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.
Contents
- 1 Math competition classes
- 2 Math competition problems
- 3 Articles
- 4 A Huge List of Links
- 5 See also
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.
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 examples:
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. (Currently offline. Mirror can be found at this page)
- 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.
- Clevermath 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
- Do you still have trouble deciding which course? Ask for personal recommendations!
AMC 8 Preparation
Problems
AMC 8 Problems in the Resources Section
Problem and Solutions: AMC 8 Problems in the AoPS wiki
AMC 10/12 Preparation
How preparing for the AIME will help AMC 10/12 Score
AIME/AMC 10 Overlap and Preparation
How to prepare for amc10 and aime?
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
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
AIME problems by sorted by difficulty
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
- USAMO Prep
- USAMO Prep
- USAMO
- Usamo prep
- USAMO Prep
- Counting down to USAMO
- USAMO Preparation
- USAJMO prep
- USAMO Preparation
- USAJMO Prep
- How to prepare for the USAMO/Making Red MOP
- Preparing in a hardcore way
- USAMO and JMO prep
- USAMO PREP
- Beginner to USAMO
- What should I be doing?
- Improve to USAMO and IMO level
- Prep for USA(J)MO
- contest math stuff/some advice on how to get good
- Olympiad Prep
- Olympiad Prep
- USAJMO Prep
- The Right Training
- What Leads to Success
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
- Lemmas in Olympiad Geometry article
- 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
- Practice problems from around the world
- General problems in Olympiad Mathematics
- 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)