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Mathematical Association of America -- American Mathematics Competitions

AMC

FAQ - Frequently Asked Questions

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Topic Areas: General AMC 8 AMC 10/12 AIME USAMO & USAJMO MOSP

This page was last updated March 6, 2013.

General

Q. #1. I don't know about the American Mathematics Competitions. What are they? What are the different contests?
A. #1. The mission of the MAA's American Mathematics Competitions is to increase interest in mathematics and to develop problem solving through a fun competition. Teachers and schools benefit from the chance to challenge students with interesting mathematical questions that are aligned with curriculum standards at all levels of difficulty. In addition, students gain the opportunity to learn and achieve through competition with students in their school and around the world.

  • The AMC 8 is a 25-question multiple-choice contest for middle-school students in grades 8 and below. The material covered is the middle school mathematics curriculum. Topics include probability, estimation, percentages, spatial visualization, everyday applications and reading and interpreting graphs. The AMC 8 is for students in the sixth through eighth grade, although accelerated fourth and fifth graders can also take part. The AMC 8 is 25 questions in length and is multiple choice with no penalty for guessing. The contest takes only 40 minutes. A student's score is the number of problems correctly answered. The AMC 8 is administered in schools in November.
  • The AMC 12 covers high school mathematics, and is for students in high school who are under 19.5 years of age. The AMC 10 covers mathematics normally associated with grades 9 and 10 and is for students under 17.5 years of age who are not enrolled in grades 11, 12 or equivalent. Both contests are given in a convenient 75-minute interval, is 25 questions in length, with approximately 12 questions in common to both contests. The AMC 10 and AMC 12 are administered in schools in February.
  • The American Invitational Mathematics Examination (AIME) is a 3-hour integer answer contest. Students will qualify for the AIME and can participate in the AIME only they score 120 or above on finish in the top 2.5% of the AMC 10, or if a student scores 100 or above or finishes in the top 5% of the AMC 12. The AIME is administered in schools in March.
  • The USAMO is a six question, two day, 9 hour essay/proof examination. The Junior Mathematical Olympiad or USAJMO contest better meets the level of young students. The USAJMO new contest bridges the computational solution process of the AIME and the proof orientation of the USAMO. Both are administered the last week of April. All problems can be solved with pre-calculus methods. Approximately 270 of the top scoring AMC 12 participants (based on a weighted average) are invited to take the USAMO. Approximately 230 of the top scoring AMC 10 participants (based on a weighted average) are invited to take the USAJMO. U.S. citizens and students legally residing in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO.

Q. #2. All the problems seem really difficult. What should I do to learn how to solve them?
A. #2. We recommend studying the problems and solutions from previous tests. These previous tests are available from the AMC at http://amc.maa.org/d-publication/publication.shtml

Q. #3. What books should I buy to study from or to improve my scores?
A. #3. There are many fine books to study. We suggest you start by looking through the Problem Books Section at the MAA Bookstore. Currently, the Contest Problem Books Volumes I - IX catalog all the AMC contest problems from 1950 to 2007 and these books are a good place to start. Another suggestion is to use the search and recommendation features of Amazon.com.

Q. #4. Who can take the AMC contests?
A. #4. Any student in any registered school who meets the respective age/grade restrictions for the AMC 8, AMC 10 and AMC 12 may take the respective contests. Students may take the AIME after qualification by being in the (approximately) top 2.5% of scorers on the AMC 10 and the (approximately) top 5% of scorers on the AMC 12. The USAMO is restricted by invitation to students attending school in the United States or Canada and citizens of the United States living abroad. The only requirement for participation in the AMC 8, AMC 10 and AMC 12 is registration by the participating school.

Q. #5. How young can a person start in the AMC program?
A. #5. Students can begin at any age that they and their parent/teacher/mentor believes them to be ready respectively for the AMC 8, AMC 10, or AMC 12. Students as young as 8 have participated in the AMC contests.

Q. #6. What are the tests that lead to the United States of America Mathematics Olympiad (USAMO) and USA Junior Mathematical Olympiad (USAJMO)?
A. #6. The AMC 8 is a standalone contest with benefits of its own (listed in the AMC 8 section of the FAQ). The path to the USAMO and USAJMO begins with either the AMC 10 or AMC 12. Approximately the top 2.5% of AMC 10 students and top 5% of AMC 12 students qualify to take the American Invitation Mathematics Examination (AIME). Students with the top 270 10*AIME + AMC 12 scores are then invited to take the USAMO. The 230 students with the 10*AIME + AMC 10 scores are then invited to take the USAJMO. Taking it a step farther, the top 12 students named USAMO winners take the Team Selection Test (TST) to determine the 6 member United States International Mathematics Olympiad team.

Q. #7. What if my school does not offer the AMC tests?
A. #7. Urge your principal, math teacher, gifted education coordinator or anyone else you can think of at your school to help your school register for the contest. If your school doesn’t offer the AMC tests, then one option would be to offer the tests to your school. You could offer to pay for the registration and material cost for the school, making it hard for them to refuse. Organize a math club, or get the existing Math Club to sponsor and fund the registration for the contest. Please make arrangements for your school to register as we must send the contest materials to the school directly. Some colleges and universities also host the contests, particularly the “B” date of the AMC 10/12. Check our web pages for a list of participating Institutions of Higher Learning.

Q. #8. How can I get all my scores from past years if our school didn't keep everything?
A. #8. Write a letter or an email to the AMC office with your request. Our postal address and our email address are on all of our literature.

  • Be sure to specify your name, exactly as it was used on the contest, the years that you took the contests, which contest you took, the name of the school where you participated (the school’s CEEB will help us look it up faster, if you know it), the city, the state and the Zip/Postal Code.
  • Requests for scores are answered only for the student who took the test and received the scores, their parent/guardian, or school counselor.
  • Please allow up to two weeks for an answer.

Q. #9. Where can I get past AMC papers and solutions?
A. #9. You can order copies of problem papers and solutions directly from the AMC office. See http://amc.maa.org/d-publication/publication.shtml
You can also order CDs that have all the AHSMEs from 1950 - 1974 (the AHSME Volume I CD, item 9) and the AHSMEs from 1975-1999 (the AHSME Volume II, item 10) and a CD that has all the AIMEs from 1984 and all the USAMOs from 1972 on, item 11. 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 2009. We have not yet added the 2009 -2010 contests.
You can find the order form here: http://amc.maa.org/d-publication/publication.shtml

Q. #10. How do we get our organization (home schools, learning centers, testing center, etc.) involved in the AMC contests?
A. #10. We prefer to offer our contest to public schools, a few government accredited private schools, colleges and universities. Before allowing other organizations to register for the contests, we would like to do further research about your academic structure. In order for us to do the required research, please provide American Math Competitions with complete information about your organization, including:

  • Organization Name
  • Contact Person
  • Email Address
  • Complete Address, City, State and Zip
  • Accreditation
  • Student Population
  • Website
  • Also include any other information helpful in our research.

