11–19 PROGRESSION
Edexcel GCSE (9–1)
Mathematics
Higher
Practice, Reasoning and Problem-solving Book
Confidence • Fluency • Problem-solving • Reasoning
ALW AY S L E A R N I NG i
,11–19 PROGRESSION
Edexcel GCSE (9–1)
Mathematics
Higher
Practice, Reasoning and Problem-solving Book
Confidence • Fluency • Problem-solving • Reasoning
ALW AY S L E A R N I NG i
,Published by Pearson Education Limited, 80 Strand, London A note from the publisher
WC2R 0RL. In order to ensure that this resource offers high-quality
support for the associated Pearson qualification, it has
www.pearsonschoolsandfecolleges.co.uk
been through a review process by the awarding body.
Copies of official specifications for all Edexcel qualifications This process confirms that; this resource fully covers the
may be found on the website: www.edexcel.com teaching and learning content of the specification or part
of a specification at which it is aimed. It also confirms
Text © Pearson Education Limited 2015
that it demonstrates an appropriate balance between the
Edited by ProjectOne Publishing Solutions, Scotland
development of subject skills, knowledge and understand-
Typeset and illustrated by Tech-Set, Gateshead
ing, in addition to preparation for assessment. Endorse-
Original illustrations © Pearson Education Limited 2015
ment does not cover any guidance on assessment activities
The rights of Bola Abiloye, Gemma Batty, Phil Boor, Cath- or processes (e.g. practice questions or advice on how to
erine Murphy and Claire Powis to be identified as authors of answer assessment questions), included in the resource nor
this work have been asserted by them in accordance with does it prescribe any particular approach to the teaching
the Copyright, Designs and Patents Act 1988. or delivery of a related course. While the publishers have
made every attempt to ensure that advice on the qualifica-
First published 2015
tion and its assessment is accurate, the official specification
18 17 16 15 and associated assessment guidance materials are the only
10 9 8 7 6 5 4 3 2 1 authoritative source of information and should always be
referred to for definitive guidance. Pearson examiners have
British Library Cataloguing in Publication Data not contributed to any sections in this resource relevant
A catalogue record for this book is available from the British to examination papers for which they have responsibility.
Library Examiners will not use endorsed resources as a source of
ISBN 9781292190242 material for any assessment set by Pearson. Endorsement
of a resource does not mean that the resource is required to
Copyright notice achieve this Pearson qualification, nor does it mean that it
All rights reserved. No part of this publication may be repro- is the only suitable material available to support the quali-
duced in any form or by any means (including photocopy- fication, and any resource lists produced by the awarding
ing or storing it in any medium by electronic means and body shall include this and other appropriate resources.
whether or not transiently or incidentally to some other use
of this publication) without the written permission of the
copyright owner, except in accordance with the provisions
of the Copyright, Designs and Patents Act 1988 or under the
terms of a licence issued by the Copyright Licensing Agency,
Saffron House, 6–10 Kirby Street, London EC1N 8TS (www.
cla.co.uk). Applications for the copyright owner’s written
permission should be addressed to the publisher.
Acknowledgements
We would like to thank Glyn Payne for his work on this book.
The publisher would like to thank the following for their
kind permission to reproduce their photographs:
Cover images: Front: Created by Fusako, Photography by
NanaAkua
Every effort has been made to contact copyright holders
of material reproduced in this book. Any omissions will be
rectified in subsequent printings if notice is given to the
publishers.
