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Contest Problem Book VI chronicles the high school competitions sponsored by the Mathematical Association of America. It contains 180 challenging problems from the six years of the American High School Mathematics Examination [AHSME], 1989 through 1994, as well as a selection of other problems. Many problem solving techniques for problems in this book show alternative approaches that appear in print for the first time. Some aspects of mathematical problem solving unique to competitions is discussed. Useful tools are selected from important areas of high school mathematics. A Problems Index classified the 180 problems in the book into subject areas: Algebra (with 65 subclasses), Complex Numbers (with 11 subclasses), Discrete Mathematics (with 20 subclasses), Geometry (with 43 subclasses), Number Theory (with 24 subclasses), Statistics (with 5 subclasses), and Trigonometry (with 12 subclasses). Many subclasses have sub-subclasses, some with over a dozen. The Pigeon Hole Principle proves that some problems must appear in more than one class. That, in fact, is the case! Outstanding problems combine elementary techniques from diverse areas of mathematics, occasionally three or more. You will find many of them here.
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Over the years perhaps the most popular of the MAA problem books have been the high school contest books, covering the yearly American High Mathematics Examinations (AHSME) that began in 1950, co-sponsored from the start by the MAA. Book V also includes the first six years of the American Invitational Mathematics Examination (AIME) which was developed as an intermediate step between the AHSME and the USA Mathematical Olympiad (USAMO). The AIME has a unique answer format-all answers are integers between 0 and 999. The editors of this volume, George Berzsenyi and Stephen B. Maurer, were respectively the chair of the AIME and the AHSME during this period. In addition to a thorough index, they have added much material not included in Contest Books I-IV: a comprehensive guide to other problem materials world wide, additional solutions, dropped problems, statistical information, and information on test development and history. This is a must volume for avid fans of elementary problems, young and old.
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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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