The American Invitational Mathematics Examination — a 15-problem, 3-hour fill-in test that AMC 10/12 high scorers take. Answers are integers from 000 to 999.

How do I qualify for the AIME?

Score in the top ~2.5% on the AMC 10 (typical cutoff ~105–115 out of 150) or top ~5% on the AMC 12 (typical cutoff ~93–100 out of 150). Cutoffs change each year.

+1 for each correct answer, 0 for blanks, 0 for wrong answers. Maximum score is 15. There is no partial credit and no penalty for guessing.

What's a USAMO/USAJMO index?

USAMO index = AMC 12 score + 10 × AIME score. USAJMO index = AMC 10 score + 10 × AIME score. The MAA picks roughly the top 250–270 USAMO and 250–270 USAJMO students by index.

Is AIME multiple choice?

No — answers are integers from 0 to 999, written in three boxes. There are no answer choices and no way to back-solve from options.

Are AIME I and AIME II the same difficulty?

Officially yes — AIME II exists for students who couldn't take AIME I (typically due to scheduling conflicts). Both are weighted equally for USAMO/USAJMO indexes.

How AIME Scoring Works

The AIME — American Invitational Mathematics Examination — is the second test in the AMC pipeline, but the first one with no multiple-choice. Every answer is a 3-digit integer from 000 to 999. That single design choice changes how you prepare for it.

The format

15 problems, all fill-in-the-integer
3 hours (180 minutes — about 12 minutes per problem on average)
Answer range: integers from 000 to 999, written in three answer boxes
Calculator: not allowed
Scoring: +1 correct, 0 blank, 0 wrong (always guess if you have a candidate)
Maximum score: 15

Two sittings exist: AIME I (about a month after the AMC 10/12) and AIME II (two weeks later, for students who missed AIME I). They are weighted equally for downstream qualification.

How qualification works

The AIME is invitation-only. You qualify by performing well on the AMC 10 or AMC 12 in the same competition cycle. The MAA publishes a cutoff each year; rough recent ranges:

AMC 10 → AIME: top ~2.5%, typically a score of 105–115 out of 150
AMC 12 → AIME: top ~5%, typically a score of 93–100 out of 150

Both AMC 10 A/B and AMC 12 A/B count, and you only need to qualify through one. If you take both AMC 10 and AMC 12, the higher-yielding result is used.

How AIME scores combine with AMC scores

AIME scores by themselves do not determine the next round. Qualification for the USAMO and USAJMO uses an index that combines both tests:

USAMO index = AMC 12 score + (10 × AIME score)
USAJMO index = AMC 10 score + (10 × AIME score)

Each AIME point is worth 10 AMC points in the index, so once you've qualified for AIME, the AIME score dominates whether you advance. Concretely, going from a 5 to a 6 on AIME is the same boost as gaining 10 points on the AMC.

The USAMO and USAJMO each invite roughly the top 250–270 students by index, with the exact cutoffs varying by year and by which sitting (A or B / I or II) you took.

What "a good AIME score" means

Because AIME problems get sharply harder as the test goes on, scores cluster at the low end. Useful reference points:

3–5 — typical for first-time qualifiers
6–8 — competitive index for USAJMO selection
9–11 — competitive index for USAMO selection
12+ — top-tier; perfect 15s exist but are rare

Problems are roughly ordered by difficulty. Most students don't attempt the last 3 in earnest the first time they take AIME — there's more value in spending time double-checking the first 10 than in sketching toward problem 14.

Why integer answers change preparation

AMC 10/12 has a useful trick: when you see five answer choices, you can sometimes back-solve, eliminate, or estimate. AIME's 0–999 range kills that path entirely. Three implications for prep:

Arithmetic rigor matters more. A computational slip on AMC might land on a wrong answer choice (still 0 points), but you knew you were close. On AIME, slipping a sign or dropping a factor of 2 produces a number indistinguishable from a random guess. Your last 5 minutes are best spent re-doing arithmetic, not attacking new problems.
Modular checks become essential. Every answer is an integer from 0–999. Computing your candidate answer mod 9 (or mod 11) before bubbling is a 30-second sanity check that catches a surprising fraction of computation errors.
Constructive problems get harder.When the answer is "the number of ways to..." or "the largest n such that...", you can no longer guess from the choices. AIME drills should bias toward problems that produce a number rather than identify one.

Where to start

Take a past AIME timed and untimed, then compare:

The timed score tells you how AIME-ready you are today.
The untimed score tells you how much room there is for pure pacing improvement vs. genuine new content learning.

If your untimed score is 4–5 points higher than timed, the limiting factor is pacing under pressure, not knowledge. The fix is more full-length AIME mocks. If both scores are close, you have specific topical gaps; the right move is targeted drills on those topics. The topics page sorts knowledge points by category so you can pick what's hurting you.

The AIME papers in Amc2Aime are organized year-by-year. After each attempt, the AI coach generates an L3 error-mode diagnosis showing where you keep losing points across attempts — the most useful single view if you want to spend your prep time efficiently.