The Problems

About the contests

Click on the name of a competition for more information about it.

USA Mathematical Olympiad

The USA Mathematical Olympiad (USAMO) is an exam taken by several hundred U.S. high school students each April. Students qualify by scoring well on the American Mathematics Contests (AMC 10 or AMC 12) and the American Invitational Mathematics Examination (AIME). The top six scorers on the USAMO are invited to represent the United States at the International Mathematical Olympiad; the U.S. team members and about 24 other high scorers train for the IMO at the Math Olympiad Summer Program (MOSP; also referred to by its historical acronym MOP, for Math Olympiad Program).

Team Selection Test

The Team Selection Test (TST) was introduced in 2000. It is used in conjunction with the USAMO to select the USA team for the IMO. It is administered at the start of the MOSP to the winners (the top 12 scorers) on the USAMO; the top 6 scorers on the USAMO/TST combination are selected for the team.

In 2007 we have posted a set of MOSP Practice Tests.

International Mathematical Olympiad

The International Mathematical Olympiad (IMO) is the premier math competition for high school students. Up to six students from each participating country are selected for the competition, held each July in a different location. (The selection procedure varies by country. In the United States, selection is based on the USAMO and the TST as described above.)

Thanks to Naoki Sato for providing TeX versions of the 1986-1990 IMOs.

Note that IMO problems not posted here can be found here in HTML.

Asian Pacific Mathematical Olympiad

The Asian Pacific Mathematical Olympiad (APMO) is a regional olympiad among countries on the Pacific Rim (and lately beyond). Each country selects up to about 30 students to write the exam sometime in March, the top 10 of which comprise that country's team score. In the United States, invitations go primarily to past participants of the MOSP.

Thanks to David Radcliffe for providing PostScript versions of the 1989-1996 APMOs (except 1990, provided by Reid Barton). Note that 1989 is the first year the competition was held.