The annual American Mathematics Competitions are a program of the Mathematical Association of America for pre-college students. Great care is taken to create new and interesting problems for these competitions. After each examination, all the problems and their solutions are made public in individual pamphlets so students can learn mathematics by practicing for future contests, and to give teachers new and exciting problems for their classes.

The oldest of the American Mathematics Competitions is the American High School Mathematics Examination [AHSME], first given in 1949. This book presents the problems and solutions from the 40th through 45th annual AHSMEs, the examinations administered 1989 through 1994. All the statements of the problems appear in this book exactly as they appeared on the examinations.

The solutions in this book include all the official solutions originally made available after the competitions, many enhanced. In addition, this book includes many alternative solutions that have never been published before.

How To Use This Book

Students who will participate in the American Mathematics Competitions and many other mathematics contests can use the problems in this book for practice. The rules for the AHSME appear on the page xix, preceding the statements of the AHSME problems so students can try the examinations under simulated contest conditions. Answers follow the questions from each competition, together with the percentage of times honor roll students used each answer choice. A few comments calling attention to unusually attractive ‘distractors’ are also included. One or more complete solutions to each problem are given in the section following all the examination questions and answers.