The AIME (American Invitational Mathematics Examination) is the bridge between the multiple-choice AMC 10/12 and the proof-based USA(J)MO. You qualify by scoring in roughly the top 2.5% of AMC 10 takers or the top 5% of AMC 12 takers; the AIME itself is a 15-question, 3-hour exam where every answer is an integer from 0 to 999. Your AMC score and AIME score then combine into a single index that decides whether you advance.
Who qualifies for the AIME
The AIME is invitation-only. Per the MAA, AMC 10 students qualify if they score in at least the top 2.5% of all AMC 10 scorers, and AMC 12 students qualify at at least the top 5% of all AMC 12 scorers. There is also a fixed-score path on the AMC 12 in some years. Because these are percentile-based, the exact cutoff score moves every year and differs between the A and B dates — so treat any specific number you see online as historical, and confirm the current thresholds on maa.org.
Two practical consequences follow for students at international schools in China. First, qualifying is a relative game: you are ranked against the full national pool of test-takers for your exam, not against your classmates. Second, the AMC 12 path (top 5%) is numerically wider than the AMC 10 path (top 2.5%), which matters when you are choosing which exam to sit. We cover that trade-off in our guide library.
The AIME format, exactly
The MAA describes the AIME as “a 15-question, 3-hour examination, in which each answer is an integer number between 0 to 999.” There are no multiple-choice options and no answer bubbles for letters — you write a three-digit integer for each problem. Scoring on the exam itself is straightforward: one point per correct answer, for a maximum AIME score of 15, with no penalty for wrong or blank answers. Calculators are not permitted.
| Attribute | AIME | Why it changes your prep |
|---|---|---|
| Questions | 15 | Each problem is worth ~6.7% — single questions swing your index hard |
| Time | 3 hours | ~12 minutes per problem; depth over speed, unlike the AMC |
| Answer form | Integer 0–999 | No guessing from options; arithmetic slips cost a full point |
| Scoring | 1 pt correct, 0 wrong/blank | No risk to attempting; never leave a solvable problem blank |
| Calculators | Not allowed | Hand-computation accuracy is itself a scored skill |
| Window | Administered 1:30–5:30 pm ET on competition day | China sits it via a school proctor; confirm local timing on maa.org |
Because the answer is a bounded integer, the AIME rewards a different reflex from the AMC. On the AMC you can sometimes back-solve from the five options; on the AIME you must produce the number outright, then sanity-check it against the 0–999 range. A surprising share of lost points are not conceptual — they are sign errors, off-by-one counting, or a final integer that falls outside the allowed range, which is an immediate signal to recheck.
AIME I vs AIME II: one shot only
The AIME runs on two dates: a primary date (AIME I) and an alternate date (AIME II). The alternate exists for scheduling conflicts and access reasons — it is not a second attempt. The MAA is explicit: “Students may only take the AIME once; any student who takes both the AIME I and II will be disqualified.” For a China-based test-taker, this means coordinating early with whoever proctors your exam so that you, your school, and the date all line up before registration closes. There is no make-up for a missed single attempt beyond the alternate-date mechanism your test center offers.
- AIME I — the primary administration date.
- AIME II — the alternate date, for those who cannot sit AIME I.
- Hard rule — sitting both leads to disqualification. Pick one with your proctor.
- Logistics — exact dates change yearly; verify on maa.org and with your school coordinator.
The index that actually decides your season
Qualifying for the AIME is a milestone, but advancing past it depends on a combined number called the qualification index. The MAA computes it by weighting your AIME score heavily against your AMC score:
| Next round | Index formula | Reads as |
|---|---|---|
| USAMO | AMC 12 score + 20 × AIME score | For students who took the AMC 12 |
| USAJMO | AMC 10 score + 20 × AIME score | For students who took the AMC 10 |
The “20 ×” multiplier is the headline. Every single AIME point is worth 20 index points, while an AMC point is worth one. That is why two students with identical AMC scores can land on opposite sides of the cutoff because of a one-question difference on the AIME. The practical takeaway for planning: once you are AIME-qualified, marginal hours are usually better spent raising your AIME floor than squeezing the last few AMC points. The exact index cutoffs for USAMO and USAJMO are set after the exams each year and are not published in advance — so plan around the structure of the formula, and read the current cutoffs on maa.org when they are released.
A realistic prep frame for AIME-bound students
From coaching China-based international-school students through the AMC ladder, the pattern we see is that AIME progress comes from accuracy under length, not raw new content. The exam draws on the same topic families as the hard end of the AMC 12 — number theory, combinatorics, and geometry — but asks you to hold a multi-step argument together for ten minutes without a multiple-choice safety net. Three habits tend to move scores:
- Full-length timing. Three hours is long; pacing and focus fade differently than on a 75-minute AMC. Practice complete past papers under time, not just isolated problems.
- Integer discipline. Build a final-answer checklist: is it an integer, is it within 0–999, does its size make sense for the problem? Many lost points die here, not in the setup.
- Topic triage. Identify your two strongest topic families and bank those problems first, since each is worth 20 index points downstream. Leave nothing solvable blank.
None of this guarantees a USAMO or USAJMO invitation — the cutoffs are competitive and set against a national field. But understanding that the index, not the AMC alone, is the real gate tends to change how students allocate their final months, and that allocation is something you control.
FAQ
How many questions is the AIME and what kind of answers?
Fifteen questions in three hours; every answer is an integer from 0 to 999, with one point per correct answer and no penalty for blanks.
What score do I need to qualify for the AIME?
Roughly the top 2.5% of AMC 10 scorers or top 5% of AMC 12 scorers. Cutoffs are percentile-based and change yearly — confirm on maa.org.
Can I take both AIME I and AIME II to improve my score?
No. You may take the AIME only once; sitting both dates leads to disqualification. The alternate date is for scheduling conflicts only.
How is the USAMO or USAJMO qualifier decided?
By an index: AMC 12 + 20 × AIME for USAMO, AMC 10 + 20 × AIME for USAJMO. Each AIME point is worth twenty index points.
This is an independent guide operated by Hanlin Education for China-based international-school students. It is not affiliated with, endorsed by, or sponsored by the Mathematical Association of America (MAA). The AMC ladder (AMC 8 → AMC 10/12 → AIME → USA(J)MO) is run by the MAA in the United States; note that the US AMC (MAA) is distinct from the Australian AMC (AMT) and from AMO (SIMCC, Singapore). Exam dates, qualification thresholds, scoring, and index cutoffs change every year — always confirm current details on maa.org. Any factual error will be corrected within 7 working days.