The Contest Problem Book I: Annual High School Mathematics Examinations 1950-1960 (New Mathematical Lib)

Anneli Lax New Mathematical Library

by Charles T. Salkind (Compiler)

A great many students have participated annually in the Annual High School Mathematics Examination (AHSME) sponsored by the Mathematical Association of America (MAA) and four other national organizations in the mathematical sciences.* In 1960, 150,000 students participated from about 5,200 high schools. In 1980, 416,000 students participated from over 6,800 high schools.

Since 1950, when the first of these examinations was given., American high school students have tested their skills and ingenuity on such problem as:

The rails on a railroad are 30 feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in how many seconds?

and many others, based on the high school curriculum in mathematics.

Genres: Mathematics

154 pages, Paperback

First published January 1, 1975

Reviews

[Beau · Rating 3 out of 5]

Excellent historical resource. The book contains 11 contest exams, 50 multiple-choice questions each (except for 1960 exam, which had 40 questions). The questions cover these high school topics: algebra, geometry, and coordinate geometry. Occasionally there is a question covering a more advanced topic. There is an answer key and complete solutions for every question. There is also a nice preface and a useful index of questions by topic.

Overall the exams would be considered too easy for serious math contest students today. Here's a sample algebra question (middle difficulty):

In the equation [x(x-1)-(m+1)]/[(x-1)(m-1)] = x/m the roots are equal when
(A) m = 1 (B) m = 1/2 (C) m = 0 (D) m = -1 (E) m = -1/2

Here's one of the harder geometry questions:

AB is a fixed diameter of a circle whose center is O. From C, any point on the circle, a chord CD is drawn perpendicular to AB. Then, as C moves over a semicircle, the bisector of angle OCD cuts the circle in a point that always:
(A) bisects the arc AB (B) trisects the arc AB (C) varies (D) is as far from AB as from D
(E) is equidistant from B and C

I found the wording and notation in some of the questions a little less than precise.