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Competitions for High School Students

Australian Maths Trust Competitions Administers the Australian Maths Competition, Australia's entry in the International Mathematical Olympiad and conducts enrichment programs such as the Mathematics Challenge for Young Australians.
MathMagic! Mathmagic invites students from around the world to work cooperatively to solve maths problems.
Brain Teasers A weekly competition, open to all students who have completed grades 3 to 8.
WebSolve A web-based mathematics competition. Open to all students in years 6 to 9, though only Queensland students are eligible for prizes.
Algebra Problem of the Week A weekly competition for students studying introductory algebra.
Geometry Forum - Problem of the Week A weekly geometry problem for high school students. This has been going for years, so there is also a large collection of past problems, with solutions. And your students may be able to win a T-Shirt!
Geometry Forum - Project of the Month A more challenging problem than the Problem of the Week. There is an archive of past problems and solutions.