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

Quick Start Video Introduction to the AMC

A quick video overview of the AMC and AIME.

Training Websites

• AMC Problem Trainer: https://amctrainer.com/play
• Trainer like MathCounts trainer and past contest taker: https://amctrainer.org/
• Problem generator and AoPS Wiki Reader: https://vqbc.github.io/trivial/
• mathRanks contests: https://mathranks.net/
• [Registration Open]Elementary/middle school contests: https://www.beestar.org/math-competition/

Free Math Books

Ritvik Rustagi's ACE The AMC 10 and 12 book

Mastering AMC 8: https://www.omegalearn.org/mastering-amc8

Mastering AMC 10/12: https://www.omegalearn.org/mastering-amc1012

The Book of Formulas: https://www.omegalearn.org/thebookofformulas

Free Math Courses

AMC 8 Fundamentals Course: https://www.omegalearn.org/amc8-fundamentals

AMC 8 Advanced/MATHCOUNTS: https://www.omegalearn.org/amc8-advanced

AMC 10/12 Fundamentals: https://www.omegalearn.org/amc10-12

Introduction To Number Theory: https://thepuzzlr.com/math-courses

Free AMC 8 Bootcamp covering all the essential concepts: https://thepuzzlr.com/courses/amc-8-bootcamp/

Free AMC 10 Course: https://thepuzzlr.com/courses/amc-10-crash-course/

List of Resources

All AMC 8 essentials: https://thepuzzlr.com/courses/amc-8-bootcamp/

All AMC 10 essentials: https://thepuzzlr.com/courses/amc-10-crash-course/

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.

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 .
• 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 Problem Solvers

• 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 Problem Solvers

• 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. Site has been replaced by a 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

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 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

BOGTRO's AIME list of topics: https://www.dropbox.com/s/icds9u5yo0xypyf/AIMElist.pdf?dl=0

Problems

AIME Problems in the Resources Section

AIME Problems in the AoPS Wiki

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

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
• Evan Chen OTIS-Excerpts
• The Basics of Olympiad Number Theory
• Olympiad Number Theory Through Challenging Problems
• Modern Olympiad Number Theory

Not Free

• Plane Euclidean Geometry: Theory and Problems
• Euclidean Geometry in Mathematical Olympiads
• 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

• Collection of Past Papers in PDF Format
• Practice problems from around the world
• General problems in Olympiad Mathematics
• Conditional Probability Problem Set
• 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
• How should I prepare