Cambridge IGCSE™ and O Level
Additional
Mathematics
COURSEBOOK
Sue Pemberton
Third edition
Digital Access
Contents
Contents
Introduction00
How to use this book
00
1 Functions00
1.1
Mappings00
1.2
Definition of a function
00
Composite functions
00
1.3
Modulus functions
00
1.4
1.5
Graphs of y = |f(x)| where f(x) is linear 00
Inverse functions
00
1.6
1.7
The graph of a function and its inverse
Summary00
Past-paper questions
00
2 Simultaneous equations and
quadratics00
2.1
Simultaneous equations (one linear
and one non-linear)
00
2.2
Maximum and minimum values of a
quadratic function
00
2.3
Graphs of y = |f(x)| where f(x) is
quadratic00
2.4
Quadratic inequalities
00
2.5
Roots of quadratic equations
00
2.6
Intersection of a line and a curve
00
Summary00
Past-paper questions
3 Factors and polynomials
00
00
3.1
Adding, subtracting and multiplying
polynomials00
3.2
Division of polynomials
00
3.3
The factor theorem
00
3.4
Cubic expressions and equations
00
3.5
The remainder theorem
00
Summary00
Past-paper questions
4 Equations, inequalities and
graphs00
4.1
Solving equations of the type
|ax + b| = |cx + d|
4.2
Solving modulus inequalities
00
4.3
Sketching graphs of cubic polynomials
and their moduli
00
Solving cubic inequalities graphically
4.4
4.5
Solving more complex quadratic
equations00
Summary00
Past-paper questions
00
5 Logarithmic and exponential
functions00
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
Logarithms to base 10
00
Logarithms to base a00
The laws of logarithms
00
Solving logarithmic equations
00
Solving exponential equations
00
Change of base of logarithms
00
Natural logarithms
00
Practical applications of exponential
equations00
5.9
The graphs of simple logarithmic and
exponential functions
00
nx
5.10
The graphs of y = k e + a and
y = k ln (ax + b) where n, k, a and b
are integers
00
5.11
The inverse of logarithmic and
exponential functions
00
Summary00
Past-paper questions
00
00
i
CAMBRIDGE IGCSE™ AND O LEVEL ADDITIONAL MATHEMATICS: COURSEBOOK
6 Straight-line graphs
00
6.1
Problems involving length of a line and
midpoint00
Parallel and perpendicular lines
00
6.2
6.3
Equations of straight lines
00
6.4
Areas of rectilinear figures
00
Converting from a non-linear equation to
6.5
linear form
00
6.6
Converting from linear form to a nonlinear equation
00
6.7
Finding relationships from data
00
Summary00
Past-paper questions
00
7 Coordinate geometry of the
circle00
7.1
7.2
The equation of a circle
00
Problems involving intersection of lines
and circles
00
Summary00
Past-paper questions
00
8 Circular measure
00
8.1
Circular measure
00
8.2
Length of an arc
00
8.3
Area of a sector
00
Summary00
Past-paper questions
00
9 Trigonometry00
9.1
9.2
9.3
9.4
9.5
Angles between 0° and 90°
00
The general definition of an angle
00
Trigonometric ratios of general angles 00
Graphs of trigonometric functions
00
Graphs of y = |f(x)|, where f(x) is a
trigonometric function
00
9.6
Trigonometric equations
00
9.7
Trigonometric identities
00
Further trigonometric equations
00
9.8
9.9
Further trigonometric identities
00
Summary00
Past-paper questions
ii
00
10 Permutations and combinations
00
10.1
Factorial notation
00
Arrangements00
10.2
10.3
Permutations00
10.4
Combinations00
Summary00
Past-paper questions
00
11 Series00
11.1
Pascal’s triangle
00
11.2
The binomial theorem
00
11.3
Arithmetic progressions
00
Geometric progressions
00
11.4
11.5
Infinite geometric series
00
11.6
Further arithmetic and geometric series 00
Summary00
Past-paper questions
12 Calculus – Differentiation 1
00
00
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
The gradient function
00
The chain rule
00
The product rule
00
The quotient rule
00
Tangents and normals
00
Small increments and approximations 00
Rates of change
00
Second derivatives
00
Stationary points
00
Practical maximum and minimum
problems00
Summary00
Past-paper questions
00
13 Vectors00
13.1
Further vector notation
00
13.2
Position vectors
00
13.3
Vector geometry
00
13.4
Constant velocity problems
00
Summary00
Past-paper questions
00
Contents
14 Calculus – Differentiation 2
00
14.1
Derivatives of exponential functions
00
Derivatives of logarithmic functions
00
14.2
14.3
Derivatives of trigonometric functions 00
14.4
Further applications of differentiation 00
Summary00
Past-paper questions
15 Calculus – Integration
15.1
15.2
15.3
15.4
15.5
15.6
00
00
Differentiation reversed
00
Indefinite integrals
00
Integration of functions of the form
(ax + b)n00
Integration of exponential functions
00
Integration of sine and cosine
functions00
1
Integration of functions of the form __
​​ x
​​
and ______
​​  1  ​​
ax + b
15.7
15.8
15.9
15.10
15.11
Further indefinite integration
00
Definite integration
00
Further definite integration
00
Area under a curve
00
Area of regions bounded by a line and a
curve00
Summary00
Past-paper questions
00
16 Kinematics00
16.1
Applications of differentiation in
kinematics00
16.2
Applications of integration in kinematics
00
Summary00
Past-paper questions
00
Answers000
Index000
iii
CAMBRIDGE IGCSE™ AND O LEVEL ADDITIONAL MATHEMATICS: COURSEBOOK
Introduction
This highly illustrated coursebook covers the Cambridge IGCSE TM Additional
Mathematics and O Level syllabuses (0606/4037). The course is aimed at students who
are currently studying or have previously studied Cambridge IGCSE TM Mathematics
(0580/0980) or Cambridge O Level Mathematics (4024).
