Math Competitions

last update March 2007

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AMC – American Mathematics Competitions

The AMC tests are national competitions offered by the Mathematical Association of America for the purpose of identifying, recognizing, and rewarding excellence in mathematics and stimulating interest in solving mathematical problems. AMC 8 (American Mathematics Contest 8) is available for students in grade 8 and younger, AMC 10 (American Mathematics Contest 10) for students in grade 10 and younger, and AMC 12 (American Mathematics Contest 12) for students in grade 12 and younger. Students who achieve a qualifying score on the AMC 10 (top 1% or 120+) or AMC 12 (top 5% or 100+) may take the more difficult AIME (American Invitational Mathematics Examination - see below). A selection of top scoring students on both of those exams (using a weighted average that gives 10 times the value to the points scored on the AIME and also favors students who took the more mathematically comprehensive AMC 12 over the AMC 10) may take the USA Mathematics Olympiad exam.

AMC 8

The AMC 8 exam is intended for junior high school students (grades 6, 7, and 8), and students above grade 8 are ineligible to participate. The test takes 40 minutes and consists of 25 multiple choice questions covering fractions and decimals, percent and proportion, perimeter, area, volume, probability and statistics, and logical reasoning. Calculators are allowed but not necessary. Algebra questions are not part of the test. Each problem correctly solved gets one point, with no points taken off for incorrect answers. The school that administers the exam receives the written report and any awards earned by the students. . A score of 20 or better on the AMC 8 results in an invitation to take the next set of contests, the AMC 10 and/or AMC 12.

The AMC 8 is held on a national test date in November (a Tuesday in the week before Thanksgiving) during the school day. It is not given within the Eden Prairie school district, but MCGT has proctored some testing in the past, so it may be possible to arrange to test through that avenue. EPCGT members who have also joined the MCGT.net group will be notified of the test availability by early October and must pre-register about that time to ensure that enough exam packets are ordered and that you receive a study guide.

Because this exam occurs during the school day, tests knowledge at a high level of problem solving, and is not available onsite at CMS or Oak Point, a student would probably want to be seriously interested in mathematics competitions and/or camps to take part.

More on AMC 8: www.unl.edu/amc/e-exams/e4-amc08/amc8.shtml

Sample questions can be found at:
www.unl.edu/amc/a-activities/a7-problems/problem81012archive.shtml

AMC 10 / AMC 12

AMC 10 and AMC 12 are 75 minutes long, with 25 multiple choice problems that can be solved with knowledge of mathematical concepts through pre-Calculus. The AMC 10 is for high school freshmen and sophomores. Older, more advanced students are ineligible to take the exam. The AMC 12 is intended for high school juniors and seniors, but may be taken by high school freshmen and sophomores.* The two tests are given on two different exam dates about 2 weeks apart in February during the school day, with the first date on a Tuesday and the second on a Wednesday. The first date will offer the AMC 10A and the AMC 12A, while the second date will offer the AMC 10B and the AMC 12B. A student may take one contest, such as the AMC 10, on both dates, in which case he will be getting two different exams testing the same knowledge. Freshmen or sophomores may elect to take the AMC 10 on one date and the AMC 12 on a second date. The school or organization that administers the test will receive the results about 3 weeks later.

Eden Prairie High School administers only the AMC 12, and only on one date. The date and registration information is disseminated to students who participate on the Math Team. If your EPHS student is not on the Math Team but would like to take the AMC 12 at EPHS, please contact the Math Department in early December to see about making arrangements. Another option may be to take the test through MCGT. Information would be disseminated through the MCGT.net group, so contact MCGT by early December if you have not heard anything.

There are 150 possible points in each of the AMC 10 and AMC 12 exams. AMC 12 students who rank in the top 5% nationally or score at least 100 will qualify for the American Invitational Mathematics Exam (AIME), as will AMC 10 students who rank in the top 1% nationally or score at least 120.

*Those highly gifted math students who are freshmen or sophomores and stand a realistic chance of scoring very highly on the AMC may want to take the AMC 12 to increase their chances of qualifying for the USAMO after taking the AIME. See USAMO below.

More on AMC 10: www.unl.edu/amc/e-exams/e5-amc10/amc10.shtml

More on AMC 12: www.unl.edu/amc/e-exams/e6-amc12/amc12.shtml

AIME – American Invitational Mathematics Examination

www.unl.edu/amc/e-exams/e7-aime/aime.shtml

The AIME (American Invitational Mathematics Examination) is a test available to students who have achieved a qualifying score on the AMC 12 (top 5% or 100+) or the AMC 10 (top 1% or 120) (see AMC info above). Together with the AMC test, it qualifies students for the United States of America Mathematical Olympiad (USAMO).

Students are given 3 hours to answer 15 questions. The answers are not multiple choice, but rather in the form of an integer between 0 and 999. The difficulty level is significantly higher on this examination than on the AMC exams.

The AIME is given on a national test date in March with an alternate date a couple of weeks later for students unable to take the exam at the first sitting. The school administering the exam sends the answer forms in, and results are received in about 3 weeks.

U.S.A. Mathematical Olympiad (USAMO)

www.unl.edu/amc/e-exams/e8-usamo/usamo.shtml

The USAMO is a 2-day, 9-hour examination consisting of 6 questions in essay/proof form. All problems can be solved with pre-Calculus knowledge. Students who are top scorers on the AMC and AIME exams are invited to take this exam (usually about 250 students, using selection criteria that give AIME scores 10 times the value of AMC 10 or 12 and consider AMC 12 scores before AMC 10). They must also be legal residents of the United States or Canada.

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ARML – American Regions Math League

www.arml.com

ARML Competition

The ARML competition is a national mathematics competition for high school students (with some exceptional junior high students included) held the first weekend in June at the University of Iowa (and Penn State and San Jose State U.). Students who qualify to compete for Minnesota through previous High School Mathematics League competition are offered the opportunity to join the team(s). Three weekend practices are made available for these students (generally at Macalester College), and the practice results are an additional help in determining the final team placement(s). Each team consists of 15 students.

The competition consists of:

• Individual round – 4 sets of questions with 10 minutes per set, and question difficulty increasing as you go
• Team round – 20 minutes to work together to answer 10 short-answer questions
• Power round – 1 hour for the team to work together to answer 10 proof-style questions
• Relay rounds (2) – each team is divided into 5 groups of 3. The first person of each threesome solves the first part of the problem (same problem given to each of the people who are first in their groups) and gives the variable answer to the second person who uses the answer in the second part of the problem. The second people in turn give their variable answers to the third people in their groups. The third people use those answers as part of their problems. Only the answers from the third people (within the 6-minute time limit) are graded. Double points are given for answers turned in before 3 minutes.

Calculators are permitted only on the Team and Power Rounds.

ARML Power Contest

The Math Team at EPHS participated in the ARML Power Contest for the first time in 2005-06. This test is completely separate from the ARML competition. The students participate as a team, with no limit to the number of team members. If at least 15 Math Team members can commit to participating in the two-part contest, EPHS will take part. The contest consists of two problem sets, the first of which is held in November, and the second of which is held in February, with some flexibility on the part of the Math Team coach as to the particular date. They are administered after school. Each problem set has a 45-minute time limit. Students group together to work on different parts of the problem sets which are more challenging than regular Math Team contests. It is possible for students who are not on Math Team to participate, but they must contact the Math Team coach in October to indicate interest.

More info: www.arml.com/power.htm

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FERMI Off-the-Wall Math Leagues

Grades 1-2, 3-4, 5-6, 7-8
District 287

Fermi* Off-the-Wall Math Leagues provide excellent mathematical problems to ponder such as “How many water balloons would fill the school gymnasium?” The problem, with its limited information, requires students to pose intelligent questions to elicit needed information. Part of the process involves constructing a FERMI model showing the mathematical thinking that helped to solve the problem. Students may work solo or in teams of up to four students. There are divisions for grades 1-2, 3-4, 5-6 and 7-8. All work is done on the internet via e-mail – no boundaries; no carpools! Grade 1-2 problems are “family math” oriented – perfect as an enrichment model or for independent study.

Problems are offered each week and students are given a week to work on the solution.

Check with the gifted and talented coordinator at your school to see if Fermi is currently being offered as a school activity. If not, sign up as an individual at the District 287 website listed above.

*The math leagues are named after Nobel award-winning physicist Enrico Fermi to honor his “ability to estimate and ‘play around’ with problem solving.”

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Math League / MathCounts

(7th & 8th graders)
www.mathcounts.org
http://members.aol.com/mathleague/

For more details on these extra-curricular opportunities for middle school students and particularly how the program is offered at Central Middle School, see Math League / MathCounts.

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Math Masters

Grades 5 and 6

For more details on this program for 5th and 6th graders and particularly how it is offered at Oak Point, see Math Masters.

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Minnesota State High School Mathematics League

www.macalester.edu/mathleague/

For more details on how the EPHS Math Team participates in the MSHSML, see Math Team

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Siemens Westinghouse Competition in Math, Science and Technology

High school students
www.siemens-foundation.org/competition

The Siemens Westinghouse Competition is a research-based competition. Students may compete individually or on a team. Those who compete individually must be high school seniors. Teams may have two or three high school members from one or more schools and do not need to include a senior. The research may be related to any one of a number of disciplines.

Projects are judged on originality, creativity, academic rigor and clarity of communication. The initial screening is done by panels of research scientists in a blind reading. Those students selected for further competition are invited to give an oral and poster presentation at one of the six regional events held in November. One individual and one team will be selected as Regional Winners. Each high school with a regional finalist receives a $2000 award per project.

Regional winners are invited to advance to the National Competition in New York City in early December, where their presentations are judged by research scientists recruited for their specific expertise in the area of research for each project.

Scholarships of $1,000-$100,000 are awarded. Online registration begins in May, with a deadline of the beginning of October.

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Trig-Star

www.nspsmo.org/trig_star/scholarship.shtml

Trig-Star is an annual competition sponsored by the National Society of Professional Surveyors that tests practical application of Trigonometry. The Level 1 contest is given at local high schools in April. Any student at EPHS who is interested may take the exam, but those who are not on the Math Team should talk to the Math Team coach to be placed on the list of applicants. Each high school has a top winner (top 3 are given recognition), and these winning scores are compared to arrive at the winner for the state. State winners may compete for National Awards of $2000 for 1st place, $1000 for 2nd place, and $500 for 3rd place.

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USA Mathematical Talent Search

Middle school* and high school students
www.usamts.org

The USA Mathematical Talent Search provides challenging mathematical problems free of charge to middle and high school students who register for the program. *It is “intended for high school students, but exceptionally strong middle school students should be able to tackle many of the problems."

The talent search began in 1989 as a column in a quarterly newsletter published by the Consortium for Mathematics and Its Applications (COMAP). It has gone through different administrative and mathematical organizers, but since 2004 has been administered by the Art of Problem Solving Foundation, with financial support and some grading and problem generation from the National Security Agency.

There are four rounds of problems, with deadlines in October, November, early January, and mid March. The first round is generally available in August. Students may register for the problems at any time at the website. The problems (and later, the solutions) may be found at the website, but only students who are registered may submit their solutions for grading. Submission may happen via mail, email, or FAX, with various rules for each.

The top 30 male and top 30 female participants in the talent search receive partial scholarships to attend the Canada/USA Math Camp. Other prizes awarded may include subscriptions to mathematical journals, books, or software. Participants who score well after 3 rounds of the USAMTS are invited to participate in the American Invitational Mathematics Examination (AIME - see above under AMC), which is the second step in the process of selecting the USA Mathematical Olympiad team.

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