Resources for mathematics competitions
The Art of Problem Solving hosts this AoPS Wiki 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
Free Math Books
- CompetifyHub's Problem Sets Free Competition Resources for Grades 1-12
- Ritvik Rustagi's ACE The AMC 10 and 12 book
- Mastering AMC 8
- Mastering AMC 10/12
- The Book of Formulas
Free Math Courses
- AMC 8/10/12 Course
- AMC 8/10/12 Practice
- AMC 8 Fundamentals Course
- AMC 8 Advanced/MATHCOUNTS
- AMC 10/12 Fundamentals
- Introduction To Number Theory
- AMC 8 Bootcamp covering all the essential concepts
- AMC 10 Course
- Free MOEMS Course
List of Resources
- All AMC 8 essentials
- All AMC 10 essentials
- A list of handouts (Here's another)
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.
- AMC Academy hosts private AMC10/12 and AIME Classes taught by USAMO Qualifiers from UCBerkeley, UofToronto, and many more. AMC Academy Info Link.
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
- CompetifyHub has Free Competition Math resources for students grades 1-4
- Mu Alpha Theta.org and Math.llmlab.io hosts past contest problems.
- Noetic Learning Challenge Math - Problem Solving for the Gifted Elementary Students .
- Beestar.org - 1st to 8th grades Weekly problem solving challenges and honor roll ranking.
- Introduction to MathCounts video.
- Elias Saab's MathCounts Drills page.
- List of all MathCounts competitions from 2000 to 2017.
- Alabama Statewide High School Mathematics Contest homepage.
- The South African Mathematics Olympiad (see here) includes many years of past problems with solutions.
Intermediate
- CompetifyHub has Free Competition Math resources for students grades 5-8 and 9-12
- AoPS math contest problems and solutions
- Past USAMTS problems can be found at the USAMTS homepage.
- Ivana Alexandrova's Weekly Math Problems for High School Students contains good problems that will make you think and that will teach you new skills and material
- 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
- CompetifyHub has Free Competition Math resources for students grades 9-12
- AoPS math contest problems and solutions
- Math and CS Research is a math and computer science publication with articles and problem sets on a wide range of topics.
- 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 and has been replaced by this web capture]
Articles
- Time Management
- Pros and Cons of 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.
- What Questions Really Are the Stupid Questions? by Richard Rusczyk.
- Learning Through Teaching
- How to Write a Math Solution by Richard Rusczyk and Mathew Crawford.
- Inequalities by Dr. Kiran Kedlaya
- Olympiad Inequalities by Thomas J. Mildorf
- Olympiad Number Theory: An Abstract Perspective by Thomas J. Mildorf
- Number Theory by Naoki Sato
- Olympiad Number Theory Through Challenging Problems by Justin Stevens
- Barycentric Coordinates in Olympiad Geometry by Max Schindler and Evan Chen
- Lifting the Exponent (LTE) by Amir Hossein Parvardi
- The uvw Method by Mathias Bæk Tejs Knudsen
- The Chinese Remainder Theorem by Evan Chen
- Contest Reflections by Wanlin Li
A Huge List of Links
AoPS Course Recommendations
- Art of Problem Solving Course Recommendations
- Do you still have trouble deciding which course? Go to the above link and click contact us at the bottom of the Course Map section to ask for personal recommendations!
AMC 8 Preparation
Problems
- CompetifyHub has Free Competition Math resources problems for AMC 8 Prep
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
- 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 AMC 10 and AIME
- Preparation for AMC 10
Problems
CompetifyHub has Free Competition Math resources problems for AMC 10/12 Prep
AMC 10 Problems in the Resources Section
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
- BOGTRO's AIME list of topics
Problems
CompetifyHub has Free Competition Math resources problems for AIME Prep AIME Problems in the Resources Section
AIME problems 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
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
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 and Solutions]]
- IMO Problems in the Resources Section
- IMO Problems and Solutions
