Math Competitions

See the following websites as well as the attachments below.
American Mathematics Competitions
The American Mathematics Competitions (AMC) seek to increase interest in mathematics and to develop problem solving ability through a series of friendly mathematics contests for junior (grades 8 and below) and senior high school students (grades 9 through 12). 
American Regions Mathematics League
The American Regions Mathematics League (ARML) is an annual national mathematics competition. High school students form teams of 15 to represent their city, state, county or school and compete against the best in the from the United States and Canada.
AMTNJ Secondary School Mathematics Contest
The Bay Area Mathematical Olympiad and Mathematical Circles
The Bay Area Mathematical Olympiad (BAMO) is a contest for high school students sponsored jointly by the Mathematical Sciences Research Institute (MSRI), the American Institute of Mathematics (AIM), the University of California at Berkeley (UCB), and the University of San Francisco (USF).
California State University - Mathematics Field Day
The Field Day is an event designed to stimulate interest in mathematics and to give recognition to mathematical ability and achievement.
Canadian Mathematics Competition
Contains a listing of mathematics competitions for Canadian high school students.
Colorado Mathematical Olympiad
The COLORADO MATHEMATICAL OLYMPIAD is the largest essay-type mathematical competition in the United States, with 600 to 1,000 participants competing annually for prizes
Descartes Mathematics Contest
The Contest is designed primarily for outstanding students in their graduating year of high school, but should also be considered for other exceptional students. The aim of the contest is to provide these students with an opportunity to test their mathematical ability.
Great Plains Math League
The Great Plains Math League will be sponsoring a series of high school math contests to determine the individual and team state champions for Missouri, Iowa and Kansas in several math events.
Harvard-MIT Math Tournament
The Harvard-MIT Math Tournament is an annual math tournament for high school students, held in alternating years at MIT and at Harvard. It is run by MIT and Harvard students who participated in math contests in high school, so try to incorporate what we liked best about math contests when we were in high school.
High School Mathematical Contest in Modeling
The purpose of The High School Mathematical Contest in Modeling is to offer students the opportunity to compete in a team setting using mathematics to present solutions to real-world modeling problems.
Indiana State Mathematics Contest
International Mathematical Olympiad
The aims of the International Mathematical Olympiad are: to discover, encourage and challenge mathematically gifted young people in all countries; to foster friendly relations between mathematicians of all countries; to create an opportunity for the exchange of information on school mathematics syllabi and practice in mathematics education throughout the world. To achieve these aims, an international contest for secondary students in solving mathematical problems is held each year.
Related sites:
Asia Pacific Mathematics Olympiad
Argentina - Olimpíada Matemática
Australian Mathematics Trust
Balkan Mathematical Olympiad
Belgium - L'Olympiade Mathématique Belge
Brazil - Olimpíada de Matemática
Bulgarian Competitions in Mathematics and Informatics
Canadian Mathematical Olympiad
Colombia - Olympiad's Colombianas
Czech Republic - Matematická Olympiáda
Estonia - Matemaatikaol\374mpiaadid
Flanders Mathematics Olympiad
Germany - Mathematik-Olympiad
Irish Mathematical Olympiad
Italy - Olimpiadi Della Matematica
Luxembourg - Olympiade mathématique
Nederlandse Wiskunde Olympiade
Norwegian Mathematical Olympiad
Olimpíadas Iberoamericanas de Matemática
Peru - Math Olympiads
Poland in Mathematical Olympiads
Portugal - Olympiad's Portuguesa de Matemática (OPM)
South Africa and the International Mathematical Olympiad
Olimpiada Matemática Española

International Mathematics Tournament of Towns
The International Mathematics Tournament of Towns is a mathematics problem-solving competition in which towns throughout the world can participate on an equal basis. The Tournament is open to all high school students, with the highest age of students being about 17 years old.
Los Alamos National Laboratory Mathematics Contests
Web-based math contest for grades 7-12 in NM and CA.
The aim of the Mandelbrot Competition since its inception nine years ago has been to provide a challenging, engaging mathematical experience which is both competitive and educational.
Math Field Day - Southeast Missouri State University
Mathematical Challenge
Mathematical Challenge is a problem-solving competition for individual pupils in Scottish secondary schools and upper primary schools (mainly P7). The aim is to promote mathematics as a source of interest and pleasurable achievement.
Mathematics Olympiad Learning Centre
A commercial site operated by Arkadii Slinko who has had experiences with the Math Olympiads in both Russia and New Zealand. A lot of free material is available from the site including Problems of the IMO 2001 (with official solutions), NZ Math Olympiads, tutorials, and articles. In addition, a Monthly Internet Olympiad is supported.
North Carolina State High School Mathematics Contest
Oklahoma State University High School Math Contest
OSU's Math Department has sponsored a High School Math Contest bringing Oklahoma high school students to Stillwater for a day of serious mathematical problem-solving.
Pomona College / University of Wisconsin Mathematical Talent Search
The Pomona College Mathematical Talent Search sends out five sets of problems to high school students each school year. The top entrants and their teachers are recognized by Pomona College.
Queensland Association of MathematicsTeachers - Problem Solving Competition
Rice University Mathematics Tournament
The Rice University Mathematics Tournament is an annual event for high school students and teams from schools in the Texas/Louisiana area. Organized by Rice undergraduate students, the Rice Mathematics Tournament has been held almost every year at the Rice University campus in Houston since 1981. The contest includes individual written tests as well as group events.
Santa Clara University High School Mathematics Contest
This is a three-hour exam which tests problem-solving skills and mathematical ingenuity rather than being directed toward the content of a specific course.
St. Cloud State University Math Contest
For the past 34 years, the St. Cloud State departments of mathematics, statistics, and computer science have held a mathematics contest for students in grades 7-12.
Stanford Math Tournament
This contest brings together students from the greater Bay Area for a day of challenging problems and mathematical fellowship. The tournament is composed of four subject area tests (algebra, geometry, advanced topics, and calculus), a general test, and a team test.
Sheffield Pop Maths Quiz
Shippensburg University High School Internet Math Contest
Southern Illinois University Mathematics Field Day
Each Spring, the Mathematics Department sponsors a mathematics contest, called Math Field Day, for regional high school students. Schools from the southern part of Illinois, ranging from Edwardsville to Fairfield to Cairo, as well as a few schools from Missouri, Kentucky, and Tennessee participate.
Tennessee Mathematics Teachers Association Annual Math Contests
Each year the Tennessee Mathematics Teachers Association holds a competition for high school mathematics students.
University of Canberra Maths Day
The best Year 12 mathematics students from 37 schools from the ACT and southern NSW tested their wits in a variety of team events.
USA Mathematical Talent Search (USAMTS)
The purpose of the USAMTS is to encourage and assist the development of problem-solving skills of talented high school students. While most other competitions have stringent time limits, the USAMTS allows for more reflection on the part of the participants. We wish to foster not only insight, ingenuity, quick thinking, and creativity, but also writing skills and the virtue of perseverance.
Washburn University Math Day - High School Mathematics Competition
L'Australian Mathematics Competition en Nouvelle-Calédonie
Report of WFNMC : The World Federation of National Mathematical Competitions
The American Mathematics Competitions 
The Mandelbrot Competition
The Harvard-MIT Mathematics Tournament 
The University of North Carolina Charlotte High School Math Contest (UNCC) 
The American Regions Math League (ARML) 

Middle School
MATHCOUNTS is the national math coaching and competition program for 7th and 8th grade students. Some statewide sites:

Mathematical Oympiads for Elementary and Middle Schools

St. Louis Community College, Florissant Valley, Excellence in Math Contest
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