Senior Mathematical Challenge contains the British National Mathematical Contest papers from the years 1988 - 1996 and ten short problem papers consisting of ten problems apiece that are composed of problems that were considered, but not selected, for those contests. The problems, which draw upon algebra, geometry, number theory, sequences and series, trigonometry, estimation, probability, and mathematical puzzles, require the reader to use skills learned in General Comprehensive School Examination and A level classes in unexpected ways. They range in difficulty from fairly routine problems to those that require considerable ingenuity to solve. Working through this book is a great way to develop your problem solving skills.
Answers are provided for all the problems. However, full solutions are provided only for those problems that appeared in the actual contests. The lack of solutions to the short problem papers is the chief limitation of the book.
The tests are arranged in reverse chronological order. This is because the first three competitions consisted of 30 multiple-choice problems that were, on average, somewhat harder than those problems given in subsequent years. After 1990, the number of problems was reduced to 25 and some easier problems were introduced to make the test more accessible to typical A level students. All problems are meant to be done without a calculator. The test lasts 90 minutes. According to a problem in the 1995 competition, students receive 25 free points, earn four points for each correct answer, lose one point for each wrong answer, and no points if a problem is left unanswered. Thus, scores can range from 0 to 125.
The solutions are clearly written. In some cases, one or more alternate solutions are provided. The alternate solutions tend to employ more advanced techniques or clever insights. Also, in some solutions, references are given to books where one can explore a topic further.
The book also contains a list of resources. Among these resources are information about how to obtain problems from the American Mathematics Contest, Australian Mathematics Competition, Canadian Mathematics Competition, and Scottish Mathematical Challenge, and Mathematical Olympiad problems. There are also references for students to puzzle books, books about mathematics for the general reader, books that provide mathematical enrichment, and books about specific mathematical subjects that appear in the mathematics contests.
Readers who have not lived in Britain may encounter occasional difficulties with references to British culture ranging from the mix of English and metric units to the fact that coins come in 1 p, 2 p, 5 p, 10 p, 20 p, and 50 p denominations.
If you can handle these problems with ease, you may wish to consider working through the The Mathematical Olympiad Handbook: An introduction to problem solving based on the first 32 British Mathematical Olympiads 1965-1996 (Oxford Science Publications).