Higher
Maths
For SQA 2019 and beyond
Revision + Practice
2 Books in 1
65233_P001_007.indd 1 03/10/19 6:03 PM
, © 2019 Leckie & Leckie Ltd
001/02102019
10 9 8 7 6 5 4 3 2 1
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted in any form or by any
means, electronic, mechanical, photocopying, recording or
otherwise, without the prior written permission 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.
The author asserts his moral rights to be identified as the
author of this work.
ISBN 9780008365233
Published by
Leckie & Leckie Ltd
An imprint of HarperCollinsPublishers
Westerhill Road, Bishopbriggs, Glasgow, G64 2QT
T: 0844 576 8126 F: 0844 576 8131
www.leckieandleckie.co.uk
Publisher: Sarah Mitchell
Project Manager: Gillian Bowman
Special thanks to
Jouve (layout and illustration); Louise Robb (proof editing)
A CIP Catalogue record for this book is available from the British
Library.
Acknowledgements
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 would gladly
receive any information enabling them to rectify any error or
omission at the first opportunity.
ebook
To access the ebook version of this Success Guide visit
www.collins.co.uk/ebooks
and follow the step-by-step instructions.
65233_P001_007.indd 2 03/10/19 6:03 PM
, Contents
INTRODUCTION5
PART 1: REVISION GUIDE
Chapter 1
Functions and graphs
Some preliminary notation 10
Functions and their graphs 11
Composite and inverse functions 12
Quadratic functions 14
Related graphs 16
Exponential and logarithmic functions
Exponential functions 18
Logarithmic functions 20
Working with logs 22
Problem solving with logs 24
Trigonometric functions
Using radians 26
Related trig graphs 28
Problem solving using trig 30
Trig formulae 32
The wave function 34
Vectors
Vectors: basic properties 36
Position vectors and applications 39
The scalar product and applications 42
Working with vectors 45
Chapter 1 Assessment 48
Chapter 2
Polynomials
Quadratic theory revisited I 52
Quadratic theory revisited II 55
Polynomials and synthetic division 58
Factors, roots and graphs 60
Trigonometric equations
Solving trig equations 62
Equations involving the wave function 64
Differentiation
Basic rules and techniques 66
Tangents and stationary points 68
Graph sketching and gradients 70
Further rules and techniques 72
Rates of change 74
Integration
Basic integration rules and techniques 77
Definite integrals and special integrals 80
Chapter 2 Assessment 82
3
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, Contents
Chapter 3
The straight line
Gradient and the straight line revisited 86
Working with the gradient 88
Problem solving using the gradient 91
The circle
The circle equation 94
Lines and circles 96
Problem solving with circles 99
Sequences and recurrence relations
Notation and calculation 102
Limits and context problems 104
Applications of differentiation and integration
Applications of differentiation 107
Applications of integration 109
Chapter 3 Assessment 112
Answers to quick tests 116
Solutions to check-up questions 122
Index 137
PART 2: PRACTICE TEST PAPERS
Revision advice 141
Topic Index 144
Practice Paper A 145
Practice Paper B 157
Answers to Exam A 171
Answers to Exam B 187
4
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Maths
For SQA 2019 and beyond
Revision + Practice
2 Books in 1
65233_P001_007.indd 1 03/10/19 6:03 PM
, © 2019 Leckie & Leckie Ltd
001/02102019
10 9 8 7 6 5 4 3 2 1
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted in any form or by any
means, electronic, mechanical, photocopying, recording or
otherwise, without the prior written permission 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.
The author asserts his moral rights to be identified as the
author of this work.
ISBN 9780008365233
Published by
Leckie & Leckie Ltd
An imprint of HarperCollinsPublishers
Westerhill Road, Bishopbriggs, Glasgow, G64 2QT
T: 0844 576 8126 F: 0844 576 8131
www.leckieandleckie.co.uk
Publisher: Sarah Mitchell
Project Manager: Gillian Bowman
Special thanks to
Jouve (layout and illustration); Louise Robb (proof editing)
A CIP Catalogue record for this book is available from the British
Library.
Acknowledgements
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 would gladly
receive any information enabling them to rectify any error or
omission at the first opportunity.
ebook
To access the ebook version of this Success Guide visit
www.collins.co.uk/ebooks
and follow the step-by-step instructions.
65233_P001_007.indd 2 03/10/19 6:03 PM
, Contents
INTRODUCTION5
PART 1: REVISION GUIDE
Chapter 1
Functions and graphs
Some preliminary notation 10
Functions and their graphs 11
Composite and inverse functions 12
Quadratic functions 14
Related graphs 16
Exponential and logarithmic functions
Exponential functions 18
Logarithmic functions 20
Working with logs 22
Problem solving with logs 24
Trigonometric functions
Using radians 26
Related trig graphs 28
Problem solving using trig 30
Trig formulae 32
The wave function 34
Vectors
Vectors: basic properties 36
Position vectors and applications 39
The scalar product and applications 42
Working with vectors 45
Chapter 1 Assessment 48
Chapter 2
Polynomials
Quadratic theory revisited I 52
Quadratic theory revisited II 55
Polynomials and synthetic division 58
Factors, roots and graphs 60
Trigonometric equations
Solving trig equations 62
Equations involving the wave function 64
Differentiation
Basic rules and techniques 66
Tangents and stationary points 68
Graph sketching and gradients 70
Further rules and techniques 72
Rates of change 74
Integration
Basic integration rules and techniques 77
Definite integrals and special integrals 80
Chapter 2 Assessment 82
3
65233_P001_007.indd 3 03/10/19 6:03 PM
, Contents
Chapter 3
The straight line
Gradient and the straight line revisited 86
Working with the gradient 88
Problem solving using the gradient 91
The circle
The circle equation 94
Lines and circles 96
Problem solving with circles 99
Sequences and recurrence relations
Notation and calculation 102
Limits and context problems 104
Applications of differentiation and integration
Applications of differentiation 107
Applications of integration 109
Chapter 3 Assessment 112
Answers to quick tests 116
Solutions to check-up questions 122
Index 137
PART 2: PRACTICE TEST PAPERS
Revision advice 141
Topic Index 144
Practice Paper A 145
Practice Paper B 157
Answers to Exam A 171
Answers to Exam B 187
4
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