One thing I do when I'm bored is to prove the equations I've been taught in my math classes but have never seen derived (like many people, I often skip past the proofs in the textbook when I'm in a rush to finish my homework). Deriving these is enlightening and gives me a nice feeling of "oh, that's why." Also, understanding the derivation of the fundamental math theorems can actually come in handy, in contrast to some contest questions, which can be contrived and arcane in comparison.