Past papers ·
USA(J)MO Past Papers
USAMO and USAJMO are the proof-based olympiad that follows the AIME — six problems written out in full over nine hours across two days. This page gathers the past problems and official solutions for both contests, organised by year.
This page provides access to past problems and official solutions from the United States of America Mathematical Olympiad (USAMO) and the USA Junior Mathematical Olympiad (USAJMO).
USAJMO was introduced later; therefore, only USAMO papers are available for earlier years.
USA(J)MO past exams by year
| Year | USAMO | USAJMO |
|---|---|---|
| 2022 | USAMO | USAJMO |
| 2021 | USAMO | USAJMO |
| 2020 | USAMO | USAJMO |
| 2019 | USAMO | USAJMO |
| 2018 | USAMO | USAJMO |
| 2017 | USAMO | USAJMO |
| 2016 | USAMO | USAJMO |
| 2015 | USAMO | USAJMO |
| 2014 | USAMO | USAJMO |
| 2013 | USAMO | USAJMO |
| 2012 | USAMO | USAJMO |
| 2011 | USAMO | USAJMO |
| 2010 | USAMO | USAJMO |
| 2009 | USAMO | — |
| 2008 | USAMO | — |
| 2007 | USAMO | — |
| 2006 | USAMO | — |
| 2005 | USAMO | — |
| 2004 | USAMO | — |
| 2003 | USAMO | — |
| 2002 | USAMO | — |
| 2001 | USAMO | — |
| 2000 | USAMO | — |
| 1999 | USAMO | — |
| 1998 | USAMO | — |
| 1997 | USAMO | — |
| 1996 | USAMO | — |
| 1995 | USAMO | — |
| 1994 | USAMO | — |
| 1993 | USAMO | — |
| 1992 | USAMO | — |
| 1991 | USAMO | — |
| 1990 | USAMO | — |
| 1989 | USAMO | — |
| 1987 | USAMO | — |
| 1986 | USAMO | — |
| 1985 | USAMO | — |
| 1984 | USAMO | — |
| 1983 | USAMO | — |
| 1982 | USAMO | — |
| 1981 | USAMO | — |
| 1980 | USAMO | — |
| 1979 | USAMO | — |
| 1978 | USAMO | — |
| 1977 | USAMO | — |
| 1976 | USAMO | — |
| 1975 | USAMO | — |
| 1974 | USAMO | — |
| 1973 | USAMO | — |
| 1972 | USAMO | — |
About USAMO & USAJMO
- USAMO is the highest-level mathematics olympiad for high school students in the United States.
- USAJMO is the junior counterpart, introduced to recognize top-performing younger students.
- Both competitions focus on proof-based problems in algebra, geometry, number theory, and combinatorics.
- Past problems are widely used for olympiad training and advanced mathematical development.