You can find official past problems and solutions for mathematics competitions organized by the Mathematical Association of America (MAA) on the following pages.
AMC 8 – American Mathematics Competition 8
The AMC 8 is an annual mathematics competition organized by the Mathematical Association of America (MAA) for students in Grade 8 and below. It is primarily intended for middle school students, though outstanding students in Grades 4–6 may also participate.
Students who achieve high scores on the AMC 8 may, with school approval, be invited to participate in the AMC 10.
The competition was first held in 1985. Prior to 1998, the AMC 8 was known as the American Junior High School Mathematics Examination (AJHSME). In 1998, it was officially renamed AMC 8.
Below is a complete collection of AMC 8 and AJHSME past contest problems and official solutions dating back to 1985:
AMC 8 Past Problems and Solutions Archive
AMC 10 – American Mathematics Competition 10
The AMC 10 is designed for students in Grade 10 and below, corresponding to middle and early high school students. High-performing AMC 8 students may also be eligible to participate.
The first AMC 10 was held in 2000. Beginning in 2002, the competition was divided into AMC 10A and AMC 10B, traditionally held in early and mid-February, with participants choosing to take either one. Since Fall 2021, both contests have been moved to early and mid-November each year.
AMC 10 problems range from introductory to highly challenging. While all questions are within students’ mathematical reach, they test a broad range of skills and concepts. Typically, only a small percentage of participants score above 120 points.
Top-performing students are invited to the American Invitational Mathematics Examination (AIME). The qualifying cutoff score usually falls between 105 and 110, though it varies slightly each year depending on overall performance.
Below is a complete archive of AMC 10 past problems and solutions since 2000:
AMC 10 Past Problems and Solutions Archive
AMC 12 – American Mathematics Competition 12
The AMC 12 is intended for students in Grade 12 and below, typically upper high school students.
The competition traces its origins to the American High School Mathematics Examination (AHSME), first held in 1950. In 2000, AHSME was officially renamed AMC 12. Starting in 2002, the contest was divided into AMC 12A and AMC 12B, traditionally held in early and mid-February. Since Fall 2021, these have been rescheduled to early and mid-November, similar to AMC 10.
Below is a comprehensive collection of AMC 12 past problems and solutions since 2000:
AMC 12 Past Problems and Solutions Archive
AIME – American Invitational Mathematics Examination
The AIME is an invitational competition for top-performing students from the AMC 10 and AMC 12.
Typical qualification standards are:
-
Top 2.5% worldwide on AMC 10
-
Top 5% worldwide on AMC 12
Exact qualification thresholds may vary each year depending on participation and performance.
AIME serves as an intermediate step between the AMC 10/12 and the USA Mathematical Olympiad (USAMO). Its primary purpose is to help identify students eligible for USAMO, and ultimately for the Mathematical Olympiad Program (MOP), which selects the six-member U.S. team for the International Mathematical Olympiad (IMO).
The AIME began in 1983. Starting in 2000, the competition was split into AIME I and AIME II. Prior to 2021, the contests were held in March. Since the 2021 reform, AIME I and II have been held annually in mid to late February starting in 2022.
Below is a complete archive of AIME past problems and solutions dating back to 1983:
AIME Past Problems and Solutions Archive
USA(J)MO – United States of America Mathematical Olympiad / Junior Mathematical Olympiad
The USAMO and USAJMO represent the third round of the U.S. mathematics competition pathway.
Qualification is determined by combined AMC and AIME performance:
-
USAMO Index = AMC 12 score + 10 × AIME score
-
USAJMO Index = AMC 10 score + 10 × AIME score
These competitions follow the format of the International Mathematical Olympiad (IMO), emphasizing proof-based problem solving.
-
USAMO began in 1972
-
USAJMO began in 2010
Below is a complete collection of USA(J)MO past problems and solutions since 1972:
USA(J)MO Past Problems and Solutions Archive