American Mathematics Competitions
Encyclopedia
The American Mathematics Competitions (AMCs) are the first of a series of competitions in high school mathematics
that determine the United States team for the International Mathematical Olympiad
(IMO). This team, consisting of six high school students, competes in the IMO and has traditionally performed well. The United States Math Team of 1994 is the only team ever to achieve a perfect score (all six members earned perfect marks), and is colloquially 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:
Students who perform well on the AMC 10 or AMC 12 exams are invited to participate in the American Invitational Mathematics Examination
. Students who perform well on the American Invitational Mathematics Examination
(AIME) are then invited to the United States of America Mathematical Olympiad
(USAMO). Students who do exceptionally well on the USAMO (typically around 30 students) are invited to go to the Mathematical Olympiad Summer Program (MOSP or more commonly, MOP), and six students are selected from the top twelve scorers on the USAMO (through yet another exam, the Team Selection Test (TST)) to form the United States Math Team.
American Mathematics Competitions is also the name of the organization, based in Lincoln, Nebraska
, responsible for creating, distributing and coordinating the American Mathematics Competitions contests, which include the American Mathematics Contest, AIME, and USAMO.
, 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 (or 2.5% as of 2011), 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 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). All students must be in 9th grade or higher to be admitted into MOSP.
During this summer camp, a series of exams are given to finally pick the 6 member US Mathematics Team. The current head coach of the US Math Team is 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 an AoPS Wiki
.
Last year's(2010) test was taken on November 16, also a Tuesday.
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. This is not a standardized test; i.e. no school has to take it, but some schools choose to, mainly to encourage growth in mathematics among their students. Full scorers on the AMC 8 (25/25) get recognition and their picture on the AMCs web site as a top scorer.
This year, anyone who scores 17-21 is considered the top 5% and people who score 22 and above are considered the top 1%.
Since the 2007-2008 school year, calculators have been disallowed on all of the selection tests for the International Math Olympiad Team (including AIME, USAMO, TST)
Qualifications for the AMC 10 or AMC 12 depend on the previous test score. A 22 or above on the AMC 8 usually is enough to take the AMC 10. But students should study hard for these tests. They are not as easy as they think.
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, 1.5 points for each question left blank, and no points for incorrect answers. Thus, a student who answers 18 correctly, leaves 5 blank, and misses 2 gets 18*6 + 5*1.5 = 115.5 points. The maximum possible score is 6*25 = 150 points; in 2006, the AMC 12 had a total of 17 perfect scores between its two administrations, while the AMC 10 had 89.
Until 1999, the exam had 30 questions and was 90 minutes long, scoring 5 points for correct answers and 2 points for omitted questions. When the exam was shortened as part of the 2000 rebranding, the value of a correct answer was increased to 6 points (keeping 150 as a perfect score). In 2001, the score of a blank was increased to 2.5 to penalize guessing. The 2007 exams were the first with only 1.5 points awarded for a blank, to discourage students from leaving a large number of questions blank in order to assure qualification for the AIME. For example, on the AMC 12, a student could advance with only 11 correct answers, presuming the remaining questions were left blank. Now, a student must answer at least 14 questions correctly to reach 100 points.
The exams overlap somewhat, with the medium-hard AMC 10 questions being the same as the medium-easy ones on the AMC 12. Since 2002, two administrations have been scheduled, so as to avoid conflicts with school breaks. The A contests are held on the first Tuesday in February, with the B contests 15 days later. Students are eligible to take an A exam and a B exam, and may even take the AMC 10-A and the AMC 12-B, though they may not take both the AMC 10 and AMC 12 from the same date. If a student takes both exams, they may use either score towards qualification to the AIME or USAMO.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
that determine the United States team for the International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
(IMO). This team, consisting of six high school students, competes in the IMO and has traditionally performed well. The United States Math Team of 1994 is the only team ever to achieve a perfect score (all six members earned perfect marks), and is colloquially 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 any student grade 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
American Invitational Mathematics Examination
The American Invitational Mathematics Examination is a 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics contest , and starting in 2010, those who rank in the top 2.5% on the AMC 10.The AIME is the second of two tests used to determine...
