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The Contest Problem Book VII: American Mathematics Competitions, 1995-2000 Contests

The Mathematical Association of America, 2006 - 200 pages

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An excellent study guide for coaches preparing their students for the AHSME exams

These collections of problems are those used in the American High School Mathematics Examinations (AHSME) for the years 1995-2000. Each examination has thirty questions and detailed solutions to the problems are given. I was especially interested in the classification of problems by type and by decade in the preface. From this, you can see the dramatic change in the topics covered on the exams. Probability, statistics and trigonometry problems did not appear on the exams in the decades 1950-59, 1960 - 69 and 1970 - 79. The significant drops in percentage appearing on the exam were in geometry and logarithms.
When I started reading this book, I was solving the problems in my head, but it wasn't long before I grabbed a pad and pen and starting writing out the solutions. While all of the problems are within the grasp of the advanced high school student, some require a clever insight if you want to solve it in a reasonable amount of time. At the end of each chapter, there is a chart listing the percentage of qualifiers who gave that answer to the question. While rare, there are occasions when a wrong answer was given more often than the correct one. It is interesting to note the general decline in the sum of the percentages as you go down the list to later in the test.
This book is the best study material available for people getting ready for a future AHSME exam. I strongly recommend it for all teachers working to prepare their students for the exams. When you look through the problems over the five years, there are some similarities that repeat on a regular basis.

Published in Journal of Recreational Mathematics, reprinted with permission


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This is the seventh book of problems and solutions from the Mathematics Competitions (published by the MAA.

Contest Problem Book VII chronicles 275 problems from the American Mathematics Contests (AMC 12 and AMC 10 for the years 1995 through 2000, including the 50th Anniversary AHSME issued in 1999. Twenty-three additional problems with solutions are included. A Problem Index classifies the 275 problems in to the following subject areas: Algebra, Complex Numbers, Discrete Mathematics (including Counting Problems), Logic, and Discrete Probability, Geometry (including Three Dimensional Geometry), Number Theory (including Divisibility, Representation, and Modular Arithmetic), Statistics, and Trigonometry.

For over 50 years many excellent exams have been prepared by individuals throughout our mathematical community in the hope that all secondary school students will have an opportunity to participate in these problem solving and enriching mathematics experiences. The American Mathematics Contests are intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school.


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