Grade
Mat h e m a t i c s
Study Guide 12
,© Department of Basic Education 2015
This content may not be sold or used for commercial purposes.
Curriculum and Assessment Policy Statement (CAPS) Grade 12
Mind the Gap study guide for Mathematics
ISBN 978-1-4315-1935-4
This publication has a Creative Commons Attribution NonCommercial Sharealike license. You can use, modify,
upload, download, and share content, but you must acknowledge the Department of Basic Education, the authors
and contributors. If you make any changes to the content you must send the changes to the Department of Basic
Education. This content may not be sold or used for commercial purposes. For more information about the terms of
the license please see:
http://creativecommons.org/licenses/by-nc-sa/3.0/.
Copyright © Department of Basic Education 2015
222 Struben Street, Pretoria, South Africa
Contact person: Dr Patricia Watson
Email:
Tel: (012) 357 4502
http://www.education.gov.za
Call Centre: 0800202933
The first edition, published in 2012, for the Revised National Curriculum Statement (RNCS) Grade 12 Mind the
Gap study guides for Accounting, Economics, Geography and Life Sciences; the second edition, published in 2014 ,
aligned these titles to the Curriculum and Assessment Policy Statement (CAPS) and added more titles to the series
in 2015, including the CAPS Grade 12 Mind the Gap study guide for Mathematics.
ISBN 78-1-4315-1935-4
Mind the Gap team
Series managing editor: Dr Patricia Watson
Production co-ordinators: Lisa Treffry-Goatley and Radha Pillay
Production assistants: Nomathamsanqa Hlatshwayo and Motshabi Mondlane
Authors: Lynn Bowie, Ronald Peter Jacobs, Sue Jobson, Terrence Mongameli Mbusi, Sello Gert Motsoane,
Nonhlanhla Rachel Mthembu, Ntshengedzeni Steven Muthige, Mpho Francis Phatlane,
Josephina Mamaroke Phatlane, Peter Ketshepile Raadt, Percy Stephen Tebeila, Anita van Heerden and
Carol Wyeth.
Expert readers: Prof Bruce Watson, Leonard Mudau and Karen van Niekerk
Proofreaders: John Ostrowick and Angela Thomas
Designers: Sonja McGonigle and Erika van Rooyen
Illustrators: Michele Dean, Vusi Malindi, Khosi Pholosa, John Ostrowick, Kenneth Tekane
Cover illustration: Alastair Findlay
Afrikaans Translation: Marga Vos
Onsite writers’ workshop IT support: Wayne Cussons
Special thanks to Winning Teams, CEO Denzil Hollis, for the organisation’s subject expertise and workshop support
Winning Teams board game facilitators: Mantse Khoza and Sue Jobson
, © Department of Basic Education 2015
Ministerial foreword
The Department of Basic Education (DBE) has pleasure in releasing the second
edition of the Mind the Gap study guides for Grade 12 learners. These study
guides continue the innovative and committed attempt by the DBE to improve the
academic performance of Grade 12 candidates in the National Senior Certificate
(NSC) examination.
The study guides have been written by teams of exerts comprising teachers,
examiners, moderators, subject advisors and coordinators. Research, which
began in 2012, has shown that the Mind the Gap series has, without doubt, had
a positive impact on grades. It is my fervent wish that the Mind the Gap study
guides take us all closer to ensuring that no learner is left behind, especially as
we celebrate 20 years of democracy. Matsie Angelina Motshekga, MP
The second edition of Mind the Gap is aligned to the 2014 Curriculum and Minister of Basic Education
Assessment Policy Statement (CAPS). This means that the writers have considered
the National Policy pertaining to the programme, promotion requirements and
protocols for assessment of the National Curriculum Statement for Grade 12 in
2014.
The CAPS aligned Mind the Gap study guides take their brief in part from the
2013 National Diagnostic report on learner performance and draw on the Grade
12 Examination Guidelines. Each of the Mind the Gap study guides defines key
terminology and offers simple explanations and examples of the types of questions
learners can expect to be asked in an exam. Marking memoranda are included to
assist learners to build their understanding. Learners are also referred to specific
questions from past national exam papers and examination memos that are
available on the Department’s website – www.education.gov.za.
The CAPS editions include Accounting, Economics, Geography, Life Sciences,
Mathematics, Mathematical Literacy and Physical Sciences Part 1: Physics and
Part 2: Chemistry. The series is produced in both English and Afrikaans. There are
also nine English First Additional Language (EFAL) study guides. These include
EFAL Paper 1 (Language in Context); EFAL Paper 3 (Writing) and a guide for each
of the Grade 12 prescribed literature set works included in Paper 2. These are
Short Stories, Poetry, To Kill a Mockingbird, A Grain of Wheat, Lord of the Flies,
Nothing but the Truth and Romeo and Juliet. (Please remember when preparing
for EFAL Paper 2 that you need only study the set works you did in your EFAL class
at school.)
The study guides have been designed to assist those learners who have been
underperforming due to a lack of exposure to the content requirements of the
curriculum and aim to mind-the-gap between failing and passing, by bridging
the gap in learners’ understanding of commonly tested concepts, thus helping
candidates to pass.
All that is now required is for our Grade 12 learners to put in the hours required
to prepare for the examinations. Learners, make us proud – study hard. We wish
each and every one of you good luck for your Grade 12 examinations.
