Well, I learned about the modulo concept from reading about it in a previous year of the USAMO. (In fact, this year in taking the USAMO I used the modulo concept for one of my proofs.) I'm only in 10th grade, talking only Honors Algebra II... although I've taught myslef sumation notation (And the multiplication version, as well), arithmatic and geometric sequences, the basic trig functions, and a few other things they don't teach you.
In a twist of irony, geometry is my major mathematical weakness. In the AIME (15 questions, I got 8/15 right) I got:
7/9 non-geometry questions right:
1/6 geometry questions right:
And in the USAMO, I couldn't even write a whole page on either of the 2 geometry proofs. In contrast, I wrote 5-page proofs for 2 of the other questions.
And my biggest mathematical strength is DEFINATELY combinations & probablity (especially the latter). I am AMAZING at probability problems for some reason.
Congratulations! You have just been blessed by the wisdom of Steve.