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Difference between revisions of "Resources for mathematics competitions"
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The [[Art of Problem Solving]] hosts this [[AoPSWiki]] as well as many other online resources for students interested in [[mathematics competitions]].
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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 AoPS Wiki.  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]]
 
* [[Math books]]
 
* [[Mathematics forums]]
 
* [[Mathematics forums]]
−
* [[Mathematics news]]
 
 
* [[Mathematics websites]]
 
* [[Mathematics websites]]
  
 +
== Free Math Books ==
  
−
== Math competition classes ==
+
* CompetifyHub's Problem Sets [//competifyhub.com/resources/ Free Competition Resources for Grades 1-12]
−
* [[Art of Problem Solving]] hosts classes that are popular among many of the highest performing students in the United States.  [http://www.artofproblemsolving.com/Classes/AoPS_C_PSeries.php AoPS Problem Series].
+
* Ritvik Rustagi's [//www.tmasacademy.com/ace-the-amc10-12-free-book ACE The AMC 10 and 12 book]
−
* [[EPGY]] hosts classes for [[AMC]] students.
+
* [//www.omegalearn.org/mastering-amc8 Mastering AMC 8]
 +
* [//www.omegalearn.org/mastering-amc1012 Mastering AMC 10/12]
 +
* [//www.omegalearn.org/thebookofformulas The Book of Formulas]
  
 +
== Free Math Courses ==
 +
 +
* [//math.llmlab.io/courses AMC 8/10/12 Course]
 +
* [//math.llmlab.io/alcumus AMC 8/10/12 Practice]
 +
* [//www.omegalearn.org/amc8-fundamentals AMC 8 Fundamentals Course]
 +
* [//www.omegalearn.org/amc8-advanced AMC 8 Advanced/MATHCOUNTS]
 +
* [//www.omegalearn.org/amc10-12 AMC 10/12 Fundamentals]
 +
* [//thepuzzlr.com/math-courses Introduction To Number Theory]
 +
* [//thepuzzlr.com/courses/amc-8-bootcamp AMC 8 Bootcamp covering all the essential concepts]
 +
* [//thepuzzlr.com/courses/amc-10-crash-course AMC 10 Course]
 +
* [//www.youtube.com/watch?v=bIipw2XSMgU Free MOEMS Course]
 +
 +
== List of Resources ==
 +
* CompetifyHub's Problem Sets [//competifyhub.com/resources/ Free Math Resources for Grades 1-12]
 +
* [//thepuzzlr.com/courses/amc-8-bootcamp All AMC 8 essentials]
 +
* [//thepuzzlr.com/courses/amc-10-crash-course All AMC 10 essentials]
 +
* [//mathgauss.com/ MathGauss: Free AMC/AIME/USAJMO Lessons, Grading, and Problem Trainer ]
 +
* A list of [{{SERVER}}/community/c1967976h2550333 handouts] (Here's [{{SERVER}}/community/c5h1578191p15903900 another])
 +
 +
== Math Competition Classes ==
 +
 +
* [[Art of Problem Solving]] hosts classes that are popular among many of the highest performing students in the United States.  [{{SERVER}}/Classes/AoPS_C_PSeries.php AoPS Problem Series].
 +
* [[AMC Academy]] hosts private AMC10/12 and AIME Classes taught by USAMO Qualifiers from UCBerkeley, UofToronto, and many more.  [//www.amcacademy.ca AMC Academy Info Link].
 +
 +
== Math Competition Problems ==
 +
 +
=== Problem Books ===
  
−
== 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.
 
Many mathematics competitions sell books of past competitions and solutions.  These books can be great supplementary material for avid students of mathematics.
−
* [[MOEMS]] books are available [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MOEMS.php here] at [[AoPS]].
+
* CompetifyHub's Problem Sets [//competifyhub.com/resources/ Free Competition Resources for Grades 1-12]
−
* [[MathCounts]] books are available [http://www.artofproblemsolving.com/Books/AoPS_B_CP_MC.php here] at [[AoPS]].
+
* [[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 [//www.arml2.com/arml_2018/page/index.php?page_type=public&page=books here].
−
* [[AMC]] books are available [http://www.artofproblemsolving.com/Books/AoPS_B_CP_AMC.php here] at [[AoPS]].
+
* [[MOEMS]] books are available [{{SERVER}}/store/list/other-products#MOEMS here] at [[AoPS]].
−
* [[Mandelbrot Competition]] books are available [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Mand.php here] at [[AoPS]].
+
* [[MATHCOUNTS]] books are available [{{SERVER}}/store/list/other-products#MATHCOUNTS here] at [[AoPS]].
−
* [[Putnam Competition]] books are available [http://www.artofproblemsolving.com/Books/AoPS_B_CP_Putnam.php here] at [[AoPS]].
+
* [[AMC]] books are available [{{SERVER}}/store/list/other-products#American Mathematics Competitions here] at [[AoPS]].
 +
* [[Mandelbrot Competition]] books are available [{{SERVER}}/store/list/other-products#Mandelbrot here] at [[AoPS]].
 +
 
