Paper 1: 150 Assessment
marks:
Trial
Term
3:marks:
Assessment
Term
3: 3:
33 hours
Assessment
Term
3:Exam
of the
tower,
(C) 3 hours
Paper
1: 150
3 hours
Paper 2: 150 marks:
1.
Assignment
/ test
(at
least TP.
50 marks)
1.
Assignment
/
test
(at
marks)
1.
Assignment
/
test
(at
least
50
marks)
1.
Assignment
/
least
50
Algebraic expressions,
equations,
and
inequalities
(nature
of
roots,
logs
and
complex
numbers)
(
50
 3), Functions and graphs (35  3), 25  3
1.
Assignment
/
test
(at
least
50
marks)
1.
Assignment
/
test
(at
least
50
marks)
Assessment
Term
3:
Revision 2.
Algebraic
expressions, equations
Analytical Geometry
50  3
Trial
examination
2.
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examination
2.
Trial
examination
2.
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examination
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examination
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examination
1.
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test
(at3Differential
least
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marks)
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roots,
logs and and Integration (25 Trigonometry
50  3
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marks:
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1:
150
marks:
3
hours
2.
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examination
complex
numbers)
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40graph
3
Paper 2: 150 marks:
3 hoursexpressions, equations, and inequalities (nature of roots, logs and complex numbers) (50  3), Functions and
Algebraic
Algebraic
expressions,
equations,
and
inequalities
(nature
of
roots,
and
complex
Functions
and
graphs
Algebraic
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equations,
and
inequalities
(nature
logs
numbers)
,
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(
50

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),
(350
35
Algebraic
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equations,
and
inequalities
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logs
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Algebraic
expressions,
equations,
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inequalities
(nature
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roots,
logs
and
complex
numbers)
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and
graphs
(
50

3
),
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expressions,
equations,
and
inequalities
(nature
of
roots,
logs
and
complex
numbers)
(
50

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150
marks:
3 hours (40  3), Euclidean
Functions
and
graphs
circles, angles
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35 Geometry
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Page 51
of 59
Page 51 of 59
Page 51 of 59
44
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
12:
GRADE
12:4TERM
TERM44
GRADE GRADE
12:
TERM
Curriculum
statement
Curriculum
statement
Curriculum
statement
Weeks
Topic
Weeks Weeks
Topic Topic
Weeks
Topic
Weeks
Topic
GRADE
12:4TERM
TERM444
12:
GRADE GRADE
12:
TERM
GRADE
12:
TERM
Curriculum
statement
Clarification
Curriculum
statement
Curriculum
statement
Curriculum
statement
Clarification
GRADE
12: TERM
4Clarification
Clarification
Clarification
Clarification
Clarification
Where
an
isisthe
given,
the
cognitive
demand
suggested:
Where
ansuggested:
example
isthe
given,
thecognitive
cognitive
demand
Where
anexample
example
given,
the
cognitive
demand
suggested:
Where
an
example
is
given,
the
demand
is
Curriculum
statement
Clarification
Where
an example
isisisgiven,
cognitive
demand
is suggest
Where
an
example
is
given,
the
cognitive
demand
isissss
Where
an example
is given,
cognitive
demand
is
knowledge
(K),
routine
procedure
(R),
complex
procedure
(C)
or
knowledge
(K),
routine
procedure
(R),
complex
proce
knowledge
(K), routine
procedure
(R),
complex
procedure
or (R), complex
knowledge
(K),
routine
procedure
(R), complex
proced
knowledge
(K),
routine
procedure
procedure
(C
knowledge
(K),
routine
procedure
proced
knowledge
(K), routine
procedure
complex
procedure
(C)
or (C)
Where(R),
an
example
is
given,
the
cognitive
demand(R), complex
problem-solving
(P).
problem-solving
(P).
problem-solving
(P).
problem-solving
(P).
problem-solving
(P).
problem-solving
(P). procedure (R),
problem-solving (P).
is suggested: knowledge
(K), routine
complex procedure (C) or problem-solving (P).
Revision
Revision
RevisionRevision
Revision
Revision
Revision
Revision
Revision
Revision
Revision
Revision
nnRevision
333
3
3
Assessment
Term4:
4:
Assessment
Assessment
Term 4:Term
Assessment
Term
4:
Assessment
Term
4:
Finalexamination:
examination:
Final
Final examination:
Final
examination:
ours Paper 1:
Paper
Paper
1:150
150marks:
marks:
hours
Paper
2:marks:
150marks:
marks:
hours
hours
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2:150
150marks:
marks:
hours Paper
Paper
333hours
Paper
150
333hours
Paper2:
2:150
1502:
hours
150 1:
marks:
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marks:
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1:
150
marks:
hours
Paper
2:
150
marks:
hours
Paper
2:
150 2:
marks:
3 hours33 hours
equations
Analytical
Geometry
50

