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== Introduction ==
 
== Introduction ==
−
The best way to prepare for math contests is to do lots of practice problems and learn the material necessary to solve the problems. There are also many books and online handouts/lectures you can use to improve your problem solving skills.  Depending on your current abilities, you will want to start out with different practice problems, different books, and in different areas of the forums. This guide is intended to help you get started.
+
The best way to prepare for math contests is to '''do lots of practice problems''' and learn the material necessary to solve the problems. There are also many books and online handouts/lectures you can use to improve your problem-solving skills.  Depending on your current abilities, you will want to start out with different practice problems, different books,
 +
 
 +
== High Level Overview ==
 +
If you don't feel like going too deep and want a straightforward answer, here it is:
 +
 
 +
- '''Beginner''' To score well on the low level competitions(like Mathcounts and AMC 8), first read the following AOPS books and take their AOPS Academy/Online classes simultaneously in this order:
 +
  - Pre Algebra
 +
  - Introduction to Algebra
 +
  - Introduction to Geometry
 +
  - Introduction to Number Theory
 +
  - Introduction to Counting & Probability
 +
  - Volume 1
 +
Then head on over to AOPS's Alcumus tool and practice all of these topics constantly. When you are practicing, you will come over problems you miss. When you do, re-read the part in the book that corresponds with that question. The more you do this, the better your skills will get.
 +
 
 +
- '''Advanced''' To score well on the high level competitions(like AMC 10 and AIME), first read the following AOPS books and take their AOPS Academy/Online classes simultaneously in this order:
 +
  - Intermediate Algebra
 +
  - Intermediate Counting and Probability
 +
  - Volume 2
 +
  - Precalculus
 +
  - Calculus
 +
Then head on over to AOPS's Alcumus tool and practice all of these topics constantly. When you are practicing, you will come over problems you miss. When you do, re-read the part in the book that corresponds with that question. The more you do this, the better your skills will get.
  
 
== Books ==
 
== Books ==
−
AoPS has a list of books available through the website, separated by contest level,  [http://www.artofproblemsolving.com/Books/AoPS_B_CP.php here].
 
  
 
The '''Art of Problem Solving books''' are an excellent resource to help prepare for math contests.  They cover a broad range of topics, from algebra to geometry to number theory to combinatorics and much much more.  
 
The '''Art of Problem Solving books''' are an excellent resource to help prepare for math contests.  They cover a broad range of topics, from algebra to geometry to number theory to combinatorics and much much more.  
  
−
* Art of Problem Solving Volume 1 - MathCounts, AMC 8, AMC 10, AMC 12
+
* Art of Problem Solving Volume 1 - [[Mathcounts]], [[AMC 8]], [[AMC 10]]
−
* Art of Problem Solving Volume 2 - AMC 12, AIME, USAMO
+
* Art of Problem Solving Volume 2 - [[AMC 12]], [[AIME]], [[USAMO]], [[MOP]]
  
−
The '''AoPS textbooks''' break down specific areas of mathematics. These books are on 3 levels, Introductory, Intermediate, and Advanced.  The Advanced series, as well as part of the Intermediate series, has not yet been published.  These books are indexed [https://artofproblemsolving.com/store/recommendations.php#state/240 here].  Excerpts are provided, as well as pretests and posttests to see if the books are on the right level for you. '''Alcumus''' is a good resource even if you do not own any of the AoPS books.
+
The '''AoPS textbooks''' break down specific areas of mathematics. These books are on 3 levels, Introductory, Intermediate, and Advanced.  The Advanced series, as well as part of the Intermediate series, has not yet been published.  These books are indexed [https://artofproblemsolving.com/store/recommendations.php#state/240 here].  Excerpts are provided, as well as pretests and posttests to see if the books are on the right level for you. '''Alcumus''' is a good resource even if you do not own any of the AoPS books. A very important note is that the prealgebra series will cover everything from algebra, number theory, geometry, and counting & probability, but justs skims through the important parts. Theoretically, with extensive(and we mean loads) of practice and going over the book multiple times(yes, the entire book), you could score well on the basic level competitions like Mathcounts or AMC 8.
  