 +
=== Problems Online ===
 +
* CompetifyHub's Problem Sets [//competifyhub.com/resources/ Free Competition Resources for Grades 1-12]
 +
[[Art of Problem Solving]] maintains a very large database of [{{SERVER}}/resources 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.com/resources/ CompetifyHub] has Free Competition Math resources for students grades 1-4
 +
* [[Mu Alpha Theta]].org and [//math.llmlab.io/ Math.llmlab.io] hosts past [//www.mualphatheta.org/index.php?chapters/national-convention/past-tests contest problems].
 +
* Noetic Learning [//www.noetic-learning.com/gifted/index.jsp Challenge Math] - Problem Solving for the Gifted Elementary Students  .
 +
* [[Beestar]].org - 1st to 8th grades Weekly problem solving challenges and honor roll ranking [//www.beestar.org/exercise all  subjects].
 +
* [//www.youtube.com/watch?v=1EpNaRaQnVM Introduction to MathCounts] video.
 +
* Elias Saab's [[MATHCOUNTS]] [//mathcounts.saab.org/ Drills page].
 +
* [//mathteamnyc.weebly.com/mathcounts.html List of all MathCounts competitions from 2000 to 2017].
 +
* [[Alabama Statewide High School Mathematics Contest]] [//mcis.jsu.edu/mathcontest/ homepage].
 +
* The [[South African Mathematics Olympiad]] ([//www.samf.ac.za/QuestionPapers.aspx see here]) includes many years of past problems with solutions.
 +
 
 +
==== Intermediate ====
 +
* [//competifyhub.com/resources CompetifyHub] has Free Competition Math resources for students grades 5-8 and 9-12
 +
* [[AoPS]] [{{SERVER}}/resources math contest problems and solutions]
 +
* Past [[United States of America Mathematical Talent Search|USAMTS]] problems can be found at the [//usamts.org USAMTS homepage].
 +
* [//www.albany.edu/ialexandrova/HS.html 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 [//www.kalva.demon.co.uk Kalva site] is one of the best resources for math problems on the planet. (Currently offline. Mirror can be found at [//mks.mff.cuni.cz/kalva/ this page])
 +
* Past [[Colorado Mathematical Olympiad]] (CMO) problems can be found at the [//www.uccs.edu/%7Easoifer/olympiad.html CMO homepage].
 +
* Past [[International Mathematical Talent Search]] (IMTS) problems can be found [//www.cms.math.ca/Competitions/IMTS/ here]
 +
* [//brilliant.org Brilliant] is a website where one can solve problems to gain points and go to higher levels.
 +
*[//www.clevermath.org Clevermath] Is similar to above
 +
 
 +
==== Olympiad ====
 +
* [//competifyhub.com/resources/ CompetifyHub] has Free Competition Math resources for students grades 9-12
 +
* [[AoPS]] [{{SERVER}}/resources math contest problems and solutions]
 +
* [//mathgauss.com/ MathGauss: Free AMC/AIME/USAJMO Lessons, USA(J)MO Grading, and Problem Trainer ]
 +
* [//mathcsr.org Math and CS Research] is a math and computer science publication with articles and problem sets on a wide range of topics.
 +
* Past [[United States of America Mathematical Talent Search | USAMTS]] problems can be found at the [//usamts.org USAMTS homepage].
 +
* The [//www.kalva.demon.co.uk/ Kalva site] is one of the best resources for math problems on the planet. (Currently offline - but a few mirrors are available, e.g [//mks.mff.cuni.cz/kalva/ here].)
 +
* [//www.qbyte.org/puzzles/ Nick's Mathematical Puzzles] -- Challenging problems with hints and solutions.
 +
* [[Canadian Mathematical Olympiad]] are hosted [//www.cms.math.ca/Competitions/CMO/ here by the Canadian Mathematical Society].
 +
* [//web.archive.org/web/20120825124642/http://pertselv.tripod.com/RusMath.html 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 [//www.cms.math.ca/Competitions/IMTS/ here]
 +
* [//web.archive.org/web/20091027032345/http://geocities.com/CapeCanaveral/Lab/4661/ Olympiad Math Madness] - Stacks of challenging problems, no solutions. [Site no longer exists and has been replaced by this web capture]
 +
 