Please allow 4 to 6 weeks for the research to be complete and a decision or determination to be made. You will be contacted by email.

Q. #11. Could you please clarify how the Gold, Silver and Bronze medals (Intramural school awards) are awarded?
A. #11.

  • To earn a medal requires taking the same test consecutively: AMC 10 or AMC 12
  • There are no medals for the AMC 8
  • Earning top place on the AMC 8 Middle School Contest does not qualify you for earning a consecutive medal on the AMC 10 or AMC 12
  • Earning top place on the AMC 10 does not qualify you for earning a consecutive medal on the AMC 12.
  • Awards are earned in consecutive years, not consecutive tests, so if a student earns a top score in 2005 on the AMC 10B, and earns a top score on the 2006 AMC 10A and AMC 10B, they would receive 2 Bronze medals. If in 2007 they receive the top score on only the AMC 10A they would receive 1 Silver Medal. Then if in 2008 they earn the top score in both the AMC 10A and AMC 10B they would receive 2 gold medals.
  • All top scores do not have to be at the same school as long as the student is the top score at the school they are currently attending, they will earn the appropriate award. The challenge to us comes with matching a student name from two different schools, and we generally need to be told. For example: we would have trouble matching top scorer Suzie Quezy at Lincoln High School in 2007, with the name Suzie Quezy at Omaha Central in 2005 and sometimes we know a student has moved (because the parents call us) but most of the time we don't. There are many similar names that have no relation to each other, even within the same school, let alone across the country, so generally we need to be told.

In General:

  • If you take one of the high school contests (AMC 10 or AMC 12) in either middle school or high school, and you are the top student, you receive a pin (first year top award for a specific contest).
  • If in the second year in a row you take the same contest and are again the top student, you receive a bronze medal ( 2nd year top award for a specific contest).
  • If in the third year in a row you take the same contest and are again the top student, you receive a silver medal ( 3rd year top award for a specific contest).
  • If in the fourth year in a row you take the same contest and are again the top student, you receive a gold medal ( 4th year top award for a specific contest).
  • If in the fifth year in a row you take the same contest and are again the top student, you receive a another gold medal.

In this way it is possible for one person to earn top honors in a school every year they take a specific contest.

  • If they start in 6th grade winning top school honors for the AMC 12 there would be 7 first place finishes. They would have received a pin, a bronze medal, a silver medal, and 4 gold medals.
  • If they start in 6th grade winning top school honors for the AMC 10 there would be 5 first place finishes on the AMC 10. They would have received a pin, a bronze medal, a silver medal, and 2 gold medals. Then they would have to take the AMC 12, and they would receive 2 first place finishes, but the tally starts over again, and they would receive a pin and a bronze medal for those two years

Q. #12. What AMC 12 (or AIME) score do you need to get into University X
A. #12. From the February 14, 2006 blog of Ben Jones, in Admissions at MIT: "A good AIME score will certainly help you. I can't give you an exact number because it depends on how it fits into the overall context of your application, but you should report any AIME scores to us - they can never hurt you.''

Q. #13. Do you have any philosophical advice for students, parents and teachers about the AMC contests?
A. #13. Here are some principles that we think are useful advice.

  1. Remember, the process is not about you or about "notching your belt" with accomplishments and honors. The contests are to provide high quality, challenging math problems aligned with the high school curriculum. The purpose is to increase interest in mathematics and to develop problem solving through a fun competition. We aim to challenge students with interesting mathematics questions at all levels of difficulty. This gives students the opportunity to learn and achieve through competition.
  2. Teachers and parents should help students prepare but let the students perform at the appropriate level and take pleasure in solving challenging mathematics problems.
  3. Encourage students to do their own preparation at their own pace.
  4. Prepare students for occasional disappointment and discouragement. The contest problems are often much harder than the math that is typically covered in school.
  5. Do not let stereotypes or misguided information steer students away from either studying for the contests or pursuing other additional interests that they may have.
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AMC 8

Q. AMC 8 #1. What score do you have to get on the AMC 8 to be invited to take the AMC 10?
A. There is no invitation from the AMC 8 to the AMC 10 or AMC 12, Rather, with the AMC 8 Reports we send an AMC 10/12 information brochure, and an AMC 10/12 registration form to the Contest Manager of ALL schools which participate in the AMC 8. No school or student needs a special invitation, nor is any minimum score required. The AMC 10 and AMC 12 are open competitions. Specifically, in the AMC 8 report which is sent to ALL participating schools is the following message:

"An AMC 10/AMC 12 Invitation Brochure has been included in this mailing. ... Any of your students may participate in the AMC 10/12. High scoring AMC 8 students should find the AMC 10 interesting and instructive."

Q. AMC 8 #2. What’s covered on the AMC 8?
A. The material covered is the middle school mathematics curriculum. No problem requires the use of algebra or a calculator. This includes, but is not limited to, such topics as:

  • Probability
  • Estimation
  • Percents
  • Elementary geometry including the Pythagorean Theorem
  • Spatial Visualization
  • Everyday Applications
  • Reading/Interpreting Graphs

Q. AMC 8 #3. What calculators are allowed?
A. The 2007 AMC 8 was the last exam to allow the use of a calculator. All subsequent exams at all levels do not allow calculator usage. No problems on the contest require the use of a calculator.

Q. AMC 8 #4. What accommodations for students with disabilities are there?
A. For the AMC 8 students with learning disabilities we allow a 70-minute time allowance to take the AMC 8. The time limit set by the Committee on the American Mathematics Competitions for visually impaired students is also 70 minutes. Please note that a teacher or a school administrator may read the questions to the student and mark the answers as directed by the student. Braille and Large Print exams are available at an additional cost. Note that since we only order exactly the number of Braille and Large Print tests that we need, orders for them must be received no later than three weeks prior to the contest date. Please email us at amcinfo@maa.org before October 15.

Q. AMC 8 #5. What accommodations are there for English Language Learners?
A. English Language Learners may use a book or dual-language nontechnical dictionary between their native language and English. A student may use the dictionary only the first time that he/she takes the AMC 8. The dictionary must be given to the school contest manager to examine and retain for the 24-hour period preceding the test. The proctor must announce to other students that the student(s) has/have been given special permission to use the dictionary during the contest.