3
25

3
Algebraic
expressions,
equations
Analytical
Geometry
50

3
25
equations
Analytical
Geometry
50

3
25

3
Algebraic
expressions,
equations
Analytical
Geometry
50

3
Algebraic
equations
Analytical
Geometry
25  3 25
Analytical
Geometry
Algebraic
equations
Analytical
ns
Analytical
Geometry50  3 50  3
25
333
50expressions,
 3 expressions,
25Geometry
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of
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and
inequalities
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and
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50
ets,
oflogs
roots,
logs
andinequalities
Trigonometry
5033
and
of
roots,
logs
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and
inequalities
(nature(nature
of
roots,
logs
and
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Trigonometry
50  3 50
and
inequalities
(nature
of
roots,
logs
and
Trigonometry
and
Trigonometry
50
333
50  3 50
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Geometry
40

3
complex
numbers)
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Geometry
40
Euclidean
Geometry
40

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complex
numbers)
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Geometry
40
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Geometry
complex
numbers)
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Geometry
40

3
complex numbers)Euclidean Geometry
Euclidean40Geometry
40 
333
3
Mensuration,
circles,
angles
and
angular
movement
35

3
35

3
Functions
and
graphs
Mensuration,
circles,
angles
and
angular
movement
35

3
35
Mensuration,
circles,
angles
and
angular
movement
35

3
35

3
Functions
and
graphs
Mensuration,
circles,
angles
and
angular
movement
35

3
35

Functions
Mensuration,
circles,
angles
and
movement
35angles
 3 35and
35  3 35 333
Functions
and graphs
Mensuration,
circles,
anglesangles
andangular
angular
movement
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and angular
movement
Mensuration, circles,
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35 and
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35  3circles,
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Finance,
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15
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15  3 15
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15
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50

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50
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and Integration
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50
 3Calculus
Page
52 ofof59
59
Page 52Page
of 5952
CAPS
TECHNICAL MATHEMATICS
45
Section 4
Curriculum and Assessment Policy Statement (CAPS)
FET TECHNICAL MATHEMATICS ASSESSMENT GUIDELINES
4.1INTRODUCTION
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 conjectures 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.
46
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
4.2 INFORMAL OR DAILY ASSESSMENT
The aim of assessment for learning is to continually collect information on a learner’s achievement that can be used to
improve individual learning.
Informal assessment involves daily monitoring of a learner’s progress. This can be done through
observations, discussions, practical demonstrations, learner-teacher conferences, informal classroom interactions, etc,
although informal assessment may be as simple as stopping during the lesson to observe learners or to discuss with
learners how learning is progressing. Informal assessment should be used to provide feedback to the learners and to
inform planning for teaching, and it need not be recorded. This should however 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.
CAPS
TECHNICAL MATHEMATICS
47
PROGRAMME OF ASSESSMENT
4.4 PROGRAMME OF ASSESSMENT
4.4 to
PROGRAMME
OF ASSESSMENT
four cognitive levels used
guide all assessment
tasks are based on those suggested in the TIMSS
The
four cognitive
levelslevel
used and
to guide
assessmentpercentages
tasks are based
on those
suggested
in the TIMSS
dy of 1999.Formal
Descriptors
for each
the aall
approximate
of tasks,
tests
and
assessments
need to
accommodate
range of cognitive
levels and abilities
of learners
as shown below:
study
of
1999.
Descriptors
for
each
level
and
the
approximate
percentages
of
tasks,
tests and
cognitive
levels
used
to guide all assessment tasks are based on those suggested
in the TIMSS
minations which shouldThe
be four
at each
level are
given
below:
examinations
which
should
be
at
each
level
are
given
below:
study of 1999.
Descriptors for each level and the approximate percentages of tasks, tests and
4.4 PROGRAMME
OF ASSESSMENT
examinations
which
be at each level are given below:
ognitive levels
Description of skills to beshould
demonstrated
Examples
Cognitive
levels
Description
of
skills
to be demonstrated
The four cognitive levels used to guide all assessment
tasks are based on those suggestedExamples
in the TIMSS study of 1999.
owledge
1. Write down the domain of the
 Straight recall
Descriptors
for
each
level
and
the
approximate
percentages
of
tasks,
tests
and
examinations
should
be at each
KnowledgeCognitive levels
1. Write down thewhich
domain
of the
Description
be demonstrated
Examples
recall on of skills tofunction
 Identification of Straight
correct formula
level are given
below:  Identification
of correct
Knowledge
1. Write down the domain of the
 Straight
recall
%
3 function
the
information
sheet (no
changing
of formula on
y