−
* Prealgebra - [[Mathcounts]], [[AMC 8]]  
+
* Prealgebra - [[Mathcounts]], [[MOEMS]]  
−
* Introduction to Algebra - Mathcounts, AMC 8, [[AMC 10]]
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* Introduction to Algebra - [[Mathcounts]], [[AMC 8]]
−
* Introduction to Number Theory - Mathcounts, AMC 8, AMC 10, [[AMC 12]]
+
* Introduction to Number Theory - [[Mathcounts]], [[AMC 8]], [[AMC 10]], [[AMC 12]], [[AIME]]
−
* Introduction to Geometry - Mathcounts, AMC 8, AMC 10, AMC 12
+
* Introduction to Geometry - [[Mathcounts]], [[AMC 8]], [[AMC 10]], [[AMC 12]], [[AIME]], [[HMMT]]
−
* Introduction to Counting & Probability - Mathcounts, AMC 8, AMC 10, AMC 12
+
* Introduction to Counting & Probability - [[Mathcounts]], [[AMC 8]], [[AMC 10]], [[AMC 12]], [[AIME]]
−
* Intermediate Algebra - AMC 10, AMC 12, [[AIME]], [[USAMO]]
+
* Intermediate Algebra - [[AMC 10]], [[AMC 12]], [[AIME]], [[USAMO]], [[HMMT]]
−
* Intermediate Counting & Probability - AMC 12, AIME, USAMO
+
* Intermediate Counting & Probability - [[AMC 12]], [[AIME]], [[HMMT]], [[USAMO]]
−
* Precalculus - AMC 12, AIME, USAMO
+
* Precalculus - [[AMC 12]], [[AIME]], [[USAMO]]
−
* Calculus - [[Putnam]]
+
* Calculus - [[HMMT]], [[Putnam]]
  
 
Here are a few more '''books good for preparation for higher level contests''' such as AMC 12, AIME, and USAMO (though some can be found online):
 
Here are a few more '''books good for preparation for higher level contests''' such as AMC 12, AIME, and USAMO (though some can be found online):
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* [http://www.maa.org/press/ebooks/euclidean-geometry-in-mathematical-olympiads Euclidean Geometry in Math Olympiads] by Evan Chen
 
* [http://www.maa.org/press/ebooks/euclidean-geometry-in-mathematical-olympiads Euclidean Geometry in Math Olympiads] by Evan Chen
 +
 +
 +
===AMC 8:===
 +
 +
Algebra: Introduction to Algebra
 +
 +
Geometry: Introduction to Geometry
 +
 +
Combinatorics: Introduction to Counting & Probability
 +
 +
General: Math competitions-Middle School
 +
 +
-Note:(Not much Number Theory is asked on the AMC 8).
 +
 +
 +
===AMC 10: (Good to review volume 1)===
 +
 +
Algebra: Intermediate Algebra
 +
 +
Geometry: Introduction to Geometry
 +
 +
Combinatorics: Introduction to Counting & Probability
 +
 +
Number Theory: Introduction to Number Theory
 +
 +
General: Volume 1
 +
 +
===AMC 12: ===
 +
 +
Algebra:  Intermediate Algebra
 +
 +
Geometry: Introduction to Geometry
 +
 +
Combinatorics: Intermediate Counting & Probability (review Introduction to Counting and Probability if needed)
 +
 +
Number Theory: Introduction to Number Theory
 +
 +
General: Volume 2
 +
 +
Extra: Precalculus
  
 
== Practice Problems ==
 
== Practice Problems ==
 
Old practice problems (with solutions) sorted by contest and year are available on the Wiki and the Resources section. Many practice problems are also available on the forums.
 
Old practice problems (with solutions) sorted by contest and year are available on the Wiki and the Resources section. Many practice problems are also available on the forums.
−
 
−
[https://www.clevermath.org/ Clevermath] provides weekly problems. (Currently, Clevermath is not available.)
 
  
 
Here are some old contest archives that may be useful for practicing with:
 
Here are some old contest archives that may be useful for practicing with:
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Harvard-MIT Mathematics Tournament:
 
Harvard-MIT Mathematics Tournament:
−
* [http://web.mit.edu/hmmt/www/datafiles/problems/ HMMT] is a nice contest on a hard AIME level.
+
* [https://www.hmmt.co/archive/problems/ HMMT] is a nice contest on a hard AIME level.
  