, Contents
1 Number 1 6.2 More linear graphs 46
1.1 Number problems and reasoning 1 6.3 Graphing rates of change 47
1.2 Place value and estimating 1 6.4 Real-life graphs 49
1.3 HCF and LCM 2 6.5 Line segments 51
1.4 Calculating with powers (indices) 3 6.6 Quadratic graphs 52
1.5 Zero, negative and fractional indices 4 6.7 Cubic and reciprocal graphs 53
1.6 Powers of 10 and standard form 5 6.8 More graphs 54
1.7 Surds 6 Problem-solving 56
Problem-solving 7 7 Area and volume 58
2 Algebra 9 7.1 Perimeter and area 58
2.1 Algebraic indices 9 7.2 Units and accuracy 59
2.2 Expanding and factorising 9 7.3 Prisms 60
2.3 Equations 10 7.4 Circles 61
2.4 Formulae 11 7.5 Sectors of circles 63
2.5 Linear sequences 12 7.6 Cylinders and spheres 64
2.6 Non-linear sequences 13 7.7 Pyramids and cones 65
2.7 More expanding and factorising 15 Problem-solving 66
Problem-solving 15 8 Transformations and constructions 68
3 Interpreting and representing data 17 8.1 3D solids 68
3.1 Statistical diagrams 1 17 8.2 Reflection and rotation 68
3.2 Time series 19 8.3 Enlargement 70
3.3 Scatter graphs 20 8.4 Translations and combinations of
3.4 Line of best fit 21 transformations 72
3.5 Averages and range 23 8.5 Bearings and scale drawings 73
3.6 Statistical diagrams 2 25 8.6 Constructions 1 74
Problem-solving 26 8.7 Constructions 2 75
8.8 Loci 77
4 Fractions, ratio and percentages 29
Problem-solving 78
4.1 Fractions 29
4.2 Ratios 30 9 Equations and inequalities 80
4.3 Ratio and proportion 31 9.1 Solving quadratic equations 1 80
4.4 Percentages 32 9.2 Solving quadratic equations 2 81
4.5 Fractions, decimals and percentages 33 9.3 Completing the square 81
Problem-solving 34 9.4 Solving simple simultaneous equations 82
9.5 More simultaneous equations 83
5 Angles and trigonometry 35
9.6 Solving linear and quadratic
5.1 Angle properties of triangles and
simultaneous equations 84
quadrilaterals 35
9.7 Solving linear inequalities 85
5.2 Interior angles of a polygon 37
Problem-solving 86
5.3 Exterior angles of a polygon 38
5.4 Pythagoras’ theorem 1 39 10 Probability 88
5.5 Pythagoras’ theorem 2 40 10.1 Combined events 88
5.6 Trigonometry 1 41 10.2 Mutually exclusive events 89
5.7 Trigonometry 2 42 10.3 Experimental probability 90
Problem-solving 44 10.4 Independent events and tree diagrams 91
10.5 Conditional probability 92
6 Graphs 45
10.6 Venn diagrams and set notation 94
6.1 Linear graphs 45
Problem-solving 95
iii
Edexcel GCSE (9–1)
Mathematics
Higher
Practice, Reasoning and Problem-solving Book
Confidence • Fluency • Problem-solving • Reasoning
ALW AY S L E A R N I NG i
,11–19 PROGRESSION
Edexcel GCSE (9–1)
Mathematics
Higher
Practice, Reasoning and Problem-solving Book
Confidence • Fluency • Problem-solving • Reasoning
ALW AY S L E A R N I NG i
,Published by Pearson Education Limited, 80 Strand, London A note from the publisher
WC2R 0RL. In order to ensure that this resource offers high-quality
support for the associated Pearson qualification, it has
www.pearsonschoolsandfecolleges.co.uk
been through a review process by the awarding body.
Copies of official specifications for all Edexcel qualifications This process confirms that; this resource fully covers the
may be found on the website: www.edexcel.com teaching and learning content of the specification or part
of a specification at which it is aimed. It also confirms
Text © Pearson Education Limited 2015
that it demonstrates an appropriate balance between the
Edited by ProjectOne Publishing Solutions, Scotland
development of subject skills, knowledge and understand-
Typeset and illustrated by Tech-Set, Gateshead
ing, in addition to preparation for assessment. Endorse-
Original illustrations © Pearson Education Limited 2015
ment does not cover any guidance on assessment activities
The rights of Bola Abiloye, Gemma Batty, Phil Boor, Cath- or processes (e.g. practice questions or advice on how to
erine Murphy and Claire Powis to be identified as authors of answer assessment questions), included in the resource nor
this work have been asserted by them in accordance with does it prescribe any particular approach to the teaching
the Copyright, Designs and Patents Act 1988. or delivery of a related course. While the publishers have
made every attempt to ensure that advice on the qualifica-
First published 2015
tion and its assessment is accurate, the official specification
18 17 16 15 and associated assessment guidance materials are the only
10 9 8 7 6 5 4 3 2 1 authoritative source of information and should always be
referred to for definitive guidance. Pearson examiners have
British Library Cataloguing in Publication Data not contributed to any sections in this resource relevant
A catalogue record for this book is available from the British to examination papers for which they have responsibility.
