Resources for mathematics competitions

The Art of Problem Solving hosts this AoPSWiki as well as many other online resources for students interested in mathematics competitions. Look around the AoPSWiki. Individual articles often have sample problems and solutions for many levels of problem solvers. Many also have links to books, websites, and other resources relevant to the topic.

• Math books
• Mathematics forums
• Mathematics websites

Math competition classes

• Art of Problem Solving hosts classes that are popular among many of the highest performing students in the United States. AoPS Problem Series.
• EPGY hosts classes for AMC students.

Math competition problems

Problem books

Many mathematics competitions sell books of past competitions and solutions. These books can be great supplementary material for avid students of mathematics.

• ARML has four problem books covering most ARML as well as some NYSML competitions. However, they are generally difficult to find. Some can be ordered here.
• MOEMS books are available here at AoPS.
• MathCounts books are available here at AoPS.
• AMC books are available here at AoPS.
• Mandelbrot Competition books are available here at AoPS.
• Putnam Competition books are available here at AoPS.

Problems online

Art of Problem Solving maintains a very large database of math contest problems. Many math contest websites include archives of past problems. The List of mathematics competitions leads to links for many of these competition homepages. Here are a few exmaples:

Introductory Problem Solvers

• Mu Alpha Theta.org hosts past contest problems.
• Noetic Learning Challenge Math - Problem Solving for the Gifted Elementary Students .
• Elias Saab's MathCounts Drills page.
• Alabama Statewide High School Mathematics Contest homepage.
• The South African Mathematics Olympiad here includes many years of past problems with solutions.
• Beestar.org - Beestar weekly problem solving tests for grade 1 - 8

Intermediate Problem Solvers

• AoPS math contest problems and solutions
• Past USAMTS problems can be found at the USAMTS homepage.
• The Kalva site is one of the best resources for math problems on the planet.
• Past Colorado Mathematical Olympiad (CMO) problems can be found at the CMO homepage.
• Past International Mathematical Talent Search (IMTS) problems can be found here
• Brilliant is a website where one can solve problems to gain points and go to higher levels.
• [1] Is similar to above

Olympiad Problem Solvers

• AoPS math contest problems and solutions
• Past USAMTS problems can be found at the USAMTS homepage.
• The Kalva site is one of the best resources for math problems on the planet. (Currently offline - but a few mirrors are available, e.g here.)
• Nick's Mathematical Puzzles -- Challenging problems with hints and solutions.
• Canadian Mathematical Olympiad are hosted here by the Canadian Mathematical Society.
• Problems of the All-Soviet-Union math competitions 1961-1986 - Many problems, no solutions. [Site no longer exists. Site has been replaced by a web capture]
• Past International Mathematical Talent Search (IMTS) problems can be found here
• Olympiad Math Madness - Stacks of challenging problems, no solutions. [Site no longer exists. Site has been replaced by a web capture]

Articles

• Pros and Cons and Math Competitions by Richard Rusczyk.
• Establishing a Positive Culture of Expectation in Math Education by Sister Scholastica Award winner Darryl Hill.
• Stop Making Stupid Mistakes by Richard Rusczyk.
• Stupid Questions by Richard Rusczyk.
• Learning Through Teaching
• How to Write a Solution by Richard Rusczyk and Mathew Crawford.

A Huge List of Links

AoPS Course Recommendations

Art of Problem Solving Course Recommendations Still have trouble deciding which course? Ask for personal recommendations.

AMC 8 Preparation

Problems

AMC 8 Problems in the Resources Section AMC 8 Problems in the AoPS wiki

AMC 10/12 Preparation

How preparing for the AIME will help AMC 10/12 Score What class to take? AMC 10 for AMC 12 practice AMC prep AMC 10/12 Preparation AIME/AMC 10 Overlap and Preparation How to prepare for amc10 and aime? Preparation for AMC 10?

Problems

AMC 10 Problems in the Resources Section AMC 10 Problems in the AoPS Wiki AMC 12 Problems in the Resources Section AHSME (Old AMC 12) Problems in the AoPS Wiki AMC 12 Problems in the AoPS Wiki

AIME Preparation

Studying to qualify for USAMO How to prepare for the AIME Preparation for the AIME Using non-AIME questions to prepare for AIME Best books to prepare for AIME? How to improve AIME score to make JMO? Preparation for AIME and USAMO

Problems

AIME Problems in the Resources Section AIME Problems in the AoPS Wiki

Beginning Olympiad Preparation

General General How to Prepare for USAJMO? USAMO preparation/doing problems Easier Olympiads for USAJMO practice? For the USAMO: ACoPS or Engel? Olympiad problems- how to prepare USAMO/Olympiads Preparation: Where to start? USAJMO prep

Bunch of General links

[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

Problems

USAJMO Problems in the Resources Section USAJMO Problems in the AoPS Wiki USAMO Problems in the Resources Section USAMO Problems in the AoPS Wiki

Middle/Advanced Olympiad Preparation

Problems

Practice Olympiad 1 Practice Olympiad 2 Practice Olympiad 3 Practice Olympiad Solutions USAMO Problems in the Resources Section USAMO Problems in the AoPS Wiki IMO Problems in the Resources Section IMO Problems in the AoPS Wiki

Book Links:

Olympiad Level

Free

Plane Geometry Hidden Discoveries -- How To Infinity Number Theory Diophantine Number Theory More Diophantine Number Theory

Not Free

Plane Euclidean Geometry: Theory and Problems Complex Numbers and Geometry Geometry of Complex Numbers Complex Numbers from A to …Z 103 Trigonometry Problems: From the Training of the USA IMO Team An Introduction to Diophantine Equations: A Problem-Based Approach Introductions to Number Theory and Inequalities 104 Number Theory Problems: From the Training of the USA IMO Team 102 Combinatorial Problems A Path to Combinatorics for Undergraduates: Counting Strategies -fkmr1 USA Mathematical Olympiads 1972-1986 Problems and Solutions Art and Craft of Problem Solving Problem Solving Strategies

Problem Sets

• 31 Olympiad problems about Probabilistic Method
• 567 Nice and Hard Inequalities
• Inequalities
• 100 Polynomial Problems
• Trigonometry Problems
• General all levels
• Number Theory
• Olympiad Problems
• 33 Functional Equations
• Induction Problems
• Induction Solutions
• 260 Geometry Problems
• 150 Geometry Problems
• 50 Diophantine Equation Problems
• 60 Geometry Problems
• 116 Problems
• Algebraic Inequalities
• 100 Combinatorics Problems
• 100 Problems
• Number Theory
• Geometry
• General
• 100 Number Theory Problems
• 100 Functional Equation Problems
• Beginning/Intermediate Counting and Probability
• 40 Functional Equations
• 100 Geometric Inequalities
• 10 Fun Unconventional Problems :)
• 169 Functional Equations
• Triangle Geometry
• Probability
• Algebra
• Number Theory
• Circle Geometry
• Other Geometry

Ranking of all Olympiads (Difficulty Level)

See also

• List of mathematics competitions
• Mathematics scholarships
• Science competitions
• Informatics competitions