The AIME (American Invitational Mathematics Examination) is invitation-only. To qualify, you must score in the top 2.5% on the AMC 10 or the top 5% on the AMC 12. Cutoff scores vary each year—recent AMC 10 cutoffs have ranged from 100.5 to 106.5 (out of 150). Approximately 6,000–8,000 students qualify annually across all AMC administrations. AIME participation is free once you qualify. The exam is 15 questions, 3 hours, with integer answers from 000 to 999.
The American Invitational Mathematics Examination (AIME) is the second tier in the USA’s most prestigious high school mathematics competition pathway. It sits between the AMC 10/12 exams (the first qualifying round, open to all students) and the USA(J)MO (the invitation-only national olympiad, open only to the highest scorers on AIME). You cannot register for AIME directly—you must first earn a qualifying score on the AMC 10 or AMC 12.
The AIME is administered by the Mathematical Association of America (MAA) through its AMC program. Each year, two versions of AIME are offered: AIME I (typically in February) and AIME II (typically in March). A student who qualifies for AIME may take either version, but not both.
Most schools register students for AIME I as the primary sitting, with AIME II available for students who couldn’t attend AIME I or for schools that prefer the later date. Your best AIME score from either sitting in the same competition year counts for the USAMO/JMO index calculation if you qualify for the olympiad round.
What makes AIME unusual compared to most math competitions is its answer format. There are no multiple choice options. Each of the 15 questions requires an integer answer between 000 and 999 (inclusive). Answers are entered as three-digit integers, with leading zeros where necessary (e.g., 7 is entered as 007). There is no partial credit and no penalty for wrong answers, which means guessing at the end of the exam is always worth attempting. A correct answer on any question, regardless of difficulty, earns exactly 1 point.
For students who have reached AIME eligibility, understanding what happens next is as important as knowing how to qualify. AIME scores contribute to the USAMO/JMO qualification index in combination with your AMC score. The cutoff for USAMO/JMO is substantially higher than just qualifying for AIME—only approximately 500 students advance to the USA(J)MO each year, compared to the thousands who reach AIME. A thorough AIME exam overview covers the full competition structure from AMC through olympiad level in detail.
Achieving AIME eligibility is a significant milestone for any high school math student. It places you in the top few percent of math students in the country who participate in AMC competitions, and it opens the door to the olympiad pipeline. Even if you don’t ultimately qualify for USAMO or earn a medal, AIME participation demonstrates mathematical ability at a level that college admissions offices and scholarship programs recognize. The problems on AIME require creative problem-solving at a level substantially above standard high school mathematics—earning a qualifying score is an achievement in itself.
This guide covers everything you need to know about AIME eligibility: how the qualification system works, what AMC scores you need, how cutoff scores are determined, what the AIME exam itself involves, and how your AIME performance connects to the USAMO and the broader mathematics olympiad pipeline. Whether you’re a student, parent, or coach planning a competition math pathway, understanding these mechanics makes preparation more strategic and goal-oriented.
There are two pathways to AIME eligibility, corresponding to the two AMC exams available to high school students: the AMC 10 (for students in 10th grade or below, under age 17.5) and the AMC 12 (for all high school students up to 12th grade).
The AMC 10 pathway requires a score in the top 2.5% of all AMC 10 participants nationally. In practice, this means scoring above the AMC 10 cutoff score for that year’s competition.
The AMC 10 is scored with 1.5 points for each correct answer and 0 points for incorrect or omitted answers, out of a possible 150 points (30 questions × 1.5 points each, minus no deductions). Note: some competition years have adjusted the scoring rubric slightly—always confirm the current year’s scoring with the MAA. Recent AMC 10A and 10B cutoff scores have typically ranged from 100 to 108, though this varies meaningfully year to year based on exam difficulty.
The AMC 12 pathway uses a more generous threshold: the top 5% of AMC 12 participants qualify. The AMC 12 is also scored out of 150 points and covers more advanced material including precalculus. AMC 12 cutoff scores tend to be lower in absolute terms than AMC 10 cutoffs because the AMC 12 content is harder—recent AMC 12 cutoffs have typically ranged from 83 to 96.
If a student is eligible for both AMC 10 and AMC 12, taking the AMC 12 and using the 5% threshold can be strategically advantageous if their score would comfortably clear the AMC 12 cutoff.
Students can take both the A and B versions of the AMC 10 or AMC 12 offered in the same year (AMC 10A and 10B are offered a few weeks apart, as are AMC 12A and 12B). If you qualify for AIME on any of these sittings, you qualify. However, you still take AIME only once (either AIME I or AIME II). Attempting both AMC 10A and 10B (or 12A and 12B) gives you two chances to clear the cutoff but does not change your AIME eligibility—one qualifying score is sufficient.
