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 (MOP), 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:
●the AMC 8, for students under the age of 14.5 and in grades 8 and below
●the AMC 10, for students under the age of 17.5 and in grades 10 and below
●the AMC 12, for students under the age of 19.5 and in grades 12 and below
Students who perform well on the AMC 10 or AMC 12 competitions 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 competition, the Team Selection Test (TST)) to form the United States International Math Olympiad Team.