 
* [http://www.artofproblemsolving.com/Forum/resources.php More Contests].
 
* [http://www.artofproblemsolving.com/Forum/resources.php More Contests].
  
 
* [http://www.artofproblemsolving.com/wiki/index.php?title=AoPS_Past_Contests User-Created Contests].
 
* [http://www.artofproblemsolving.com/wiki/index.php?title=AoPS_Past_Contests User-Created Contests].
 +
 +
 +
There are certain strategies in preparing for the AMC 10/12- especially qualification for the AIME.
 +
 +
 +
The AIME cutoff has ranged 84-95 on AMC 12.since 2020 when the qualification was loosened to "5% of scorers". In order to get a score in the range, a simple way is to answer 13 questions right (check your work carefully!) and leave the rest blank, which earns a score of 96. In the past, since the 2020  cutoffs have beenontests have been getting slightly harder each year, and new generations of competitors don't always match the new level. This means, since the first 10 questions are solvable in half the test time by most people who prepare, they are 60 easy points. Throughout questions #10-#20, answering 3-5 shall be enough to qualify.
 +
 +
Beware, though, that the AIME question #1 is harder than AMC question #10, so this strategy presumes that you *could* solve more than 15 AMC problems, but you are choosing to reduce your time/difficulty pressure and increase your confidence, to guarantee a qualifying score but not get your highest possible score.
 +
 +
 +
 +
Qualification for the USAMO, however, is much harder. Only 260-270 people qualify every year. USAMO qualifiers need a good combination of AMC & AIME scores. The average score on the AMC 12 for a USAMO qualifier is around 114-132. There are simple ways to do this but it takes a lot of work. Answering the first 15 right, and then getting 5 out of the 10 left would usually qualify.
 +
 +
 +
 +
 +
The AIME cutoff on the AMC 10 have ranged throughout (96-104) in recent years. The top 2.5% of scorers qualify. The AMC 10 does test less topics than the AMC 12 but many questions go into much more depth. Cutoffs on the AMC 10 are higher since the testing only tests topics up to Geometry. AIME ranges from Algebra to precalculus, which means only very elite scorers make it. Though the qualifying scores are high, there is indeed a good strategy. Since you get 1.5 points for each question blank, it’s good just to do what you know. Answering 15 questions right and leaving the rest blank would earn a score of 105 while answering 20 right and leaving the rest blank would earn a score of 127.5. Since contests are getting harder as said earlier, 15-18 right should be enough.
 +
 +
 +
 +
 +
Qualifications for the USAJMO is similar to that for the USAMO except they use AMC 10 scores.
 +
 +
 +
 +
 +
 +
 +
Top 10 most Difficult math Competitions(National) in The USA:
 +
 +
10. MATHCOUNTS - Pre-Algebra, Geometry, Number Theory, Combinatorics, Logic
 +
 +
 +
9. AMC 10 - Intermediate Algebra, Geometry, Number Theory, Combinatorics
 +
 +
 +
8. AMC 12 - Intermediate Algebra, Geometry, Number Theory, Combinatorics, Pre-Calculus
 +
 +
 +
7. ARML - Advanced Algebra, Geometry, Number Theory, Combinatorics
 +
 +
 +
6. AIME - Advanced Algebra, Advanced Geometry, Number Theory, Combinatorics, Pre-Calculus
 +
 +
 +
5. USAMTS - Advanced Algebra, Advanced Geometry, Number Theory, Combinatorics, Pre-Calculus
 +
 +
 +
4. USAJMO - Advanced Algebra, Advanced Geometry, Advanced Number Theory, Combinatorics
 +
 +
 +
3. USAMO - Advanced Algebra, Very Advanced Geometry, Advanced Number Theory, Combinatorics, Advanced Pre-Calculus
 +
 +
 +
1 (tie). IMO - Very Advanced Algebra, Very Advanced Geometry, Very Advanced Number Theory, Advanced Combinatorics, Advanced Pre-Calculus
 +
 +
 +
1 (tie). PUTNAM - Advanced Algebra, Geometry, Number Theory, Advanced Combinatorics, Advanced Calculus
  
 
== Forums ==
 
== Forums ==
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* The [https://artofproblemsolving.com/community/c6_high_school_olympiads Olympiad] forum is a forum for problems at the olympiad level.
 
