Preface

Summary

A Brief History of the American Mathematics Competitions

In the last year of the second millennium, the American High School Mathematics Examination, commonly known as the AHSME, celebrated its fiftieth year. It began in 1950 as a local exam in the New York City area, but within its first decade had spread to most of the states and provinces in North America, and was being administered to over 150,000 students. A third generation of students is now taking the competitions.

The examination has expanded and developed over the years in a number of ways. Initially it was a 50-question test in three parts. Part I consisted of 15 relatively routine computational problems; Part II contained 20 problems that required a thorough knowledge of high school mathematics, and perhaps some ingenuity; those in Part III were the most difficult, although some of these seem, based on the latter problems on the modern examination, relatively straightforward. The points awarded for success increased with the parts, and totaled 150.

The exam was reduced to 40 questions in 1960 by deleting some of the more routine problems. The number of questions was reduced again, to 35, in 1968, but the number of parts was increased to four. The number of problems on the exam was finally reduced to 30, in 1974, and the division of the exam into parts with differing weights on each part was eliminated. After this time, each problem would be weighted equally. It continued in this form until the end of the century, by which time the exam was being given to over 240,000 students at over 5000 schools.

One might get the impression that with a reduction in the number of problems the examination was becoming easier over the years, but a brief look at the earlier exams (which can be found in The Contest Problem Book, Volumes I through V) will dissuade one from this view. The number of problems has been reduced, but the average level of difficulty has increased. There are no longer many routine problems on the exams, and the middlerange problems are more difficult than those in the early years.

Since 1974, students from the United States have competed in the International Mathematical Olympiad (IMO), and beginning in 1972 students with very high scores on the AHSME were invited to take the United States of America Mathematical Olympiad (USAMO).