vi Introduction Structure of the bookTh e book is split roughly into four blocks. Chapters 1 to 7 cover algebra and functions, chapters 8 to 11 cover geometry, chapters 12 to 15 cover calculus, and chapters 16 to 18 cover probability and statistics. Chapter 19 contains questions that mix together diff erent parts of the course – a favourite trick in International Baccalaureate®(IB) examinations.You do not have to work through the book in the order presented, but given how much the IB likes to mix up topics, you will fi nd that some questions refer to material in previous chapters. In such cases, a ‘rewind panel’ will tell you that the material has been covered earlier, so that you can decide whether to remind yourself or move on.In the book we have tried to include only material that will be examinable. Th ere are many proofs and ideas that are useful and interesting but which are not included in the main text; these can be found on the CD-ROM should you wish to explore them.Each chapter starts with a list of learning objectives which give you an idea about what the chapter contains. Th ere is also an introductory problem that illustrates what you will be able to do aft er you have completed the chapter. Some introductory problems relate to ‘real life’ situations, while others are purely mathematical. You should not expect to be able to solve the problem at the start, but you may want to think about possible strategies and what sort of new facts and methods would help you. Th e solution to the introductory problem is provided at the end of the chapter, aft er the summary of the chapter contents.Key point boxesTh e most important ideas and formulae are emphasised in the Key point boxes. Th ey also highlight which formulae are given in the Formula booklet.Worked examplesEach worked example is split into two columns. On the right is what you should write down in your solution. Sometimes examples may go into more detail than you strictly need, but they are designed to give you an idea of what is required to score full method marks in examinations. Mathematics, however, is about much more than remembering methods and preparing for examinations. So, on the leftof each worked example are notes that describe the thought processes and suggest which approach you could use to tackle the question. We hope that these will Introduction© Cambridge University Press 2012.Not for printing, sharing or distribution.