Cambridge IGCSE and O Level Additional Mathematics Workbook

97 Pages·2018·7.321 MB·English

by  Val Hanrahan, Wall

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Cambridge
IGCSE®
and O Level
Additional
Mathematics
Val Hanrahan
Jeanette Powell
9781510421653.indd 1 07/09/18 9:27 PM
Welcome to the Cambridge IGCSE and O Level Additional Mathematics Workbook. The aim of this
Workbook is to provide you with further opportunity to practise the skills you have acquired while
using the Cambridge IGCSE and O Level Additional Mathematics Student’s Book. It is designed to
complement the Student’s Book and to provide additional exercises to support you throughout the
course and help you to prepare for your examination.
The chapters in this Workbook reflect the topics in the Student’s Book. There is no set way to
approach using this Workbook. You may wish to use it to supplement your understanding of the
different topics as you work through each chapter of the Student’s Book, or you may prefer to use
it to reinforce your skills in dealing with particular topics as you prepare for your examination. The
Workbook is intended to be sufficiently flexible to suit whatever you feel is the best approach for
your needs.
All exam-style questions and sample answers in this title were written by the author(s). In
examinations, the way marks are awarded may be different.
Every effort has been made to trace all copyright holders, but if any have been inadvertently
overlooked, the Publishers will be pleased to make the necessary arrangements at the first
opportunity.
Although every effort has been made to ensure that website addresses are correct at time of going
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© Roger Porkess, Val Hanrahan & Jeanette Powell 2018
First published 2018 by
Hodder Education
An Hachette UK Company
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www.hoddereducation.com
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Printed in Great Britain by Hobbs the Printers Ltd, Totton, Hampshire, SO40 3WX.
A catalogue record for this title is available from the British Library.
ISBN: 978 1 5104 2165 3
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Contents
CHAPTER 1 Functions 4
CHAPTER 2 Quadratic functions 11
CHAPTER 3 Equations, inequalities and graphs 16
CHAPTER 4 Indices and surds 24
CHAPTER 5 Factors of polynomials 29
CHAPTER 6 Simultaneous equations 34
CHAPTER 7 Logarithmic and exponential functions 38
CHAPTER 8 Straight line graphs 46
CHAPTER 9 Circular measure 51
CHAPTER 10 Trigonometry 54
CHAPTER 11 Permutations and combinations 62
CHAPTER 12 Series 64
CHAPTER 13 Vectors in two dimensions 70
CHAPTER 14 Differentiation 75
CHAPTER 15 Integration 85
CHAPTER 16 Kinematics 92
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1
Functions
1 For the function f(x) = 2x − 5 find:
a) f(2) b) f(0) c) f(−3)
2 For the function g(x) = (2x − 2)2 find:
a) g(0) b) g(0.5) c) g(−2)
3 For the function h:x → x2 − 2x find:
a) h(2) b) h(−2) c) h(0)
4 For the function f:x → 5 − 3x find:
a) f(3) b) f(−3) c) f(1)
5 For the function g(x) = 2x+1 find:
Remember that the
√ symbol means the
a) g(0) b) g(4) c) g(12) positive square root
of a number.
6 For the function f(x) = x2 − 2
Draw a mapping diagram when the inputs are:
a) the numbers in the set {1, 2, 3} b) the numbers in the set {−1, −2, −3}.
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Questions 1–8
7 Find the range of the following functions:
a) f(x) = 2x + 1 Domain {0, 1, 2}
b) g(x) = 3x2 − 1 Domain {2, 4, 6}
2x−1
c) h(x) = Domain {1, 3, 6}
5
d) f(x) = 4x Domain ℤ+
The symbol ℤ means the
set of all integers, and ℤ+
means the set of positive
integers.
e) f:x → x2 − 5 Domain ℤ
8 What values must be excluded from the domain of the following functions and
why must they be excluded?
a) f(x) = 2x−1
3
b) f(x) =
x2
2x−1
c) f(x) =
x+1
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1 Functions
y
9 a) On the axes provided, plot the graph of y = f(x),
where f(x) = x2 − 4, for 0 ≤ x ≤ 4. 5
4
b) Add the line y = x to your graph. 3
2
1
0 x
–5 –4 –3 –2 –1 1 2 3 45
–1
–2
–3
–4
–5
c) Given that f−1(x) = x+4, calculate the values of:
(i) f−1(−4) (ii) f−1(−3) (iii) f−1(0) (iv) f−1(5)
d) Use these to add the graph of y = f−1(x) to the graph you drew in part a).
e) What you notice?
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Questions 9–10

10 Given that f(x) = 2x − 3; g(x) = x2 and h(x) = 3x − 2 find the following:
a) fg(3) e) fgh(0)
b) gf(3) f) hgf(0)
c) fh(2) g) fgh(x)
d) hf(2) h) hgf(x)
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1 Functions
11 Given f(x) = 2x + 1 and g(x) = 3x+1 find:
a) fg(5) c) fg(0)
b) gf(5) d) gf(0)
1
12 Given f(x) = x + 3, g(x) = x2 − 3 and h(x) = for x ≠ −3, find:
x+3
a) fg(x) d) hf(x)
b) gf(x) e) hfg(x)
c) fh(x) f) hgf(x)
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Questions 11–14
13 a) Find the inverse for the following functions:
(i) f(x) = 2x − 3 (ii) f(x) = x2 − 4 for x  0
b) On the axes below, plot the graphs of y = f(x) and y = f−1(x).
y
5
4
3
2
1
0 x
–5 –4 –3 –2 –1 1 2 3 45
–1
–2
–3
–4
–5

14 The first graph shows the line y = 2 − x and the other graphs are related to this.
Write down their equations.
y y y a) y y y y b)y y
6 6 6 6 6 6 6 6 6
5 5 5 5 5 5 5 5 5
4 4 4 4 4 4 4 4 4
3 3 3 3 3 3 3 3 3
2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1
–3 –2––110–31–22––1130–341–252–x–1130–34–1252–x1–103–341–252–1x–130–341–252–x1–130–34–1252–x1–103–341–252–1x–310–431–252–x1–310 4152x3 4 5 x
–2 –2 –2 –2 –2 –2 –2 –2 –2
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