Purpose
The main purpose of the AMC 10 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult. Students who participate in the AMC 10 should find that most of the problems are challenging but within their grasp. The contest is intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school.Learning
Although the excitement of testing one's mettle is naturally directed toward the contest itself, it is what happens before and after the contests which can have lasting educational value. Talents are enhanced with practice beforehand. This might be done by working through previous examinations, by participating in math leagues and, most importantly, by studying mathematics more intensely than one normally does in high school. Learning will take place if students singly, jointly and, especially with their teachers, strive to solve those contest problems they did not see how to solve in the allotted time as well as to understand the solutions to those problems that they did not solve correctly. The problems on the AMC 10 are chosen so that the solutions illustrate important mathematical principles. Occasionally, problems are chosen so that certain subtle but significant confusions, as well as some common computational errors, will be identified by the wrong answers listed. These principles and confusions are highlighted in the carefully prepared solutions manual. Some problems have quick solutions which seem like "tricks". What appears to be a trick the first time it is encountered often becomes a technique for solving other problems. A student’s mathematical tool kit for solving problems can be greatly expanded by the acquisition of these techniques.Difficulty
Since the AMC 10/12 covers such a broad spectrum of knowledge and ability there is a wide range of scores. The National Honor Roll cut off score for the AMC 12, 100 out of 150 possible points, is typically attained or surpassed by about 5% of all participants. For many students and schools only relative scores are significant, and so lists of top individual and team scores on regional and local levels are compiled. These regional lists and information on score distributions appear in the yearly summary sent to all participating schools. The more valuable comparison students can make is between their own level of achievement and their levels in previous years. In particular, they are encouraged to begin taking the contests early in their mathematics studies and to look back with pride each year on how they have learned to answer questions that they could not have answered previously.A special purpose of the AMC 10 is to help identify those few students with truly exceptional mathematics talent. Students who are among the very best deserve some indication of how they stand relative to other students in the country and around the world . The AMC 10 provides one such indication, and it is the first in a series of examinations. In this way the very best young mathematicians are recognized, encouraged and developed.
The AMC 10 is not an end in itself. Outstanding performance on it is neither necessary nor sufficient for becoming an outstanding mathematician. The ability to gain insights and do computations quickly are wonderful talents, but many eminent mathematicians are not quick in this way. Also, the multiple-choice format (necessary for the prompt scoring of over 400,000 examinations) benefits those who are shrewd at eliminating wrong answers and guessing, but this is not particularly a mathematical talent. In short, students who do not receive nationally recognized scores should not shrink from pursuing mathematics further, and those who do receive such high scores should not think that they have forever proved their mathematical merit. This examination, like all mathematical competitions, remains but a means for furthering mathematical development.
