From Wikiversity - Reading time: 2 minEach country typically has its own set of contests. For high school, these usually include one national Mathematics Olympiad and one or more qualifier contests intended to help select students to invite to the national Olympiad. The top six students of every country are then invited to participate in the International Mathematics Olympiad (IMO).
In the United States:
Middle School
High School
Undergraduate
More Listings:
http://k12mathcontests.wikispaces.com/
http://homeschoolmathcontests.com/
There are many problem solving books available for students. The list is broken up into three levels by difficulty. Most of these books can be purchased online.
Art of Problem Solving, Volume 1, by Richard Rusczyk
To practice math facts - KENKEN squares challenge you to think spatially while practicing math facts. www.kenken.com
Art of Problem Solving, Volume 2, by Richard Rusczyk
The Art and Craft of Problem Solving, by Paul Zeitz
Problem-Solving through Problems, by Loren C. Larson
Problem Solving Strategies, by Arthur Engel
http://www.aplusclick.com/grade15.htm