__________________________________
Matsie Angelina Motshekga, MP
Minister of Basic Education
2015
, © Department of Basic Education 2015
Mat h e m a t i c s
Study Guide 12
,© Department of Basic Education 2015
This content may not be sold or used for commercial purposes.
Curriculum and Assessment Policy Statement (CAPS) Grade 12
Mind the Gap study guide for Mathematics
ISBN 978-1-4315-1935-4
This publication has a Creative Commons Attribution NonCommercial Sharealike license. You can use, modify,
upload, download, and share content, but you must acknowledge the Department of Basic Education, the authors
and contributors. If you make any changes to the content you must send the changes to the Department of Basic
Education. This content may not be sold or used for commercial purposes. For more information about the terms of
the license please see:
http://creativecommons.org/licenses/by-nc-sa/3.0/.
Copyright © Department of Basic Education 2015
222 Struben Street, Pretoria, South Africa
Contact person: Dr Patricia Watson
Email:
Tel: (012) 357 4502
http://www.education.gov.za
Call Centre: 0800202933
The first edition, published in 2012, for the Revised National Curriculum Statement (RNCS) Grade 12 Mind the
Gap study guides for Accounting, Economics, Geography and Life Sciences; the second edition, published in 2014 ,
aligned these titles to the Curriculum and Assessment Policy Statement (CAPS) and added more titles to the series
in 2015, including the CAPS Grade 12 Mind the Gap study guide for Mathematics.
ISBN 78-1-4315-1935-4
Mind the Gap team
Series managing editor: Dr Patricia Watson
Production co-ordinators: Lisa Treffry-Goatley and Radha Pillay
Production assistants: Nomathamsanqa Hlatshwayo and Motshabi Mondlane
Authors: Lynn Bowie, Ronald Peter Jacobs, Sue Jobson, Terrence Mongameli Mbusi, Sello Gert Motsoane,
Nonhlanhla Rachel Mthembu, Ntshengedzeni Steven Muthige, Mpho Francis Phatlane,
Josephina Mamaroke Phatlane, Peter Ketshepile Raadt, Percy Stephen Tebeila, Anita van Heerden and
Carol Wyeth.
Expert readers: Prof Bruce Watson, Leonard Mudau and Karen van Niekerk
Proofreaders: John Ostrowick and Angela Thomas
Designers: Sonja McGonigle and Erika van Rooyen
Illustrators: Michele Dean, Vusi Malindi, Khosi Pholosa, John Ostrowick, Kenneth Tekane
Cover illustration: Alastair Findlay
Afrikaans Translation: Marga Vos
Onsite writers’ workshop IT support: Wayne Cussons
Special thanks to Winning Teams, CEO Denzil Hollis, for the organisation’s subject expertise and workshop support
Winning Teams board game facilitators: Mantse Khoza and Sue Jobson
, © Department of Basic Education 2015
Ministerial foreword
The Department of Basic Education (DBE) has pleasure in releasing the second
edition of the Mind the Gap study guides for Grade 12 learners. These study
guides continue the innovative and committed attempt by the DBE to improve the
academic performance of Grade 12 candidates in the National Senior Certificate
(NSC) examination.
The study guides have been written by teams of exerts comprising teachers,
examiners, moderators, subject advisors and coordinators. Research, which
began in 2012, has shown that the Mind the Gap series has, without doubt, had
a positive impact on grades. It is my fervent wish that the Mind the Gap study
guides take us all closer to ensuring that no learner is left behind, especially as
we celebrate 20 years of democracy. Matsie Angelina Motshekga, MP
The second edition of Mind the Gap is aligned to the 2014 Curriculum and Minister of Basic Education
Assessment Policy Statement (CAPS). This means that the writers have considered
the National Policy pertaining to the programme, promotion requirements and
protocols for assessment of the National Curriculum Statement for Grade 12 in
2014.
The CAPS aligned Mind the Gap study guides take their brief in part from the
2013 National Diagnostic report on learner performance and draw on the Grade
12 Examination Guidelines. Each of the Mind the Gap study guides defines key
terminology and offers simple explanations and examples of the types of questions
learners can expect to be asked in an exam. Marking memoranda are included to
assist learners to build their understanding. Learners are also referred to specific
questions from past national exam papers and examination memos that are
available on the Department’s website – www.education.gov.za.
The CAPS editions include Accounting, Economics, Geography, Life Sciences,
Mathematics, Mathematical Literacy and Physical Sciences Part 1: Physics and
Part 2: Chemistry. The series is produced in both English and Afrikaans. There are
also nine English First Additional Language (EFAL) study guides. These include
EFAL Paper 1 (Language in Context); EFAL Paper 3 (Writing) and a guide for each
of the Grade 12 prescribed literature set works included in Paper 2. These are
Short Stories, Poetry, To Kill a Mockingbird, A Grain of Wheat, Lord of the Flies,
Nothing but the Truth and Romeo and Juliet. (Please remember when preparing
for EFAL Paper 2 that you need only study the set works you did in your EFAL class
at school.)
The study guides have been designed to assist those learners who have been
underperforming due to a lack of exposure to the content requirements of the
curriculum and aim to mind-the-gap between failing and passing, by bridging
the gap in learners’ understanding of commonly tested concepts, thus helping
candidates to pass.
All that is now required is for our Grade 12 learners to put in the hours required
to prepare for the examinations. Learners, make us proud – study hard. We wish
each and every one of you good luck for your Grade 12 examinations.
__________________________________
Matsie Angelina Motshekga, MP
Minister of Basic Education
2015
, © Department of Basic Education 2015
