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Q. USAMO #1. How do I qualify for the USAMO/USAJMO?
A. The 2013 USAMO/JMO Selection Protocol is as follows:

USAMO and USA Junior Mathematical Olympiad Selection Protocol:

  1. U.S. citizens and students residing in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO.
  2. Selection to the USAMO will be based on the USAMO index which is defined as AMC 12 Score + 10 * AIME Score. Selection to the USAJMO will be based on the USAJMO index which is defined as AMC 10 Score + 10 * AIME Score.
  3. Only AMC 12 A or AMC 12 B takers who are U.S. citizens and students residing in the United States and Canada will be eligible for the USAMO.
  4. Only AMC 10 A or AMC 10 B takers who are U.S. citizens and students residing in the United States and Canada will be eligible for the USAJMO. This automatically limits Junior Math Olympiad participation to 10th graders and below. Students who take ONLY the AMC 10 test, whether AMC 10 A or AMC 10 B or both, will NOT be eligible for the USAMO regardless of their score on the AMC 10 or the AIME.
  5. The approximately 260-270 individual students with the top AMC 12 based USAMO indices will be invited to take the USAMO. These indices will be selected from the pool of AMC 12 takers with an AIME score.
  6. The approximately 230-240 individual students with the top AMC 10 based USAMO indices will be invited to take the USAJMO. These indices will be selected from the pool of AMC 10 takers with an AIME score after removing students who also took an AMC 12 test and qualified for the USAMO in rule 5. This means young students MUST take the USAMO if they qualify through an AMC 12 index.
  7. We will select the student with the numerically largest index, whether AMC 10 based USAJMO index or AMC 12 based USAMO index, from each US state not already represented in either the USAMO or the USAJMO. The student will be invited to the USAMO if the numerically highest index in the state is AMC 12 based, and invited to the USAJMO if the index is AMC 10 based.

Q. USAMO #2. What USAMO index will I need to be invited to the USAMO?
A. If you take the average of the USAMO invitation indices for 2000-2009, the result is 213. If you take the average of the USAMO invitation indices for 2000, 2001, 2003, 2004, 2005 when we invited about 250-260 participants the result is 217. Using the average like this is not perfect, but year-by-year values and the overall average are consistent with my estimate based on 2008 and 2009 results that an index of 210 will be the approximate invitation level for 2013. Of course, the precise value will depend on the variability in difficulty of the 2013 AMC 10 and AMC 12 and the AIME compared to previous years. The committees do an excellent job of calibrating the difficulty level given that there are 6 contests each year, each with new problems, but the contests do vary in overall difficulty with a standard deviation which is about one problem from an overall average.

Q. USAMO #3. What index will I need to be invited to the USAJMO?
A. In 2011 for the USAJMO, the required index on the AMC 10 and AIME I combination was 179.0. The required index on the AMC 10 and AIME II combination was 196.5.

Q. USAMO #4. When do we get our USAMO Scores?
A. Grading of the USAMO takes place about 10 days after the test with results posted on the web site soon thereafter. Note that in the Teachers' Manual in the Sample S-I letter which all USAMO and USAJMO participants receive: "USAMO winners and MOSP invitations will be telephoned after grading." About 2-3 weeks after the USAMO and USAJMO we will send a copy of the USAMO, USAMO Solutions, the USAJMO and the USJAMO 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 USAMO papers to you. Of course, you can also obtain a copy of the USAMO problems and solutions on our website.

Q. USAMO #5. When are the solutions to the USAMO and USAJMO available?
A. We will not post any official solutions on the AMC website until after the grading which takes place about 10 days after the contest.

Q. USAMO #6. What calculators are allowed on the USAMO and USAJMO?
A. No calculators are allowed on the USAMO or USAJMO. No notes, books, headphones, cell phones, ipods, slide rules, mathematical tables, computers, calculators or calculator watches are allowed during the exam. The only instruments permitted are writing and drawing instruments (ruler, compass, protractor, graph paper, carbon paper).

Q. USAMO #7. What accommodations for English Language Learners are there?
A. For the USAMO Students learning English as a second language, who are taking the USAMO or USAJMO for the first time, are permitted to use a non-technical translation dictionary during the exam. However, the proctor must examine and keep the dictionary in his or her possession for the 24 hours preceding the USAMO or USAJMO, and the proctor must announce to any other participants that the student has been given special permission to use the dictionary.

Q. USAMO #8. Who can proctor the USAMO and USAJMO contest?
A. The USAMO and USAJMO must be taken on the official days under the supervision of an educator-absolutely no exceptions. It is possible, however, for a student to take the test under the supervision of a teacher at a site other than the student’s school for valid reasons. The student’s teacher must call the AMC national office for permission.

