GCSE Maths - 2tier-foundation for Edexcel A (Collins, 2006).pdf - Algebra & Trigonometry - Amiga78

BRIAN SPEED

KEITH GORDON

KEVIN EVANS

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

77–85 Fulham Palace Road

Hammersmith

London

W6 8JB

Acknowledgements

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.

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.

Browse the complete Collins catalogue at

www.collinseducation.com

10 9 8 7 6 5 4 3 2 1

ISBN-13: 978-0-00-721560-7

ISBN-10: 0-00-721560-6

Collection / Getty Images

p49, p67, p95, p143, p167, p195, p213, p257, p275, p299, p327, p355,

p427, p453, p473, p483, p523, p549

The author asserts his moral right to be identified as the author of this

work.

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 Joan Miller and Peta Abbott

Additional proof reader: Ruth Burns

Indexer: Dr Laurence Errington

Internal design by JPD

Cover design by JPD

Cover illustration by Andy Parker, JPD

Page make-up by Gray Publishing

Page make-up of Really Useful Maths! spreads by EMC Design

Illustrations by Gray Publishing, EMC Design, David Russel, Lazlo Veres,

Lisa Alderson, Roger Wade Walker, Bob Lea, Peter Cornwell, Martin

Sanders and Peters and Zabranksy

Production by Natasha Buckland

Printed and bound in Italy by Eurografica SpA

CONTENTS

Chapter 1 Basic number

Chapter 2 Fractions

Chapter 3 Negative numbers

Chapter 4 More about number

Chapter 5 Perimeter and area

Chapter 6 Statistical representation

119

Chapter 7 Basic algebra

143

Chapter 8 Further number skills

167

Chapter 9 Ratios, fractions, speed and proportion

195

Chapter 10 Symmetry

213

Chapter 11 Averages

225

Chapter 12 Percentages

257

Chapter 13 Equations and inequalities

275

Chapter 14 Graphs

299

Chapter 15 Angles

327

Chapter 16 Circles

355

Chapter 17 Scale and drawing

373

Chapter 18 Probability

397

Chapter 19 Transformations

427

Chapter 20 Constructions

453

Chapter 21 Units

473

Chapter 22 Pie charts, scatter diagrams and surveys

483

Chapter 23 Pattern

505

Chapter 24 Surface area and volume of 3-D shapes

523

Chapter 25 Quadratic graphs

539

Chapter 26 Pythagoras’ theorem

549

Answers

563

Index

599

iii

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.

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

marks.

Throughout the textbook you will find

Puzzles and Activities – highlighted in

the green panels – designed to

challenge your thinking and improve

your understanding.

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

progress.

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

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

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