Series Editor: Harry Smith
系列编辑：Harry Smith
Authors: Greg Attwood, Jack Barraclough, Ian Bettison, Lee Cope, Charles Garnet Cox, Daniel Goldberg, Alistair Macpherson, Bronwen Moran, Su Nicholson, Laurence Pateman, Joe Petran, Keith Pledger, Harry Smith, Geoff Staley, Dave Wilkins
作者：格雷格·阿特伍德、杰克·巴拉克劳、伊恩·贝蒂森、李·科普、查尔斯·加内特·考克斯、丹尼尔·戈德堡、阿利斯泰尔·麦克弗森、布朗文·莫兰、苏·尼科尔森、劳伦斯·帕特曼、乔·佩特兰、基思·普莱杰、哈里·史密斯、杰夫·斯塔利、戴夫·威尔金斯

Published by Pearson Education Limited, 80 Strand, London WC2R ORL.
由 Pearson Education Limited， 80 Strand， London WC2R ORL 出版。
www.pearsonschoolsandfecolleges.co.uk
Copies of official specifications for all Pearson qualifications may be found on the website: qualifications.pearson.com
所有 Pearson 资格证书的官方规格副本可在网站上找到：qualifications.pearson.com

Text © Pearson Education Limited 2017
文 © 培生教育有限公司 2017
Edited by Tech-Set Ltd, Gateshead
由盖茨黑德的 Tech-Set Ltd 编辑
Typeset by Tech-Set Ltd, Gateshead
由盖茨黑德的 Tech-Set Ltd 排版
Original illustrations © Pearson Education Limited 2017
原创插图 © 培生教育有限公司 2017
Cover illustration Marcus@kja-artists
封面插图 Marcus@kja-艺术家
The rights of Greg Attwood, Jack Barraclough, Ian Bettison, Lee Cope, Charles Garnet Cox, Daniel Goldberg, Alistair Macpherson, Bronwen Moran, Su Nicholson, Laurence Pateman, Joe Petran, Keith Pledger, Harry Smith, Geoff Staley, Dave Wilkins to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Greg Attwood、Jack Barraclough、Ian Bettison、Lee Cope、Charles Garnet Cox、Daniel Goldberg、Alistair Macpherson、Bronwen Moran、Su Nicholson、Laurence Pateman、Joe Petran、Keith Pledger、Harry Smith、Geoff Staley、Dave Wilkins 有权根据 1988 年《版权、设计和专利法》主张被确定为本作品的作者的权利。

First published 2017  首次发布于 2017 年
20191817
10987654321

A catalogue record for this book is available from the British Library
本书的目录记录可从大英图书馆获得
ISBN 9781292183336  国际标准书号9781292183336

All rights reserved. No part of this publication may be reproduced in any form or by any means (including photocopying or storing it in any medium by electronic means and 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, Barnards Inn 86 Fetter Lane, London EC4A 1EN (www.cla.co.uk). Applications for the copyright owner’s written permission should be addressed to the publisher.
保留所有权利。未经版权所有者的书面许可，不得以任何形式或任何方式复制本出版物的任何部分（包括通过电子方式将其影印或存储在任何媒体中，无论是否暂时或偶然地用于本出版物的其他用途），除非符合版权的规定， 1988 年设计和专利法或版权许可机构颁发的许可条款，Barnards Inn 86 Fetter Lane， London EC4A 1EN （www.cla.co.uk）。版权所有者书面许可的申请应提交给出版商。
Printed in the UK by Bell and Bain Ltd, Glasgow
由格拉斯哥的 Bell and Bain Ltd 在英国印刷

