This third edition of Core Maths for Advanced Level has been extensively revised to cover the pure mathematics for AS and A Levels in Mathematics based on the subject criteria specified by QCA. The material is dealt with in a progressive and logical way so that the knowledge and skills acquired for AS stage are used and developed in later topics for A2. Because this book is not limited to any specific scheme, it also covers material that some boards may not examine. Specific syllabuses need to be looked at in order to identify topics that are optional: a syllabus map is included.
As a starting point, the book assumes the minimum level of success on the national curriculum for access to A-level. Many of you will have reached a higher level, particularly in algebraic skills and so will find an overlap between some work in this book and what you already know. For you the early chapters provide useful revision but they also contain some work that you are unlikely to have covered. We suggest using the mixed exercises at the ends of these chapters to identify unfamiliar topics, so that you can, if you wish, restrict your study to these sections.
All too many students regard A-level mathematics as being intrinsically difficult. We strongly disagree with this opinion. Part of the reason for this myth may be that students, at an early stage in their course, tackle problems that are too sophisticated. The exercises in this book are designed to overcome this problem, all starting with straightforward questions. There are many A-level examination questions at regular intervals throughout the book. These extensive exercises are intended for use at a later date, to give practice in examination questions when confidence and sophistication have been developed. The summary sections also include a brief recap of the work in preceding chapters and a set of multiple choice questions, which are useful for selftesting even if they do not form part of the examination to be taken.
There are many computer programs that help with the understanding of mathematics. In particular, good graph drawing software is invaluable for investigating graphical aspects of functions. Graphics calculators are also invaluable and some of them are now available with facilities to link them to computers and printers. However, as their use is forbidden in certain examination papers, you should not get into the habit of relying on them too much.
Another very valuable aid, particularly for investigating sequences and analysing data, is a computer spreadsheet. In a few places we have indicated where such aids can be used effectively, but this should be regarded as a minimum indication of the possible use of technology. We would like to thank Alison Gee for her thorough work in checking the book. We are grateful to the following examination boards for giving their permission to reproduce questions from past examination papers.
- London Examinations, a division of Edexcel Foundation (Edexcel)
- Oxford, Cambridge and RSA Examinations (OCR)
- Assessment and Qualifications Alliance (AQA)
- Welsh Joint Education Committee (WJEC)