AIME Past Papers & Solutions
American Invitational Mathematics Examination
AIME I and II past papers with full worked solutions — the bridge between AMC speed problems and USAMO proof writing.
- Eligibility
- AMC 10 / AMC 12 qualifiers
- Format
- 15 questions, each with an integer answer from 000 to 999
- Duration
- 3 hours
- Scoring
- 1 point per correct answer, no penalty and no partial credit (15 max)
The AIME removes multiple-choice safety nets: every answer is an integer between 000 and 999, so an arithmetic slip costs the whole question. Three hours for fifteen problems means you are expected to think, not race — but you are also expected to finish computations perfectly. Past papers are how you learn the standard AIME toolkit and, just as importantly, how you build the checking habits that turn near-misses into points.
Past papers by year
Each year page lists the official paper source (paper I and paper II), the answer key location, difficulty notes and how to review your solutions.
Stuck on a AIME question?
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What the paper tests
Algebra
Number theory
Combinatorics
Geometry
Accuracy discipline
Where it leads: A high AMC + AIME index invites you to USAJMO or USAMO. See our coaching programme.
Book personalised AIME classes
Past papers show you the gap; a mentor closes it. Our AIME mentors are medal winners who walk through every solution 1-to-1, then set targeted practice on the archetypes you lost marks on.
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Frequently asked questions
- How do I qualify for the AIME?
- By scoring in roughly the top 2.5% on the AMC 10 or the top 5% on the AMC 12. Cut-offs are published by the MAA each year and vary by paper.
- What AIME score do I need for USAMO?
- Selection uses a combined index of your AMC 12 score plus ten times your AIME score, with the cut-off set annually by state and year group. Most qualifiers score at least 8–10 on the AIME.
- How should I practise AIME papers?
- Sit full three-hour papers rather than isolated problems. The skill being tested is sustained accuracy, and that only shows up over a complete paper.
Related paper libraries
Preparing beyond past papers? See our 1-to-1 Maths Olympiad tutoring hub for the full UKMT, BMO, AMC and AIME pathway with verified expert mentors.