AIME prep
The AIME is a 15-question, three-hour exam by invitation, open to students who score high enough on the AMC 10 or AMC 12. Every answer is a whole number from 0 to 999.
AIME at a glance
- Length
- 15 questions in about three hours, which is twelve minutes each.
- Answers
- Integers from 0 to 999, so there are no choices to work backward from.
- How you qualify
- From the 2026-27 cycle, 100 or above on the AMC 10 or 85 or above on the AMC 12.
12 minutes a problem
The AIME gives 180 minutes for 15 questions, which is 12 minutes each. The ratings rise from a median of 39 on problems 1 to 5 to 61 on problems 11 to 15.
- Problems 1 to 5, median rating
- 39
- Problems 6 to 10, median rating
- 49
- Problems 11 to 15, median rating
- 61
The first problem alone has a median of 32, against 28 for the AMC 12 as a whole.
Who this is for
A single AIME problem can take half an hour, and a slip anywhere along the way costs the whole answer. Students who have qualified, and those who are close, use it to see what the jump from the AMC feels like.
Take a full paper in one three-hour sitting, then go back to the late problems you could not finish.
The AIME paper preset in Arena deals official problems on the three-hour clock. AIME bridge is different: it draws on Lemmas originals pitched between the late AMC and the early AIME, and it is not an official paper. For long problems with no multiple choice, the Laboratory holds unranked HMMT problems.
What Lemmas has for the AIME
- Problems in the bank
- 1,065
- Years covered
- 1983 to 2026
- Median difficulty, out of 100
- 48
Lemmas has 1,065 AIME problems from 1983 to 2026, 71 papers in all, rated from 21 to 81. The median is 48, 20 points above the AMC 12's 28, and half of the problems fall between 42 and 58.
Arena sets each of the 71 AIME papers against the full 180-minute clock, with the answers sealed until time is up. To see how a rating is worked out, read how difficulty is measured.
AIME problems by subject
Geometry has the most AIME problems at 361, Algebra follows with 296, and Combinatorics has the fewest at 137.
- Geometry, 34% of the bank
- 361
- Algebra, 28% of the bank
- 296
- Number Theory, 25% of the bank
- 271
- Combinatorics, 13% of the bank
- 137
Past the AIME: HMMT
HMMT answers are exact values, so a fraction or a radical can be correct, where every AIME answer is an integer from 0 to 999. The February tournament also adds subject tests, a proof-based team round and a Guts round beside the individual papers, where the AIME is one paper sat alone.
Questions about the AIME
How is the AIME scored?
Each of the 15 answers is a whole number from 0 to 999 and a correct one earns a point, so the top score is 15. There is no penalty for a wrong answer.
How do I qualify for the AIME?
From the 2026-27 cycle, score 100 or above on the AMC 10 or 85 or above on the AMC 12. The MAA's AIME page lists later cycles.
How should I prepare for the AIME?
Practice by problem number as well as by year. The early problems are quick and the late ones decide papers, and Lemmas rates every problem from 1 to 100 so you can find the hard ones.
Where the AIME problems come from
The MAA, as the AIME's rights holder, allows Lemmas to use these problems with written permission, and each carries its own source line.
AIME on the Mathematical Association of America website (opens in a new tab)
Make an account and try your first problem.
Username, email and password. No card.