Note that we offer the AMC 8 Contest in Spanish, see the Registration Form for details.

Q. AMC 8 #6. Who can proctor the contest?
A. The proctoring of the AMC 8 contest should be by:

  1. In the first preference, a math teacher at the registered school
  2. In the second preference, a teacher or administrator at the registered school
  3. In the third preference, a college or university teacher of mathematics or a responsible adult not associated with or related to any of the participants who is a math club or team coach for the group of participants.
  4. In the fourth preference, a responsible adult not associated with or related to any of the participants such as librarian, clergy, etc.
  5. The proctoring of the contest must take place in a public building, (e.g. school, library, college or university, church).
  6. The proctor should not be related to any of the participants.

Q. AMC 8 #7. Why take the AMC 8? It’s a one shot test, so what’s the reward?
A. The AMC 8 can discover mathematical talent at a time when it really matters and encourage those students to continue on to the higher level tests. Furthermore, the AMC 8 has recognition and awards for schools and individual students as listed in the Teachers’ Manual, for example - School Certificate of Honor — awarded to schools with a team score (AMC 8, top 3 students scores) of 66 or greater.

  • School Certificate of Merit — awarded to schools with a team score (AMC 8, top 3 students scores) between 50 and 65, inclusive.
  • Certificate of Distinction — is given to all students who receive a perfect score.
  • AMC 8 Winner Pin — given to the student(s) in each school with the highest score.
  • Certificate for Outstanding Achievement — the top three students in each of your assigned sections will receive, respectively, a gold, silver, or bronze certificate. In case of a tie, additional certificates will be included with your results.
  • AMC 8 Distinguished Honor Roll Certificate — given to all students who score in (approximately) the top 1%.
  • AMC 8 Honor Roll Certificate is given to all students who score in (approximately) the top 5%.
  • AMC 8 Achievement Roll Certificate — given to all students in 6th grade and below who score in (approximately) the top 40%. 15 points or more.
  • A Certificate of Participation is included in this Teachers manual, and will be included in your school results. This may be reproduced and given to the other students so that every student taking the AMC 8 will receive recognition. An Order Form will be included with your results in case you wish to purchase a set of these Certificates.
  • Achievement Award Pins, Certificates of Merit, t-shirts, and neckties are available for purchase if your school wishes to recognize other outstanding students. Ordering information for these awards will be sent along with your school’s results.

Q. AMC 8 #8. When do we get official scores and reports for the AMC 8?
A. The AMC office will begin mailing official scores and reports in early to mid-December following the AMC 8 in late November. The precise start of mailing depends on the volume of scoring and processing and how fast schools return the forms for scoring. Most schools in the US should have results before the end-of-year holidays.

The email reports go out roughly in the order that we process the reports sent back from the schools. Processing and reporting from start to finish takes about 3 to 4 weeks. Scoring reports on 150,000 students from over 2200 schools in 50 US states, all US territories and over 30 countries outside the US takes time. Please be patient.

Note that the AMC 8 is centrally scored at the AMC office. Each school report includes the following data: 1. A list of the top 20 students in your school. 2. A report for each section with a minimum of 10 students. This report lists the score of each student. 3. One combined report for all sections with fewer than 10 students. 4. Tables of Item Difficulty for the participants in your school. 5. A "next year" AMC 8 Registration Form for AMC 8 School Contest Managers who wish to register before the beginning of the next school year. 6. A "next year" AMC 10/AMC 12 Brochure will be included with your results. 7. The summary of results and awards will include the names of the top-scoring students and a listing of the national award winners and will be posted on our web site each year.

Q. AMC 8 #9. What if I don't receive my official scores and reports for the AMC 8?
A. If you do not receive your current year AMC 8 school report of results by mid-January following the AMC 8 administration in late November please call the AMC office at 800-527-3690 or email amcinfo@maa.org

Q. AMC 8 #10. Can the contest manager provide unofficial scores?
A. Some students might wish to keep a personal record of their answers by circling their answers on the contest booklet before they are marked on the form. This procedure is acceptable provided it does not consume too much time. However, the official answers will be the ones blackened on the answer form.

After the contest manager has delivered all of the Answer Forms to the school office to be mailed, the manager may discuss the contest and solutions with your students. Remember that there will be schools taking the contest in other locations at different times, and some will be taking the contest on other “window” dates, which are currently extend for the next 7 days following the official contest date. a. Inform the students that the contest and solutions may not be discussed with anyone outside of their contest administration either orally, via email, internet, copier or media of any type until after the contest administration period. b. The contest booklets must be collected from the students. They may be returned after the contest administration period.

Q. AMC 8 #11. How do I make a request for a rescore of my answer forms?
A. Use the form included in the Teachers' Manual. There is a $10.00 charge for each student answer form rescored. The official answers will be the ones blackened on the answer form. All student answer forms returned for grading will be recycled 80 days after the AMC 8.

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AMC 10/12

Q. AMC 10/12 #1. What score do you have to get on the AMC 8 to be invited to take the AMC 10?
A. There is no invitation from the AMC 8 to the AMC 10 or AMC 12, Rather, with the AMC 8 Reports we send an AMC 10/12 information brochure, and an AMC 10/12 registration form to the Contest Manager of ALL schools which participate in the AMC 8. No school or student needs a special invitation, nor is any minimum score required. The AMC 10 and AMC 12 are both open competitions. Specifically, in the AMC 8 report which is sent to ALL participating schools is the following message:

"An AMC 10/AMC 12 Invitation Brochure has been included in this mailing... Any of your students may participate in the AMC 10/12. High scoring AMC 8 students should find the AMC 10 interesting and instructive."

The AMC 10 is significantly more difficult than the AMC 8. Teachers should evaluate the maturity of a specific student before suggesting participation. See FAQ AMC10/12 #9 as it would apply to young students.

