California Math League, which gives challenging math tests to 6-12th grades for fun (and bragging rights). In high school, there are 6 tests each year, with 6 math problems each, ranging from almost trivial to damn near impossible and including algebra and geometry. (All the problems are solvable without higher math than that, but the reasoning skills developed in higher math are almost required to do well.) Almost anyone can get number 1; I am darn proud when I get number 6, and I pride myself in my math skills. (The math teacher at my school gets number 6 right about half the time.) This and the AMC 10 and 12 tests (formerly both the AHSME) are great for students who want to stretch their mathematical skills, and make sure those same skills can be put to good use on a college application. (The tests provide quantitative measurements of mathematical skill, which colleges like; high performers on these tests get awards, which colleges like even more.)