How should I prepare?
Contents
Introduction
The best way to prepare for math contests is to do lots of practice 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.
Books
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.
- Prealgebra - Mathcounts, AMC 8
- Introduction to Algebra - Mathcounts, AMC 8, AMC 10
- Introduction to Number Theory - Mathcounts, AMC 8, AMC 10, AMC 12
- Introduction to Geometry - Mathcounts, AMC 8, AMC 10, AMC 12
- Introduction to Counting & Probability - Mathcounts, AMC 8, AMC 10, AMC 12
- Intermediate Counting & Probability - AMC 12, AIME, USAMO
- Precalculus- AMC 12, AIME, USAMO
- Calculus- Putnam
Here are a few more books good for preparation for higher level contests such as AMC 12, AIME, and USAMO:
- [1] by Paul Zeitz
- (Note: There is also an online version at https://kheavan.files.wordpress.com/2010/06/paul-zeitz-author-the-art-and-craft-of-problem-solving-2edwiley20060471789011.pdf)
- 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
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:
- AMC 8 Problems and Solutions - AMC 8 is a national contest for grades 8 and younger.
- AMC 10 Problems and Solutions - AMC 10 is a national contest for grades 10 and younger.
- AMC 12 Problems and Solutions - AMC 12 is a national contest for grades 12 and younger.
- AIME Problems and Solutions - AIME is a contest administered to those who qualify with a high score on the AMC 10/12.
- USAMO Problems and Solutions - USAMO is a proof-based contest which must be qualified for through a combination of AMC & AIME scores.
- HMMT is a nice contest on a hard AIME level.
- USC is a contest with a lot of problems based on common concepts you will see over and over.
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 MathCounts forum is for MathCounts-level problems.
- The High School Basics forum is a good place to find AMC-level and easy AIME-level problems.
- Intermediate Topics has hard AMC-level problems, as well as all levels of AIME topics. There is not a clear line between Intermediate and High School basics, but Intermediate is generally harder.
- Pre-Olympiad is a forum for problems just below olympiad level. Here you will find a lot of easy USAMO-level proofs, and problems as tough as the last few AIME problems.
- The LaTeX forum is a place to get help with LaTeX, which is what you use to type things like
on the forums.
on the forums.Cheat Sheets
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
Classes
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:
Past AoPS Topics
AMC
- Best Ways to Prepare
- AMC prep.
- AoPS is too hard for me......
- 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
AIME
- 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...
