Woah - unrelated, but my school lost to Blair at the national science bowl finals. I've just started math competitions recently too, but I'm nowhere near that level, congrats. I'm just hoping for top 100 at the michigan competition.
I don't think my school does math competitions (or, at least, I haven't heard anything about it), but they sound interesting. What exactly do you do in them?
There is some variety, but most of the time you just sit and take a math test for a while, except the problems are way more fun than the math tests you take at school. Sometimes they are written tests and sometimes they are multiple choice or short answer. Usually the problems are based on "classical math" like algebra, geometry, combinatorics, or number theory and are designed so that all you need is cleverness to solve them, rather than knowledge of advanced calculus. Extra knowledge can never hurt though. A few competitions are a little more exciting and are live or have team rounds or other exciting things.
If you are interested in trying them, I would suggest that you ask if your school offers the AMC 12, or see if it is offered at a local university. Also you should look into the Idaho ARML (American Regions Math League) team and see if you can join it, because ARML is a lot of fun and you get to meet a lot of people who like math competitions.
You can find a lot of information and problems from past competitions at
http://www.artofproblemsolving.com/.
Most of the problems posted in the maths thread could be competition problems or are competition problems.