# 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 prestigeous 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 American Mathematics Competitions (AMC). Art of Problem Solving (AoPS) is a proud sponsor of the AMC!

## 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 0 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.

### 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.

- 1983 AIME
- 1984 AIME
- 1985 AIME
- 1986 AIME
- 1987 AIME
- 1988 AIME
- 1989 AIME
- 1990 AIME
- 1991 AIME
- 1992 AIME
- 1993 AIME
- 1994 AIME
- 1995 AIME
- 1996 AIME
- 1997 AIME
- 1998 AIME
- 1999 AIME
- 2000 AIME I
- 2000 AIME II
- 2001 AIME I
- 2001 AIME II
- 2002 AIME I
- 2002 AIME II
- 2003 AIME I
- 2003 AIME II
- 2004 AIME I
- 2004 AIME II
- 2005 AIME I
- 2005 AIME II
- 2006 AIME I
- 2006 AIME II
- 2007 AIME I
- 2007 AIME II
- 2008 AIME I
- 2008 AIME II
- 2009 AIME I
- 2009 AIME II
- 2010 AIME I
- 2010 AIME II
- 2011 AIME I
- 2011 AIME II
- 2012 AIME I
- 2012 AIME II
- 2013 AIME I
- 2013 AIME II
- 2014 AIME I
- 2014 AIME II
- 2015 AIME I
- 2015 AIME II
- 2016 AIME I
- 2016 AIME II
- 2017 AIME I
- 2017 AIME II