* The [https://artofproblemsolving.com/community/c6_high_school_olympiads Olympiad] forum is a forum for problems at the olympiad level.
  
−
* The [http://www.artofproblemsolving.com/community/c68_latex_and_asymptote LaTeX] forum is a place to get help with LaTeX, which is what you use to type things like <math>2^3</math> on the forums.
+
* The [http://www.artofproblemsolving.com/community/c68_latex_and_asymptote LaTeX and Asymptote] forum is a place to get help with <math>\text{\LaTeX}</math>, which is what you use to type things like <math>2^3</math> on the forums. It's also for Asymptote, which is what we use to make diagrams, like: <asy>
 +
draw((0,0)--(2,0)--(0,2)--cycle);
 +
label("A",(0,0),SW);
 +
label("B",(2,0),SE);
 +
label("C",(0,2),NW);
 +
</asy>
 +
 
 +
== Books ==
 +
* Ritvik Rustagi's [https://www.tmasacademy.com/ace-the-amc10-12-free-book ACE The AMC 10 and 12 book] is a great resource to use for AMC 10 and AMC 12. The book has over 200 page and contains 250+ problems with detailed solutions.
 +
 
 +
* Free [https://www.omegalearn.org/mastering-amc8 Mastering AMC 8 book] is a good way to learn and review the topics on the AMC 8
 +
 
 +
* Free [https://www.omegalearn.org/mastering-amc1012 Mastering AMC 10/12 book] is a good way to learn and review the topics on the AMC 10/12
  
 
== Cheat Sheets ==
 
== Cheat Sheets ==
 
Many great reference guides are available for free on the internet.
 
Many great reference guides are available for free on the internet.
 +
* Ritvik Rustagi's 53-page long handout has all the formulas for the AMC 10 and AMC 12. The handout was made alongside a 4 hour long review seminar for AMC 10 and AMC 12. It's a great way to review and learn new topics for the AMC 10 and AMC 12. [https://www.tmasacademy.com/amcseminar]
 +
 +
* BOGTRO's list of theory relevant to the AIME. https://www.dropbox.com/s/icds9u5yo0xypyf/AIMElist.pdf?dl=0
 +
 +
* Sohil Rathi's [https://www.omegalearn.org/thebookofformulas The Book of Mathematical Formulas & Strategies] is a great way to review all formulas on math contests like AMCs, AIME, MATHCOUNTS, etc
  
 
* Coach Monk's [http://mathweb.scranton.edu/monks/courses/ProblemSolving/MathCountsPlaybookBW.pdf MathCounts Playbook] is a good place to start for MathCounts-level material.
 
* Coach Monk's [http://mathweb.scranton.edu/monks/courses/ProblemSolving/MathCountsPlaybookBW.pdf MathCounts Playbook] is a good place to start for MathCounts-level material.
Line 85: Line 217:
 
*The Mandelbrot Competition maintains a nice list of topics you need to know for high school math competitions called [http://www.mandelbrot.org/resources/forms/indivtopics.pdf All of Math in 3 Pages].
 
*The Mandelbrot Competition maintains a nice list of topics you need to know for high school math competitions called [http://www.mandelbrot.org/resources/forms/indivtopics.pdf All of Math in 3 Pages].
 