. Students who perform well on the American Invitational Mathematics Examination
American Invitational Mathematics Examination
The American Invitational Mathematics Examination is a 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics contest , and starting in 2010, those who rank in the top 2.5% on the AMC 10.The AIME is the second of two tests used to determine...
(AIME) are then invited to the United States of America Mathematical Olympiad
United States of America Mathematical Olympiad
The United States of America Mathematical Olympiad is a high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the AMC series of contests...
(USAMO). Students who do exceptionally well on the USAMO (typically around 30 students) are invited to go to the Mathematical Olympiad Summer Program (MOSP or more commonly, MOP), and six students are selected from the top twelve scorers on the USAMO (through yet another exam, the Team Selection Test (TST)) to form the United States Math Team.
American Mathematics Competitions is also the name of the organization, based in Lincoln, Nebraska
Lincoln, Nebraska
The City of Lincoln is the capital and the second-most populous city of the US state of Nebraska. Lincoln is also the county seat of Lancaster County and the home of the University of Nebraska. Lincoln's 2010 Census population was 258,379....
, responsible for creating, distributing and coordinating the American Mathematics Competitions contests, which include the American Mathematics Contest, AIME, and 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 MathPathMathPath
MathPath is a mathematics enrichment summer program for students ages 11–14 . It is four weeks long, and moves to a different location each year. MathPath is visited by world-renowned mathematicians such as John H...
, 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 (or 2.5% as of 2011), 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
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
between 0 and 999 inclusive
Inclusive
Inclusive may refer to:* Inclusion * inclusive disjunction, A or B or both* inclusive fitness, in evolutionary theory, how many kin are supported including non-descendants* inclusive interval includes its endpoints...
, 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 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). All students must be in 9th grade or higher to be admitted into MOSP.
During this summer camp, a series of exams are given to finally pick the 6 member US Mathematics Team. The current head coach of the US Math Team is Zuming Feng from Phillips Exeter Academy
Phillips Exeter Academy
Phillips Exeter Academy is a private secondary school located in Exeter, New Hampshire, in the United States.Exeter is noted for its application of Harkness education, a system based on a conference format of teacher and student interaction, similar to the Socratic method of learning through asking...
.
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 an AoPS Wiki
Wiki
A wiki is a website that allows the creation and editing of any number of interlinked web pages via a web browser using a simplified markup language or a WYSIWYG text editor. Wikis are typically powered by wiki software and are often used collaboratively by multiple users. Examples include...
.
AMC 8
The AMC 8 has 25 multiple-choice questions and is to be taken in 40 minutes. No problems require the use of a calculator, and calculators are not allowed starting in 2008. The contest is held on a Tuesday in November; in the case of 2007, on Tuesday, November the 13th.Last year's(2010) test was taken on November 16, also a Tuesday.
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. This is not a standardized test; i.e. no school has to take it, but some schools choose to, mainly to encourage growth in mathematics among their students. Full scorers on the AMC 8 (25/25) get recognition and their picture on the AMCs web site as a top scorer.
Rankings
Based on questions correct:- 22 and up: Distinction
- 17 and up: Honor Roll
- 15 and up (or anybody 6th grade and under): Merit
This year, anyone who scores 17-21 is considered the top 5% and people who score 22 and above are considered the top 1%.
AMC 10 and AMC 12
The AMC 10 and AMC 12 each have 25 questions, and each is to be taken in 75 minutes. Until 2007, calculators were allowed, but like the AMC 8, supposedly unneeded.Since the 2007-2008 school year, calculators have been disallowed on all of the selection tests for the International Math Olympiad Team (including AIME, USAMO, TST)
Qualifications for the AMC 10 or AMC 12 depend on the previous test score. A 22 or above on the AMC 8 usually is enough to take the AMC 10. But students should study hard for these tests. They are not as easy as they think.
