The American Mathematics Competitions (AMC)

The American Mathematics Competitions (AMC) is dedicated to the goal of strengthening the mathematical capabilities of our nation’s youth. We believe that one　　　　　　　 way to meet this goal is to identify, recognize and reward excellence in mathematics through a series of national contests called the:

• American Mathematics Contest 8 (AMC 8),
• American Mathematics Contest 10 (AMC 10),
• American Mathematics Contest 12 (AMC 12),
• American Invitational Mathematics Examination (AIME), and
• United States of America Mathematical Olympiad (USAMO).

In addition to the 5 contests listed above, we also have a summer program, and choose the final six contestants for an international competition:

• Mathematical Olympiad Summer program (MOSP), and the
• International Mathematical Olympiad (IMO)

For over 50 years many excellent exams have been prepared by individuals throughout our mathematical community in the hope that all secondary students will have an opportunity to participate in these problem solving and enriching mathematics experiences. The AMC contests are intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school. To insure this mission is served, each year the AMC solicits enrollment by mailing an Invitation Brochure to all schools in the United States teaching grades six through twelve.

HISTORICAL BEGINNING

On Thursday, May 11, 1950 the first Mathematical Contest, sponsored by the New York Metropolitan Section of the Mathematics Association of America (MAA) took place. It was given in approximately 238 schools to around 6,000 students in the New York area onl　　　　　　　y. The following exerpt is taken from the Report of the Committee addressed to that year’s participating teachers:

“The first mathematics contest sponsored by the New York Metropolitan Section of the MAA is now history. It was a lot of work getting the contest organized and finally holding it. Like all new projects, we worried about it. Would the High Schools participate? Would they like the test? Is it worth while? Will any good be produced by it? Will it be a success?”

Today, over fifty years and three generations later we can answer all of the Committee's questions with a resounding Yes! Yes! Yes! The overall success of this program can be viewed by simply looking at our growth in numbers. This year over 413,000 students in over 5100 schools participated in the AMC Contests. Another 10,000 students have qualified to participate in the AIME scheduled for late March and early April. From this qualifying round another 250 students will be invited to take the prestigous USAMO in early May.