* [http://web.archive.org/web/20060518133620/http://staff.imsa.edu/math/journal/volume4/articles/NoahSheets.pdf The Noah Sheets]
 
* [http://web.archive.org/web/20060518133620/http://staff.imsa.edu/math/journal/volume4/articles/NoahSheets.pdf The Noah Sheets]
 +
 +
* The Popular Elementary Math Competitions [https://medium.com/@edustar/popular-elementary-school-math-competitions-do-you-know-them-7298dc1d3108 Contests to build Math Interests]
  
 
== Classes ==
 
== Classes ==
 +
 +
Free AMC 8 Fundamentals Class: https://www.omegalearn.org/amc8-fundamentals
 +
 +
Free AMC 8 Advanced/Mathcounts Class: https://www.omegalearn.org/amc8-fundamentals
 +
 +
Free AMC 10/12 Class: https://www.omegalearn.org/amc10-12
 +
 +
Free AMC 8/10 Class: https://www.youtube.com/channel/UC-Nt9Uo03VSo2QTNIzsE_cA (Some special seminars occasionally with Olympiad Winners)
  
 
If you are serious about improving your problem-solving skills, AoPS offers several online classes, available [http://www.artofproblemsolving.com/Classes/AoPS_C_About.php here].
 
If you are serious about improving your problem-solving skills, AoPS offers several online classes, available [http://www.artofproblemsolving.com/Classes/AoPS_C_About.php here].
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Summer programs are also a great way to improve problem-solving skills.  Some of these include:
 
Summer programs are also a great way to improve problem-solving skills.  Some of these include:
  
 +
* [https://rossprogram.org/ Ross Mathematics Program]
 
* [http://www.promys.org/ PROMYS]  
 
* [http://www.promys.org/ PROMYS]  
 
* [http://www.mathcamp.org/ MathCamp]
 
* [http://www.mathcamp.org/ MathCamp]
 
* [http://www.mathpath.org/ MathPath]
 
* [http://www.mathpath.org/ MathPath]
−
* [http://www.awesomemath.org/index.shtml AwesomeMath]
+
* [https://www.awesomemath.org/ AwesomeMath]
−
 
+
* [http://ideamath.org IdeaMath]
−
== Past AoPS Topics ==
 
−
=== Mathcounts ===
 
−
* '''[http://artofproblemsolving.com/community/q1h1217349p6066794 How to Prepare for Mathcounts]'''
 
−
 
 
−
=== AMC ===
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=174272 Best Ways to Prepare]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=139495 AMC prep.]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=210890 too late to prepare?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=209162 Preparing book questions]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=208696 amc 10 prep course?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=194187 Torn between books]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=193636 studying for AMC 10 for next year]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=191604 advice for AMC success]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=189902 Advice for a newbie?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=187851 Which AOPS book to buy?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=186820 I need help with AMC10!]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=181662 How would you prepare for the AMC10 these next weeks?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=169323 Best way to prepare for the AMC 10]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=170137 amc 10??]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=148196 Algebra 2 and Preparation for AIME/AMC]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=136730 Getting High Scores on AMC]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=194022 Advice for AMC12]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=132677 getting better at math...fast]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=132374 Improving your AMC score!!!]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=133900 I finally got hold of the AoPS V2]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=181707 How to prepare for the AMC 12?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184350 AMC 12 Preparation]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=174299 help w/ AMC12 and AIME?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=173664 Practicing By Taking Older Contests]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=152170 how should I study for the AMC 12/AIME?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=152414 Preparing for AMC12/AIME]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=1361994 attacking the later problems in the AMC 10/AMC 10 advice]
 
−
 
 
−
=== AIME ===
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=193085 AIME Prep: for newbies]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=173323 About preparing]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=169466 AoPS books are useless?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=170179 Book for AIME]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=136183 Concepts to know for the AIME...]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=136810 Trig functions to know for AIME?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=136536 Tips, Formulas, Must-knows, hard previous questions 4 AIME?]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=132916 Easiest Subject to Improve In]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=132563 AIME prep...]
 
−
 
 
−
=== USAMO ===
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=199616 What to study]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=196885 Please Help!!!]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=172265 Recommended USAMO Prep?]
 
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* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=149393 Memorization]
 
−
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=142476 USAMO Help!]
 
  
 
== See Also ==
 
== See Also ==

Revision as of 18:32, 19 August 2024

Introduction

The best way to prepare for math contests is to do lots of practice problems and learn the material necessary to solve the problems. There are also many books and online handouts/lectures you can use to improve your problem-solving skills. Depending on your current abilities, you will want to start out with different practice problems, different books,

High Level Overview

If you don't feel like going too deep and want a straightforward answer, here it is:

- Beginner To score well on the low level competitions(like Mathcounts and AMC 8), first read the following AOPS books and take their AOPS Academy/Online classes simultaneously in this order: 

 - Pre Algebra
 - Introduction to Algebra
 - Introduction to Geometry
 - Introduction to Number Theory
 - Introduction to Counting & Probability
 - Volume 1

Then head on over to AOPS's Alcumus tool and practice all of these topics constantly. When you are practicing, you will come over problems you miss. When you do, re-read the part in the book that corresponds with that question. The more you do this, the better your skills will get.