f
x


2
20%


3
the
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sheet
(no
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 Identification of correct formula
thelevels
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2
x ony f  x function
Cognitive20%
of
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to
be
demonstrated
Examples
the subject)
3
x
(no
changing
of
Use of mathematical
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(Grade 10)
y

f
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
2


1.
Write
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domain
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Knowledge
• Use
Straight
recall
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(Grade 10)
the subject)
x
ˆ

Appropriate
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mathematical
AOB subtended byˆarc
2. The
angle
20%
•
Identification
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on
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Useuse
ofcorrect
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(Grade
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2. The
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vocabulary  Appropriate
at the centre
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.......
information sheet (no changing AB
of the
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 Appropriate use of mathematical2 AB at2.
theThe
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utine
 Estimation and appropriate
rounding
x
5
x

14
1. Solve for x : x  (Grade
10)
Routine of numbers• Estimation
and appropriate
centre
: x 2atthe
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14 O of a circle .......
1. Solve for xAB
Use of vocabulary
mathematical
facts rounding
cedures
(Grade
10)
ˆ
AOB
2.
The
angle
subtended
Procedures
of
numbers
Routine
 Estimation
and appropriate rounding
•
Appropriate
useand
of mathematical
(Grade1.10)Solve for x : x 2 by
5xarc

14
 Proofs
of prescribed
theorems
AB at the centre O of a circle .......
vocabulary

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of
prescribed
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and
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of
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%
(Grade
derivation of formulae
2. Determine the general solution
of10)
35%
derivation
of
Routine
•
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andformulae
rounding
of
2.
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the
general
solution of
 use
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of prescribed
theorems
and
 Identification
and
direct
of appropriate
correct
2
the equation 1. Solve for x : x − 5 x =
14
Procedures
numbers derivation

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and
direct
use
of
correct
35%
the
equation
of
formulae
2.10)Determine
the general solution of
formula on the information sheet (no
2 sin(
x  30)  1 (Grade
0 (Grade
11)
•
Proofs ofon
prescribed
theoremssheet
and (no
formula
the
information
2
sin(
x

30

)

1

0
(Grade

Identification
and
direct
use
of
correct
the
equation
changing of the subject)
2. Determine the general solution11)
of the
35%
derivation of formulae
changing
of
the
subject)
formula
on
the
information
sheet
(no
equation
(Grade
2
sin(
x

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
)
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(Grade 11)
 Perform well-known
procedures
ˆ
•
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and direct use3.of Prove
correctthat the angle AOB
11)

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well-known
procedures
ˆ
changing
of
the
subject)
that
 Simple applications
and calculations
formula
on the information sheet
(no
subtended
by3.arcProve
thethe angle AOB
AB at

Simple
applications
and
calculations
ˆ the

Perform
well-known
procedures
changing
of
the
subject)
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Prove 3.
thatProve
the
angle
subtended
subtended
bythe
arc
at
AB
which might involve few steps
AOB
that
the
angle
centre O of a 3.
circle
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which
might
involve
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steps

Simple
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and
calculations
•
Perform
well-known
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by
arc
at
the
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of
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circle
AB
centre
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a circle is by
double
theat the
 Derivation from given information
subtended
arc AB
ˆ which
size
ofwhich
the angle ACB
the ˆ