Q. AMC 10/12 #2. What is the frequency of different types of problems on the AMCs?
A. In the AMC 10/12 Math Club Package, we have a chart of problem type frequency by year using the categories from the NCTM Standards
AMC 10 NCTM Standards Avg 02A 02B 03A 03B 04A 04B 05A 05B 06A 06B 07A 07B 08A 08B 09A 09B total
Algebra 6.8125 8 13 5 6 7 7 2 5 5 4 7 3 8 9 9 11 109
Connections 0.125 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2
Data and Probability 2.1875 1 1 3 1 2 1 2 6 4 2 0 5 1 4 1 1 35
Geometry 8.1875 9 5 6 7 9 10 8 5 6 10 9 12 9 6 10 10 131
Measurement 0.6875 0 0 0 0 1 0 1 0 2 4 0 0 2 1 0 0 11
Number Operations 5.25 6 6 10 9 4 6 8 5 3 2 4 4 5 4 5 3 84
Problem Solving 1.75 1 0 1 2 2 1 2 4 5 3 5 1 0 1 0 0 28
Totals 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 400
                                     
AMC 12 NCTM Standards Avg 02A 02B 03A 03B 04A 04B 05A 05B 06A 06B 07A 07B 08A 08B 09A 09B total
Algebra 6.9375 8 9 4 6 6 5 4 9 5 3 10 5 10 10 8 9 111
Connections 0.125 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2
Data and Probability 1.6875 1 2 2 3 1 3 2 2 1 5 0 3 0 1 0 1 27
Geometry 8.75 8 5 10 11 10 9 8 7 6 7 10 12 8 10 10 9 140
Measurement 0.5625 0 0 0 0 0 0 1 0 1 4 0 0 2 1 0 0 9
Number & Operations 5.375 7 7 7 5 7 6 6 6 4 4 2 4 5 3 7 6 86
Problem Solving 1.5625 1 2 2 0 1 2 2 1 8 2 3 1 0 0 0 0 25
Totals 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 400

Note 1: AMC problems often involve several topics. What we have labeled as Number Theory, you might
consider as something else. Likewise for probability and trigonometry.
Note 2: Many problems can be worked in several ways, e.g. with trig functions and also without.

Q. AMC 10/12 #3. When will the AMC 10/12 results come back by email?
A. It takes about 3 weeks after the contest date to score and report the AMC 10 and AMC 12 contests. The AMC office will send results by email (if provided on the registration form) and first class mail as soon as the answer forms are scored. If you have not received your results from our office within 30 days after the AMC 10/AMC 12 please contact us to verify that your answer forms were in fact received. The email report is sent to the school contest manager whose email is listed on the registration form used to order the contest. The official hard copy report is postal mailed to the address on the registration form soon after the email is sent. Reports with AIME qualifiers are mailed first, followed later by school reports with no AIME Qualifiers.

Q. AMC 10/12 #4. What’s covered on the AMC 10?
A. The AMC 10 covers mathematics normally associated with grades 9 and 10. To challenge students at all
grade levels, and with varying mathematical skills, the problems range from fairly easy to extremely difficult. Approximately 12 questions are common to the AMC 10 and AMC 12. The AMC 10 assumes knowledge of elementary algebra; basic geometry knowledge including the Pythagorean Theorem, area and volume formulas; elementary number theory; and elementary probability. What are excluded are trigonometry, advanced algebra, and advanced geometry. We recommend students study prior year copies of the AMC 10 contest and solutions. You can purchase a CD from the AMC with all the previous decade's contests to see what the AMC 10 contest is like.

Q. AMC 10/12 #5. What’s covered on the AMC 12?
A. The AMC 12 covers the high school mathematics curriculum, excluding calculus. To challenge students at all grade levels, and with varying mathematical skills, the problems range from fairly easy to extremely difficult. Approximately 12 questions are common to the AMC 10 and AMC 12.

Q. AMC 10/12 #6. Are logarithms covered on the AMC 10?
A. Since logarithms are not usually considered part of the grades 9 and 10 mathematics curriculum, and are usually considered part of advanced algebra, logarithms do not appear on the AMC 10.

Q. AMC 10/12 #7. What calculators are allowed on the AMC 10 and the AMC 12?
A. Calculators are not allowed on the AMC 10 and AMC 12 contests. The 2007 AMC 10 and 12 were the last contests to allow the use of a calculator. All subsequent exams at all levels will not allow calculator usage.

Q. AMC 10/12 #8. What accommodations for students with disabilities are there?
A. For the AMC 10/12 the time limit set by the CAMC for students who are visually impaired or learning disabled
is 120 minutes. A teacher or a school administrator may read the questions to the student and mark the
answers as directed by the student. Braille and Large Print exams are available at an additional cost.

We only order the number of Braille and Large Print tests that we need, so orders for them must be received
no later than three weeks prior to the contest date. Please see the registration form for more information on ordering Braille and Large Print tests.

Q. AMC 10/12 #9. What accommodations are there for English Language Learners?
A. Students learning “English as a Second Language” (ESL) may use a book dual-language non-technical dictionary between their native language and English. A student may use the dictionary only the first time that he/she takes the AMC 10/AMC 12. The dictionary must be given to the school contest manager to examine and retain for the 24-hour period preceding the contest. The proctor must announce to other students that the student(s) has/have been given special permission to use the dictionary during the contest. The AMC 10 and
AMC 12 are also available in Spanish and French. Please see the registration and order form for more
information on obtaining these materials.

Note that we offer the AMC 10 and AMC 12 Contests in Spanish and in French, see the Registration Form for details.

Q. AMC 10/12 #10. Should I take the AMC 10 or AMC 12?
A. The answer probably depends as much on the personality of the student as on the mathematical ability and training of the student. Some students can take a very difficult examination, not score as well as they had expected, and take the experience as incentive for future study. The same experience for another student could be devastating and lead to a decreased interest in mathematical problem solving, and perhaps even in the
study of mathematics. The latter situation should, of course, be avoided at all cost. When advising students regarding the choice of contests, please keep in mind that the primary goal of all the American Mathematics Competitions contests is to provide students with a positive experience in mathematical problem solving. The awards that can sometimes accompany this experience are nice, but distinctly secondary.

Q. AMC 10/12 #11. Can a student take both contests?
A. Yes, as long as a student is eligible to take the appropriate contests. That is:

  • A 10th grader or below can take the AMC 10 A and the AMC 10 B
  • A 10th grader or below can take the AMC 10 A and the AMC 12 B
  • A 10th grader or below can take the AMC 12 A and the AMC 10 B
  • A 10th grader or below can take the AMC 12 A and the AMC 12 B
  • An 11th or 12th grader can take the AMC 12 A and the AMC 12 B

However, in order to do this the school would have to register for both dates and order contest bundles to
have the contests on hand.

Q. AMC 10/12 #12. Who can proctor the contests?
A. The proctoring of the AMC 10 and AMC 12 contest should be by

  1. In the first preference, a math teacher at the registered school
  2. In the second preference, a teacher or administrator at the registered school
  3. In the third preference, a college or university teacher of mathematics or a responsible adult not
    associated with or related to any of the participants who is a math club or team coach for the group of participants.
  4. In the fourth preference, a responsible adult not associated with or related to any of the participants such as librarian, clergy, etc.
  5. The proctoring of the contest must take place in a public building, (e.g. school, library, college or university, church).
  6. The proctor should not be related to any of the participants.