- Advanced To score well on the high level competitions(like AMC 10 and AIME), first read the following AOPS books and take their AOPS Academy/Online classes simultaneously in this order: 

 - Intermediate Algebra
 - Intermediate Counting and Probability
 - Volume 2
 - Precalculus
 - Calculus

Then head on over to AOPS's Alcumus tool and practice all of these topics constantly. When you are practicing, you will come over problems you miss. When you do, re-read the part in the book that corresponds with that question. The more you do this, the better your skills will get.

Books

The Art of Problem Solving books are an excellent resource to help prepare for math contests. They cover a broad range of topics, from algebra to geometry to number theory to combinatorics and much much more.

The AoPS textbooks break down specific areas of mathematics. These books are on 3 levels, Introductory, Intermediate, and Advanced. The Advanced series, as well as part of the Intermediate series, has not yet been published. These books are indexed here. Excerpts are provided, as well as pretests and posttests to see if the books are on the right level for you. Alcumus is a good resource even if you do not own any of the AoPS books. A very important note is that the prealgebra series will cover everything from algebra, number theory, geometry, and counting & probability, but justs skims through the important parts. Theoretically, with extensive(and we mean loads) of practice and going over the book multiple times(yes, the entire book), you could score well on the basic level competitions like Mathcounts or AMC 8.

Here are a few more books good for preparation for higher level contests such as AMC 12, AIME, and USAMO (though some can be found online):


AMC 8:

Algebra: Introduction to Algebra

Geometry: Introduction to Geometry

Combinatorics: Introduction to Counting & Probability

General: Math competitions-Middle School

-Note:(Not much Number Theory is asked on the AMC 8).


AMC 10: (Good to review volume 1)

Algebra: Intermediate Algebra

Geometry: Introduction to Geometry

Combinatorics: Introduction to Counting & Probability

Number Theory: Introduction to Number Theory

General: Volume 1

AMC 12:

Algebra: Intermediate Algebra

Geometry: Introduction to Geometry

Combinatorics: Intermediate Counting & Probability (review Introduction to Counting and Probability if needed)

Number Theory: Introduction to Number Theory

General: Volume 2

Extra: Precalculus

Practice Problems

Old practice problems (with solutions) sorted by contest and year are available on the Wiki and the Resources section. Many practice problems are also available on the forums.

Here are some old contest archives that may be useful for practicing with:

American Mathematics Competitions:

American Invitational Mathematical Examination:

United States of America Mathematical Olympiad:

Harvard-MIT Mathematics Tournament:

  • HMMT is a nice contest on a hard AIME level.


There are certain strategies in preparing for the AMC 10/12- especially qualification for the AIME.


The AIME cutoff has ranged 84-95 on AMC 12.since 2020 when the qualification was loosened to "5% of scorers". In order to get a score in the range, a simple way is to answer 13 questions right (check your work carefully!) and leave the rest blank, which earns a score of 96. In the past, since the 2020 cutoffs have beenontests have been getting slightly harder each year, and new generations of competitors don't always match the new level. This means, since the first 10 questions are solvable in half the test time by most people who prepare, they are 60 easy points. Throughout questions #10-#20, answering 3-5 shall be enough to qualify.

Beware, though, that the AIME question #1 is harder than AMC question #10, so this strategy presumes that you *could* solve more than 15 AMC problems, but you are choosing to reduce your time/difficulty pressure and increase your confidence, to guarantee a qualifying score but not get your highest possible score.


Qualification for the USAMO, however, is much harder. Only 260-270 people qualify every year. USAMO qualifiers need a good combination of AMC & AIME scores. The average score on the AMC 12 for a USAMO qualifier is around 114-132. There are simple ways to do this but it takes a lot of work. Answering the first 15 right, and then getting 5 out of the 10 left would usually qualify.