An important rule: once you exceed the age or grade eligibility limit for the AMC 10 (over 10th grade or age 17.5 on the day of the competition), you can only use the AMC 12 pathway. Many students who qualified for AIME via AMC 10 in their freshman and sophomore years switch to AMC 12 in junior and senior year—it’s the only available route.
The AMC registration process itself deserves attention for first-time participants. Students register for AMC through their high school, which serves as an administering institution under MAA authorization. If your school is not registered as an AMC administering site, you can sometimes take the exam at a nearby school that is registered, or in some cases register as a home-school student through the MAA’s individual registration process.
Deadlines for AMC registration typically fall in late September or October for the February competition date, which is earlier than many students expect. Don’t discover in January that your school never registered for AMC 10A.
For students aiming to qualify for AIME, the year before the competition is the critical preparation window. Students who begin systematic AMC preparation in middle school or early in their freshman year have a substantial advantage over students who start late. The AMC 10 content ceiling includes topics through Algebra II and introductory combinatorics—material that most students don’t encounter in standard curriculum until junior or senior year. Self-directed study of this content one or two years ahead of when school teaches it is the single biggest competitive advantage in AMC and AIME preparation.
AIME qualifying cutoffs are not fixed. They are set after each competition sitting based on the actual score distribution of all participants nationally. This means you can’t know the exact cutoff before you take the exam—you know the approximate range based on historical patterns, but the actual cutoff depends on how difficult the exam turns out to be and how all participants perform.
Historically, AMC 10 cutoffs have ranged from approximately 99 to 111 across recent competition years, with most years falling in the 100–108 range. AMC 12 cutoffs have ranged from approximately 81 to 99. These ranges exist because exam difficulty varies year to year—a particularly hard exam results in lower overall scores and thus a lower cutoff, while an easier exam drives scores up and pushes the cutoff higher.
The MAA also sometimes implements a fixed “floor score” rule as a secondary qualification pathway. Under this rule, students scoring at or above the floor (for example, 100 on the AMC 10 or 100 on the AMC 12) automatically qualify regardless of whether their percentile reaches the 2.5% or 5% threshold. The floor score provides a deterministic target to aim for during preparation. Check the current year’s AMC bulletin for whether a floor score rule applies and at what level it is set.
For context on aime cutoff targets in practice: a score of 108 on the AMC 10 would have safely qualified in nearly every recent year. A score of 96 on the AMC 12 would have comfortably qualified in most years. These are ambitious targets—they represent roughly 20–22 correct answers on a 30-question exam where many problems are deliberately challenging. Students who aim to clear the cutoff consistently typically need 2–3 years of systematic AMC preparation to reach this level reliably.
Tracking historical cutoff scores is useful for calibrating preparation goals. The MAA publishes official cutoff scores for each competition year, and AoPS maintains archived records going back many years. Looking at the last 5–7 years of cutoffs for the specific exam version you’re targeting (AMC 10A, 10B, 12A, 12B) gives you a realistic target range. For most students, aiming for 108+ on AMC 10 or 96+ on AMC 12 provides a comfortable cushion above historical cutoffs in all but the easiest competition years, when cutoffs have occasionally reached 111 or 99 respectively.
Score percentiles don’t translate directly between different AMC versions in the same year. AMC 10A and AMC 10B typically have different difficulty levels and thus different cutoffs, despite both using the 2.5% threshold. Similarly, AMC 12A and 12B set cutoffs independently.
This means that if you’re strategic, you might try AMC 10A first and then AMC 10B if needed, comparing difficulty levels reported by students on AoPS after AMC 10A is released (before AMC 10B is administered). Many students use this information to decide whether AMC 10B or AMC 12B represents a better shot at qualifying, though ultimately each exam’s cutoff is set post-administration.
AIME I is offered in late January or early February, a few weeks after the AMC exams. It is the primary sitting for most schools and typically has higher registration numbers than AIME II. AIME I problems are set independently from AIME II—neither is consistently harder or easier than the other, though individual years vary.
Best for: Most students, since your school is more likely to be registered for AIME I as the default. AIME I is often the choice for students who want maximum preparation time before the olympiad index calculation deadlines.
Note: If you take AIME I and are unhappy with your score, you cannot retake AIME I. AIME II is a separate exam, not a retake. Taking AIME II uses a different set of problems and your AIME II score replaces AIME I for USAMO index purposes only if AIME II is also your designated sitting.
AIME II is offered in late February or early March, approximately 4–6 weeks after AIME I. AIME II was historically called AIME II or the “alternate AIME.” It serves students who couldn’t attend AIME I due to schedule conflicts, illness, or school availability, and students whose schools only register for the later sitting.
Best for: Students who missed AIME I, students at schools that offer only AIME II, or students who strategically prefer the later date for additional preparation time after seeing their AMC score and confirming qualification.
