STEP, MAT, TMUA: Skills for success in University Admissions Tests for Mathematics PDF
Preview STEP, MAT, TMUA: Skills for success in University Admissions Tests for Mathematics
Every effort has been made to trace all copyright holders, but if any have been inadvertently overlooked, the Publishers will be pleased to make the necessary arrangements at the first opportunity. Although every effort has been made to ensure that website addresses are correct at time of going to press, Hodder Education cannot be held responsible for the content of any website mentioned in this book. It is sometimes possible to find a relocated web page by typing in the address of the home page for a website in the URL window of your browser. Hachette UK’s policy is to use papers that are natural, renewable and recyclable products and made from wood grown in well-managed forests and other controlled sources. The logging and manufacturing processes are expected to conform to the environmental regulations of the country of origin. Orders: please contact Hachette UK Distribution, Hely Hutchinson Centre, Milton Road, Didcot, Oxfordshire, OX11 7HH. Telephone: +44 (0)1235 827827. Email [email protected] Lines are open from 9 a.m. to 5 p.m., Monday to Friday. You can also order through our website: www.hoddereducation.co.uk ISBN: 978 1 3983 2331 5 eISBN: 978 1 3983 2219 6 © David Bedford, Phil Chaffé, Tim Honeywill and Richard Lissaman 2021. Selected STEP questions reproduced with the permission of Cambridge Assessment Admissions Testing. (Permission to use the material does not imply that Cambridge Assessment Admissions Testing endorses the content of the book/resource.) First published in 2021 by Hodder Education, An Hachette UK Company Carmelite House 50 Victoria Embankment London EC4Y 0DZ www.hoddereducation.co.uk Impression number 10 9 8 7 6 5 4 3 2 1 Year 2025 2024 2023 2022 2021 All rights reserved. Apart from any use permitted under UK copyright law, no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or held within any information storage and retrieval system, without permission in writing from the publisher or under licence from the Copyright Licensing Agency Limited. Further details of such licences (for reprographic reproduction) may be obtained from the Copyright Licensing Agency Limited, www.cla.co.uk Cover photo © Mark Roper - stock.adobe.com Illustrations by Integra Services Ltd. Typeset in Pondicherry, India. Printed in Italy. A catalogue record for this title is available from the British Library. Contents How to use this book Section 1: Getting started with problem solving 1 An introduction to the Mathematics Admissions Tests 2 Mathematical problem solving in admissions tests Section 2: Problem solving in multiple choice questions 3 Introductory number and algebra techniques 4 Geometry and coordinate geometry 5 Functions 6 Calculus 7 Graph sketching, identification and transformation 8 Sequences and series 9 Trigonometry 10 Logic and proof Section 3: Problem solving in extended questions 11 Getting started with longer questions 12 Number theory and combinatorics 13 Further trigonometry 14 Calculus – integration and differential equations 15 Complex numbers 16 Matrices Answers How to use this book Hello and welcome to this book about the mathematics used in admissions tests. It is designed to grow with you from the start of your post-16 mathematics studies. The content of the early chapters will be accessible to you even if you have not covered much in your school studies to date. As you progress through your school course, you will be able to engage with more and more of the book. The later chapters require knowledge from most of a two-year course, including some further mathematics. You should attempt each chapter as soon as you feel confident that you have covered enough in your school mathematics lessons. The book is in three sections Section one describes the main mathematics admissions tests, giving information about the papers, how they are graded, their syllabus and some of the universities that require students to sit an admissions test or will lower their admission requirements for good results in an admissions test. Admissions tests are meant to be difficult and place a high value on problem solving skills. Section one concludes with some key techniques for developing those skills. Section two focuses on the MAT and TMUA examinations. Students who will be sitting the STEP examination will also find this part useful, particularly early on in their studies. The chapters in this section cover some key topics that frequently occur in admissions tests. There are also worked examples accompanied by explanations of the thought processes required to solve them. You should read these examples carefully as there are many useful techniques within them. There are questions to try as you go along as well as exercises to reinforce your skills. Each chapter closes with some questions that are written in the same style as the MAT and TMUA questions. Section three covers the longer questions that you find on the MAT papers and the STEP papers. Chapters 11 to 13 are aimed at students preparing for either the MAT or STEP examinations. Chapters 14 to 16 are aimed at students preparing for the STEP papers. Chapter 11 is an introduction to the algebraic skills required for admissions tests and forms the bridge between the earlier MAT and TMUA chapters and the more advanced chapters at the end of the book. Each chapter includes annotated examples and exercises before concluding with a MAT or STEP style question. If at any stage you find that you are struggling with any of the problems, put them to one side and come back to them later. It is often a good idea to let your ideas settle before coming back to an initially intractable problem.
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