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Invitational Competitions

Information Overview

For students who perform exceptionally well on the AMC 10/12, they are invited to continue participating in the AMC series of examinations that culminate with the International Mathematical Olympiad (IMO). The first in this series is the American Invitational Mathematics Exam (AIME), followed by the USA Mathematical Olympiad and Junior Mathematical Olympiad (USAMO and USAJMO). The top participants from the USA(J)MO are invited to the Mathematical Olympiad Program in the summer after the competition. Participants from the Mathematical Olympiad Program are then eligible to be selected for the following summer’s six-member team that will represent the United States of America at the IMO.

Competition Cycle 2019-2020 

After the AIME I and AOIME are scored, the USAMO committee and MAA AMC program will determine the cutoff indexes that will qualify students for USAMO or USAJMO. USA(J)MO qualification scores are determined by AMC 10/12 and AIME scores. For this 2019-2020 competition cycle, the AMC will uphold this process to determine USO(J)MO qualifiers. Acknowledging that some students may have taken both AIME I and AOIME, both scores will be considered when setting cut-offs for those students. The AIME I and AOIME cutoff scores will be split. The student’s USO(J)MO indexes are calculated as follows:

USOMO Index = AMC 12 Score + 10 x AIME I/ AOIME Score
USOJMO Index = AMC 10 Score + 10 x AIME I/ AOIME Score

A Hypothetical Example

For instance, if a student took the AMC 12 A and 12 B, and the AIME I and AOIME, that student could have the following index scores This student would qualify for the USO(J)MO with Index Score 3.

NOTE: ALL VALUES BELOW ARE PURELY HYPOTHETICAL. OFFICIAL CUTOFFS WILL BE ANNOUNCED THE SECOND WEEK OF JUNE ON THE MAA AMC WEBSITE

Example Student Scores

Student: Jonathan Nathan
AMC 12 A: 87
AMC 12 B: 110
AIME I: 11
AOIME: 12

Index score 1: 12 A + (10*AIME I) = 87 + 110 = 197
Index score 2: 12 A + (10*AOIME) = 87 + 120 = 207
Index score 3: 12 B + (10*AIME I) = 110 + 110 = 220* [qualifying score]
Index score 4: 12 B + (10*AOIME) = 110 + 120 = 230

Example of Cutoff Scores

  AMC 10 A AMC 10 B AMC 12 A AMC 12 B
AIME I 203 210 218 215
AOIME 215 220 227 235

 

To learn more about each competition within the MAA AMC Program follow the links below:

American Invitational Mathematics Exam

The American Invitational Mathematics Examination (AIME) is a challenging competition offered for those who excelled on the AMC 10 and/or AMC 12. The AIME is a 15 question, 3-hour examination, each answer is an integer number between 0 to 999. The questions on the AIME are much more difficult than those on the AMC 10 and AMC 12. Top scoring participants on the AIME are invited to take the USAMO or USAJMO.

AIME Competition Dates:

  • AIME I (main AIME competition date): Wednesday, March 10, 2021
  • AIME II (alternate AIME competition date): Thursday, March 18, 2021

AIME Administration Resources:

USA Mathematical Olympiad and Junior Mathematical Olympiad

The United States of America Mathematical Olympiad (USAMO) and the United States of America Junior Mathematical Olympiad (USAJMO) are six question, two day, 9-hour essay/proof examinations. The top scoring AMC 12 participants (based on a combination of AMC 12 and AIME score) are invited to take the USAMO. The top scoring AMC 10 participants (based on a combination of AMC 10 and AIME score) are invited to take the USAJMO. U.S. citizens and students studying in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO.

The MAA AMC champions inclusivity within our program and competitions. As we work towards creating a mathematical community to empower students of all genders, we invite the top-scoring AMC female students to our USA(J)MO each year. These students are placed on an ambitious path to potentially qualify for MOP, EGMO, and ultimately IMO.

