High School Math Olympiad Pipeline: AMC 10/12 → AIME → USAMO
Published · Grade band: High School (9–12) · Topic: Mathematics
The AMC/AIME/USAMO pipeline is the most searched high school math competition pathway in the United States, and also the most misunderstood. The confusion is understandable: the same organization runs three different contests that feed into each other, with cutoffs that change year to year, two test dates for the first round, and two separate olympiad tracks (USAJMO for younger students, USAMO for older). This page maps the whole structure.
All contests in this pipeline are administered by the Mathematical Association of America (MAA) through its AMC program. Always verify current test dates, registration procedures, and qualifying cutoffs on the official MAA AMC website — cutoffs shift every cycle based on score distributions.
Step 1: AMC 10 or AMC 12
The pipeline begins with the AMC 10 (for students in grade 10 or below who have not yet turned 17.5) or the AMC 12 (open to all students in grade 12 or below who have not yet turned 19.5). Both are 30-question, 75-minute multiple-choice contests. Each is offered on two separate test dates: an “A” date and a “B” date, typically offered about a week apart in November. Students may take both A and B, and their better score is used for qualification purposes.
AMC 10A, 10B, 12A, and 12B are different exams with different problems, though similar difficulty. A student can take AMC 10A and AMC 10B, or AMC 10A and AMC 12B, or AMC 12A and AMC 12B — any two tests on different dates from the same competition year.
Registration: schools register with MAA to become official contest sites. Students take the exam at school. If your school does not offer the AMC, you can locate a nearby official site through the MAA website or contact the MAA to request that your school register.
Step 2: AIME
Students who score above a certain threshold on the AMC 10 or AMC 12 qualify for the AIME (American Invitational Mathematics Examination). The AIME is a 15-question, 3-hour exam — answers are integers from 000 to 999 rather than multiple choice. It is significantly harder than the AMC.
Like the AMC, the AIME runs on two dates: AIME I (typically in February) and AIME II (typically in March). Students who qualified via either AMC contest may take either AIME, and their better score is used for olympiad selection.
The AMC/AIME combination index (a weighted sum of AMC score and AIME score) determines who is invited to the next round. The formula and weights are published by MAA and are worth understanding before test day — the AMC score matters more than many students realize even after they qualify for the AIME.
Step 3: USAJMO or USAMO
Students with the highest AMC + AIME combined indices are invited to either the USAJMO (US Junior Mathematical Olympiad, for AMC 10 qualifiers or students in grade 10 or below) or the USAMO (US Mathematical Olympiad, for AMC 12 qualifiers). Invitations are extended in late March.
Both the USAJMO and USAMO are two-day, nine-hour proof-based competitions. A student writes mathematical proofs — not just computes answers — for six problems over two sessions. The style of thinking required is fundamentally different from AMC/AIME problem-solving; most serious competitors prepare specifically for proof-writing well in advance.
Top scorers at the USAMO are invited to the Mathematical Olympiad Summer Program (MOP) and are considered for the US team at the International Mathematical Olympiad (IMO).
Where the cutoffs come from
AMC qualification cutoffs for the AIME, and AIME cutoffs for the olympiads, are set after each exam based on score distributions rather than being fixed in advance. This means that a score of 100 on the AMC 12 qualifies for the AIME in some years but not others. The MAA publishes the cutoffs for the current year promptly after scores are released; historical cutoffs are available on AoPS and elsewhere.
The practical implication: do not plan your year around “I just need to score X” without checking recent history. Cutoffs on the AMC 10 and AMC 12 have varied meaningfully year to year. Aim to understand the material deeply rather than to hit a target number.
Preparation resources
The Art of Problem Solving (AoPS) community publishes archived AMC, AIME, and USAMO problems going back many years, with full solution discussions. Past AMC exams are the best preparation for future AMC exams. See the AoPS review on this site for a longer discussion of the platform.
Middle school students
A strong 8th-grader who has done serious MATHCOUNTS preparation can take the AMC 8 (the non-pipeline benchmark test) or, if ready, the AMC 10. There is no age floor on the AMC 10 beyond the grade/age maximums; a seventh-grader who qualifies for the AIME through the AMC 10 is genuinely eligible. The contest community includes students who reach AIME at very young ages. See the middle school math directory for the MATHCOUNTS and AMC 8 context.
About this directory: Meli Review publishes an independent directory of academic contests for students from primary school through university. Contest details were accurate to the best of our review at publication. The AMC program structure and cutoffs change annually — always confirm on the official MAA website.