Work Out Applied Mathematics: ‘A’ Level PDF
Preview Work Out Applied Mathematics: ‘A’ Level
MACMILLAN MASTER SERIES Work Out Applied Mathematics 'A' Level The titles in this . sertes For examination at 16+ Biology Mathematics Chemistry Physics Computer Studies Principles of Accounts English Language Spanish French Statistics German For examinations at 'A' level Applied Mathematics Physics Biology Pure Mathematics Chemistry Statistics English Literature For examinations at college level Operational Research Mathematics for Economists MACMILLAN MASTER SERIES Applied Mathematics R. Haines and B. Haines M MACMILLAN © R. Haines and B. Haines 1986 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 Act 1956 (as amended). 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 1986 Published by MACMILLAN EDUCATION LTD Houndmills, Basingstoke, Hampshire RG21 2XS and London Companies and representatives throughout the world Typeset and illustrated by TecSet Ltd, Wallington, Surrey British Library Cataloguing in Publication Data Haines, R. Work out applied mathematics 'A' level. (Macmillan master series) 1. Mathematics-Examinations, questions, etc. I. Title II. Haines, B. 510'.76 QA43 ISBN 978-0-333-39767-1 ISBN 978-1-349-08213-1 (eBook) DOI 10.1007/978-1-349-08213-1 vii Acknowledgements viii Examination Boards for Advanced Level 1 Introduction 1 How to Use this Book 1 Revision 2 The Examination 3 1 Vector Dynamics 15 2 Relative Motion 29 3 Systems of Coplanar Forces. Frameworks 47 4 Friction. Equilibrium of Bodies in Contact 63 5 Composite Centres of Mass 6 Constant Acceleration. Velocity-Time Graphs. Power 78 90 7 Projectiles 106 8 Motion in a Circle 121 9 Differential Equations 10 Work. Energy. Simple Harmonic Motion. Elastic Strings. 136 154 11 Impulses. Connected Particles 172 12 Probability 187 Index To Kevin, Sarah and Nicholas Acknowledgements Over many years the questions set by the various Examination Boards have stimulated and enhanced the teaching of mathematics throughout education. Everyone involved in mathematics, both the teachers and the taught, owes a debt to the Boards for the ever-present challenge that new examination questions bring to mathematics education. Once again our thanks go to everyone who has helped with the preparation of this book, especially to Nicholas who, with nimble fingers, processed our indifferent typing into an acceptable form. We shall be greatly indebted to anyone notifying us of any errors. The author and publishers wish to thank the following who have kindly given permission for the use of copyright material: The Associated Examining Board, the Southern Universities' Joint Board, the University of London School Examinations Board and the University of Oxford Delegacy of Local Examinations for questions from past examination papers. Every effort has been made to trace all the copyright holders but if any have been inadver tently overlooked the publishers will be pleased to make the necessary arrangement at the first opportunity. Examination Boards for Advanced level Syllabuses and past examination papers can be obtained from: The Associated Examining Board (AEB) Stag Hill House Guildford Surrey GU2 SXJ University of Cambridge Local Examinations Syndicate (UCLES) Syndicate Buildings Hills Road Cambridge CB 1 2EU Joint Matriculation Board (JMB) 78 Park Road Altrincham Cheshire WA14 SQQ University of London School Examinations Board (L) University of London Publications Office 52 Gordon Square London WClE 6EE University of Oxford Delegacy of Local Examinations (OLE) Ewert Place Summertown Oxford OX2 7BZ vii Oxford and Cambridge Schools Examination Board (0 & C) I 0 Trumpington Street Cambridge CB2 IQB Scottish Examination Board (SEB) Robert Gibson & Sons (Glasgow) Ltd 17 Fitzroy Place Glasgow G3 7SF Southern Universities' Joint Board (SUJB) Cotham Road Bristol BS6 6DD Welsh Joint Education Committee (WJEC) 245 Western Avenue Cardiff CF5 2YX Northern Ireland Schools Examination Council (NISEC) Examinations Office Beechill House Beechill Road Belfast BT8 4RS Introduction The Work Out series are not 'just textbooks'. They are based on the revision needs of 'A' level students and have been designed to help students obtain the best possible grades in their examinations. This applied mathematics book is based on the mechanics and probability content of 'single subject' mathematics syllabuses. Coupled with Work Out Pure Mathematics 'A' Level by the same authors, most of the topics likely to be encountered in 'A' level mathematics examinations have been covered. Additionally, students entering higher education to read mathematics and associated topics often find they are unfamiliar with topics which their new lecturers assume they have already covered. Typically, students who have studied mathematics and/or statistics for 'A' level find themselves at a loss when their lecturer embarks on dynamics. This book provides a bridge which will allow students to rapidly familiarise themselves, through examples, with standard topics of applied mathematics. Each chapter in the book starts with a brief list of formulae and is followed by many 'A' level type questions, each with a complete solution. At the end of each chapter more 'A' level questions are set as exercises with the important steps in the working of each one being given to facilitate easy reference. How to the Book Us~ (a) By repeated use and practice, endeavour to become familiar with the fre quently used formulae listed in the Fact Sheets. (b) Practice in answering examination questions is important. Open the book at a definite topic, choose a question and cover over the solution until you have tried to do it by yourself. If you get really stuck your mind will be receptive when you uncover the solution. (c) The methods used in the book are not necessarily the shortest. Always be on the lookout for shorter and neater solutions. 'There is always a shorter way' is an excellent maxim to adopt throughout mathematics. Revision (a) Your school or college should be able to supply you with a syllabus and typi cal examination papers. If not, you should write to the secretary of the examination board. A list of addresses is given on pages ix and x. (b) Use the book to revise topics before trying past papers. (c) Familiarise yourself with the contents of your formula booklet (if one is provided) well before the examination. There are always some candidates who fail to answer questions because they are not aware that a vital formula which escapes them at that instant is to be found in the booklet so thoughtfully provided by the board! 1
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