GCSE Maths - 2tier-higher 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.

Browse the complete Collins catalogue at

www.collinseducation.com

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

p209, p300, p315, p333, p363, p415, p509, p519, p531, p543, p559,

p573

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 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

CONTENTS

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

111

Chapter 7 Geometry

149

Chapter 8 Transformation geometry

171

Chapter 9 Constructions

191

Chapter 10 Powers, standard form and surds

209

Chapter 11 Statistics 1

237

Chapter 12 Algebra 2

279

Chapter 13 Real-life graphs

303

Chapter 14 Similarity

315

Chapter 15 Trigonometry

333

Chapter 16 Linear graphs and equations

363

Chapter 17 More graphs and equations

385

Chapter 18 Statistics 2

415

Chapter 19 Probability

437

Chapter 20 Algebra 3

479

Chapter 21 Dimensional analysis

509

Chapter 22 Variation

519

Chapter 23 Number and limits of accuracy

531

Chapter 24 Inequalities and regions

543

Chapter 25 Vectors

559

Chapter 26 Transformation of graphs

573

Chapter 27 Proof

585

Answers

597

Index

635

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

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-higher for Edexcel A (Collins, 2006).pdf

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