How should I prepare?
A common question that regularly comes up on the forum is "How can I prepare for MathCounts/AMC/ARML/AIME/USAMO?" This page is intended to answer these questions.
Introduction
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 10, 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.
- Introduction to Algebra - Mathcounts, AMC 8, AMC 10, AMC 12
- 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 Algebra - AMC 12, AIME, USAMO
- Intermediate Counting & Probability - AMC 12, AIME, USAMO
Here are a few more books good for preparation for higher level contests such as AMC 12, AIME, and USAMO:
- 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
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.
