Math Practice Problems

Art of Problem Solving's Intermediate Counting and Probability starts on June 19. Learn about one-to-one correspondences, the principle of inclusion-exclusion, generating functions, pigeonhole principle, recursion, and conditional probability. Click here to enroll today!

Below is a list of sites which are good resources for those seeking practice problems. Some sites have problems spanning multiple difficulty levels and have been included in more than one list. (This list initially compiled almost entirely by AoPS Community member mathfanatic.)

Getting Started

These sites contain some problems appropriate for middle school students or others just getting started in problem solving.

MATHCOUNTS Practice Problems - Answers, some solutions.
Math Drills for MATHCOUNTS - Problems and solutions.
Bay Area Math Meet - Some solutions.
South African Mathematics Olympiad - Problems and solutions.

Intermediate

These sites contain some problems appropriate for high schoolers who have some experience problem solving.

South African Mathematics Olympiad - Problems and solutions.
Canadian Open Mathematics Challenge - Problems and solutions.
Kömal. Problems with some solutions.
Bay Area Math Meet - Some solutions.
Colorado Mathematical Olympiad - Some solutions.
International Mathematics Talent Search - Problems only.
Flanders Mathematics Olympiad

Advanced

AoPS hosts a large database of Olympiad and undergraduate competition problems and solutions. The following sites contain problems appropriate for students preparing for Olympiad-level compeitions.

Large archive of Olympiad problems (and other competitions) from around the world by John Scholes. Many with solutions.
Nick's Mathematical Puzzles. A collection of challenging problems with hints and solutions.
Canadian Mathematical Society Olympiads - CMO, APMO, and other contests.
South African Mathematics Olympiad - Problems and solutions.
Singapore International Mathematical Olympiad - Problems and solutions.
Eastern European Olympiads - Some solutions.
Problems of the All-Soviet-Union math competitions 1961-1986 - Many problems, no solutions.
International Mathematics Talent Search - Problems only.
Olympiad Math Madness - Stacks of challenging problems, no solutions.
US Olympiad Team Selection Test - Problems only, other olympiads here as well.
Irish Mathematical Olympiad
India Math Olympiads - Problems only
A variety of past olympiads of various nations - No solutions.
Flanders Mathematics Olympiad

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