Q. USAMO #9. Where can I get past copies of the USAMO problems and solutions?
A. You can purchase from the AMC a CD that has all the AIMEs from 1984 and all the USAMOs from 1972 on it. Furthermore, the problems and solutions are reproduced from the original source, so there are no typos, no edits, and the original solutions. The CD that comes with the Math Club Package contains all the contests, AMC 8, 10, 12, AIME and USAMO from 2000 to the present.

A more specific link to the order form: see item 11 on the form.

Don't forget all the USAMO and IMO books from the MAA. Go to then click on the Bookstore link, and go to the Problem Books Series.

Q. USAMO #10. On the USAMO and USAJMO, if one proves a result using a completely different method, but still makes sense, would graders still give that a 0?
A. The graders are all experienced mathematicians, all very capable and intelligent. Many, even most, are former USAMO and IMO participants and winners. All are familiar with reading and evaluating mathematical arguments, including novel and unexpected proofs. All papers are read at least twice, independently. If a proof is significantly different or unusual, it may be read by several more graders independently. If a proof is fully correct, it will be awarded full points. The rubrics establish a guide for consistency in awarding points, not a rigid template for grading.

Note also that there is a citation for the most elegant proof, often it is very different from the official proof. See for example, the last paragraph of the article: "38th United States of America Mathematical Olympiad", Mathematics Magazine, April 2010, volume 83, number 2, pages 155-158.

Q. USAMO #11. Will our papers have comments on them, so that we can see our errors and improve next year?
A. No. The comments on the papers (if any, and there are very few) would be useless to you. Each paper is read twice and independently and the two opinions have to be reconciled against a standard rubric and the graders must agree before a score is assigned. Then all papers in the top 25% are read again and the second reading must agree with the standard rubric. Your score is correctly and fairly assigned. Incidentally, all grading is blind grading, all we have is the student number, nothing else. Therefore, it takes detailed explanation and work to interpret a mark on a paper. I suggest you compare your solution to the official solution and try to understand the differences and similarities. It is a long-standing policy of the AMC that decisions of USAMO graders are final.

Q. USAMO #12. What if none of the AMC 12 scores qualify for the AIME? Then, does the top score in the state on the AMC 12 automatically make it to USAMO? If not what will happen?
A. In the case that a state has no AIME qualifiers, then that state will not have a USAMO or USAJMO qualifier either. That is, an AIME score is a necessary condition for qualifying for USAMO. or USAJMO. In 9 years of making the invitations for USAMO, for 50 states, I recall seeing that happen once. The existing rules are sufficient to cover the situation, and something that happens once in a decade, or once in 450 cases does not need a special rule.

Q. USAMO #13. Can a non-US-citizen outside North America in an American international school participate in the USAMO?
A. The answer is no. See the USAMO Teachers' Manual: Section 1, second paragraph, on page 4. You should participate in the Mathematical Olympiad selection process for the country of your nationality.

For US-citizen students outside the U.S. we require proof of citizenship using a U.S. State Department issued passport, or a birth certificate.

Q. USAMO #14. Is there a Certificate of Participation for those who participate in the USAMO or USAJMO?
A. Yes, the AMC office creates and sends a Certificate of Participation with the USAMO and USAJMO results and the solutions. This material will be sent sometime in late May, after the grading is complete and all results have been compiled.

Q. USAMO #15. What time is the USAMO and USAJMO given?
A. See page 5, Section V. line 6 of the USAMO Teachers' Manual where the testing time frame for each continental time zone is listed explicitly. For all other time zones, please contact the AMC office.

Q.  USAMO #16.  Which contest should young, advanced students take?
A. A student in 10th grade or below who wishes to qualify for the USAMO must take either the AMC 12 A or the AMC 12 B contests in order to be considered for USAMO selection. We recommend that such a student take an AMC 10 contest on one date if possible. A student in 10th grade or below wishing to take the AMC 12 and qualify for the USAMO should have a good problem solving knowledge in advanced algebra, analytic geometry, function notation, logarithms, trigonometry, and complex numbers in order to score well on the AMC 12, AIME and USAMO. The student must also be prepared to compete with 11th and 12th grade students on an equal basis since USAMO qualification is based on score only with no consideration for grade in school.

The minimum USAMO qualifying index for the last years have been:
2010, 208.5, 277 students
2009, 201.5, 514 students
2008, 204.0, 503 students
2007, 197.5, 505 students
2006, 217, 432 students

We recommend students aim for an AMC 12 based index of at least 210 in order to qualify for the USAMO.

Based on the single year experience of 2010, we recommend students aim for an AMC 10 based index of at least 200 in order to qualify for the USAJMO.

Exact invitation levels will vary each year depending on the difficulty of the contests and the pool of participating students. The historical minimum qualifying scores here are for planning purposes only and do not necessarily indicate future qualifying scores.