The Contest Problem Book IV: Annual High School Examinations, 1973-1982

This text contains the problems from the (American) Annual High School Mathematics Examinations (AHSME), from the years 1973 - 1982, their answers, and their solutions. The problems, which range from relatively straightforward calculations to fiendishly difficult problems that require considerable ingenuity to solve, draw upon algebra, geometry, trigonometry, number theory, combinatorics, probability, and logic. No calculus is assumed, but it can sometimes be employed to solve a problem. The problems, which are meant to be done without a calculator, increase in difficulty within each examination. The 1973 examination consisted of 35 questions. It had four parts of 10, 10, 10, and 5 questions, worth 3, 4, 5, and 6 points each. A wrong answer resulted in a deduction of 1/4 of the point value of the question. From 1974 - 1982, the examinations consisted of 30 questions. From 1974 - 1977, each question was worth five points, with one point deducted for wrong answers. From 1978 - 1982, the score was obtained by adding 30 points to four times the number of correct responses and then subtracting the number of wrong answers. Thus, starting in 1978, it was no longer possible to obtain a negative score. From 1973 - 1977, students were given 80 minutes to complete the examination. From 1978 - 1982, they had 90 minutes to complete the examination. Thus, speed was essential. After working through a test, you can check your answers against the key, determine if you wish to retry a problem, then read the solutions that are provided. Reading the solutions given in the text is instructive since they are clearly written and tend to be elegant. Moreover, in some cases, alternate solutions are given or the solutions include comments about relevant theorems or related problems. However, you will not find the solutions useful if you are not familiar with the theorems used in solving the problems. Working through this book is a great way to develop your problem-solving skills. However, it is no longer as useful for preparing for the American Mathematics Competition (AMC), as the AHSME is now called. The format and contents of the examination have changed. For instance, questions about non-decimal bases would not be familiar to current students given changes in the curriculum. If you are interested in preparing for the current examination, you would benefit from working through The Contest Problem: Book VIII (MAA Problem Book Series) if you are preparing for the AMC 10 or The Contest Problem Book IX (Maa Problem Books) (Bk. 9) if you are preparing for the AMC 12. Top scorers on those examinations qualify for the American Invitational Mathematics Examination (AIME). Of the books in this series, only The Contest Problem Book V: American High School Mathematics Examinations (AHSME) / American Invitational Mathematics Examinations (AIME) 1983-1988 (Anneli Lax New Mathematical Library) contains problems from the AIME.

The problems are interesting and give you a good idea of the AHSME and the solutions are generally clear.