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The MAA American Mathematics Competitions (AMC) is comprised of several contests based on age and invitational competitions based on results from the AMC 10/12, AIME, and/or USAMO.

The AMC 8 is a 25-question, 40-minute, multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem-solving skills. The contest is held in November every year. All USA, USA embassy, Canadian, and foreign school students in grade 8 or below are eligible to participate as long as they are under 14.5 years of age on the day of the contest.

The AMC 10 is a 25-question, 75-minute, multiple choice examination in secondary school mathematics containing problems which can be understood and solved with algebra and geometry concepts. Two different versions of the contests are given on two dates, about two weeks apart, in February. All USA, USA embassy, Canadian, and foreign school students in grade 10 or below are eligible to participate as long as they are under 17.5 years of age on the day of the contest.

The AMC 12 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. Two different versions of the contests are given on two dates, about two weeks apart, in February. All USA, USA embassy, Canadian, and foreign school students in grade 12 or below are eligible to participate as long as they are under 19.5 years of age on the day of the contest.

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. 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, all problems on the AIME can be solved by pre-calculus methods.

The AIME is intended to provide further challenge and recognition, beyond that provided by the AMC 10 or AMC 12, to the many high school students in North America who have exceptional mathematical ability. All students who took the AMC 12 and achieved a score of 100 or more out of a possible 150 or were in the top 5% are invited to take the AIME. All students who took the AMC 10 and had a score of 120 or more out of a possible 150, or were in the top 2.5% also qualify for the AIME. Two versions of the AIME are given on two different dates, about two weeks apart, in late March. Unlike the AMC 10/12, a student can only take the AIME once, and is encouraged to do so on the first date offered.

The Putnam Competition is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada. The Putnam Competition is considered to be the most prestigious university-level mathematics examination in the world, and its difficulty is such that the median score is often zero or one (out of 120) despite being attempted by students specializing in mathematics.

The Putnam Competition awards scholarships with cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 to the departments of mathematics of the institutions with the five winning teams. The MAA designates the five highest ranking individuals as Putnam Fellows. The Putnam awards prizes to each of these individuals and to each of the next twenty highest ranking contestants. The trustees of the Putnam Fund also will award at Harvard University or at Radcliffe College the annual William Lowell Putnam Prize Scholarship to one of the Putnam Fellows. This scholarship is available either immediately or upon completion of the undergraduate course of the successful candidate and carries a value of up to $12,000 plus tuition at Harvard.

The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the MAA.

The Putnam Competition now takes place on the first Saturday in December, and consists of two three-hour sittings separated by a lunch break. The test is supervised by faculty members at the participating schools.

Visit Putnam Competition to register and for more information.

The United States of America Mathematical Olympiad (USAMO) and the United States of America Junior Mathematical Olympiad (USAJMO) are six question, two day, 9 hour essay/proof examinations. All problems can be solved with pre-calculus methods. Approximately 270 of the top scoring AMC 12 participants (based on a weighted average of AMC 12 and AIME score) are invited to take the USAMO. Approximately 230 of the top scoring AMC 10 participants (based on a weighted average of AMC 10 and AIME score) are invited to take the USAJMO. The USAMO and USAJMO are given on two consecutive days in late April. U.S. citizens and students legally residing in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO.

The Mathematical Olympiad Summer Program (MOSP) is a three-to-four week intensive summer program held immediately after the USAMO Award Ceremony to prepare students for possible participation on the team that will represent the USA at the International Mathematical Olympiad (IMO). 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. Participants are invited to attend this free program based on the results of the USAMO. The top 12 students are automatically invited to attend.

The International Mathematical Olympiad (IMO) is a two day math competition held each summer. Participating countries send teams of up to six students. In addition to the students, there is one team leader, one deputy leader, and observers. Each day participants take a 4.5 hour, 3 question essay exam. The participating countries trade off in hosting the event, which in its entirety usually lasts 10- 14 days. The most talented high school students from over 90 nations compete in an extremely challenging two day examination. The examination is constructed by the leaders of the participating teams from a pool of problems submitted earlier by the invited nations.