How should I prepare?
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. You should also try to strengthen in the areas you are not as good at. This guide is intended to help you get started.
AoPS has a list of books available through the website, separated by contest level, 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.
- Art of Problem Solving Volume 1 - MathCounts, AMC 8, AMC 10, AMC 12
- Art of Problem Solving Volume 2 - AMC 12, AIME, USAMO
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.
- Prealgebra - Mathcounts, AMC 8
- Introduction to Algebra - Mathcounts, AMC 8
- Introduction to Number Theory - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
- Introduction to Geometry - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
- Introduction to Counting & Probability - Mathcounts, AMC 8, AMC 10, AMC 12, AIME
- Intermediate Algebra - AMC 10, AMC 12, AIME, USAMO
- Intermediate Counting & Probability - AMC 12, AIME, USAMO
- Precalculus - AMC 12, AIME, USAMO
- Calculus - Putnam, IMO
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):
- The Three-Year MATHCOUNTS Marathon by Karen Ge (It is intended for Mathcounts, but it could potentially help in AMC 10 and 12.)
- Art and Craft of Problem Solving by Paul Zeitz
- Problem-Solving Strategies by Arthur Engel
- Geometry Revisited by H.S.M. Coxeter & Samuel L. Greitzer
- 102 Combinatorial Problems by Titu Andreescu & Zuming Feng
- 103 Trigonometry Problems by Titu Andreescu & Zuming Feng
- 104 Number Theory Problems by Titu Andreescu & Zuming Feng
- Euclidean Geometry in Math Olympiads by Evan Chen
For the AMC 8, the Pre-Algebra book should be enough. Algebraic problems are asked more simpler than ones of the advanced competitions. AMC 8: (Algebra: Introduction to Prealgebra), (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: (Algebra: Intermidiate Algebra), (Geometry: Introduction to Geometry), (Number Theory: Introduction to Number Theory), (Combinatorics: Introduction to Counting & Probability), (General: Volume 1)-Note:(Introduction to Algebra is not needed much for competitions other than ARML)
AMC 12: (Algebra: Intermidiate Algebra), (Geometry: Introduction to Geometry), (Number Theory: Introduction to Number Theory), (Combinatorics: Intermidiate Counting & Probability), (General: Volume 2), (Extra: Introduction to Precalculus).
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.
Clevermath provides weekly problems. (Currently, Clevermath is not available.)
Here are some old contest archives that may be useful for practicing with:
American Mathematics Competitions:
American Invitational Mathematical Examination:
- AIME Problems and Solutions - AIME is a contest administered to those who qualify with a high score on the AMC 10/12.
United States of America Mathematical Olympiad:
- USAMO Problems and Solutions - USAMO is a proof-based contest which must be qualified for through a combination of AMC & AIME scores.
Harvard-MIT Mathematics Tournament:
- HMMT is a nice contest on a hard AIME level.
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 forum is a place to get help with , which is what you use to type things like on the forums.
Many great reference guides are available for free on the internet.
- Coach Monk's MathCounts Playbook is a good place to start for MathCounts-level material.
- Coach Monk's High School Playbook goes a little more in depth, and is useful for all levels of high school mathematics.
- The Mandelbrot Competition maintains a nice list of topics you need to know for high school math competitions called All of Math in 3 Pages.
- The Noah Sheets
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 programs are also a great way to improve problem-solving skills. Some of these include:
Past AoPS Topics
- Best Ways to Prepare
- AMC prep.
- too late to prepare?
- Preparing book questions
- amc 10 prep course?
- Torn between books
- studying for AMC 10 for next year
- advice for AMC success
- Advice for a newbie?
- Which AOPS book to buy?
- I need help with AMC10!
- How would you prepare for the AMC10 these next weeks?
- Best way to prepare for the AMC 10
- amc 10??
- Algebra 2 and Preparation for AIME/AMC
- Getting High Scores on AMC
- Advice for AMC12
- getting better at math...fast
- Improving your AMC score!!!
- I finally got hold of the AoPS V2
- How to prepare for the AMC 12?
- AMC 12 Preparation
- help w/ AMC12 and AIME?
- Practicing By Taking Older Contests
- how should I study for the AMC 12/AIME?
- Preparing for AMC12/AIME
- attacking the later problems in the AMC 10/AMC 10 advice
- AIME Prep: for newbies
- About preparing
- AoPS books are useless?
- Book for AIME
- Concepts to know for the AIME...
- Trig functions to know for AIME?
- Tips, Formulas, Must-knows, hard previous questions 4 AIME?
- Easiest Subject to Improve In
- AIME prep...