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, 1.5 points for each question left blank, and no points for incorrect answers. Thus, a student who answers 18 correctly, leaves 5 blank, and misses 2 gets 18*6 + 5*1.5 = 115.5 points. The maximum possible score is 6*25 = 150 points; in 2006, the AMC 12 had a total of 17 perfect scores between its two administrations, while the AMC 10 had 89.
Until 1999, the exam had 30 questions and was 90 minutes long, scoring 5 points for correct answers and 2 points for omitted questions. When the exam was shortened as part of the 2000 rebranding, the value of a correct answer was increased to 6 points (keeping 150 as a perfect score). In 2001, the score of a blank was increased to 2.5 to penalize guessing. The 2007 exams were the first with only 1.5 points awarded for a blank, to discourage students from leaving a large number of questions blank in order to assure qualification for the AIME. For example, on the AMC 12, a student could advance with only 11 correct answers, presuming the remaining questions were left blank. Now, a student must answer at least 14 questions correctly to reach 100 points.
The exams overlap somewhat, with the medium-hard AMC 10 questions being the same as the medium-easy ones on the AMC 12. Since 2002, two administrations have been scheduled, so as to avoid conflicts with school breaks. The A contests are held on the first Tuesday in February, with the B contests 15 days later. Students are eligible to take an A exam and a B exam, and may even take the AMC 10-A and the AMC 12-B, though they may not take both the AMC 10 and AMC 12 from the same date. If a student takes both exams, they may use either score towards qualification to the AIME or USAMO.
History
| Years | Name | No. of questions | Comments |
|---|---|---|---|
| 1950–1951 | Annual High School Contest | 50 | New York state only |
| 1952–1959 | Nationwide | ||
| 1960–1966 | 40 | ||
| 1967–1972 | 35 | ||
| 1973 | Annual High School Mathematics Examination | 35 | |
| 1974–1982 | 30 | ||
| 1983–1999 | American High School Mathematics Examination | 30 | AIME American Invitational Mathematics Examination The American Invitational Mathematics Examination is a 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics contest , and starting in 2010, those who rank in the top 2.5% on the AMC 10.The AIME is the second of two tests used to determine... introduced in 1983, now is a middle step between AHSME and USAMO AJHSME, now AMC 8, introduced in 1985 |
| 2000–present | American Mathematics Contest | 25 | AHSME split into AMC10 and AMC12 A&B versions introduced in 2002. USAMO split into USAJMO and USAMO in 2010. AMC 10 qualifiers who pass AIME go to USAJMO |
See also
- American Invitational Mathematics ExaminationAmerican Invitational Mathematics ExaminationThe American Invitational Mathematics Examination is a 15-question 3-hour test given since 1983 to those who rank in the top 5% on the AMC 12 high school mathematics contest , and starting in 2010, those who rank in the top 2.5% on the AMC 10.The AIME is the second of two tests used to determine...
(AIME) - United States of America Mathematical OlympiadUnited States of America Mathematical OlympiadThe United States of America Mathematical Olympiad is a high school mathematics competition held annually in the United States. Since its debut in 1972, it has served as the final round of the AMC series of contests...
(USAMO) - Mathematical Olympiad Summer Program (MOSP or MOP)
- International Mathematical OlympiadInternational Mathematical OlympiadThe International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
(IMO) - Mandelbrot CompetitionMandelbrot CompetitionNamed in honor of the Mandelbrot set, the Mandelbrot Competition is a mathematics competition founded by Sam Vandervelde, Richard Rusczyk and Sandor Lehoczky that allows high school students to compete individually and in four-person teams.-Competition:...
- Art of Problem Solving (AoPS)
- List of mathematics competitions
External links
- The Official AMC Home Page
- Problems and Solutions from past AMC exams
- The Art of Problem Solving: AMC Forum Artofproblemsolving Is a very useful link