Mind-Action-Series-Book-11-1

i
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Maths Textbook/Workbook Grade 11 NCAPS
ISBN 13: 978-1-86921-464-7
Product Code: M A T 9 1
Authors: M.D Phillips
J. Basson
C. Botha
First Edition: May 2012
PUBLISHERS
ALLCOPY PUBLISHERS
P.O. Box 963
Sanlamhof, 7532
Tel: [phone], Fax: [phone]
Email: [e-mail]
Website: www.allcopypublishers.co.za

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MATHS GRADE 11 NCAPS
TEXTBOOK INFORMATION
MARK DAVID PHILLIPS
B.SC, H Dip Ed, B.Ed (cum laude) University of the Witwatersrand.
The author has over twenty years of teaching experience in both state and private schools. He has led the
Mathematics Department in two schools and is currently teaching at The King’s School West Rand. The author has
presented teacher training and learner seminars for various educational institutions including Excelearn, Isabelo,
Kutlwanong Centre for Maths, Science and Technology, Learning Channel, Oracle and UJ. Mark is currently a TV
presenter for “Matrics Uploaded” on SABC 1. He has previously published highly successful Mathematics
textbooks through Allcopy Publishers and is a qualified assessor. Mark has travelled extensively in the
United Kingdom, Europe and America, gaining invaluable international educational experience. The textbook
contains methods used in top schools all over the world.
JURGENS BASSON
BA (Mathematics and Psychology) HED Randse Afrikaanse Universiteit (UJ)
Jurgens Basson has over twenty years of teaching experience in secondary and tertiary education. He is the
founder of The Maths Centre, a private study centre which offers extra maths and science tuition to more than 500
students in two different areas in Gauteng. In 2003, he established the RAU/Oracle School of Maths. Over 2000
previously disadvantaged students have had the opportunity to benefit from this programme. With the introduction
of the new curriculum in 2006, Jurgens saw the need to train and empower educators to implement the new
curriculum. He obtained a sponsorship from Oracle to do educator development workshops in five of the nine
provinces to date. Jurgens is a highly sought after educational consultant with a passion for Maths and the new
curriculum. In 2010, he served on the panel to finalise the CAPS curriculum for Maths.
CONRAD BOTHA
Maths Hons, PGCE, B.Sc (Mathematics and Psychology) Rand Afrikaans University.
Conrad Botha has been an educator in both state and private schools for the past eight years. He is currently Head
of Department at The King’s School West Rand and has also been extensively involved in teaching Maths at The
Maths Centre (Grades 4-12). The institution tutors both primary and high school learners in Maths, Science as well
as conducts examination training sessions for Grade 11 and 12 learners. The experience he obtained at The Maths
Centre resulted in him gaining valuable knowledge and teaching methodology, particularly in the implementation of
the new curriculum. Conrad has also done editing work for the Learning Channel.
The purpose of this publication is to cover all Maths topics in the new curriculum (CAPS) using a user-friendly,
modern approach. The examples presented in each chapter of the textbook cover all of the main concepts in each
topic. There is a logical, to-the-point, progression from one example to the next and the exercises reinforce the
concepts inherent in the particular topic dealt with.
At the end of each chapter there is a mixed revision exercise. This exercise is for revising all of the concepts dealt
with in the chapter. There is also a “Some Challenges” exercise which provides invaluable extension and problem
solving for top learners. At the end of the book, short answers to all of the exercises have been provided.
“This textbook has always been a life-saver for me. I just don’t have the time to waste trying to create my
own lessons using other books and then still trying to get to assess my learners in the way that we are
supposed to. This textbook has helped me to get through the content as quickly and effectively as possible
leaving more time for me to assess my learners. I can also have a life outside of school and not get so
wrapped up with so much work. I like the assessment tasks in the Teacher Guide. I have used them to
meet the requirements in the policy documents.”
Hester Jansen Van Vuuren, Educator
The CONCEPT
ENDORSEMENT
The AUTHORS

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MATHEMATICS
TEXTBOOK/WORKBOOK
GRADE 11 NCAPS
CONTENTS
CHAPTER 1 EXPONENTS AND SURDS
1
CHAPTER 2 EQUATIONS AND INEQUALITIES 20
CHAPTER 3 NUMBER PATTERNS 54
CHAPTER 4 ANALYTICAL GEOMETRY 62
CHAPTER 5 FUNCTIONS 83
CHAPTER 6 TRIGONOMETRY 135
CHAPTER 7 MEASUREMENT 199
CHAPTER 8 EUCLIDEAN GEOMETRY 207
CHAPTER 9 PROBABILITY 264
CHAPTER 10 FINANCIAL MATHEMATICS 284
CHAPTER 11 STATISTICS 310
SOLUTIONS TO EXERCISES 337

1
CHAPTER 1 – EXPONENTS AND SURDS
REVISION OF THE BASICS
The basic theory of exponents that you studied in Grade 10 is extremely
important. We will now revise these important concepts.
EXPONENTIAL LAWS
Law Example
1. .
mn mn
aa a
+
=
34 7
3.3 3
=
2.
m
mn
n
aa
a
−
=
884 4
4
2
2216
2
−
===
3.
() ()
mn mn nm
aa a
×
==
34 34 12 43
(3 ) 3 3 (3 )
×
===
4.
()
m
mm
ab a b
=
432 12 42 32 86
(3 ) 3 . . 9
xy x y xy
×× ×
==
5.
m
m
m
aa
b
b
=
313
2236
4464
xxx
×
×
==
EXPONENTIAL DEFINITIONS (COROLLARIES FROM THE LAWS)
Definition Example
1. 0
1
a
=
0
31
=
2.
11
a
=
, with
a
∈
R
2008
11
=
3.
1
n
n
x
x
−
=
4
4
1
x
x
−
=
4.
n
n
a
ax
x
−
=
4
4
3
3x
x
−
=
5.
() ()
1
n
n
ax
ax
−
=
() ()
4
4
1
3
3
x
x
−
=
6. 1
n
n
x
x
−
=
4
4
1
x
x
−
=
7.
n
n
a
ax
x
−
=
4
4
3
3
x
x
−
=
8. 1
n
n
x
a
ax
−
=
4
4
1
3
3
x
x
−
=
9.
() ()
1
n
n
ax
ax
−
=
() ()
4
4
1
3
3
x
x
−
=
10.
nn
ab
ba
−
=
22
34
43
−
=
11.
mn
nm
ab
ba
−
−
=
34
43
xy
yx
−
−
=