American Mathematics Competitions

The American Mathematics Contest (AMC) is the first of a series of competitions in high school mathematics that determines the United States Math Team, which competes in the International Mathematical Olympiad (IMO). This team, consisting of 6 high school students, competes in the International Mathematics Olympiad (IMO), and traditionally has performed well. The United States Math Team is the only team ever to achieve a perfect score (all six members earned perfect marks) at the 1994 IMO. That team is known as the "dream team".

Until 2000, the American Mathematics Contest was known as the American High School Mathematics Examination (AHSME). The contest was established in 1950.

There are three levels:

the AMC 8 is for students in grades 8 and below
the AMC 10 is for students in grades 10 and below
the AMC 12 is for students in grades 12 and below

Students who perform well on the AMC 10 or AMC 12 exams are invited to participate in the American Invitational Mathematics Examination.

The American Mathematics Competitions is also the name of the organization, based in Lincoln, Nebraska, responsible for creating, distributing and coordinating the AMC contests, which include the American Mathematics Contest (AMC), the American Invitational Mathematics Examination (AIME), and the United States of America Mathematical Olympiad (USAMO).

Benefits of participating

There are certain rewards for doing well on the AMC tests. For the AMC 8, a perfect score may earn a book prize or a plaque (as it did for the students who achieved perfect scores in 2002); a list of high scoring students is also available to colleges, institutions, and programs who want to attract students strong in mathematics. This may earn a high scorer an invitation to places like MathPath, a summer program for middle schoolers. The top-scoring student in each school is also awarded a special pin.

For the AMC 10 and AMC 12, a high score earns recognition (in particular, perfect scorers' names and pictures are published in a special awards book); as with the AMC 8, a list of high-scoring students is also available to colleges, institutions, etc. The top-scoring student in each school is awarded a special pin, or a bronze, silver, or gold medal, depending on how many times he or she was the top scorer. For more information on awards, visit Awards for the AMC.

In addition, high scorers on the AMC 10 and AMC 12 qualify to take the next round of competitions, the 3-hour long American Invitational Mathematics Examination (AIME), typically held in March or April. Any student who scores in the top 1% on the AMC 10, scores in the top 5% on the AMC 12, scores at least 100 points on the AMC 12, or scores at least 120 on the AMC 10 is invited to take the AIME. The answer to each of the 15 questions on the AIME is an integer between 0 and 999 inclusive, so while it is technically a multiple-choice test, it is not one in practice.

The combined scores of the AMC and the AIME are used to determine those that will be invited back to take a grueling 9-hour, 2-day, 6-problem session of proofs known as the United States of America Mathematical Olympiad (USAMO). Approximately thirty students are selected based on their USAMO performance to be trained at the Mathematical Olympiad Summer Program, or MOSP (better known as MOP to its participants). In addition, in 2004, twenty-five 9th grade students were selected to participate in MOSP.

During this summer camp, a series of exams are given to finally pick the 6 member US Mathematics Team. The current coaches of the US Math Team are Titu Andreescu, director of the AMC, and Zuming Feng, from Phillips Exeter Academy.

Major universities such as MIT are beginning to ask applying students for their AMC scores. Since the AMC tests a deeper level of math than the SAT, this can help identify students who are ready for a rigorous undergraduate curriculum. Many top students appreciate the elevated difficulty and attention given to AMC exams and take preparation courses with Art of Problem Solving, EPGY, and other specialized instructional institutions. Students even write their own mock AMC exams to challenge each other, and post them on the Art of Problem Solving website, where the mock exams get organized into the AoPSWiki.

Note: Some of this material is taken from How to Prepare for the AMC Exams, with permission from the original author.

Rules and scoring

AMC 8

The AMC 8 has 25 multiple-choice questions and is to be taken in 40 minutes. Calculators are allowed.

The AMC 8 is scored based on the number of questions answered correctly only. There is no penalty for getting a question wrong, and each question has equal value. Thus, a student who answers 23 questions correctly and 2 questions incorrectly receives a score of 23.

AMC 10 and AMC 12

The AMC 10 and AMC 12 each have 25 questions, and each is to be taken in 75 minutes. Calculators are allowed.

Each exam is scored based on the number of questions answered correctly and the number of questions left blank. A student receives 6 points for each question answered correctly and 2.5 points for each question left blank. (Incorrect answers contribute 0 points). Thus, a student who answers 18 correctly, leaves 5 blank, and misses 2 gets 18*6 + 5*2.5 = 120.5 points. The maximum possible score is 6*25 = 150 points.

In 2000 and 2001, 2.0 points were given for each question left blank. The number was changed to 2.5 in order to increase the penalty for random guessing, and to make the scoring system more consistent with the AHSME scoring of the 1990's, in which 2 points were given for a question left blank and 5 points were given for a correct answer (the AHSME had 30 questions instead of 25, so a perfect score was still 150).

Starting in 2007, the point value for a blank response will be reduced to 1.5. According to the 2005 awards booklet, this is to discourage students from leaving a large number of questions blank in order to assure qualification for the AIME.

Note: Some of this material is taken from How to Prepare for the AMC Exams, with permission from the original author.

History

Years	Name	No. of questions	Comments
1950-1951	Annual High School Contest	50	New York state only
1952-1959		50	Nationwide
1960-1966		40
1967-1972		35
1973	Annual High School Mathematics Examination	35
1974-1982	Annual High School Mathematics Examination	30
1983-1999	American High School Mathematics Examination	30	AIME introduced in 1983 AJHSME introducted in 1985
2000-present	American Mathematics Contest	25	AHSME split into AMC10 and AMC12

External links

The Official AMC Home Page
Problems and Solutions from past AMC exams
The Art of Problem Solving: AMC Forum
How to Prepare for the AMC Exams
The IMO Compendium - huge collection of problems from mathematical competitions, and the most complete collection of IMO shortlists and longlists.

Mathematics competitions