TODAY

The AMC year begins in the fall with the American Mathematics Contest 8 (AMC 8, originally called the AJHSME - American Junior High School Mathematics Examination). The AMC 8 is for students in the sixth, seventh or eighth grade; accelerated fourth and fifth grade students also take part. It is a 25-question, 40-minute multiple-choice contest, given the Tuesday before Thanksgiving week. A student’s score is the number of problems correctly solved, there is no penalty for guessing. The material covered is the middle school mathematics curriculum. No problem requires the use of algebra or a calculator. AMC 8 Eligibility extends to any student 14.5 years of age or younger on the day of the contest, and not enrolled in grades 9, 10, 11 or 12 or equivalent. After the contest is taken in the school, the contest administrator sends AMC the answer forms, and we score, compile and send email results back to the school, usually within 3 weeks. We then follow up with a written report, accompanied by the awards for the school. Students who score 20 or better on the AMC 8 are invited to take the next set of contests, the AMC 10/AMC 12.
The American Mathematics Contest 12 (AMC 12, originally called the AHSME - American High School Mathematics Examination), is a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. The AMC 12 is designed for students in a program leading to a high school diploma, and under 19.5 years of age on the day of the contest.
The American Mathematics Contest 10 (AMC 10, added in 2000, when the names of the AMC 8 and AMC 12 were updated) is also a 25 question, 75 minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. The AMC 10 is designed for students in a program leading to a high school diploma, under 17.5 years of age on the day of the contest, and not enrolled in grades 11 or 12 or equivalent.
The AMC 12 and AMC 10 Contests are given on two different dates, (designated by the use of the "A" and "B" suffix on the contest names - AMC 12A, AMC 10A, AMC 12B or AMC 10B) about two weeks apart, in February. A student may choose to take one　　　　　　　 contest on both dates. Another words, an 11th or 12th grader may take the AMC 12 on both dates. A student in 10th grade or below may choose whether he will take the AMC 10 or the AMC 12 on each date , so a 10th grader can take the AMC 10 A and the AMC 12B, the AMC 12A and the AMC 10B, the AMC 12A and the AMC 12B or the AMC 10A and the AMC 10B. After the contest is taken in the school, the contest administrator sends AMC the answer forms, and we score, compile and send email results back to the school, usually within 3 weeks. We then follow up with a written report, accompanied by the awards for the school. AMC 12 students who rank in the top 5% nationally (or score at least 100) will qualify for the American Invitational Mathematics Exam (AIME). AMC 10 students who rank in the top 1% nationally (or score at least 120) will also qualify for the AIME.
The American Invitational Mathematics Examination (AIME), is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. It is given on two different dates, (designated by the use of the "I" and "II" suffix on the contest names - AIME-I and AIME -II) about two weeks apart, in March. The questions on the AIME are much more difficult and students are very unlikely to obtain the correct answer by guessing. As with the AMC 10 and AMC 12 (and the USAMO), all problems on the AIME can be solved by pre-calculus methods. Unlike on the AMC 10 and the AMC 12 a student can onl　　　　　　　y take the AIME onc　　　　　　　e, and the student/school must make the decision as to whether they will take the AIME-I or the AIME-II. Again, after the contest is taken in the school, the contest administrator sends AMC the answer forms, and we score, compile and send email results back to the school, usually within 3 weeks. We then follow up with a written report, accompanied by the awards for the school. AMC 12 students who rank in the top 5% nationally (or score at least 100) will qualify for the American Invitational Mathematics Exam (AIME). AMC 10 students who rank in the top 1% nationally (or score at least 120) will also qualify for the AIME.
The United States of American Mathematical Olympiad (USAMO), is a six question, two day, 9 hour essay/proof examination. All problems can be solved with pre-calculus methods. Approximately 250 of the top scoring AMC participants (based on a weighted average) are invited to take the USAMO. U. S. citizens and students legally residing in the United States and Canada (with qualifyng scores) are eligible to take the USAMO. This is given on two consecutive days (usually a Tuesday and Wednesday) in mid-late April. The twelve top scoring USAMO students are invited to a two day Olympiad Awards Ceremony in Washington, DC sponsored by the MAA, the Akamai Foundation, the Microsoft Corporation and the Matilda Wilson Foundation. Six of these twelve students will comprise the United States team that competes in the “International Mathematical Olympiad (IMO). The IMO began in 1959; the USA has participated since 1974.
The Mathematical Olympiad Summer Program (MOSP) is a 3-4 week, intensive training program in June, which will give all participants, including the six IMO team members and two alternates, extensive practice in solving mathematical problems which require deeper analysis than those solved by students in even the best American high schools. Full days of classes and extensive problem sets give students thorough preparation in several important areas of mathematics which are traditionally emphasized more in other countries than in the United States. Traditionally there are 25 openings for the IMO team, alternates, and a select group of younger students. For the past several years The Akamai Foundation has sponsored an additional 25 openings for students just finishing ninth grade.
The AMC year culminates with the International Mathematical Olympiad (IMO) which is a 10-14 day trip and contest for the top 6 students, who comprise the US IMO team and represent the United States at IMO. The 2006 team competed against over 90 countries in Ljubljana, Slovenia, in July 2006 and placed Fifth.

The American Mathematics Competitions:

• Is dedicated to the goal of strengthening the mathematical capabilities of our nation's youth. We believe that one　　　way to meet this goal is to identify, recognize and reward excellence in mathematics through a serics of national contests.
• What happens before and after the AMC Contests can have lasting educational value. Talents will be enhanced if one　　　 practices beforehand, by working through previous examinations, by participating in math leagues and, most importantly, by studying mathematics more intensely than one　　　normally does in school.

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