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 Mathematical 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 Problem 6-9: 4 Problem 10-12: 5 Problem 13-15: 6

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

• The MAA's official webpage for the AMC and its Invitational Competitions page
• The AoPS Wiki's AIME Problems and Solutions page
• The AoPS Contest's AIME Problems folder
• Statistics for the past AMC and AIME exams
• The AoPS Contests & Programs Forum for contest related discussions
• AoPS User created mock AIMEs, an abundance of mocks designed to mimic real AIME tests, compiled here in AoPS Contests (some of the original mock pdf files are compiled here)
• Past SMT, HMMT, PUMaC, CMIMC and other college hosted contests
• Evan Chen's Math Contest Platitudes blog, a guide to contest preparation, and Math Contest FAQs
• Math.llmlab.io, an online contest training platform
• BOGTRO's AIME Study guide
• Dylan Yu's AIME Study guide, accessed through his website here
• Omega Learn's AIME webpage

Books & Classes

• The Art of Problem Solving Volume 1 by Sandor Lehoczky and Richard Rusczyk
• The Art of Problem Solving Volume 2 by Richard Rusczyk and Sandor Lehoczky
• Intermediate Algebra by Richard Rusczyk and Mathew Crawford
• Intermediate Counting & Probability by David Patrick
• Precalculus by Richard Rusczyk
• A Gentle Introduction to the American Invitational Mathematics Exam by Scott Annin
• The AoPS Online School, with AIME preparation classes and other classes on AIME topics
• The AoPS Math Jams, some of which are devoted to discussing problems of the AIME

See also

• American Mathematics Competitions
• AIME Problems and Solutions
• AMC historical results
• Resources for mathematics competitions
• How should I prepare?
• Mathematics Olympiads