Where the content in one chapter includes topics that should have already been covered
in previous studies, a prerequisite knowledge section has been provided so that you can
build on your prior knowledge.
‘Discussion’ sections have been included to provide you with the opportunity to discuss
and learn new mathematical concepts with your classmates.
‘Challenge’ questions have been included at the end of most exercises to challenge and
stretch you.
Towards the end of each chapter, there is a summary of the key concepts to help you
consolidate what you have just learnt. This is followed by a ‘Past paper’ questions
section, which contains questions taken from past papers for this syllabus.
A Practice Book is also available in the IGCSE TM Additional Mathematics series, which
offers you further targeted practice. This book closely follows the chapters and topics
of the coursebook, offering additional exercises to help you to consolidate concepts
you have learnt and to assess your learning after each chapter.
iv
How to use this book
How to use this book
Throughout this book, you will notice lots of different features that will help your learning. These are explained below.
THIS SECTION WILL SHOW YOU HOW TO:
ACTIVITY
These set the scene for each chapter, help with
navigation through the Coursebook and indicate
the important concepts in each topic.
Activities give you an opportunity to apply your
understanding of a concept to a practical task.
When activities have answers, you can find these in
the digital version of the Coursebook.
PRE-REQUISITE KNOWLEDGE
This feature shows how your understanding or use
of a topic covered in another area of the book will
help you with the concepts in this chapter.
WORKED EXAMPLE
These boxes show you the step-by-step process to
work through an example question or problem, giving
you the skills to work through questions yourself.
TIP
CLASS DISCUSSION
The information in this feature will help you
complete the exercises, and give you support in
areas that you might find difficult.
At certain points in the chapters you will be given
opportunities to talk about your learning and
understanding of the topic in a small group or
with a partner.
KEY WORDS
REFLECTION
The key vocabulary appears in a box at the
start of each chapter, and is highlighted in the
text when it is first introduced. You will also find
definitions of these words in the Glossary at the
back of this book.
These activities ask you to think about the
approach that you take to your work, and how
you might improve this in the future.
Exercises
Appearing throughout the text, exercises give you
a chance to check that you have understood the
topic you have just read about and practice the
mathematical skills you have learned. You can find
the answers to these questions in the digital version
of the Coursebook.
CHALLENGE QUESTIONS
These exercises will stretch your skills in the topic you
have just learned. You can find the answers to these
questions in the digital version of the Coursebook.
Past paper questions
Questions at the end of each chapter provide a
variety of past paper questions, some of which may
require use of knowledge from previous chapters.
Answers to these questions can be found in the digital
version of the Coursebook.
SUMMARY
There is a summary of key points at the end of
each chapter.
This icon shows you where you should complete
an exercise without using your calculator.
v
CAMBRIDGE IGCSE™ AND O LEVEL ADDITIONAL MATHEMATICS: COURSEBOOK
How to use this series
This suite of resources supports learners and teachers following the Cambridge
IGCSE™ and O Level Additional Mathematics syllabuses (0606/4037). Up-to-date
metacognition techniques have been incorporated throughout the resources to meet the
changes in the syllabus content and develop a complete understanding of mathematics
for learners. All of the components in the series are designed to work together.
Cambridge IGCSE™ and O Level
Additional
Mathematics
COURSEBOOK
Sue Pemberton
Third edition
Digital Access
The coursebook contains sixteen chapters that together offer
complete coverage of the syllabus. We have worked with NRICH
to provide a variety of project activities, designed to engage
learners and strengthen their problem-solving skills. Each chapter
contains opportunities for formative assessment, differentiation
and peer and self-assessment offering learners the support needed
to make progress. Cambridge Online Mathematics is available
through the digital/print bundle option or on its own without the
print coursebook. Learners can review content digitally, explore
worked examples and test their knowledge with quiz questions
and answers. Teachers benefit from the ability to set tests and
tasks with the added auto-marking functionality and a reporting
dashboard to help track learner progress quickly and easily.
The digital teacher’s resource provides extensive guidance
on how to teach the course, including suggestions for
differentiation, formative assessment and language
support, teaching ideas and PowerPoints. The Teaching
Skills Focus shows teachers how to incorporate a
variety of key pedagogical techniques into teaching,
including differentiation, assessment for learning, and
metacognition. Answers for all components are accessible
to teachers for free on the Cambridge GO platform.
Cambridge IGCSE™ and O Level
Additional
Mathematics
TEACHER’S
RESOURCE
COURSEBOOK
Sue Pemberton
Third edition
vi
Digital Access
1
Cambridge IGCSE™ and O Level
Additional
Mathematics
PRACTICE BOOK
Muriel James
Characteristics & classification
How
ofto
living
use organisms
this series
A Practice Book is available for learners that wish to have
extra questions to work through. This resource which can be
used in class or assigned as homework, provide a wide variety
of extra maths activities and questions to help learners
consolidate their learning and prepare for assessment. ‘Tips’
are also regularly featured to give learners extra advice and
guidance on the different areas of maths they encounter.
Access to the digital versions of the practice books is
included, and answers can be found either here or in the back
of the books.
Digital Access
Cambridge IGCSE™ and O Level
Additional
Mathematics
A Worked Solutions Manual has been introduced to the
series. This offers a fully worked solution, with annotated
comments, to a selection of questions for teachers or
learners to use as they work through the content.
WORKED SOLUTIONS MANUAL
Muriel James
Digital Access
vii