Q. AMC 10/12 #13. Can a school register for both dates?
A. Yes, but the school will have to pay the appropriate registration fee for each contest date, and purchase the contest bundles for each date. The problems on the A and B contest dates are different. Note that
approximately 12 questions are common to the AMC 10 and AMC 12 on a single date, so a student cannot take the AMC 10 and the AMC 12 on the same date.

Q. AMC 10/12 #14. What would stop a school from registering for both contests?
A. Nothing, except the cost in registration fees and the time to administer the contest on two separate days.

Q. AMC 10/12 #15. What if a school registers for one date, then later wants to change the registration to the other date?
A. Although we discourage a change in date because of the extra handling and potential confusion,
nevertheless a change in date is permitted, before the contest materials are sent, as long as time permits according to the registration schedule and as long as the corresponding change in registration fee (plus any change in bundles) is paid. Increases must be paid at the time with charge card, both to expedite changes
and to eliminate billing costs.

Q. AMC 10/12 #16. What do I do in the event of school closure on the day we have registered to take the Contest A date?
A. In the event school is closed due to weather or any other insurmountable situation, you will be given the option to register your school for Contest B (registration fee plus bundles), or you may elect to give Contest A
on a later date as an unofficial administration. The school contest manager MUST contact the AMC office
promptly to make appropriate arrangements. We do not have access to all school closings in the country and cannot automatically roll your registration forward. Please note that unofficial participation means students will not be eligible for national awards, nor will their scores qualify them for AIME. All schools taking Contest A unofficially will still receive a school report and all intramural awards.

Q. AMC 10/12 #17. Isn’t it unfair to allow schools and students to take the contests twice within two weeks
time?
A. Not really. The contest problems for 60 years of high school contests are available in books and in copies of
old contests. The problems are basically the same from contest to contest, so there is plenty of common
material to study. The addition of another 25 contest problems with two more weeks to study is not a
significant advantage for any student. Furthermore, it is the philosophy and purpose of the AMC to encourage students to engage in significant mathematical problem solving. If we can do this by offering more contests on additional dates, then we are better meeting our goal.

Q. AMC 10/12 #18. What if a student is sick or absent or at another school activity on the date of the A contest? Can the student take the B contest?
A. Yes, if the school has registered for the B contest date and has contest bundles available for the contest, a student can take the second contest.

Q. AMC 10/12 #19. Why do you charge registration fees for both contest dates?
A. Because we have to create, print, handle, store, ship, score, summarize and send intramural awards for an entirely distinct and new set of problems for both contests, our production and fulfillment costs are proportionately increased. In addition, in order to avoid confusion and errors in administering the two contests, we send the B contests by expedited shipping to arrive after the A contest has been given. The expedited shipping costs significantly more.

Q. AMC 10/12 #20. How can I find the answers or solutions to the questions on the current AMC 10 and
AMC 12?
A. Your contest manager has a Contest Manager's Envelope with the solutions to all the problems on the
AMC 10 and AMC 12 contests. Of course, the correct letter choices are also included. Please ask your contest manager to see the printed solutions.

Q. AMC 10/12 #21. What if I believe my answer was scored incorrectly?
A. The scoring is explained in item 4 on the front cover of every AMC 10 A, AMC 10 B, AMC 12 A, and AMC 12 B contest booklet, the item that starts with "SCORING:" Your first step should be to ask the contest manager at your school. The contest manager at the school receives an e-mail from the AMC office containing a
spreadsheet (a .CSV file, actually) showing every answer recorded by the AMC scanner for every participating student at the school. If the spreadsheet does not satisfy you, step two would be to ask your contest manager about the current rescoring options. In the AMC 10/12 Teachers' Manual is a rescoring request form to fill out
and fax or mail to the AMC office along with a $10 rescoring fee.

Q. AMC 10/12 #22. Why does it cost to have an answer form rescored?
A. It costs the AMC office about an hour of staff time to rescore a sheet. First we have to locate your individual answer sheet from over 200,000 that we have stored on shelves in our storage area. Then we hand-score it,
and compare to the records we have in the database. We examine the answer sheet very closely to determine
if the scanner made an error. Then we compose an answer and send a reply to you. The fee does not cover the staff time this requires. And in our experience, we have not yet found a case where it was our mistake, a poorly erased or poorly bubbled entry is almost always the cause.

Q. AMC 10/12 #23. Has the AIME qualification level for the AMC 10 always been 120 points?
A. From 2000-2003 the AIME qualification level from the AMC 10 was set at the top 1%. After 4 years, the
contest creation committee members felt that they had enough experience in setting the test that we could
use a fixed level of 120 (or the top 1%, whichever is lower). In 2011, the percentage was changed to the top 2.5% on the AMC 10.

Q. AMC 10/12 #24. What is the intention, purpose, and history of development behind the AMC 10, the content
in the AMC 10, and the scoring rules used in the AMC 10?
A. Here is a "Message from the AMC 10 Chair" on page 14 of the "2008 Summary of Results and Awards", summarizing the philosophy behind the AMC 10,

"The AMC 10 test was developed to provide a better experience in mathematical problem solving for students
in the lower high school grades. In years prior to 2000, students in these grades had to take a test that
included problems on topics such as logarithms and trigonometry, subjects that they had not yet studied. The AMC 10 examination contains only problems based on subject material that students in ninth and tenth grade have
likely seen, while still providing them with a challenging experience.

Our goal for the AMC 10 has been to design the contests so that the average student can work on between 15 and 20 problems and get at least 10 of those correct. This would give an average score of between 72.5 and
85, since a student receives 6 points for each correct problem and 1.5 points for each unanswered problem.
The AMC 10 and AMC 12 tests have common problems, which has the advantage of permitting students taking the AMC 10 to compare their solutions with the students taking the AMC 12, and allows teachers to better identify excellent problem solvers at a young age. However, we are concerned that if we predictably have a
large number of common problems on the exams, it might encourage younger students to take the AMC 12
before they are ready, since a larger proportion of students taking the AMC 12 qualify for the American Invitational Mathematics Examination (AIME). As a consequence, you will likely see an unpredictable fluctuation
in the number of common problems from a minimum of about nine to a maximum of about thirteen."