 +
== Articles ==
 +
 
 +
* [//thepuzzlr.com/math-kangaroo-time-management Time Management]
 +
* [{{SERVER}}/news/articles/pros-cons-math-competitions Pros and Cons of Math Competitions] by [[Richard Rusczyk]].
 +
* [{{SERVER}}/news/articles/establishing-a-positive-culture Establishing a Positive Culture of Expectation in Math Education] by [[Sister Scholastica Award]] winner Darryl Hill.
 +
* [{{SERVER}}/news/articles/stop-making-stupid-mistakes Stop Making Stupid Mistakes] by [[Richard Rusczyk]].
 +
* [{{SERVER}}/news/articles/what-are-stupid-questions What Questions Really Are the Stupid Questions?] by [[Richard Rusczyk]].
 +
* [{{SERVER}}/news/articles/learning-through-teaching Learning Through Teaching]
 +
* [{{SERVER}}/news/articles/how-to-write-a-solution How to Write a Math Solution] by [[Richard Rusczyk]] and [[User:MCrawford|Mathew Crawford]].
 +
* [{{SERVER}}/articles/files/KedlayaInequalities.pdf Inequalities] by Dr. Kiran Kedlaya
 +
* [{{SERVER}}/articles/files/MildorfInequalities.pdf Olympiad Inequalities] by Thomas J. Mildorf
 +
* [{{SERVER}}/articles/files/MildorfNT.pdf Olympiad Number Theory: An Abstract Perspective] by Thomas J. Mildorf
 +
* [{{SERVER}}/articles/files/SatoNT.pdf Number Theory] by Naoki Sato
 +
* [//s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/olympiad-number-theory.pdf Olympiad Number Theory Through Challenging Problems] by Justin Stevens
 +
* [//s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/bary.pdf Barycentric Coordinates in Olympiad Geometry] by Max Schindler and Evan Chen
 +
* [//s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/lifting-the-exponent.pdf Lifting the Exponent (LTE)] by Amir Hossein Parvardi
 +
* [//s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/uvw.pdf The uvw Method] by Mathias Bæk Tejs Knudsen
 +
* [//s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/crt.pdf The Chinese Remainder Theorem] by Evan Chen
 +
* [//s3.amazonaws.com/aops-cdn.artofproblemsolving.com/resources/articles/Recollection.pdf Contest Reflections] by Wanlin Li
 +
 
 +
== A Huge List of Links ==
 +
=== AoPS Course Recommendations ===
 +
* [{{SERVER}}/School/recommendations.php 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.com/resources/ CompetifyHub] has Free Competition Math resources problems for AMC 8 Prep
 +
[{{SERVER}}/community/c3413 AMC 8 Problems in the Resources Section]
 +
 
 +
Problem and Solutions: [[AMC_8_Problems_and_Solutions|AMC 8 Problems in the AoPS Wiki]]
 +
 
 +
=== AMC 10/12 Preparation ===
 +
 
 +
* [{{SERVER}}/community/c5h388108 How preparing for the AIME will help AMC 10/12 Score]  
 +
* [{{SERVER}}/community/c5h396741 What class to take]
 +
* [{{SERVER}}/community/c5h387918 AMC 10 for AMC 12 practice]
 +
* [{{SERVER}}/community/c5h385418 AMC prep]
 +
* [{{SERVER}}/community/c5h384828 AMC 10/12 Preparation]
 +
* [{{SERVER}}/community/c5h384747 AIME/AMC 10 Overlap and Preparation]
 +
* [{{SERVER}}/community/c4h378851 How to prepare for AMC 10 and AIME]
 +
* [{{SERVER}}/community/c4h369849 Preparation for AMC 10]
 +
 