Note: You cannot take both AIME I and AIME II in the same year as two separate scored attempts to improve your score. You may take only the sitting your school or you are registered for. Attempting to take both is a violation of AMC competition rules.
If you are eligible for both AMC 10 and AMC 12 (10th grade or below, age ≤17.5), you have a strategic choice. The AMC 10 uses a 2.5% cutoff and the AMC 12 uses a 5% cutoff, but AMC 12 is substantially harder. The question is whether you can score in the top 5% on the harder AMC 12 or the top 2.5% on the easier AMC 10.
Most students in grades 9–10 with strong AMC preparation do better strategically by focusing on the AMC 10. The 2.5% cutoff sounds tougher but the content ceiling is lower (no precalculus), which means the very best students aren’t scoring dramatically above the cutoff on the same exam, compressing the score distribution. Students in 11th or 12th grade must use AMC 12 as their only path. For USAMO index calculations, AMC 12 scores are used directly; AMC 10 scores are also accepted for USAJMO (for younger students) and USAMO qualification is based on a combined index.
Divisibility, prime factorization, modular arithmetic, and number systems appear consistently across AIME problems. Number theory problems often require finding remainders, counting divisors, or applying the Chinese Remainder Theorem.
Counting problems, combinations, permutations, and probability form a significant portion of most AIME exams. These problems often involve clever counting arguments or inclusion-exclusion principles.
AIME geometry problems involve both classical Euclidean geometry and coordinate methods. Problems frequently require finding lengths, areas, or angles using creative applications of standard theorems.
Polynomial equations, systems of equations, sequences, series, and functional equations appear regularly. AIME algebra often requires noticing clever algebraic identities or manipulations.
AIME scores combine with AMC scores to form a qualification index for USA(J)MO. The index formula is: AMC score + 10 × AIME score. Students who took AMC 10 use this index for USAJMO qualification. Students who took AMC 12 use this index for USAMO qualification. The cutoffs for olympiad selection vary each year based on the actual distribution of scores among all AIME participants, but typical recent USAMO cutoffs have been in the range of 215–230, and USAJMO cutoffs in the range of 195–215.
To put this in perspective: if you scored 108 on the AMC 12 and then score 12 on AIME, your index is 108 + 120 = 228, which in most years would qualify for USAMO. An AMC 12 score of 96 combined with an AIME score of 14 gives an index of 236, comfortably above recent USAMO cutoffs.
These combinations illustrate why both a strong AMC score and a strong AIME score matter—a significantly higher score on one can partially compensate for a lower score on the other, but the index is multiplicative on AIME, making each additional correct AIME answer worth 10 AMC points.
For students who qualify for USAMO or USAJMO, the next steps involve a two-day written olympiad in April or May, where problems require full written proofs rather than numerical answers. USAMO and USAJMO are among the most challenging math competitions in the world at the high school level.
The top finishers are invited to the Mathematical Olympiad Summer Program (MOSP/MOP), from which the USA IMO team is selected. AIME eligibility is the first step in this pathway, but the subsequent competition levels demand a qualitative shift in mathematical depth and proof-writing ability that most AIME-eligible students develop over years of dedicated practice.
For students focused on maximizing AIME performance rather than just qualifying, the preparation strategy shifts significantly from AMC prep. AMC preparation is primarily about speed and breadth—solving a wide variety of problems correctly within a strict per-problem time budget.
AIME preparation requires depth: the ability to spend 15 or more minutes working through a single difficult problem, try multiple approaches, recognize when to abandon a dead end, and synthesize techniques from multiple areas of mathematics in a single solution. Students who rely solely on AMC-style drilling often plateau in AIME performance because they haven’t developed the sustained problem-solving endurance AIME demands.
The best AIME preparation combines systematic review of past AIME problems (organized by topic), the Art of Problem Solving curriculum for deeper topic coverage (particularly in number theory, combinatorics, and geometry beyond AMC scope), and contest-specific preparation such as mock AIME exams under realistic timed conditions. The community at ArtOfProblemSolving.com (AoPS) is the premier resource for AIME-level mathematics discussion, solution review, and peer learning. Many of the top AIME scorers cite AoPS forum discussions and the Intermediate and Pre-Olympiad AoPS textbooks as their primary preparation resources.
Beyond preparation materials, developing a competition mentality for AIME is essential. Unlike AMC where skipping hard problems is often the right strategy, AIME rewards persistence on individual problems. A student who spends 25 minutes solving problems 8 and 9 on AIME earns 2 points. A student who spends the same time reading all 15 problems and answering none definitively earns 0. AIME rewards going deep rather than going wide, which is a fundamentally different skill than what AMC rewards. Students who understand this distinction early—and practice accordingly—consistently outperform peers with equivalent AMC scores when AIME day arrives.