Q. AMC 10/12 #25. Why is the AIME qualifying score for the AMC 10 set at 120 points (or the top 2.5%, whichever is more inclusive)?
A. A new policy for AIME qualifying was introduced beginning with the 2000 AMC examinations. Those students taking the AMC 12 and scoring over 100 qualify, as usual, as do those students scoring in the top 5% on the
AMC 12 examination. This new policy is more equitable since it guards against the possibility of a particularly difficult examination, one on which the scores are uniformly lower than normal, skewing the number of AIME qualifiers. Beginning with the 2004 contest we instituted a similar qualifying system for the students taking the AMC 10 contests. Students scoring in the top 2.5% of either AMC10 qualify for the AIME, as well as all those who score 120 or more on one of these contests. The requirement is set higher for AMC 10 qualifiers for two reasons:

  • First, the AIME can be quite intimidating, and we do not want young students to be discouraged by poor performance on this examination.
  • Second, we would like to ensure that any student qualifying for the AIME by virtue of placement on the
    AMC 10 would likely also qualify for the AIME in subsequent years when taking the AMC 12. It could be
    very disappointing for a student to be an AIME qualifier in grade 10 but not in subsequent high school
    years.

By restricting the number of AIME qualifiers from the AMC 10 to about the top 2.5%, we hope not to exclude any very good young students for whom the AIME would be an appropriate experience, but also not put students
in a situation where they do not have much opportunity to succeed.

Q. AMC 10/12 #26. What is the rewards structure for the two contest dates?
A. A School Winner Pin is given to the student in a school with the highest score on a given test date. Thus, it is conceivable that a student could win two School Winner Pins, if the school elects to administer both the A and B contests. It is also conceivable that a school could have two different School Winners if it elects to give both the A and B contests.

  • A Gold Medal is given to a student who achieves the highest score in his/her school for four consecutive years. The highest score could be on either the A contest or the B contest.
  • A Silver Medal is given to a student who achieves the highest score in his/her school for three consecutive years. The highest score could be on either the A contest or the B contest.
  • A Bronze Medal is given to a student who achieves the highest score in his/her school for two consecutive years. The highest score could be on either the A contest or the B contest. However, as a national award,
    a student can only win one Bronze Medal, even if the student was high score in 2007, and took both the A contest and the B contest in 2008 and was high score on both.
  • A. Honor Roll of Distinction Pin is awarded to the top scoring one percent of the AMC 12 A and the AMC 10A and the top scoring one percent of the AMC 12 B and the AMC 10B. A Certificate of Distinction is awarded
    to all students who qualify for the AIME.
  • A Certificate of Achievement is awarded to the students in grade 10 or below with a score of 90 or above
    on the AMC 12 A or AMC 12 B.
  • A Certificate of Achievement is awarded to the students in grade 8 or below with a score of 90 or above on the AMC 10 A or AMC 10 B.
  • A Certificate of Honor is awarded to schools with a team score of at least 400 on the AMC 12 A or AMC 12 B. Thus it is conceivable that a school could receive two Certificates of Merit if it chooses to register for both
    the AMC 12 A and AMC 12 B contests.
  • A Certificate of Merit is awarded to schools with a team score of at least 300 on the AMC 12 A or AMC 12 B. Thus it is conceivable that a school could receive two Certificates of Merit, or a Certificate of Honor and a Certificate of Merit if it chooses to register for both the AMC 12 A and AMC 12 B contests.

Q. AMC 10/12 #27.  My school only offers the AMC12B. Can I go to another school and take the 12A?
A. Yes, it is true that you can take the "other-date" AMC contest at another school, but only in the circumstances that
(1) you have the express permission of the other school's AMC Contest Manager, and
(2) all local school regulations and permissions allow a student from one school to enter another school.  All responsibility for see that both conditions above are fulfilled falls on the student seeking alternate date.  It may be easier to get your school to administer the A-date, see Frequently Asked Question General #7 by clicking here.
We do our best to make sure AIME qualifiers are accounted for, but we do not forward school winner scores.  Also, usually the alternate school does not count your score at their school, so you can't be a school winner there either.

Q.  AMC 10/12 #28.  What is the difference in AMC 10A and 10B?
A. Both the AMC 10 A and the AMC 10 B have the same number of questions, the same scoring and the same rules for adminstration.  The only difference is that each has a distinct set of questions, although the two contests are designed to be equal in difficulty and distribution of topics.

For national and regional awards only one award will be issued based on the higher score from the A and B contests. For intramural awards it is possible to win an award for both the A and the B contest.

Q.  AMC 10/12 #29.  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.

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AIME

Q. AIME #1. Do I have to go through precalc before I take AIME?
A. No, you do not have to go through precalc before AIME. You can see from prior years' AIME contests that a
few questions with

  • complex numbers
  • trigonometric functions, graphs and identities
  • sequences and series
  • function notation occur on the AIME. A student who wishes to solve these problems or understand the published solutions needs to be familiar with these mathematical concepts. These topics are typically, but
    not always or exclusively, covered in a "precalc" course. Of course, it does not matter where or when or
    how the student learns the concepts. You should find your best learning plan and follow that.

Remember too, AMC 10, AMC 12 and AIME questions often cross course and curricular boundaries, combining ideas that occur in several courses so a particular course is neither necessary nor sufficient.

Q. AIME #2. If you take both A-date and B-date AMC tests, both have AIME qualifying scores, but one score is higher than the other, do you get
to choose which score to use with your AIME score?
A. We use the higher numerical qualifying score, wherever it came from, whatever test it was achieved on. 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 contests 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 contest administrator, has a section for students who qualified at
multiple testing sites. Please give this important information to the AIME Contest administrator, so that we can use this important information.

Q. AIME #3. Can a student take both the AIME and the Alternate AIME (AIME II)?
A. No. Students are only allowed to take one. AIME. There are no circumstances in which this may be waived.
See the AIME Teacher's Manual, Section VIII.

Q. AIME #4. What accommodations for students with disabilities are there?
A. For the AIME if one of your AIME qualified students is visually impaired and/or learning disabled, please call
the AMC office, and we will discuss the options available to you. We do not have the AIME available in Braille or large print. The time allowance for students with learning disabilities is 4.5 hours.

Q. AIME #5. What accommodations are there for English Language Learners?
A. Students learning “English as a Second Language” (ESL) may use a book dual-language non-technical dictionary between their native language and English. A student may use the dictionary only the first time that he/she takes the AIME. The dictionary must be given to the school contest manager to examine and retain for
the 24-hour period preceding the contest. The proctor must announce to other students that the student(s) has/have been given special permission to use the dictionary during the contest.

Q. AIME #6. What calculators are allowed?
A. No calculators are allowed on the AIME. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, calculators and computers are not permitted.