 +
==== Problems ====
 +
[//competifyhub.com/resources/ CompetifyHub] has Free Competition Math resources problems for AMC 10/12 Prep
 +
 
 +
* [//mathgauss.com/ MathGauss: Free AMC/AIME/USAJMO Lessons, USA(J)MO Grading, and Problem Trainer(with helpful hints!) ]
 +
 
 +
[{{SERVER}}/community/c3414_amc_10 AMC 10 Problems in the Resources Section]
 +
 
 +
[[AMC 10 Problems and Solutions]]
 +
 
 +
[{{SERVER}}/community/c3415_amc_12ahsme AMC 12 Problems in the Resources Section]
 +
 
 +
[{{SERVER}}/wiki/index.php/AHSME_Problems_and_Solutions AHSME (Old AMC 12) Problems in the AoPS Wiki]
 +
 
 +
[[AMC_12_Problems_and_Solutions|AMC 12 Problems in the AoPS Wiki]]
 +
 
 +
===AIME Preparation===
 +
 
 +
* [{{SERVER}}/community/c5h397954 Studying to qualify for USAMO]
 +
* [{{SERVER}}/community/c5h400442 How to prepare for the AIME]
 +
* [{{SERVER}}/community/c5h399160 Preparation for the AIME]
 +
* [{{SERVER}}/community/c5h357602 Using non-AIME questions to prepare for AIME]
 +
* [{{SERVER}}/community/c4h355918 Best books to prepare for AIME]
 +
* [{{SERVER}}/community/c5h344816 How to improve AIME score to make JMO]
 +
* [{{SERVER}}/community/c5h341827 Preparation for AIME and USAMO]
 +
* [//www.dropbox.com/s/icds9u5yo0xypyf/AIMElist.pdf BOGTRO's AIME list of topics]
 +
 
 +
==== Problems ====
 +
[//competifyhub.com/resources/ CompetifyHub] has Free Competition Math resources problems for AIME Prep
 +
[{{SERVER}}/community/c3416 AIME Problems in the Resources Section]
 +
 
 +
* [//https://mathema-amc.replit.app/ Mathema] has free problem lookup, trainer, and hint generation to push you toward the solution
 +
 
 +
[[AIME Problems and Solutions]]
 +
 
 +
'''[//drive.google.com/file/d/0B8JbOaFM5Xo_bnc2NUd0dDFLY1U/view?pref=2&pli=AIME AIME problems sorted by difficulty]'''
 +
 
 +
===Beginning Olympiad Preparation===
 +
* [{{SERVER}}/community/c5h480253 General]
 +
* [{{SERVER}}/community/c5h481746 General]
 +
* [{{SERVER}}/community/c5h401061 How to Prepare for USAJMO]
 +
* [{{SERVER}}/community/c5h399023 USAMO preparation/doing problems]
 +
* [{{SERVER}}/community/c5h396736 Easier Olympiads for USAJMO practice]
 +
* [{{SERVER}}/community/c5h366383 For the USAMO: ACoPS or Engel]
 +
* [{{SERVER}}/community/c5h360619 Olympiad problems- how to prepare]
 +
* [{{SERVER}}/community/c5h354103 USAMO/Olympiads Preparation: Where to start]
 +
* [{{SERVER}}/community/c5h344929 USAJMO prep]
 +
 