Derivation
from
given
information
which
might
involve
few
steps
•
Simple
applications
and
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may be involved
centre
O
circleACB
isˆdouble the
size
ofthe
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the
is double
the
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of of
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same
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mightbe
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 Derivation
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sameofarc
atˆ the
 Identification and use (after
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atangle
the circle.
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size
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(Grade
• Identification
Derivationmay
fromand
given
information
may 11)
be
use
(after
changing
be
involved
circle.
(Grade
11)
the subject) of correct formula
(Grade
11)
same arc subtends at the circle.
involved
the
subject)
of correct formula
 Identification
and use (after changing
 Generally similar
to
those
(Grade 11)
•
Identification
and use
(after changing the
Generally
similar
to those
the
subject)
of correct formula
encounteredin class
subject) of correct formula
encountered
in classsimilar
 Generally
thoseis the average speed covered
mplex
1. toWhat
 Problems involve
complex
calculations
•
Generally
similar
to those encountered
in
Complexand/or higher order
1. to
What
Problems
involve complex
calculations
encountered
in class
cedures
on a round trip
and is the average speed covered
class
reasoning
Procedures
on
round
trip to
andaverage speed covered
and/or
higher
order
reasoning
Complex
1.the
What
is the
 Problems
involve
complex
calculations
from a destination
ifathe
average
1. What
is
average
speed covered on
Complex
• notProblems
involve
complex
calculations
 There
is often
an obvious
route
to
from
a destination
if the
average

There
is
often
not
an
obvious
route
to
Procedures
on
a
round
trip
to and
and/or
higher
order
reasoning
a
round
trip
to
andfrom
a destination
Procedures
and/or
higher
order
reasoning
%
speed
going
to
the
the solution
30%
speed
going
to
the
if
the
average
speed
going
to the
the
solution
from
a
destination
if the average
• not
There
is often
notaisan
obvious
to the route
There
often
not route
an obvious
to/ h and the
destination
is 100km
 Problems need
be based
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real
destination
is
30%
and
the
100
km
/
h
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and
the
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 Problems
need
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on a realspeed for the
30% context
speed going to the
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world
average speed
speed for
journey is
average
forthe
thereturn
•
Problems
need
not
be
based
on
a
real
world
context
is 100km / h and the
 Problems need notreturn
be based
on aisreal
80km / h ? destination
journey
(Grade
 Could involve making
significant
(Grade 11)
world context
km / h ?for
return journey
is 80speed
(Grade
average
the
Could
involve
making
significant
world
context
11)
connections•between
different
Could
involve
making
significant
11)
return
is 80km / h ? (Grade
between
different
 Could
involve
making significant (x  2)2
( x + journey
2)2
representations connections
connections between different
2.
Differentiate
2 with respect to
2.
Differentiate
with
respect
11)
representations
connections between different 2. Differentiate
xx. (Grade 12) ( x x 2) with respect
representations
 Require conceptual
understanding
2
x