Q. AIME #7. How do I qualify for the AIME?
A. Students who score 100 or above or finish in the top 5% (whichever is more inclusive) on an AMC 12 or students who score 120 or above or finish in the top 2.5% (whichever is more inclusive) on the AMC 10 are
eligible to take the American Invitational Mathematics Examination (AIME). The AMC will automatically send a
copy of the first date AIME contest to the school contest manager for each student achieving a qualifying score.

Q. AIME #8. Why is it only 2.5% (120) to qualify for AIME on the AMC 10?
A. A new policy for AIME qualifying was introduced beginning with the 2000 AMC examinations. Those students taking the AMC 12 and scoring over 100 qualify, as usual, (or the students scoring in the top 5% on the AMC 12 examination, whichever is more inclusive). This new policy is more equitable since it guards against the
possibility of a particularly difficult examination, one on which the scores are uniformly lower than normal, reducing the number of AIME qualifiers. Beginning with the 2004 contest we instituted a similar qualifying
system for the students taking the AMC 10 contests. Students scoring in the top 2.5% of either AMC10 qualify for the AIME, or those who score 120 or more on one of these contests (whichever is more inclusive). The requirement is set higher for AMC 10 qualifiers for two reasons:

  • First, the AIME can be quite intimidating, and we do not want young students to be discouraged by poor performance on this examination.
  • Second, we would like to ensure that any student qualifying for the AIME by virtue of placement on the
    AMC 10 would likely also qualify for the AIME in subsequent years when taking the AMC 12. It could be very disappointing for a student to be an AIME qualifier in grade 10 but not in subsequent high school years.

By restricting the number of AIME qualifiers from the AMC 10 to about the top 2.5%, we hope not to exclude any very good young students for whom the AIME would be an appropriate experience, but also not put students
in a situation where they do not have much opportunity to succeed.

Q. AIME #9. Who can proctor the contest?
A. The proctoring of the AIME contest should be by:

  1. In the first preference, a math teacher at the school
  2. In the second preference, a teacher or administrator at the school
  3. In the third preference, a college or university teacher of mathematics or a responsible adult not
    associated with or related to any of the participants who is a math club or team coach for the group of participants.

  4. In the fourth preference, a responsible adult not associated with or related to any of the participants such as librarian, clergy, etc.

  5. The proctoring of the contest must take place in a public building, (e.g. school, library, college or
    university, church).

  6. The proctor should not be related to any of the participants.

Q. AIME #10 Where can I get copies of the previous AIME contests?
A. You can order a CD that has all the AIMEs from 1984 and all the USAMOs from 1972. 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 currently contains all the contests, AMC 8,
10, 12, AIME and USAMO from 2000 to 2009.

Q. AIME #11. When we will get the AIME results?
A. We first need to receive the envelopes with answer forms from the schools. In spite of asking schools to
return the envelopes quickly, some schools mail them and it still takes a week to 10 days after the AIME contest to receive answer forms. After that, we need to check the envelopes in as being received, count the answer sheets inside against the number we sent out, then scan, record, match students' AMC and AIME scores, tabulate and do the statistical analysis. After that we do a preliminary analysis of USAMO indices. By that point, it is time for AIME II, and we do everything all over again for the AIME II results. Finally, we make the USAMO selection, and include the results in the AIME report. Therefore, you can expect that the AIME results will not be available until about 3 to 4 weeks after the AIME date.

Q. AIME #12. What is the deadline for ordering the AIME II, also known as the AIME Alternate, contest?
A. As soon as possible after administration of the AMC 10 and AMC 12 contests. Read the AIME Teacher's
Manual, Section VII for the exact deadline date each year. It is approximately one week before the AIME II date, but varies with the calendar, weekends, holidays, etc.

Q. AIME #13. What is the procedure for taking the AIME II or alternate test date if my school only offers the
first one?
A. Most schools offer the contest on the AIME-I date, because it's the simplest, least expensive, and most straightforward solution. If your school offers you the contest on the AIME-I date, the AMC office strongly suggests that you take it then unless you have a very compelling reason to do otherwise.

Q. AIME #14. Are some schools forced to take the AIME II, in that the B exam scores will not be processed in
time to permit administration of the AIME I?
A. No. That is false, since the AMC Office works very hard to finish processing and sending in time for all schools which desire to administer the AIME I are able to do so.

Q. AIME #15. What score do you need on USAMTS to qualify for AIME?
A. The minimum score required to qualify for AIME from USAMTS is a score of 54 out of 60 possible points
(90% of the possible points) after 2 rounds of USAMTS. In computing the USAMO index, we use the percent on the USAMTS (after two rounds) plus 10 times the AIME score. For example, if you scored 54 on the USAMTS, (90\% of a possible 60 points after two rounds), and get a score of 11 on the AIME, then your index would be 90 + 10*11 = 200. If you took both the AMC 10 or AMC 12, and the USAMTS your index is the maximum of the two ways calculating the index.

Q. AIME #16. What the cutoff score on the AMC10 and AMC 12 to get to the AIME in past years?
A. Look in the AMC 12 Archive, under General Statistics. The record is complete back to 2001. Here's how to find it: Go to the AMC page, then click AMC 12, then click Archive, then chose a year to look at the General Statistics.

Q. AIME #17. How many people qualify for USAMO and AIME each year?
A. Detailed statistics for each year are available in the Archives section of our website. Go to the AMC page,
then click AIME, then click Archive, then chose a year to look at the General Statistics.

Q. AIME #18. What are some good books to study from for the AIME?
A. Consider purchasing the AIME and USAMO CD from the AMC. See the answer to Frequently Asked Question AIME #10. Consider the Contest Problem Books I-IX and all the other books in the Problem Books category available from the MAA on-line bookstore and major on-line book retailers.

Q. AIME #19. I took the AMC 10 or AMC 12 test at a college, not at my school, and i qualified. where should I
go to take the AIME?
A. The AMC office mails a sealed envelope with the AIME and the procedures for registering for the AIME II (also known as the AIME Alternate) to each location (or locations) where you qualified for the AIME. With the active knowledge and cooperation of the administering location and your regular high school and teacher (where you have daily attendance) you can take the AIME at your school. Have the college (or other administering location) send the sealed AIME envelope to your high school teacher after you have made the arrangements. Also send an email to amcinfo@maa.org to inform our office that you will be taking the AIME at the high school, not at the qualifying location. Of course, you can also take the AIME at the qualifying location, we ask that locations administering the AMC 10 and AMC 12 also accept the possibility that they may be asked to administer the AIME, should the location have qualifiers. If you qualified on the AMC 10 or AMC 12 at a different location than where you want to take the AIME, then the responsibility is yours to make sure that all involved parties (college, high school, teacher, and AMC, as well as you) know this, and cooperate to make it happen.

