American Invitational Mathematics Examination

• 1. Introduction

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  The American Invitational Mathematics Examination has been part of American competitive mathematics since 1983. In 1994, ninety-nine students earned perfect scores on the qualifying exam, a number so large it caused delays in distributing results. The usual printed pamphlets could not accommodate the data; thick newspaper bundles replaced them. What does the AIME demand of the students who take it? Who earns a seat, and what does a strong score ultimately determine?

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• 2. Fifteen Questions

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  Fifteen questions greet each participant, arranged in order of increasing difficulty. The AIME uses no multiple-choice options. Every answer is a specific integer, recorded on an OMR answer sheet as exactly three digits. A response of 7 becomes 007; a response of 43 becomes 043. This format eliminates the element of chance from guessing while preserving the efficiency of automated grading.

  One point is awarded for each correct answer, and nothing is deducted for a wrong one. Scores run from zero to fifteen with no partial credit in between. Pencils, erasers, rulers, and compasses are the only permitted tools; calculators are barred from the room.

  Algebra, geometry, trigonometry, number theory, probability, and combinatorics all feature in the competition. Much of this material sits outside the standard high school curriculum, and competitors typically seek out supplementary resources to prepare. The 2003 AIME I opened with a problem involving positive integers and a maximization condition; the answer was 839.

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• 3. Earning a Seat

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  The AMC 12 and AMC 10 are the primary gateways into the AIME. Since 2022, students who score in roughly the top 13-15% on the AMC 12 receive an invitation. The threshold on the AMC 10 sits around the top 6-8%. Before 2022, these requirements were stricter: the top 5% on the AMC 12 and, beginning in 2010, the top 2.5% on the AMC 10.

  The USAMTS, the United States of America Mathematics Talent Search, provides a third route into the competition. It is a free, proof-based contest, and students who score at least 68 out of 75 earn a qualifying spot. Where a student earns access through both the AMC and the USAMTS, the AMC pathway is used when calculating the qualifying index.

  The AIME I and AIME II are separate sittings of the competition, offered each year. Domestic students are placed in AIME I by default and may switch to AIME II if a scheduling conflict arises. Most qualifiers ultimately sit AIME I. International students are assigned directly to AIME II. No student may sit both in the same year; participation is limited to one sitting per cycle. During the 1990s, fewer than 2,000 students typically qualified for the AIME each year.

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• 4. Road to the USAMO

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  The United States Mathematical Olympiad, commonly called the USAMO, is the competition the AIME qualifies students toward. Qualification is a two-step process. Students must first reach the AIME through the AMC or USAMTS, then earn a combined index score high enough to meet a published cutoff.

  Before the 2025-2026 competition cycle, the qualifying index was computed by adding a student's AMC score to ten times their AIME score. Starting with the 2025-2026 cycle, the AIME score is multiplied by twenty before being added to the AMC total. A single correct answer on the AIME now shifts the index by twenty points rather than ten.

  Since 2017, the USAMO and USAJMO cutoffs have been published separately by test version. Eight thresholds appear each year, split across two AMC versions and two AIME sittings. A student who takes both AMC contests can carry up to two qualifying indices. Meeting any one of the eight cutoffs earns a place in the USAMO or USAJMO. In 2026, the median AIME score was 6 on both AIME I and AIME II. At least half of all qualifiers that year answered six or more questions correctly.

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• 5. A Competition Evolves

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  In 2000, a second annual sitting was introduced to the competition. Before that, the AIME ran once per year, typically on a Tuesday or Thursday in late March or early April.

  Two weeks was the usual gap between the first and second sittings. The second date existed for students who missed the first because of illness, spring break, or other conflicts.

  COVID-19 disrupted the 2020 schedule, forcing the cancellation of the AIME II that year. Qualifying students were redirected to the American Online Invitational Mathematics Examination, which carried the problems originally written for the cancelled test. Both sittings moved fully online in 2021. In 2022, the competition ran in a hybrid format, offered both online and in person. From 2023 onward, all contests have been held in person.

  In 2019, the two sittings fell on the 13th of March and the 21st. For the 2025-2026 cycle, AIME I was held on the 5th of February 2026 and AIME II on the 11th. That cycle's AIME I returned a mean score of 6.26; the AIME II came in at 6.55.

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