This is the fifth book of problems from the American High School Mathematics Examination (AHSME), covering the six examinations from 1983–88. It is also the first book of problems for the follow-up American Invitational Mathematics Examination (AIME), which began in 1983. These are two of the four examinations in the American Mathematics Competitions (AMC); the others are the USA Mathematical Olympiad (USAMO) and the American Junior High School Mathematics Examination (AJHSME).

Each AHSME consists of 30 multiple-choice questions, and each AIME consists of 15 questions, with each answer an integer from 0 to 999. Both examinations cover precalculus material. Contestants have 90 minutes for the AHSME, 3 hours for the AIME (2.5 hours in 1983–85). During the period covered by this book, about 400,000 students took the AHSME each Spring and 1000–4000 were invited to the AIME (based on AHSME score). On both exams, problems are roughly in increasing order of difficulty, with the AIME questions, on average, much harder. The AHSME is one of the largest mathematics competitions in the world, and all the AMC exams are known and respected worldwide.

Why Buy this Book?

The immediate reason is to practice in order to do better on future offerings of these competitions. And there is no doubt that practice helps. The AHSME is a hard exam: typically the best score in a school will be less than 100 points out of 150 possible, so there is plenty of room for improvement.