The United States of America Mathematical Olympiad (USAMO) is a high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the AMC series of contests. Top scorers on the USAMO usually represent the United States at the International Mathematical Olympiad.
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In order to be eligible to take the USAMO, a participant must be either a U.S. citizen or a legal resident of the United States or Canada. [1] Only U.S. residents and citizens may join the American IMO team. In addition, all participants, regardless of geographic location, must meet qualification indices determined by previous rounds of the AMC contests. Entry to the USAMO is by invitation only.
The USAMO (and the USAJMO since 2010) is restricted to approximately 500 (250 prior to 2006) participants combined each year. To keep this quota constant, the AMC Committee uses a selection process, which has seen a number of revisions in the exam's history.
In 2011 we will have slightly revised qualification rules for the USA Mathematical Olympiad and USA Junior Mathematical Olympiad. The goal is to select approximately 500 students total for the two Olympiads, split approximately 270 for the USAMO and 230 for the USAJMO respectively. Selection for the 2011 USA Mathematical Olympiad (USAMO) and 2011 USA Junior Mathematical Olympiad (USAJMO) will be made according to the following rules: [2]
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.
Starting in 2010, the USA Mathematical Olympiad is split into two parts. The USA Mathematical Olympiad will be administered to approximately 270 students, mostly selected from top ranking AMC12 participants. The AMC10 only participants will take part in USA Junior Mathematical Olympiad.[3]
1.Selection to the USAMO and JMO will be based on the USAMO index which is defined as AMC score + 10 * AIME score.
2.Only AMC 12A or AMC 12B takers are eligible for the USAMO (with the slight exception mentioned in item 5 below).
3.Only AMC 10A and AMC 10B takers are eligible for the JMO. (This automatically limits Junior Math Olympiad participation to 10th graders and below.)
4.Approximately the top 260 AMC12 based USAMO indices will be invited to the USAMO.
5.In order to find unrecognized young talent, AMC 10 takers who score 11 or more on the AIME will be invited to the USAMO. (In 2008 and 2009 this was 5 or 6 students).
6.Select the top index from any state not already represented in the USAMO.
7.Approximately the top 220-230 students with AMC10 based USAMO indices and not already selected to the USAMO via an AMC12 based index will be invited to the JMO.
Source: [3]
Selection for the USAMO will be made according to the following rules:
1. The goal is to select about 500 of the top scorers from this years’s AIME and AMC 12A, AMC 12B, AMC 10A and AMC 10B contests to participate in the USAMO.
2. Selection will be based on the USAMO index which is defined as 10 times the student’s AIME score plus the student’s score on the AMC 12 or the AMC 10.
3. The first selection will be the approximately 330 highest USAMO indices of students taking the AMC 12A or AMC 12B contest.
4. The lowest AIME score among those 330 first selected will determine a floor value. The second selection of approximately 160 USAMO participants will be among students in the 10th grade and below who received an AIME score at least as high as the floor value. If there are more than 160 young students with a score above the floor value, then approximately 160 students will be selected from this group by using the USAMO index.
5 The student with the highest USAMO index from each state, territory, or U.S. possession not already represented in the selection of the first and second groups will be invited to take the USAMO.
6. To adjust for variations in contest difficulty, the number of students selected from A & B contests will be proportional to the number of students who took the A & B Contests.
7. In advising young students (in grade 10 or below) who desire to be selected for the USAMO whether to take the AMC 12 contest or the AMC 10 contest, please be aware of the following facts:
a. In 2007, among 506 students invited to take the USAMO, 229 were in 10th grade and below. Those students had scored 6 or greater on the AIME.
b. Among those 229 students, 87 had their AIME qualifying high score based on the AMC 12 and 142 had their AIME qualifying high score based on the AMC 10.
c. In 2007, among 8,312 students who took the AIME, 2,696 were in grades 10 and below. Of those, 998 qualified for the AIME from the AMC 12 and 1,698 qualified from the AMC 10.
