Links
Sites I send people to. Art of Problem Solving for books, classes and practice; Exeter for what a problem-based curriculum looks like end to end.
Art of Problem Solving
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Art of Problem Solving
Books, online classes and the community forums. The center of gravity for competition math in the US.
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Alcumus
Free adaptive problem sets that follow the AoPS books topic by topic. Needs a free account.
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AoPS Wiki: AMC 8 problems and solutions
Every past AMC 8, with community solutions. Also the AMC 10/12, AIME and more from the same index.
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Beast Academy
The AoPS program for grades 1–5: books plus an online version with practice.
Curricula
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Phillips Exeter Academy mathematics problem sets
Exeter teaches math entirely from problem sets (Math 1 through Math 6), discussed around a Harkness table. The sets are free PDFs and are a model of how a problem-based course is sequenced.
Competitions
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MAA American Mathematics Competitions
AMC 8, AMC 10/12 and AIME: dates, registration and the official archive.
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MOEMS (Math Olympiads for Elementary and Middle Schools)
Five short contests a year for school teams, grades 4–8.
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MATHCOUNTS
The middle-school competition series; the free Problem of the Week archive is good practice on its own.