Mastering Advanced Pure Mathematics
Mastering Advanced Pure Mathematics is not just another A-Level textbook. It contains full explanations so that it can be used in the classroom or at home as a support in the study of a wide range of syllabuses based on the common core 'A' level topic lis
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Advanced Pure Mathematics
Macmillan Master Series Accounting Advanced English Language Advanced Pure Mathematics Arabic Banking Basic Management Biology British Politics Business Administration Business Communication Business Law C Programming Chemistry COBOL Programming Commerce Communication Computers Databases Economic and Social History Economics Electrical Engineering Electronic and Electrical Calculations Electronics English as a Foreign Language English Grammar English Language English Literature English Spelling French
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Mastering
Advanced Pure
Mathematics Geoff Buckwell
MACMILLAN
© Geoff Buckwell 1996 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1P 9HE. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. First published 1996 by MACMILLAN PRESS LTD Houndmills, Basingstoke, Hampshire RG21 6XS and London Companies and representatives throughout the world ISBN 978-0-333-62049-6 ISBN 978-1-349-13551-6 (eBook) DOI 10.1007/978-1-349-13551-6 A catalogue record for this book is available from the British Library. 10 9 05 04
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Copy-edited and typeset by Povey-Edmondson Okehampton and Rochdale, England
Qcontents
ix
Introduction Acknowledgements
X
1 Number Negative and fractional indices 1.1
1.2 1.3 1.4
1
2 7 9 17
Surds Logarithms The number e and other bases
2 Polynomials 2.1 Polynomials (manipulation) 2.2 Finding linear factors of a polynomial 2.3 Solving equations 2.4 The quadratic polynomial 2.5 Non-linear simultaneous equations
22 22 26 28 31 36
3 Series 3.1 The summation notation (~] 3.2 Arithmetic Series 3.3 Geometric series 3.4 Infinite geometric series 3.5 The binomial expansion 3.6 The binomial expansion when n is not a positive integer
40
4 Coordinates 4.1 Distance between two points 4.2 Gradient of a line 4.3 Other formulae 4.4 The equation of a straight line 4.5 Perpendicular lines 4.6 Conversion of data to fit a straight line graph
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5 The differential calculus 5.1 The concept of differentiation 5.2 Differentiating a function of a function (the chain rule) 5.3 The product rule 5.4 The quotient rule
89 89 93 96 97
41 42 47 50 53 59
66 68 69 74 78 81
CONTENTS
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