Require
conceptual
understanding
representations
to x. (Grade 12)
•
Require conceptual
understanding
2. Differentiate (x  2) with respect
to x. (Grade 12)
 Require
conceptual
Suppose a piece of wire could bextied
Problem Solving
•
Non-routine
problems
(which areunderstanding
not
(Grade
12)equator.
tightly around to
thex.earth
at the
15%
necessarily difficult)
•
•
Higher order reasoning and processes are
involved
Might require the ability to break the
problem down into its constituent parts
Imagine that this wire is then lengthened
by exactly one metre and held so that it is
still around the
Pageearth
55 ofat59the equator. Would
a mouse be able to crawl between
Page the
55 ofwire
59
and the earth? Why or why not?
Page 55 of 59
(Any grade)
The Programme of Assessment is designed to set formal assessment tasks in all subjects in a school throughout the
year.
48
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
(a)
Number of Assessment Tasks and Weighting:
Learners are expected to have seven (7) formal assessment tasks for their school-based assessment (SBA). The
number of tasks and their weighting are listed below:
GRADE 10
School-based Assessment
TASKS
GRADE 11
GRADE 12
WEIGHT (%)
TASKS
WEIGHT (%)
TASKS
WEIGHT (%)
Project
or
Investigation
Test
20
Project
or
Investigation
Test
20
Test
Project or
Investigation
Assignment / Test
10
20
Term 2
Assignment or
Test
Mid-year Exam
10
10
30
Assignment or
Test
Mid-year Exam
Test
Mid-year Exam
10
15
Term 3
Test
Test
10
10
Test
Test
10
10
Test
Trial Exam
10
25
Term 4
Test
10
Test
10
Term 1
10
10
30
10
School-based
Assessment
mark
100
100
100
School-based
Assessment
mark (as % of
promotion
mark)
25%
25%
25%
End-of-year
examinations
75%
75%
Promotion mark
100%
100%
Note:
•
Although the project/investigation is indicated in the first term, it could be scheduled in term 2. Only ONE
project/investigation should be set per year.
•
Tests should be at least ONE hour long and count at least 50 marks.
•
Project or investigation must contribute 25% of term 1 marks while the test marks contribute 75% of the term
1 marks. The same weighting of 25% should apply in cases where a project/investigation is in term 2.
•
The combination (25% and 75%) of the marks must appear in the learner’s report.
•
Graphic and non-programmable calculators are not allowed (for example, calculators which factorise
, or find roots of equations). Calculators should only be used to perform standard
numerical computations and to verify calculations by hand.
Formula sheet MUST NOT be provided for tests and final examinations in Grades 10 and 11. Learners
can be with formula sheet in Grade 12 for tests and examinations.
Trigonometric functions and graphs will be examined in paper 2.
•
•
(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 Grades 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.
CAPS
TECHNICAL MATHEMATICS
49
Mark distribution for Technical Mathematics NCS end-of-year papers: Grades 10 - 12
Description
Grade 10
Grade 11
Grade. 12
Algebra ( Expressions, equations and inequalities
including nature of roots in Grades 11 & 12)
60 ± 3
90 ± 3
50 ± 3
Functions & Graphs
25 ± 3
45 ± 3
35 ± 3
Finance, growth and decay
15 ± 3
15 ± 3
15 ± 3
PAPER 1:
Differential Calculus and Integration
TOTAL
50 ± 3
100
150
150
PAPER 2 : Grades 11 and 12: theorems and/or trigonometric proofs: maximum 12 marks
Description
Grade 10
Grade 11
Grade 12
Analytical Geometry
15 ± 3
25 ± 3
25 ± 3
Trigonometry
40 ± 3
50 ± 3
50 ± 3
Euclidean Geometry
30 ± 3
40 ± 3
40 ± 3
Mensuration and circles, angles and angular
movement
15 ± 3
35 ± 3
35 ± 3
100
150
150
TOTAL
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.
•
Formula sheet must not be provided for tests and for final examinations in Grades 10 and 11 BUT for
Grade 12 formula sheet can be provided for tests and examinations.
•
Trigonometric functions and graphs will be examined in paper 2.
4.5 RECORDING AND REPORTING
•
Recording is a process in which the teacher is able to document the level of a learner’s performance in a specific
assessment task.
•
It indicates learner progress towards the achievement of the knowledge as prescribed in the Curriculum and
Assessment Policy Statements.
•
Records of learner performance should provide evidence of the learner’s conceptual progression within a grade
and her/his readiness to progress or to be promoted to the next grade.
•
Records of learner performance should also be used to monitor the progress made by teachers and learners in
the teaching and learning process.
•
Reporting is a process of communicating learner performance to learners, parents, schools and other stakeholders.
Learner performance can be reported in a number of ways.
•
These include report cards, parents’ meetings, school visitation days, parent-teacher conferences, phone calls,
letters, class or school newsletters, etc.
•
Teachers in all grades report percentages for the subject. Seven levels of competence have been described for
each subject listed for Grades R – 12. The individual achievement levels and their corresponding percentage
bands are shown in the Table below.
50
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
CODES AND PERCENTAGES FOR RECORDING AND REPORTING
RATING CODE
7
6
5
4
3
2
1
DESCRIPTION OF COMPETENCE
Outstanding achievement
Meritorious achievement
Substantial achievement
Adequate achievement
Moderate achievement
Elementary achievement
Not achieved
PERCENTAGE
80 – 100
70 – 79
60 – 69
50 – 59
40 – 49
30 – 39
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 which 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.
CAPS
TECHNICAL MATHEMATICS
51
52
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)