American Invitational Mathematics Examination
The American Invitational Mathematics Examination began in 1983 as a single annual event. It was scheduled for late March or early April on either a Tuesday or Thursday. For seventeen years, the test appeared only once per year to select high school students from the top five percent of AMC 12 participants. The format remained static until the turn of the millennium when organizers decided to expand access. Beginning in 2000, the competition split into two distinct versions called AIME I and AIME II. This change allowed students who missed the first date due to illness or spring break conflicts to compete again. International students were automatically assigned to the second version while domestic students took the first. No student could officially participate in both competitions despite the existence of two dates. The schedule shifted again in recent years with tests now occurring in early March instead of April. The second exam follows exactly two weeks after the first one. In 2020, the rapid spread of the COVID-19 pandemic led to the cancellation of the AIME II for that year.
Students qualify for this examination through specific score thresholds set by the Mathematical Association of America. Before 2010, only those ranking in the top five percent on the AMC 12 high school mathematics examination earned an invitation. Starting in 2010, the criteria expanded to include the top 2.5 percent of AMC 10 scorers as well. By 2022, the organization adjusted these percentages to invite approximately the top 13 to 15 percent of AMC 12 participants. The same adjustment invited roughly the top 6 to 8 percent of AMC 10 participants. An alternative pathway exists through the USAMTS free proof based math contest. Students who score at least 68 out of 75 points on that competition gain entry. If a student qualifies via both routes, the system prioritizes the AMC pathway when calculating index scores. This rule ensures consistency across different qualification methods. Most students who qualify choose to take the AIME I version rather than the second date. The number of qualifiers fluctuated significantly during the 1990s with fewer than 2,000 students typically participating annually. In 1994, an unprecedented 99 students achieved perfect scores on the AHSME causing delays in result distribution.
The competition consists of fifteen questions of increasing difficulty administered over three hours. Each answer must be an integer between 000 and 999 inclusive. Participants cannot use calculators but are permitted pencils erasers rulers and compasses. Answers are entered onto an OMR sheet similar to grid-in math questions on the SAT. Leading zeros must be filled in for all answers so that 7 becomes 007 and 43 becomes 043. One point is earned for each correct answer while no points are deducted for incorrect responses. No partial credit is given so final scores range from 0 to 15 inclusive. Concepts covered include elementary algebra geometry trigonometry number theory probability and combinatorics. Many topics do not appear directly in typical high school mathematics courses requiring supplementary resources. The format effectively removes chance elements found in multiple choice tests while preserving automated grading ease. Sample problems from 2003 asked participants to find a value where x equals 839. Another problem from 2012 required finding a complex number z equaling 375.
A student's score determines eligibility for the United States Mathematical Olympiad through a specific index calculation method. Before the 2025-2026 competition cycle, organizers added the AMC score to ten times the AIME score. This formula produced a single index used to set qualification cutoffs. Starting with the current cycle, the system now adds the AMC score to twenty times the AIME score. Since 2017, the USAMO and USAJMO qualification cutoff has been split between the AMC A and B contests as well as the AIME I and II versions. Hence there will be a total of eight published USAMO and USAJMO qualification cutoffs per year. A student can have up to two indices via participating in both AMC contests. The student only needs to reach one qualification cutoff to take the next level competition. If a student qualifies from both competitions using different pathways, the AMC pathway is used over the USAMTS when calculating the index scores for the cutoff. These adjustments ensure fairness across varying test dates and participant pools.
The rapid spread of the COVID-19 pandemic led to the cancellation of the AIME II for that year. Instead qualifying students were able to take the American Online Invitational Mathematics Examination which contained problems originally intended for the second date. Both 2021's AIME I and II were moved online to accommodate safety concerns. The 2022 administration offered both online and in-person options for participants. From 2023 onward all AIME contests returned to in-person formats. This shift marked a return to traditional testing environments after years of digital adaptation. The transition required significant logistical changes for organizers and schools alike. Students who missed the first date due to illness or spring break conflicts could still compete on the alternate date if available. International students remained scheduled for the second version regardless of location. The flexibility allowed the program to continue despite global health restrictions.
Mean and median score trends from 2014 through 2025 reveal shifting difficulty levels across exam versions. The mean score for 2025 I reached 6.16 while the median stood at 6. Scores for 2024 II dropped to a mean of 5.45 with a median of 5. In 2023, the mean for Part I was 4.28 and Part II averaged 4.40. The year 2022 saw means of 4.82 and 4.40 respectively with medians of 4 for both. Earlier data shows 2019 Part II had a mean of 6.47 and a median of 6. Statistical anomalies include clusters of perfect scores such as the 99 students achieving perfection in 1994. These events caused delays in result distribution requiring thick newspaper bundles instead of usual pamphlets. The mean score for 2014 I was 4.88 with a median of 5. Median scores often hover around 5 or 6 depending on the specific test version. Some years show higher averages like 2020 Part II which reached 6.13. These fluctuations reflect changes in problem difficulty and student preparation over time.
Common questions
When did the American Invitational Mathematics Examination begin and what was its original schedule?
The American Invitational Mathematics Examination began in 1983 as a single annual event scheduled for late March or early April on either a Tuesday or Thursday. For seventeen years, the test appeared only once per year to select high school students from the top five percent of AMC 12 participants.
How has the qualification criteria for the American Invitational Mathematics Examination changed since 2010?
Starting in 2010, the criteria expanded to include the top 2.5 percent of AMC 10 scorers as well as those ranking in the top five percent on the AMC 12 high school mathematics examination. By 2022, the organization adjusted these percentages to invite approximately the top 13 to 15 percent of AMC 12 participants and roughly the top 6 to 8 percent of AMC 10 participants.
What are the specific rules for answering questions on the American Invitational Mathematics Examination?
Each answer must be an integer between 000 and 999 inclusive with leading zeros filled in so that 7 becomes 007 and 43 becomes 043. Participants cannot use calculators but are permitted pencils erasers rulers and compasses while answers are entered onto an OMR sheet similar to grid-in math questions on the SAT.
How is eligibility for the United States Mathematical Olympiad calculated using the American Invitational Mathematics Examination score?
Starting with the current cycle, the system now adds the AMC score to twenty times the AIME score to produce a single index used to set qualification cutoffs. Since 2017, the USAMO and USAJMO qualification cutoff has been split between the AMC A and B contests as well as the AIME I and II versions resulting in eight published USAMO and USAJMO qualification cutoffs per year.
Why was the second version of the American Invitational Mathematics Examination cancelled in 2020 and what replaced it?
The rapid spread of the COVID-19 pandemic led to the cancellation of the AIME II for that year. Instead qualifying students were able to take the American Online Invitational Mathematics Examination which contained problems originally intended for the second date.
All sources
8 references cited across the entry
- 3webPrizes
- 4webMAA Invitational CompetitionsMathematical Association of America
- 5webAmerican Invitational Mathematics ExaminationMathematical Association of America
- 7webAMC Platform and Administeration PoliciesMathematical Association of America