AIME Exam Guide: Prep, Format & Practice Tests 2026

What Is the AIME?

The American Invitational Mathematics Examination—AIME for short—is a 15-question, three-hour competition for high school students who qualify through the AMC 10 or AMC 12. It sits in the middle tier of the US mathematical olympiad pipeline: above the AMC contests and below the USA Mathematical Olympiad (USAMO). If you're serious about competitive math, qualifying for and doing well on the AIME is a meaningful milestone.

Unlike the AMC exams, which are multiple-choice, every AIME answer is an integer from 000 to 999. That single constraint changes everything about strategy. You can't guess-and-check from five options—you have to actually solve the problem, or at least get close enough to derive the final integer.

The exam is administered twice each year: AIME I in early March and AIME II about two weeks later. Students who qualify for either version are competing for the same goal: a high enough combined AMC/AIME score (the USAMO index) to receive an invitation to the USAMO or USAJMO.

AIME Eligibility: Who Can Take It?

You qualify for the AIME by scoring above a cutoff on the AMC 10 or AMC 12. The cutoffs shift slightly each year based on difficulty, but historically they look like this:

• AMC 10: Score 120 or above (out of 150), or finish in the top 2.5% of all AMC 10 takers
• AMC 12: Score 100 or above (out of 150), or finish in the top 5% of all AMC 12 takers

These thresholds mean AIME qualification itself is an achievement—roughly 6-8% of AMC participants advance each year. If you're aiming for AIME, your AMC prep matters as much as your AIME prep. You have to earn the invitation before you can sit the main event.

There's no registration fee for the AIME beyond what your school pays for AMC participation. International students can participate through schools that register with the Mathematical Association of America (MAA), though USAMO eligibility is restricted to US citizens and permanent residents.

AIME Exam Format

Here's what you're actually dealing with on test day:

• Questions: 15 problems
• Time limit: 3 hours (180 minutes)
• Answer format: Integer from 000 to 999—you bubble in three digits, leading zeros included
• Scoring: 1 point per correct answer, 0 for incorrect or blank. No penalty for wrong answers
• Maximum score: 15
• Median score: Usually 3-5 out of 15 (yes, it's that hard)

The no-penalty scoring is worth emphasizing. If you've spent 20 minutes on a problem and have a reasonable guess, bubble it in. There's no downside. This differs from some competition formats where wrong answers cost you points.

Problems are arranged roughly in order of increasing difficulty, though experienced competitors know this is approximate—problem 10 might feel easier than problem 8 depending on topic. Don't let early hard problems derail your time management. Scan all 15 problems first, then tackle the ones you're most confident about.

AIME Scoring and the USAMO Index

Your AIME score alone doesn't determine whether you advance. What matters is your USAMO Index, which combines your AMC and AIME scores:

USAMO Index = AMC 12 score + 10 × AIME score

Or for AMC 10 qualifiers applying to the USAJMO:

USAJMO Index = AMC 10 score + 10 × AIME score

A student who scored 120 on AMC 12 and got 5 on AIME has a USAMO index of 170. The USAMO cutoff is typically around 215-230 depending on the year, which means you'd need something like a 135 AMC 12 score and an 8 on AIME. The bar is genuinely high—roughly 250-500 students qualify for USAMO each year out of over 300,000 AMC participants.

Even without USAMO qualification, an AIME score in the 8-15 range is a strong signal for college applications, particularly for STEM programs and schools that value mathematical talent. Many Ivy League and top technical schools explicitly ask about AIME performance on supplemental applications.

What Topics Does the AIME Cover?

The AIME doesn't follow a fixed syllabus, but certain topics appear consistently across every year's exam:

Number theory: Modular arithmetic, divisibility, prime factorization, floor/ceiling functions, Diophantine equations. This is probably the most consistently tested category. A solid foundation in modular arithmetic pays dividends across multiple problems.

Combinatorics: Counting principles, permutations, combinations, probability, recursion, generating functions at the harder end. Combinatorics problems often have elegant solutions once you find the right framing—brute force rarely works.

Algebra: Polynomials, Vieta's formulas, complex numbers, sequences and series, functional equations. Algebra on AIME is rarely straightforward—expect multi-step problems where you need to introduce clever substitutions.

Geometry: Triangle properties, circle theorems, coordinate geometry, trigonometry. Geometry problems tend to be either very accessible (if you spot the key construction) or very punishing (if you don't). Synthetic methods often beat coordinate-bashing on efficiency.

One topic that catches many first-timers off guard: the AIME frequently combines topics. A problem might require number theory to set up an equation that's then solved algebraically, or combinatorics applied in a geometric context. Don't silo your preparation by subject.

How to Prepare for the AIME

Effective AIME prep has three phases. Don't skip straight to phase three—the foundation matters more than most students realize.

Phase 1: Build core theory (2-3 months before exam)

Work through a structured resource covering each major topic area. The Art of Problem Solving (AoPS) Introduction and Intermediate series are the standard recommendations. You don't need to finish every chapter—prioritize the topics that appear most frequently on recent exams. Modular arithmetic, Vieta's formulas, basic combinatorics, and triangle/circle geometry should all be solid before you attempt past exams.

Phase 2: Past exams and targeted problem sets (1-2 months before)

Work through AIME I and II from the past 10 years under timed conditions. Start with full three-hour sessions to build stamina, then analyze every problem you got wrong or skipped. The mistake analysis is more important than the initial attempt—understand not just how to solve the problem, but why the solution approach works.

For each problem you missed, find three similar problems and solve them. This pattern-matching is what separates students who score 4-6 from those who score 8-10.

Phase 3: Mock exams and refinement (final 3-4 weeks)

Take full mock exams, score them, and focus remaining prep on your weakest topic. If combinatorics is consistently hurting you, spend two weeks on nothing but combinatorics problems at the AIME difficulty level. Marginal gains on your weakest topic produce more improvement than further strengthening your strengths.

Time management deserves a dedicated practice session. AIME gives you 12 minutes per problem on average. In practice, most students spend 2-3 minutes on easy problems and 20-30 minutes on hard ones. Practice explicitly skipping and returning—don't let one stubborn problem consume your session.

AIME Test Day Tips

You've done the preparation. Here's how to perform on the actual day.

Read all 15 problems in the first 10 minutes. Don't attempt to solve them during this scan—just categorize: easy (confident), medium (solvable with effort), hard (skip first round). This gives you a map of the exam before you commit time anywhere.

Work your confident problems first. Secure those points before tackling harder ones. A guaranteed 5 points beats chasing a potential 7 and ending up with 3.

Write out your work clearly. AIME graders see only your final bubbled answer—no partial credit. But clear written work helps you catch arithmetic errors before you finalize, and it makes returning to a problem faster if you skip and come back.

Watch your arithmetic. AIME problems are designed to have clean integer answers. If you get a messy decimal or a number outside 0-999, something's wrong—go back and check. The answer 000 is valid, by the way. Don't assume the answer must be large.

Use all three hours. Most students who finish early would benefit from double-checking arithmetic or reconsidering skipped problems. Time pressure at the end is more common than running out of problems to work on.

After the exam, whether you're happy with your score or not, do a thorough post-mortem. The AIME problems and official solutions are published—go through every problem you missed and understand both the solution and what mental block prevented you from finding it. That process, repeated consistently, is what drives improvement over multiple AIME seasons.