The Committee on the American Mathematics Competitions announces a new contest, the USA Junior Mathematical Olympiad, for students in 10th grade and below, beginning in April 2010.

The Junior Mathematical Olympiad contest better meets the level of young students. This new contest bridges the computational solution process of the AIME and the proof orientation of the USAMO.

Qualification Rules for the USAJMO

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:

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 AIME-qualifying AMC 12 Score + 10 * AIME Score. Selection to the USAJMO will be based on the USAJMO index which is defined as AIME-qualifying 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.

The current USA Mathematical Olympiad administered to about 500 students in all grades will split into two flights:

1. The USA Mathematical Olympiad will be administered to about 270 students, mostly in 12th grade and 11th grade, along with any extremely talented 10th graders and below who may qualify (qualification procedures below.)
2. The USA Junior Mathematical Olympiad will be administered to about 230 students in 10th grade and below who qualify (qualification procedures below.)

The USA Junior Mathematical Olympiad will have 6 problems and be administered over 2 days, the same as the USAMO. Two problems on each day will be unique to the USAJMO, and will be close in level and content to problems 13-15 on the AIME. One problem on each day will be the same as a problem appearing on the USAMO. All six problems on the USA Junior Mathematical Olympiad will require written answers, perhaps a detailed algebraic, number theoretic, combinatoric or geometric solution rather than a proof in mathematical format. Problems will be graded on the same 7 point scale (42 points total) as the USAMO, and have the same rigorous grading.

The USA Junior Mathematical Olympiad will take place at the same time as the USAMO, the last Tuesday-Wednesday of April every year and will be administered within the school, just as the USAMO is currently administered.

In parallel with the USAMO awards structure, we will announce 12 USA Junior Mathematics Olympiad Winners, and 12 Honorable Mentions, based on the 12 highest Junior Mathematical Olympiad scores and the next 12 highest Junior Mathematical Olympiad scores.  We will award certificates and prizes to the 12 winners, but we will not have a formal recognition ceremony for the 12 Junior Mathematical Olympiad winners as we do for the USAMO Winners.

Mathematical Olympiad Summer Program (MOSP) Selection:

Assuming continuing funding, under the USAMO/USAJMO division the USAMO SubCommittee and the graders will select about 12-13 top scoring 10th and 9th graders from the USAMO and will subsequently select the top-scoring  approximately 12  10th and 9th graders from the USAJMO. That is, essentially the USAJMO Winners will be invited to MOSP. The first group from the USAMO will be become the Red 1, the second from the USAJMO will become Red 2. The MOSP instruction and curriculum for these two groups remains identical.  Instructors at MOSP remain free to reassign students to groups as needed or desired.

Additional information on the selection criteria:

If an underclassman, (10th Grade or Lower) takes both the AMC 10 and AMC 12 on different dates (either AMC 10 A and AMC 12 B, or AMC 12 A and AMC 10 B) and qualifies for the AIME on both then:

The AMC 12 score and the AIME score and the corresponding USAMO index (10*AIME + AMC12) are placed in the pool of all AMC 12 takers, and sorted from highest to lowest USAMO index. We select the approximately 250-260 highest USAMO indices for invitation to the USAMO. We will then invite the highest USAMO index from each USA state not already represented in the group of invitees. This will nearly fill out the approximately 270 invitees to the USAMO.  If an underclassman took the AMC 12 and the AMC 10 and qualifies for USAMO through this first procedure by virtue of the AMC 12 score, then done. That is, a young student may not “opt down” to the USAJMO, we want students to attempt at the highest level for which they qualify.

The AMC 10 score and the AIME score and the corresponding USAJMO index (10*AIME + AMC 10) are placed in the pool of all AMC 10 takers, and sorted from highest to lowest USAJMO index. We select the approximately highest 230 highest USAJMO indices for invitation to the USAJMO. The one exception is that if a student takes the AMC 10 ONLY, and then scores 11 or better on the AIME we will call that special exceptional unanticipated ability and invite to the USAMO. We expect this to be about 5 students nationally.

Frequently Asked Questions about the USAJMO:

Q.  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 2010.  Of course, the precise value will depend on the variability in difficulty of  the 2010 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 1 problem from an overall average.

Q.  Is it true that If a student participates in the AMC12, then he/she wouldn't qualifiy for the USAJMO?

It depends on the AMC 12 score. If a young student (10th grade or below) takes the AMC 12 and qualifies for the AIME on the AMC 12, and then qualifies for the USAMO on the basis of the AMC 12 and AIME, then the student will be invited to the USAMO rather than the USAJMO.

However, there could be a situation where a student takes the AMC 10 and the AMC 12 and qualifies for the AIME by the AMC 10, and not by the AMC12, and then on the basis of the AMC 10 and AIME qualifies for the USAJMO. Such a student would be invited to the USAJMO. The fact that a young student did attempt the AMC12 but did not qualify for USAMO would NOT make a difference in selection for the USAJMO.

If a young student (10th grade and below) takes ONLY the AMC 12, and then for whatever reason does not qualify for the USAMO (either did not qualify for the AIME, or did take the AIME, but AMC 12 and AIME together did not qualify for the USAMO), then the student made a mistake in attempting tests they were not ready for, and experience shows the student would not have done well on the USAMO.

The basic idea is that a student should be invited to and take the highest level test for which they qualify.   Young students (10th grade and below) taking the AMC 12 and AIME and qualifying for the USAMO may NOT opt down to the USAJMO.

Q. Can a 10th grader or even a 9th grader lose the opportunity of being selected to JMO even though he/she may be among the top performers for AMC10?

No, see the second paragraph above. However, such a student must take the AMC 10 in order to conclusively prove they are a top performer on the AMC 10.

More information will be posted as it becomes available.