The authors and publisher would like to thank the following for their kind permission to reproduce their photographs:
作者和出版商衷心感谢以下人员允许转载他们的照片：
(Key: b-bottom; c-centre; l-left; r-right; t-top)
（键：b-底部;c-中心;l-左;r-右;t-顶部）
Alamy Stock Photo: Eric Robison 155, 209 ©, Paul Fleet 126, 209 (b), Photo12 94, 209 (a), Science History Images 17, 89 (b), Zoonar GmbH 43, 89 ©; Getty Images: Henrik Sorenson 1, 89 (a), John Foxx 167, 209 (d); Paul Nylander: 54, 89 (d); Shutterstock.com: Marc Sitkin 71, 89 (e)
Alamy Stock 照片： Eric Robison 155， 209 © ， Paul Fleet 126， 209 （b）， Photo12 94， 209 （a）， Science History Images 17， 89 （b）， Zoonar GmbH 43， 89 © ;Getty Images： Henrik Sorenson 1， 89 （a）， John Foxx 167， 209 （d）;保罗·尼兰德：54、89 （d）;Shutterstock.com：马克·西特金 71， 89 （e）

All other images © Pearson Education
所有其他图片 © Pearson Education

In order to ensure that this resource offers high-quality support for the associated Pearson qualification, it has been through a review process by the awarding body. This process confirms that this resource fully covers the teaching and learning content of the specification or part of a specification at which it is aimed. It also confirms that it demonstrates an appropriate balance between the development of subject skills, knowledge and understanding, in addition to preparation for assessment.
为了确保该资源为相关的 Pearson 资格认证提供高质量的支持，它已通过颁奖机构的审查过程。这个过程确认了该资源完全涵盖了规范的教学内容或它所针对的规范的一部分。它还证实，除了为评估做准备外，它还展示了学科技能、知识和理解的发展之间的适当平衡。
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认可不包括资源中包含的任何关于评估活动或过程的指导（例如练习题或关于如何回答评估问题的建议），也没有规定相关课程的教学或交付的任何特定方法。
While the publishers have made every attempt to ensure that advice on the qualification and its assessment is accurate, the official specification and associated assessment guidance materials are the only authoritative source of information and should always be referred to for definitive guidance.
虽然出版商已尽一切努力确保有关资格认证及其评估的建议准确无误，但官方规范和相关的评估指导材料是唯一的权威信息来源，应始终参考以获得明确的指导。
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Examiners will not use endorsed resources as a source of material for any assessment set by Pearson.
考官不会使用认可的资源作为 Pearson 设置的任何评估的材料来源。
Endorsement of a resource does not mean that the resource is required to achieve this Pearson qualification, nor does it mean that it is the only suitable material available to support the qualification, and any resource lists produced by the awarding body shall include this and other appropriate resources.
认可资源并不意味着需要该资源才能获得此 Pearson 资格，也不意味着它是支持该资格的唯一合适材料，颁奖机构制作的任何资源清单均应包括此资源和其他适当资源。

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Pearson 拥有强大的编辑流程，包括答案和事实核查，以确保本出版物内容的准确性，并尽一切努力确保本出版物没有错误。然而，我们只是人，偶尔会发生错误。对于因本出版物中的错误而引起的任何误解，Pearson 概不负责，但确保内容准确无误是我们的首要任务。如果您发现错误，请通过 resourcescorrections@pearson.com 与我们联系，以便我们确保它得到纠正。

