This text contains the problems from the U. K. Junior Mathematical Olympiad from the years 1989 - 1995 and sixty additional problems that were considered for the tests. The problems, which are meant to be done without a calculator, draw upon number sense, estimation, algebra, geometry, trigonometry, and combinatorics. To qualify for these competitions, students first had to excel on the U. K. School Mathematics Challenge. Problems from that competition can be found in Gardiner's Mathematical Challenge, which you should work through before attempting the problems in this text. Unless you can handle most of the problems in Mathematical Challenge with ease, you will find working through this book frustrating.
With the exception of the inaugural year of 1989, in which an experimental test of 13 open-ended problems was given, each test is divided into two sections. Section A consists of 10 problems for which a numerical answer is sought. Section B consists of six open-ended problems in which you are expected to justify your answers with some sort of proof. The problems increase in difficulty within each section. The problems in the second section are much more involved than those in the first. The tests are presented in reverse chronological order, presumably because the 1989 examination was harder than those given in succeeding years. Of the 60 additional problems, forty are of the first type and the remainder are of the second type. Answers are given for all the Section A problems. In addition, Gardiner includes sections containing hints and outline solutions for all the problems that appeared on the actual examinations. However, there are no solutions, answers, or even hints for the 20 additional section B problems.
The hints give you suggestions on how to approach a problem. The outline solutions lead you through the solution to a problem, with blanks left where you are expected to fill in the details and with letters of key words such as negative replaced by *'s (so that it looks like *e*a*i*e) in order to force the reader to puzzle out the word. The blanks allow you to work out the details of the problem for yourself. However, I found the use of *'s distracting. Since complete solutions are rarely given, it is not possible to fully check your work for the section B problems. That said, there is sufficient feedback for you to determine whether you are approaching a problem correctly.
American readers will notice differences in terminology (trapezium instead of trapezoid) and notation (what looks like a decimal point actually means multiplication). 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.
Working through this book is a great way to prepare for middle or high school mathematics contests.