GCSE Maths - 2tier-higher for Edexcel A (Collins, 2006).pdf

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This high quality material is endorsed by Edexcel and has been through a rigorous quality assurance
programme to ensure it is a suitable companion to the specification for both learners and teachers.
This does not mean that the contents will be used verbatim when setting examinations nor is it to be
read as being the official specification – a copy of which is available at www.edexcel.org.uk
This book provides indicators of the equivalent grade level of maths questions throughout. The publishers
wish to make clear that these grade indicators have been provided by Collins Education, and are not the
responsibility of Edexcel Ltd. Whilst every effort has been made to assure their accuracy, they should be
regarded as indicators, and are not binding or definitive.
William Collins’ dream of knowledge for all began with the publication of his first book in
1819. A self-educated mill worker, he not only enriched millions of lives, but also founded
a flourishing publishing house. Today, staying true to this spirit, Collins books are packed
with inspiration, innovation and a practical expertise. They place you at the centre of a
world of possibility and give you exactly what you need to explore it.
Collins. Do more.
Published by Collins
An imprint of HarperCollins Publishers
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With special thanks to Lynn and Greg Byrd
The Publishers gratefully acknowledge the following for permission to
reproduce copyright material. Whilst every effort has been made to trace
the copyright holders, in cases where this has been unsuccessful or if any
have inadvertently been overlooked, the Publishers will be pleased to
make the necessary arrangements at the first opportunity.
Browse the complete Collins catalogue at
© HarperCollins Publishers Limited 2006
Edexcel material reproduced with permission of Edexcel Limited.
Edexcel Ltd accepts no responsibility whatsoever for the accuracy or
method of working in the answers given.
10 9 8 7 6 5 4 3 2 1
ISBN-13 978-0-00-721564-5
ISBN-10 0-00-721564-9
Grade bar photos © 2006 JupiterImages Corporation
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p209, p300, p315, p333, p363, p415, p509, p519, p531, p543, p559,
© Mr Woolman, p42
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The author asserts his moral right to be identified as the author of this
All rights reserved. No part of this publication may be reproduced, stored
in a retrieval system or transmitted in any form or by any means –
electronic, mechanical, photocopying, recording or otherwise – without
the prior written consent of the Publisher or a licence permitting
restricted copying in the United Kingdom issued by the Copyright
Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP.
British Library Cataloguing in Publication Data. A Catalogue record for
this publication is available from the British Library
Commissioned by Marie Taylor, Vicky Butt and Michael Cotter
Project managed by Penny Fowler
Edited by Marian Bond and Paul Sterner
Answer checker: Amanda Whyte
Internal design by JPD
Cover design by JPD
Cover illustration by Andy Parker, JPD
Page make-up and indexing by Gray Publishing
Page make-up of Really Useful Maths! spreads by EMC Design
Illustrations by Gray Publishing, EMC Design, Peters and Zabransky,
Peter Cornwell, Bob Lea (Artists Partners), Martin Sanders (Beehive
Illustration) and Laszlo Veres (Beehive Illustration)
Production by Natasha Buckland
Printed and bound in Italy by Eurografica SpA
Chapter 1 Number
Chapter 2 Fractions and percentages
Chapter 3 Ratios and proportion
Chapter 4 Shape
Chapter 5 Algebra 1
Chapter 6 Pythagoras and trigonometry
Chapter 7 Geometry
Chapter 8 Transformation geometry
Chapter 9 Constructions
Chapter 10 Powers, standard form and surds
Chapter 11 Statistics 1
Chapter 12 Algebra 2
Chapter 13 Real-life graphs
Chapter 14 Similarity
Chapter 15 Trigonometry
Chapter 16 Linear graphs and equations
Chapter 17 More graphs and equations
Chapter 18 Statistics 2
Chapter 19 Probability
Chapter 20 Algebra 3
Chapter 21 Dimensional analysis
Chapter 22 Variation
Chapter 23 Number and limits of accuracy
Chapter 24 Inequalities and regions
Chapter 25 Vectors
Chapter 26 Transformation of graphs
Chapter 27 Proof
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Welcome to Collins GCSE Maths, the easiest way to learn and succeed in
Mathematics. This textbook uses a stimulating approach that really appeals to
students. Here are some of the key features of the textbook, to explain why.
Each chapter of the textbook begins with an Overview . The
Overview lists the Sections you will encounter in the chapter,
the key ideas you will learn, and shows how these ideas relate
to, and build upon, each other. The Overview also highlights
what you should already know, and if you’re not sure, there is
a short Quick Check activity to test yourself and recap.
Maths can be useful to us every day of
our lives, so look out for these Really
Useful Maths! pages. These double page
spreads use big, bright illustrations to
depict real-life situations, and present a
short series of real-world problems for
you to practice your latest mathematical
skills on.
Each Section begins first by
explaining what mathematical ideas
you are aiming to learn, and then
lists the key words you will meet and
use. The ideas are clearly explained,
and this is followed by several
examples showing how they can be
applied to real problems. Then it’s
your turn to work through the
exercises and improve your skills.
Notice the different coloured panels
along the outside of the exercise
pages. These show the equivalent
exam grade of the questions you are
working on, so you can always tell
how well you are doing.
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Every chapter in this textbook contains
lots of Exam Questions . These provide
ideal preparation for your examinations.
Each exam question section also
concludes with a fully worked example.
Compare this with your own work, and
pay special attention to the examiner’s
comments, which will ensure you
understand how to score maximum
Throughout the textbook you will find
Activities – highlighted in the green
panels – designed to challenge your
thinking and improve your
Review the Grade Yourself pages at the
very end of the chapter. This will show
what exam grade you are currently
working at. Doublecheck What you
should now know to confirm that you
have the knowledge you need to
Working through these sections in the right way should mean you achieve your very best
in GCSE Maths. Remember though, if you get stuck, answers to all the questions are at
the back of the book (except the exam question answers which your teacher has).
We do hope you enjoy using Collins GCSE Maths, and wish you every good luck in
your studies!
Brian Speed, Keith Gordon, Kevin Evans
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