When I was in high school, it was called AHSME, or "American High School Mathematics Exam." Now it's the American Mathematics Competition (AMC).

The AMC competition problems are multiple choice, but don't let that fool you into thinking that these problems don't require some careful thought and problem solving.

The solutions sections for these problems are quite detailed, so if you can't figure out the problem on your own, you can learn something by reading the solutions.