What do I study next?

Senior in high-school, finishing up AP Calculus BC. I have a book that covers multivariable calculus, and a book on linear algebra. I'm working through both on my own, and it's going great. Unfortunately, the university I'll be going to won't accept the AP for credit, and I'll obviously need to take the multivariable calculus/linear algebra in a class to prove that I can do it. It'll take about a year for me to be able to actually be able to take any "new" courses in university, essentially. I don't doubt that these courses will be a challenge, it's just that I'd like to be doing something more.

I'm just a bit stumped on what I should be trying to study next. Should I just be attempting problems from contests? Or should I be moving ahead to try and tackle some new material?

>>5
If it's the one I'm thinking of, then it's hardly technical at all.