USAMO and USAJMO Administration Resources:

FAQs for the AIME and USAMO/USAJMO

  1. Q. How do I qualify for the AIME?

    A. Qualification parameters for AIME vary with the results of the AMC 10/12 competitions. For AMC 10, invitations are issued to at least the top 2.5% of all scorers. For AMC 12, invitations are issued to at least the top 5% of all scorers. The exact cutoffs will depend on the difficulty of each competition.

  2. Q. How do I qualify for the USA(J)MO?

    A. Qualification parameters for USA(J)MO vary with the results of the AMC 10/12 competitions and AIME competitions. Selection to the USAMO will be based on the USAMO index which is defined as AMC 12 Score plus 10 * AIME Score. Selection to the USAJMO will be based on the USAJMO index which is defined as AMC 10 Score plus 10 * AIME Score. The committees calibrate the difficulty level for the 6 competitions each year and may determine different cutoffs based on the exam version if there is a significant difference in results and score distribution.

  3. Q. Who can proctor the AIME or USA(J)MO?

    A. The proctoring of any competition should be by a teacher (preferably a mathematics teacher) or administrator at the school; a college or university teacher of mathematics, or a responsible adult such as a math club coach or librarian. The proctoring of the exam must take place in a public building, (e.g. school, library, college or university, church). The proctor should not be related to any of the participants.

  4. Q. When can I see my AIME results? When can I see my USA(J)MO results?

    A. AIME Results reports are given to schools after we have received all AIME I and AIME II answer forms, scored all answer forms, and determined USA(J)MO selection indices. Therefore, you can expect that the AIME results will not be available until about 3 to 4 weeks after the AIME date.

    Grading of the USAMO takes place approximately 10 days after the test with results posted on the website soon thereafter. About 2-3 weeks after the USAMO and USAJMO we will email a copy of the USAMO, USAMO Solutions, the USAJMO, and the USAJMO solutions to your Exam Manager along with your total score. We do not report individual problem scores, only the total score. Note that the AMC does not return your USA(J)MO papers to you.

  5. Q. If you take both A-date and B-date AMC tests, but one score is higher than the other, do you get to choose which score to use with your AIME score for USA(J)MO qualification?

    A. We use the higher numerical score. We match both AMC scores with the AIME score, assuming we are able to locate both AMC scores. This means that the student spelled his/her name the same way on all exams and took both AMC exams at the same school. If one or both of these important criteria are not met we need timely notification in order to match results. The AIME certification form, filled out by the AIME competition administrator, has a section for students who qualified at multiple testing sites. Please give this important information to the AIME Competition administrator, so that we can use this important information.

  6. If I need to take the AIME at a location other than where I took the AMC 10/12, what should I do?

    A. Students are to take the AIME at the same testing location where they took the AMC 10/12 whenever possible. This is to ensure that a student’s AMC 10/12 score can be accurately matched up with their AIME score for USA(J)MO qualification. In the event that a student absolutely cannot take the AIME at the same competition location, they are to make arrangements with a different competition manager who has the materials to proctor the exam and complete the “Change of Venue” form (Coming soon!). Our customer service office cannot assist in finding new venues for the exam, instead, students should reach out to schools near them, using the AIME Venue page (Coming soon!) as a resource. Once you have made arrangements with this location, send an email to amcinfo@maa.org to inform our office that you will be taking the AIME at this new location, not at the qualifying location.

  7. Q. If I qualified with both the 12A at my own high school and the 10B at another high school, but wish to put my 10B score on the AIME I'm taking at my own school, what do I need to do?

    A. If you are taking the AIME at the school you attend daily on the basis of the AMC 12A that you took at the school, then the important thing is that the certification form, filled out by your AIME administrator, includes your name and the other school name and CEEB where you took the AMC 10B. Make sure that the other school where you qualified knows that you will NOT be taking the AIME at that school. Please make sure that the other school competition manager knows, and that your own school competition manager knows what you intend to do. We only use the AMC 10/12 score as the first check on your identity. For all other purposes, we rely on our internal record-keeping.

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