Beginning in 2006, the USAMO was expanded to include approximately 500 students (around 430 were actually invited, read below) due to a proposal and sponsorship from the Art of Problem Solving website:
Source: American Mathematics Competitions
Since 2002, the following set of guidelines have been adopted for use in determining each year's USAMO participants:
Source: American Mathematics Competitions
Prior to 2001, the following guidelines were used:
Source: American Mathematics Competitions hey hey hey hey hey america rocks
| Year | AMC 12 | AMC 10 | Total number of qualifiers |
|---|---|---|---|
| 2011 | 188.0 (AIME I); 215.5 (AIME II) for USAMO | 179.0 (AIME I); 196.5 (AIME II) for USAJMO | 282 USAMO; 222 USAJMO |
| 2010 | 208.5 (USAMO); 204.5 (USAMO -- 11th and 12th) | 11/15 on AIME (USAMO) OR 188.5+ on index (USAJMO) | 328 USAMO; 235 USAJMO |
| 2009 | 201.0 | 7/15 on AIME AND 215.0+ on index | 514 |
| 2008 | 204.0 | 6/15 on AIME AND 202.5+ on index | 503 |
| 2007 | 197.5 | 6/15 on AIME AND 181.0+ on index | 505 |
| 2006 | 217 | 8/15 on AIME | 432 |
| 2005 | 233 (AIME I); 220.5 (AIME II) | 9/15 on AIME | 259 |
| 2004 | 210 | 7/15 on AIME | 261 |
| 2003 | 226 | 8/15 on AIME | 250 |
| 2002 | 210 | 6/15 on AIME | 326 |
| 2001 | 213 | 7/15 on AIME | 268 |
| 2000 | 212 (12th); 204 (11th) | 9th grade: 7/15 on AIME AND 164+ on index; 10th grade: 8/15 on AIME AND 174+ on index | 239 |
Since 2002, the USAMO has been a six-question, nine-hour mathematical proof examination spread out over two days. (The IMO uses the same format.) On each day, four and a half hours are given for three questions.
Each question is graded on a scale from 0 to 7, with a score of 7 representing a proof that is mathematically sound. Thus, a perfect score is 42 points. The number of perfect papers each year has varied depending on test difficulty. Regardless, the top 12 scorers are all named contest winners.
The scale of 0 to 7 goes as follows:
The test consisted of two three-problem sets. Three hours were given for each set; one set was given in the morning (9:00-12:00), and the other in the afternoon (1:00-4:00).
The test consisted of five problems to be solved in three and a half hours (earlier, three hours). Each problem was worth 20 points, for a perfect score of 100.
In most years, students have taken the USAMO at their respective high schools. Prior to 2002, the problems were mailed to the schools in sealed envelopes, not to be opened before the appointed time on the test day. Since 2002, test problems have been posted on the AMC website (see links below) fifteen minutes prior to the official start of the test. Student responses are then faxed back to the AMC office at the end of the testing period.
In 2002, the Akamai Foundation, as a major sponsor of the American Mathematics Competitions, invited all USAMO participants to take the test at a central event at MIT in Cambridge, Massachusetts, all expenses paid. In addition, Akamai invited all 2002 USAMO participants who were not high school seniors (approximately 160 students) to take part in an enlarged Mathematical Olympiad Program (also known as "MOP") program. Since holding this central event every year would be prohibitively expensive, it has been discontinued. In 2004 and 2005, however, funding was found to send 30 rising freshmen to MOP as well, in a program popularly called "Red MOP."
Each year, the top 12 scorers on the USAMO are considered for selection to the IMO team for the United States. The students are trained at the MOP in Lincoln, Nebraska, and then six are selected to the team. The next approximately 18 high scorers, usually excluding high school seniors, are also invited to MOP.
Here are the subjects on the test in different years by problem number (i.e. what subject each problem was from):
2011:
2010:
2009:
2008:
2007:
2006:
2005:
2004:
2003: