American Mathematics Exams
These four exams (AJHSME, AHSME, AIME, and USAMO) are designed to interest and motivate students in math as well as to challenge better math students. Each of these exams is described below.
AJHSME - The American Junior High School Mathematics Examination
This test for middle school students is sponsored by the Mathematics Association of America (MAA) in an effort to strengthen the mathematics capability of America's youth. This is a 40 minute multiple choice exam with 25 questions.
AHSME - The American High School Mathematics Examination
This exam covers high school mathematics up to and including calculus. The problems range from easy to extremely difficult. Students have 90 minutes to answer 30 questions.
The exam is open to:
* Any student officially enrolled in high school and taking at least one course
* Students in lower grade levels
* Home school students 18 or younger
Students who score at least 100 points on the AHSME will be invited to take the American Invitational Mathematics Examination (AIME).
AIME - The American Invitational Mathematics Examination
This exam is an intermediate exam between the AHSME and the USAMO. Students who score well on the AHSME are invited to take this exam. The exam covers high school math up to and including pre-calculus. Students have 3 hours to answer 15 questions.
USA Mathematics Olympiad (USAMO)
This competition was developed as a means of discovering, challenging, and encouraging outstanding high school mathematics students. There are 5 questions in the 3.5 hour long test. The questions are essay/proof format and require math up to and including pre-calculus. Approximately 150 of the top scorers on the AHSME/AIME exams (based on a weighted average) will be invited to take this test.
Canadian Mathematics Exams
These exams are open to students outside of Canada.
These six exams (Gauss, Pascal, Cayley, Fermat, Euclid, and Descartes) are designed to interest and motivate students in math as well as to challenge better math students. The competitions are broken up by grade level. Students may compete individually or as part of a team.
Gauss Contest
This exam is for students in grades 7 and 8 (or younger at the discretion of local organizers). The test is 60 minutes long and consists of 25 multiple choice questions of increasing difficulty. There is less stress on this exam being a competition than for the upper grades.
Pascal Contest
This exam is for students in grade 9. The test is 60 minutes long and consists of 25 multiple choice questions of increasing difficulty.
Cayley Contest
This exam is for students in grade 10. Younger students may take the exam, but students may only take one of the exams open to 9–11 graders. The test is 60 minutes long and consists of 25 multiple choice questions of increasing difficulty. Canadian students who do well on this exam may be invited to the Invitation Mathematics Challenge, and may result in inclusion on the Canadian International Mathematics Olympiad team.
Fermat Contest
This exam is for students in grade 11. Younger students may take the exam, but students may only take one of the exams open to 9–11 graders. The test is 60 minutes long and consists of 25 multiple choice questions of increasing difficulty. Canadian students who do well on this exam may be invited to the Invitation Mathematics Challenge, and may result in inclusion on the Canadian International Mathematics Olympiad team.
Euclid Contest
This exam is designed for good math students in grade 12 though exceptional students in lower grades are encouraged to take it. This exam is 2.5 hours and consists of 10 questions, none of which are multiple choice.
Descartes Contest
This exam is designed for outstanding math students in grade 12 though exceptional students in lower grades are encouraged to take it. The contest is 2.5 hours longs and consists of 10 questions, none of which are multiple choice. The exam includes math through calculus.
ARML - American Regions Math League
ARML is a nationwide competition open to high school aged (or younger) students. Teams of 15 students compete in 4 rounds—Team, Individual, Power Question, and Relay. The problems require algebra, geometry, and trigonometry. The competition occurs the weekend after Memorial Day at three sites around the country.
ASMA - American Scholastic Mathematics Association
Throughout the year, students take a series of 6 exams. The exams are graded on-site and the highest 8 scores are sent to a national center to tabulate the results from schools across the country. (The scores of the same 8 people do not need to be reported each time.) There are two divisions for this competition—grades 7–9 and grades 9–12. The exams for both divisions are 35 minutes long and have 7 questions.
Continental Mathematics League
Exams are given for students in grades 2–9 and calculus. Additional competitions are held for C++ and PASCAL programming. Students should have an above-average reading and analytical reasoning ability and at least average computational ability.
For students in:
Grades 2 and 3, there are three 30-minute exams per year with 6 questions per exam.
Grades 4–9, there are five 30-minute exams per year with 6 questions per exam.
Calculus, there are four 40-minute exams per year with 8 questions per exam.
International Mathematics Olympiad (IMO)
High school students from around the world compete in this annual event. Participating countries send teams of up to six students. The competition for one of the six spots is very fierce. Students are invited to join based on their scores on the USAMO and their participation in MOP.
The Mandelbrot Competition
This difficult exam consists of two parts, an individual test and a team test. The team tests are all proofs. This fun competition is good preparation for the AHSME and AIME exams.
Math League
The Math League has math contests for students in the United States and Canada in grades 4–12. The goal is for students to develop an interest in mathematics through solving worthwhile problems.
MATHCOUNTS
MATHCOUNTS is an annual competition for 7th and 8th grade students. Teams of four students compete in local competitions. Those who do best progress to the state competition. Those who do best at the state championships progress to the national finals.
NML - National Mathematics League
The competition has 7 divisions: 6th Grade, PreAlgebra, Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus. The exams have 6 questions that students have 30 minutes to complete. There are 5 exams each year and students must work individually.
Rice Math Tournament
Each school may bring up to 20 students, no more than 10 of whom may be from any one grade level. There are 4 events which cover topics ranging from algebra to calculus and different combinations of students may particpate in different events.
Westinghouse Science Talent Search
This prestigious competition is open to all high school seniors in the U.S. To enter, students must submit a research project in math, science, or engineering.
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