Q. AIME #20. 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 12 A 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 contest manager knows, and that your own school contest manager knows what you intend
doing. What AMC score you write on the AIME answer form is definitely of lesser importance. We only use that score as a weak first check on your identity. For every other purpose, we rely on our internal record-keeping.

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USAMO and USA Junior Math Olympiad (USAJMO)

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 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.

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 1 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: http://amc.maa.org/d-publication/publication.shtml see item 11 on the
form.

Don't forget all the USAMO and IMO books from the MAA. Go to maa.org 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 can 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.

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MOSP (Mathematical Olympiad Summer Program)

Q. MOSP #1. What are the rules about eligibility for MOSP regarding citizenship?
A. Generally speaking, if a student has been attending a high school in the United States for more than one
year (e.g. is not specifically an exchange student in the US for a year or less) and has a sufficiently high score
on the USAMO or USAJMO, then the student is eligible for the Mathematical Olympiad Summer Program. See the USA(J)MO Teachers' Manual, Section VIII, page 6 for more specifics.

Q. MOSP #2. What do the color groups at MOSP mean?
A. We invite high-scoring Olympiad participants in certain categories to the MOSP. The color groups are an organizational device for the AMC office to make sure we have all the categories invited and filled. Once here, using the instructors' experience and best judgment the instructors will assign students to whatever class or activity they think will benefit the student most,. There are no rigid classifications or immutable categories. Students may be instructed to mix or match by grades, experience, or MOSP test scores according to the purposes of the instructors. Daily class composition may change, even several times, over the course of 3
weeks.

Q. MOSP #3. What are the criteria for invitation to MOSP?
A: The criteria for invitation to 2011 MOSP are:

  1. Scores of 35 and higher on USAMO, and eligible (US citizenship or permanent residency)
  2. Scores of 28 and higher on the USAMO and eligible (US citizenship or permanent residency, in 9th 10th or 11th grade and not already invited in (1).)
  3. Scores of 21 on the USAMO and higher and eligible (US citizenship or permanent residency, in 9th or 10th grade, and not already selected in (1) or (2).)
  4. Scores of 28 and higher on the USAJMO, and eligible (US citizenship or permanent residency, and in 9th or 10th grade.)
  5. Scores of 14 or higher on the USAMO, or 15 or higher on the USAJMO, and eligible (U.S. Citizenship or permanent residency, female, in 9th, 10th,
    11th or 12th grade.)

Q. MOSP #4. How will the qualifications for China Girl's Math Olympiad (CGMO) proceed?
A. Pending firm commitment of funding for the additional participation at MOSP, the plan is to select about 8 to
10 high-scoring young women from both the USAMO and the USAJMO to invite to MOSP. These will be
determined in addition to invitations to young women from the USAMO Winners, the non-senior USAMO
Honorable Mentions,and high scoring 9th and 10th graders from the USAMO and USAJMO according to
previously published criteria. (Note that this is the same number of young women that were invited from the USAMO to MOSP the past couple of years, again assuming available funding.)

However until we have some experience comparing scores from the USAMO and the USAJMO we are not going
to commit to firm numbers of participants from either contest or firm score criteria from either contest. MOSP instructors, USAMO and USAJMO graders, and the USA(J)MO committee will jointly make the determination, considering quality of written solutions, difficulty of problems solved, difficulty of problems attempted,
comparison with all USA(J)MO scores and all available other scores (AMC 10, AMC 12, AIME) in order to find and train the best possible team. The selection process will be done with Student ID Numbers only, so selection will be blind with respect to name, school, region, etc.

Performance at MOSP, mostly based on the MOSP weekly tests, among all the young women at MOSP will determine the actual team that goes to the CGMO.

Q. MOSP #5. What will the selection process be for the 2012 USA International Mathematical Olympiad team?
A. Selection of the 6 team members and 2 alternates for the 2012 USA team for the International Mathematical Olympiad will be based on a combination of the following criteria:

  1.  The Team Selection for the Team Selection Test (TSTST) given in the last week of 2011 Mathematical Olympiad Summer Program.  The 2012 Team Selection Test (taken in June 2011 at the MOSP in Lincoln) will be given over 3 days, with 3 Olympiad-style problems per day, in 4-1/2 hour blocks.  From the results of this TSTST we will choose 12-18 students with the highest scores for potential team membership in 2012.
  2. These 12-18 students will take additional Olympiad-style tests taken in the 2011-2012 academic year, including the Asia-Pacific Mathematical Olympiad, usually administered on the first or second Monday in March.
  3. Potentially an additional Olympiad-level test, given in schools, in late winter.  Details on this will be announced by January 1, so that students and schools have adequate time to schedule and prepare, including finding proctors. 
  4. The 2012 USAMO score from the 41st Annual USAMO on April 24-25, 2012.
  5. The Team Selection Index will be a sum of the scores from these 3 or 4 Olympiad-level tests in 2011-2012.  Some weighting may be used to adjust for differences in contest difficulty or other factors.
  6. An ad hoc committee consisting of the MOSP Director/IMO Team Leader, MOSP Assistant Director/Deputy Leader, AMC Director, USAMO Subcommittee Chair, CAMC Chair and others appointed by the IMO Leader for the ad hoc committee will vote for the USA IMO Team membership based on the Team Selection Index using additional information including the 2012 AMC 12 Score, the 2012 AIME score and other indications including team spirit and demonstrated work ethic and study habits through 2011-2012 as evidenced by active participation in the steps 1-4.

Note that the 12-18 students attending 2011 MOSP and scoring the highest on the TSTST at MOSP will NOT need to qualify for the 2012 USAMO by taking the 2012 AMC 12 and 2012 AIME combination.  That is, there will be “automatic qualification” for USAMO by virtue of 12-18 TSTST high scores.  However, failure to take the AMC 12 and or AIME or a low score on either without adequate explanation will put a student at a competitive disadvantage in step 6.
These changes are made for the following reasons:

  1. The current determination of the team using a TST during the first week at MOSP comes very late for purchasing air-travel tickets, planning summer family schedules, obtaining visas, and registering the team with the IMO. The new schedule allows us to determine a team by early May, allowing better scheduling for all these activities and potential cost-saving by purchasing tickets earlier.
  2. The new plan will keep students at a higher level of continuous competitive preparation throughout the year, most especially in the spring leading to the USAMO.

This spreads the selection criteria over several Olympiad-level contests, so that a single day’s performance is less likely to affect a strong competitor adversely.

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