American Mathematics Competitions

The American Mathematics Competitions (AMC) are the first of a series of competitions in secondary school mathematics that determine the United States team for the International Mathematical Olympiad (IMO). The selection process takes place over the course of roughly four stages. At the last stage, the Mathematical Olympiad Summer Program (MOSP), the United States coaches select six members to form the IMO team. The United States Math Team of 1994 is the only team ever to achieve a perfect score (all six members earned perfect marks), and is colloquially known as the "dream team".

There are three levels:

Students who perform well on the AMC 10 or AMC 12 exams are invited to participate in the American Invitational Mathematics Examination (AIME). Students who perform well on the AIME are then invited to the United States of America Mathematical Olympiad (USAMO) or United States of America Junior Mathematical Olympiad (USAJMO). Students who do exceptionally well on the USAMO (typically around 30 students) are invited to go to the Mathematical Olympiad Summer Program (MOSP or more commonly, MOP), and six students are selected from the top twelve scorers on the USAMO (through yet another exam, the Team Selection Test (TST)) to form the United States International Math Olympiad Team.

American Mathematics Competitions is also the name of the organization, based in Washington, DC, responsible for creating, distributing and coordinating the American Mathematics Competitions contests, which include the American Mathematics Contest, AIME, and USAMO.

The members of the Committee on the American Mathematics Competitions (CAMC) are dedicated to the goal of strengthening the mathematical capabilities of our nation's youth. The CAMC believes that one way to meet this goal is to identify, recognize and reward excellence in mathematics through a series of national contests called the American Mathematics Competitions. The AMC include: the American Mathematics Contest 8 (AMC 8) (formerly the American Junior High School Mathematics Examination) for students in grades 8 and below, begun in 1985; the American Mathematics Contest 10 (AMC 10), for students in grades 9 and 10, begun in 2000; the American Mathematics Contest 12 (AMC 12) (formerly the American High School Mathematics Examination) for students in grades 11 and 12, begun in 1950; the American Invitational Mathematics Examination (AIME), begun in 1983; and the USA Mathematical Olympiad (USAMO), begun in 1972.

...
Wikipedia