American Invitational Mathematics Examination
The American Invitational Mathematics Examination (AIME) is the second exam in the series of exams used to challenge bright students on the path toward choosing the team that represents the United States at the International Mathematics Olympiad (IMO). While most AIME participants are high school students, some bright middle school students also qualify each year.
High scoring AIME students are invited to take the prestigious United States of America Mathematics Olympiad (USAMO) for qualification from taking the AMC 12 or United States of America Junior Mathematics Olympiad (USAJMO) for qualification from taking the AMC 10.
The AIME is administered by the Mathematical Association of America (MAA). Art of Problem Solving (AoPS) is a proud sponsor of the AMC!
| AIME |
| Region: USA |
| Type: Free Response |
| Difficulty: 3-6 |
| Difficulty Breakdown:
Problem 1-5: 3 |
Contents
Format
The AIME is a 15 question, 3 hour exam
taken by high scorers on the AMC 10, AMC 12, and USAMTS competitions. Qualification through USAMTS only is rare, however. Each answer is an integer from 000 to 999, inclusive, making guessing almost futile. Wrong answers receive no credit, while correct answers receive one point of credit, making the maximum score 15. Problems generally increase in difficulty as the exam progresses - the first few questions are generally AMC 12 level, while the later questions become extremely difficult in comparison. Calculators are not permitted.
In the first two years (1983 and 1984) there was a 2.5 hour time limit instead of the current 3 hour limit.
Curriculum
The AIME tests mathematical problem solving with arithmetic, algebra, counting, geometry, number theory, and probability and other secondary school math topics. Problems usually require either very creative use of secondary school curriculum, or an understanding as to how different areas of math can be used together to investigate and solve a problem.
Resources
Links
- AMC homepage and their AIME page
- AIME Problems and Solutions -- A community effort to provide solutions to all AIME problems from which students can learn.
- The AoPS AIME guide.
- AMC Forum for discussion of the AMC and problems from AMC and AIME exams.
- The AoPS Contest Archive includes problems and solutions from most AMC and all AIME exams.
- Mock AIME exams by AoPSers -- A wealth of secondary practice materials.
- Past HMMT, PUMaC, and CMIMC exams (search the test up to see the link).
Recommended reading
- Problem and solution books for past AMC exams. One of these books also includes numerous past AIMEs and solutions.
- Introduction to Counting & Probability by Dr. David Patrick is recommended for students who qualify for the AIME, but feel they lag behind in their understanding of basic combinatorics and probability relative to their other areas of math. Information
- Introduction to Geometry by Richard Rusczyk. Information
- The Art of Problem Solving Volume II by Sandor Lehoczky and Richard Rusczyk. Information.
AIME Preparation Classes
- AoPS hosts an online school teaching introductory classes in topics covered by the AIME as well as AIME preparation classes.
- AoPS holds many free Math Jams, some of which are devoted to discussing problems on the AIME. Math Jam Schedule
AIME Exams in the AoPSWiki
This is a list of all AIME exams in the AoPSWiki. Some of them contain complete questions and solutions, others complete questions, and others are lacking both questions and solutions. Many of these problems and solutions are also available in the AoPS Resources section. If you find problems that are in the Resources section which are not in the AoPSWiki, please consider adding them. Also, if you notice that a problem in the Wiki differs from the original wording, feel free to correct it. Finally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
| Year | Test I | Test II |
|---|---|---|
| 2022 | AIME I | AIME II |
| 2021 | AIME I | AIME II |
| 2020 | AIME I | AIME II |
| 2019 | AIME I | AIME II |
| 2018 | AIME I | AIME II |
| 2017 | AIME I | AIME II |
| 2016 | AIME I | AIME II |
| 2015 | AIME I | AIME II |
| 2014 | AIME I | AIME II |
| 2013 | AIME I | AIME II |
| 2012 | AIME I | AIME II |
| 2011 | AIME I | AIME II |
| 2010 | AIME I | AIME II |
| 2009 | AIME I | AIME II |
| 2008 | AIME I | AIME II |
| 2007 | AIME I | AIME II |
| 2006 | AIME I | AIME II |
| 2005 | AIME I | AIME II |
| 2004 | AIME I | AIME II |
| 2003 | AIME I | AIME II |
| 2002 | AIME I | AIME II |
| 2001 | AIME I | AIME II |
| 2000 | AIME I | AIME II |
| 1999 | AIME | |
| 1998 | AIME | |
| 1997 | AIME | |
| 1996 | AIME | |
| 1995 | AIME | |
| 1994 | AIME | |
| 1993 | AIME | |
| 1992 | AIME | |
| 1991 | AIME | |
| 1990 | AIME | |
| 1989 | AIME | |
| 1988 | AIME | |
| 1987 | AIME | |
| 1986 | AIME | |
| 1985 | AIME | |
| 1984 | AIME | |
| 1983 | AIME | |