 +
==== General links ====
 +
* [{{SERVER}}/community/c5h31888 USAMO Prep]
 +
* [{{SERVER}}/community/c5h71008 USAMO Prep]
 +
* [{{SERVER}}/community/c5h79077 USAMO]
 +
* [{{SERVER}}/community/c5h81296 USAMO prep ]
 +
* [{{SERVER}}/community/c5h143168 USAMO Prep]
 +
* [{{SERVER}}/community/c5h273572 Counting down to USAMO]
 +
* [{{SERVER}}/community/c5h294132 USAMO Preparation]
 +
* [{{SERVER}}/community/c5h344929 USAJMO prep]
 +
* [{{SERVER}}/community/c5h385092 USAMO Preparation]
 +
* [{{SERVER}}/community/c5h397424 USAJMO Prep]
 +
* [{{SERVER}}/community/c5h401201 How to prepare for the USAMO/Making Red MOP]
 +
* [{{SERVER}}/community/c5h401640 Preparing in a hardcore way]
 +
* [{{SERVER}}/community/c5h406402 USAMO and JMO prep]
 +
* [{{SERVER}}/community/c5h411476 USAMO PREP]
 +
* [{{SERVER}}/community/c5h419800 Beginner to USAMO]
 +
* [{{SERVER}}/community/c5h447454 What should I be doing]
 +
* [{{SERVER}}/community/c5h453638 Improve to USAMO and IMO level]
 +
* [{{SERVER}}/community/c5h474960 Prep for USA(J)MO]
 +
* [{{SERVER}}/community/c5h385654 contest math stuff/some advice on how to get good]
 +
* [{{SERVER}}/community/c5h420845 Olympiad Prep]
 +
* [{{SERVER}}/community/c5h420845 Olympiad Prep]
 +
* [{{SERVER}}/community/c5h619416 USAJMO Prep]
 +
* [{{SERVER}}/community/c5h520900 The Right Training]
 +
* [//usamo.wordpress.com/2014/07/27/what-leads-to-success-at-math-contests What Leads to Success]
 +
* [//mathgauss.com/ MathGauss: Free AMC/AIME/USAJMO Lessons, USA(J)MO Grading, and Problem Trainer(with helpful hints!) ]
  
 +
==== Problems ====
  
−
=== Problems online ===
+
* [{{SERVER}}/community/c3420_usajmo USAJMO Problems in the Resources Section]
−
[[Art of Problem Solving]] maintains a very large database of [http://www.artofproblemsolving.com/Forum/resources.php 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:
+
* [[USAJMO Problems and Solutions]]
 +
* [//www.usamts.org/contest/past-problems USAMTS Problems]
 +
* [//mathgauss.com/ MathGauss: Free AMC/AIME/USAJMO Lessons, USA(J)MO Grading, and Problem Trainer(with helpful hints!) ]
  
−
* [[Mu Alpha Theta]].org hosts past [http://www.mualphatheta.org/National_Convention/MAO_Past_Tests.htm contest problems].
+
===Middle/Advanced Olympiad Preparation===
−
* Elias Saab's [[MathCounts]] [http://mathcounts.saab.org/ Drills page].
 
−
* [[Alabama Statewide High School Mathematics Contest]] [http://mcis.jsu.edu/mathcontest/ homepage].
 
  
 +
====Problems====
 +
* [{{SERVER}}/Forum/download/file.php?id=38803 Practice Olympiad 1]
 +
* [{{SERVER}}/Forum/download/file.php?id=38804 Practice Olympiad 2]
 +
* [{{SERVER}}/Forum/download/file.php?id=38805 Practice Olympiad 3]
 +
* [{{SERVER}}/Forum/download/file.php?id=38806 Practice Olympiad Solutions]
 +
* [{{SERVER}}/community/c3409_usamo USAMO Problems in the Resources Section]
 +
* [[USAMO Problems and Solutions]]
 +
* [{{SERVER}}/community/c3222_imo IMO Problems in the Resources Section]
 +
* [[IMO Problems and Solutions]]
 +
* [//mathgauss.com/ MathGauss: Free AMC/AIME/USAJMO Lessons, USA(J)MO Grading, and Problem Trainer(with helpful hints!) ]
  
−
== See also ==
+
== See Also ==
  
 
* [[List of mathematics competitions]]
 
* [[List of mathematics competitions]]
 +
* [[Mathematics scholarships]]
 +
* [[Science competitions]]
 +
* [[Informatics competitions]]
 +
* [[How should I prepare?]]

Latest revision as of 12:49, 24 July 2025

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 AoPS Wiki. 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.

Free Math Books

Free Math Courses

List of Resources

Math Competition Classes

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.

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

Intermediate

Olympiad

Articles

A Huge List of Links

AoPS Course 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

Problems

CompetifyHub has Free Competition Math resources problems for AMC 10/12 Prep

AMC 10 Problems in the Resources Section

AMC 10 Problems and Solutions

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

Problems

CompetifyHub has Free Competition Math resources problems for AIME Prep AIME Problems in the Resources Section

  • Mathema has free problem lookup, trainer, and hint generation to push you toward the solution

AIME Problems and Solutions

AIME problems sorted by difficulty

Beginning Olympiad Preparation

General links

Problems

Middle/Advanced Olympiad Preparation

Problems

See Also

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