Advanced Level Mathematics: Mechanics 1

Introduction Cambridge International Examinations (CIE) Advanced Level Mathematics has been written especially for the new CIE mathematics syllabus. There is one book corresponding to each syllabus unit, except that units P2 and P3 are contained in a single book. This book covers the first Mechanics unit, M1.

The syllabus content is arranged by chapters which are ordered so as to provide a viable teaching course. Occasionally a section or an example deals with a topic which goes beyond the requirements of the syllabus; these are marked with an asterisk (* ).

The treatment of force as a vector quantity introduces some simple vector notation, consistent with that in Chapter 13 of unit P1. Students may find this useful in writing out their solutions, although it is not a requirement of the examination.

Some paragraphs within the text appear in this type style. These paragraphs are usually outside the main stream of the mathematical argument, but may help to give insight, or suggest extra work or different approaches.

Numerical work is presented in a form intended to discourage premature approximation.

In ongoing calculations inexact numbers appear in decimal form like 3.456..., signifying that the number is held in a calculator to more places than are given. Numbers are not rounded at this stage; the full display could be, for example, 3.456 123 or 3.456 789.

Final answers are then stated with some indication that they are approximate, for example ‘1.23 correct to 3 significant figures’.

The approximate value of g is taken as 10 m s −2 .

There are plenty of exercises, and each chapter ends with a Miscellaneous exercise which includes some questions of examination standard. There are two Revision exercises, and two Practice examination papers.

Some exercises have a few questions towards the end which are longer or more demanding that those likely to be set in the examination. Teachers may wish to assign these questions to selected students to enhance the challenge and interest of the course.

Cambridge University Press would like to thank OCR (Oxford, Cambridge and RSA Examinations), part of the University of Cambridge Local Examinations Syndicate (UCLES) group, for permission to use past examination questions set in the United Kingdom.

The author thanks UCLES and Cambridge University Press, in particular Diana Gillooly, for their help in producing this book. However, the responsibility for the text, and for any errors, remains with the author.