Library Examiners will not use endorsed resources as a source of
ISBN 9781292190242 material for any assessment set by Pearson. Endorsement
of a resource does not mean that the resource is required to
Copyright notice achieve this Pearson qualification, nor does it mean that it
All rights reserved. No part of this publication may be repro- is the only suitable material available to support the quali-
duced in any form or by any means (including photocopy- fication, and any resource lists produced by the awarding
ing or storing it in any medium by electronic means and body shall include this and other appropriate resources.
whether or not transiently or incidentally to some other use
of this publication) without the written permission of the
copyright owner, except in accordance with the provisions
of the Copyright, Designs and Patents Act 1988 or under the
terms of a licence issued by the Copyright Licensing Agency,
Saffron House, 6–10 Kirby Street, London EC1N 8TS (www.
cla.co.uk). Applications for the copyright owner’s written
permission should be addressed to the publisher.
Acknowledgements
We would like to thank Glyn Payne for his work on this book.
The publisher would like to thank the following for their
kind permission to reproduce their photographs:
Cover images: Front: Created by Fusako, Photography by
NanaAkua
Every effort has been made to contact copyright holders
of material reproduced in this book. Any omissions will be
rectified in subsequent printings if notice is given to the
publishers.
, Contents
1 Number 1 6.2 More linear graphs 46
1.1 Number problems and reasoning 1 6.3 Graphing rates of change 47
1.2 Place value and estimating 1 6.4 Real-life graphs 49
1.3 HCF and LCM 2 6.5 Line segments 51
1.4 Calculating with powers (indices) 3 6.6 Quadratic graphs 52
1.5 Zero, negative and fractional indices 4 6.7 Cubic and reciprocal graphs 53
1.6 Powers of 10 and standard form 5 6.8 More graphs 54
1.7 Surds 6 Problem-solving 56
Problem-solving 7 7 Area and volume 58
2 Algebra 9 7.1 Perimeter and area 58
2.1 Algebraic indices 9 7.2 Units and accuracy 59
2.2 Expanding and factorising 9 7.3 Prisms 60
2.3 Equations 10 7.4 Circles 61
2.4 Formulae 11 7.5 Sectors of circles 63
2.5 Linear sequences 12 7.6 Cylinders and spheres 64
2.6 Non-linear sequences 13 7.7 Pyramids and cones 65
2.7 More expanding and factorising 15 Problem-solving 66
Problem-solving 15 8 Transformations and constructions 68
3 Interpreting and representing data 17 8.1 3D solids 68
3.1 Statistical diagrams 1 17 8.2 Reflection and rotation 68
3.2 Time series 19 8.3 Enlargement 70
3.3 Scatter graphs 20 8.4 Translations and combinations of
3.4 Line of best fit 21 transformations 72
3.5 Averages and range 23 8.5 Bearings and scale drawings 73
3.6 Statistical diagrams 2 25 8.6 Constructions 1 74
Problem-solving 26 8.7 Constructions 2 75
8.8 Loci 77
4 Fractions, ratio and percentages 29
Problem-solving 78
4.1 Fractions 29
4.2 Ratios 30 9 Equations and inequalities 80
4.3 Ratio and proportion 31 9.1 Solving quadratic equations 1 80
4.4 Percentages 32 9.2 Solving quadratic equations 2 81
4.5 Fractions, decimals and percentages 33 9.3 Completing the square 81
Problem-solving 34 9.4 Solving simple simultaneous equations 82
9.5 More simultaneous equations 83
5 Angles and trigonometry 35
9.6 Solving linear and quadratic
5.1 Angle properties of triangles and
simultaneous equations 84
quadrilaterals 35
9.7 Solving linear inequalities 85
5.2 Interior angles of a polygon 37
Problem-solving 86
5.3 Exterior angles of a polygon 38
5.4 Pythagoras’ theorem 1 39 10 Probability 88
5.5 Pythagoras’ theorem 2 40 10.1 Combined events 88
5.6 Trigonometry 1 41 10.2 Mutually exclusive events 89
5.7 Trigonometry 2 42 10.3 Experimental probability 90
Problem-solving 44 10.4 Independent events and tree diagrams 91
10.5 Conditional probability 92
6 Graphs 45
10.6 Venn diagrams and set notation 94
6.1 Linear graphs 45
Problem-solving 95
iii
