American Mathematics


American Mathematics Competitions at Carnegie Mellon University

Exam formats

The AMC 8 is a 25 question, 40 minute multiple choice test. Problems generally increase in difficulty as the exam progresses. Through 2007, calculators were permitted; though now, they are not. A correct answer scores 1 point, but unlike the AMC 10/12, no points are deducted for wrong answers.

The AMC 10/12 is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are not allowed


The AMC 8 examination provides an opportunity to apply the concepts taught at the junior high level to problems which not only range from easy to difficult but also cover a wide range of applications. Many problems are designed to challenge students and to offer problem solving experiences beyond those provided in most junior high school mathematics classes. High scoring students are invited to participate in the AMC 10.

The main purpose of the AMC 10/12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiple-choice format. What happens before and after the AMC 10/12 can have lasting educational value. Talents will be enhanced if one practices beforehand, 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.


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 examination 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. 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.


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 12 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 12 is one in a series of examinations (followed in the United States by the American Invitational Examination and the USA Mathematical Olympiad) that culminate in participation in the International Mathematical Olympiad, the most prestigious and difficult secondary mathematics examination in the world.

The AMC 10/12 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 is wonderful talent, but many eminent mathematicians are not quick in this way. Also, the multiple-choice format (necessary for the prompt scoring of over 300,000 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 contest, and all other mathematical competitions, remains but one means for furthering mathematical development.


For most students all the problems will seem really difficult. We recommend studying the problems and solutions from previous tests. These previous tests are available from the AMC There are also many books specially dedicated to AMC. We suggest you start by looking through the Problem Books Section at the MAA Bookstore . Currently, the Contest Problem Books Volumes I - IX catalog all the AMC contest problems from 1950 to 2007 and these books are a good place to start.
Carnegie Mellon University's School of Computer Science is proud to offer weekly preparation sessions for AMC 10/12 as a part of Western Pennsylvania American Regions Math League Team outreach effort.

Other Resources

There are many web resources but our favorite are: AwesomeMath, Art of Problem Solving, International Mathematical Olympiad as well as Kvant magazine for students who can read Russian.