The AIME cutoff on the AMC 10 have ranged throughout (96-104) in recent years. The top 2.5% of scorers qualify. The AMC 10 does test less topics than the AMC 12 but many questions go into much more depth. Cutoffs on the AMC 10 are higher since the testing only tests topics up to Geometry. AIME ranges from Algebra to precalculus, which means only very elite scorers make it. Though the qualifying scores are high, there is indeed a good strategy. Since you get 1.5 points for each question blank, it’s good just to do what you know. Answering 15 questions right and leaving the rest blank would earn a score of 105 while answering 20 right and leaving the rest blank would earn a score of 127.5. Since contests are getting harder as said earlier, 15-18 right should be enough.



Qualifications for the USAJMO is similar to that for the USAMO except they use AMC 10 scores.




Top 10 most Difficult math Competitions(National) in The USA:

10. MATHCOUNTS - Pre-Algebra, Geometry, Number Theory, Combinatorics, Logic


9. AMC 10 - Intermediate Algebra, Geometry, Number Theory, Combinatorics


8. AMC 12 - Intermediate Algebra, Geometry, Number Theory, Combinatorics, Pre-Calculus


7. ARML - Advanced Algebra, Geometry, Number Theory, Combinatorics


6. AIME - Advanced Algebra, Advanced Geometry, Number Theory, Combinatorics, Pre-Calculus


5. USAMTS - Advanced Algebra, Advanced Geometry, Number Theory, Combinatorics, Pre-Calculus


4. USAJMO - Advanced Algebra, Advanced Geometry, Advanced Number Theory, Combinatorics


3. USAMO - Advanced Algebra, Very Advanced Geometry, Advanced Number Theory, Combinatorics, Advanced Pre-Calculus


1 (tie). IMO - Very Advanced Algebra, Very Advanced Geometry, Very Advanced Number Theory, Advanced Combinatorics, Advanced Pre-Calculus


1 (tie). PUTNAM - Advanced Algebra, Geometry, Number Theory, Advanced Combinatorics, Advanced Calculus

Forums

The forums are one of the best ways to find problems to solve, get help with problems you cannot solve, and collaborate with people of all levels and abilities. The forum is divided into many subforums for problems of different difficulties.

  • The Middle School forum is for MathCounts and AMC 8/10-level problems.
  • The High School forum is a good place to find AMC10/12-level and AIME-level problems.
  • The Olympiad forum is a forum for problems at the olympiad level.
  • The LaTeX and Asymptote forum is a place to get help with $\text{\LaTeX}$, which is what you use to type things like $2^3$ on the forums. It's also for Asymptote, which is what we use to make diagrams, like: [asy] draw((0,0)--(2,0)--(0,2)--cycle); label("A",(0,0),SW); label("B",(2,0),SE); label("C",(0,2),NW); [/asy]

Books

  • Ritvik Rustagi's ACE The AMC 10 and 12 book is a great resource to use for AMC 10 and AMC 12. The book has over 200 page and contains 250+ problems with detailed solutions.

Cheat Sheets

Many great reference guides are available for free on the internet.

  • Ritvik Rustagi's 53-page long handout has all the formulas for the AMC 10 and AMC 12. The handout was made alongside a 4 hour long review seminar for AMC 10 and AMC 12. It's a great way to review and learn new topics for the AMC 10 and AMC 12. [1]
  • Coach Monk's High School Playbook goes a little more in depth, and is useful for all levels of high school mathematics.

Classes

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

Free AMC 8 Advanced/Mathcounts Class: https://www.omegalearn.org/amc8-fundamentals

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

Free AMC 8/10 Class: https://www.youtube.com/channel/UC-Nt9Uo03VSo2QTNIzsE_cA (Some special seminars occasionally with Olympiad Winners)

If you are serious about improving your problem-solving skills, AoPS offers several online classes, available here.

WOOT is an online class offered by AoPS for olympiad training. It has one of the best peer groups in the country, and is a great way to prepare for the USAMO.

Summer Camps

Summer programs are also a great way to improve problem-solving skills. Some of these include:

See Also

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