Overarching themes … iv  总体主题......四
6 Matrices … 94
6 矩阵 ...94
Extra online content … vi
额外的在线内容...六
1 Complex numbers … 1
1 复数 ...1
1.1 Imaginary and complex numbers … 2
1.1 虚数和复数 ...2
1.2 Multiplying complex numbers … 5
1.2 复数相乘 ...5
1.3 Complex conjugation … 6
1.3 复数偶联 ...6
1.4 Roots of quadratic equations … 8
1.4 二次方程的根 ...8
1.5 Solving cubic and quartic equations … 10
1.5 求解三次方程和四次方程 ...10
Mixed exercise 1 … 14
混合练习 1 ...14
2 Argand diagrams … 17
2 Argand 图 ...17
2.1 Argand diagrams … 18
2.1 Argand 图 ...18
2.2 Modulus and argument … 20
2.2 模数和参数 ...20
2.3 Modulus-argument form of complex numbers … 23
2.3 复数的模参数形式 ...23
2.4 Loci in the Argand diagram … 28
2.4 Argand 图中的位点 ...28
2.5 Regions in the Argand diagram … 36
2.5 Argand 图中的区域 ...36
Mixed exercise 2 … 39
混合练习 2 ...39
3 Series … 43
3 系列43
3.1 Sums of natural numbers … 44
3.1 自然数之和 ...44
3.2 Sums of squares and cubes … 47
3.2 平方和立方之和 ...47
Mixed exercise 3 … 51
混合运动 3 ...51
4 Roots of polynomials … 54
4 多项式的根 ...54
4.1 Roots of a quadratic equation … 55
4.1 二次方程的根 ...55
4.2 Roots of a cubic equation … 57
4.2 三次方程的根 ...57
4.3 Roots of a quartic equation … 59
4.3 四次方程的根 ...59
4.4 Expressions relating to the roots of a polynomial … 62
4.4 与多项式的根相关的表达式 ...62
4.5 Linear transformations of roots … 65
4.5 根的线性变换 ...65
Mixed exercise 4 … 68
混合运动 4 ...68
5 Volumes of revolution … 71
5 卷革命 ...71
5.1 Volumes of revolution around the $x$$x$xx-axis … 72
5.1 绕 $x$$x$xx 轴的公转量 ...72
5.2 Volumes of revolution around the $y$$y$yy-axis … 76
5.2 绕 $y$$y$yy 轴的公转量 ...76
5.3 Adding and subtracting volumes … 78
5.3 添加和减少体积 ...78
5.4 Modelling with volumes of revolution … 83
5.4 使用旋转体积建模 ...83
Mixed exercise 5 … 86
混合运动 5 ...86
Review exercise 1 … 89
复习练习 1 ...89
6.1 Introduction to matrices … 95
6.1 矩阵简介 ...95
6.2 Matrix multiplication … 99
6.2 矩阵乘法 ...99
6.3 Determinants … 104
6.3 行列式 ...104
6.4 Inverting a $2\times 2$$2\times 2$2xx22 \times 2 matrix … 108
6.4 反转 $2\times 2$$2\times 2$2xx22 \times 2 矩阵 ...108
6.5 Inverting a $3\times 3$$3\times 3$3xx33 \times 3 matrix … 112
6.5 反转 $3\times 3$$3\times 3$3xx33 \times 3 矩阵 ...112
6.6 Solving systems of equations using matrices … 116
6.6 使用矩阵求解方程组 ...116
Mixed exercise 6 … 121
混合练习 6 ...121
7 Linear transformations … 126
7 线性变换 ...126
7.1 Linear transformations in two dimensions127
7.1 二维线性变换127
7.2 Reflections and rotations … 131
7.2 反射和旋转 ...131
7.3 Enlargements and stretches … 136
7.3 扩大和伸展 ...136
7.4 Successive transformations … 140
7.4 连续变换 ...140
7.5 Linear transformations in three dimensions … 144
7.5 三维线性变换 ...144
7.6 The inverse of a linear transformation … 148
7.6 线性变换的逆 ...148
Mixed exercise 7 … 151
混合运动 7 ...151
8 Proof by induction … 155
8 归纳证明 ...155
8.1 Proof by mathematical induction … 156
8.1 数学归纳证明 ...156
8.2 Proving divisibility results … 160
8.2 证明可整除结果 ...160
8.3 Proving statements involving matrices … 162
8.3 涉及矩阵的证明语句 ...162
Mixed exercise 8 … 165
混合运动 8 ...165
9 Vectors … 167
9 向量 ...167
9.1 Equation of a line in three dimensions … 168
9.1 三维线的方程 ...168
9.2 Equation of a plane in three dimensions … 175
9.2 平面在三维中的方程 ...175
9.3 Scalar product … 178
9.3 标量积178
9.4 Calculating angles between lines and planes … 184
9.4 计算线和平面之间的角度 ...184
9.5 Points of intersection … 189
9.5 交点 ...189
9.6 Finding perpendiculars … 193
9.6 求垂线 ...193
Mixed exercise 9 … 202
混合练习 9 ...202
Review exercise 2 … 209
复习练习 2 ...209
Exam-style practice: Paper 1 … 215
考试式练习：试卷 1 ...215
Answers … 217  答案。。。217
Index … 249  指数。。。249