This textbook is a welcome addition to the excellent series of books which are, in effect, the modules which form the SMP 16-19 A and AS levels in Mathematics and Further Mathematics. It is specifically targeted (as are some tasksheets at the end of chapters in the component books) at higher attaining students.

The brief Introduction describes the potential audience as students on Mathematics 16-19 courses aiming for entry to Oxford and Cambridge universities. Nevertheless, the contents and approach are clearly designed to be of help to A level maths students generally. The answers given to the various problems are intended to be full enough not to require excessive input from a teacher. The “problem and solution” format gives students working independently, or in a supported self-study environment, the chance to work ahead of their classmates on particular topics or to pursue an investigation more deeply by putting in extra time and effort.

The exercises themselves have been chosen with the aim of enhancing manipulative skills in algebra and calculus “within stimulating contexts”. Inevitably though, as much of the book is about improving facility with the techniques of Pure mathematics, many of the contexts are necessarily formal or fairly abstract. Despite this limitation, the solutions illustrate the effectiveness of graphical, programmable calculators in circumventing tedious, repetitive algebra and highlighting underlying concepts. The organisation of problems into topic groups - and linking them with chapters in both the pure and applied course texts - also acts as a practical aid to those wanting to hone a specific skill to help with a broader line of enquiry.

In the end, the worth of this sort of textbook depends on how students react to it and work from it over an extended period. As far as one can tell on first reading, however, this new publication seems to be a valuable extension to a course which is at the forefront of shaping an overdue rethink of how to teach mathematics beyond GCSE.

Richard Choat is Head of Mathematics at William Ellis School, London NW5 - part of the LASWAP Sixth Form Consortium.