This is actually a bit of my story mixed with advice, so it will be somewhat lengthy, anyway, here we go...
At age seven I became very passionate about math, then physics and other topics I taught myself Algebra, Geometry, Trigonometry and Calculus in a summer. From age seven to age ten I continued this pattern, studying topics from all fields of study like differential topology, theoretical physics, etc... I concealed this the best I could though, fearing social reject, but after taking a break from academia between age ten and fourteen I decided it was time I moved forward and tried to get into college early or something. This was just last year, I showed my mathematics teachers a bit of what I could do, took the final for pre-calculus (the class that I was originally scheduled to be taking next year) and they are now considering allowing me to take AP Calculus this coming year, as a sophomore. Similar situations have arisen in all other subjects. But, although I already know the content, I want to take AP classes and stay in high school for the social experience and better chances of getting into a good school with scholarships (although I could probably go to a decent school now for free, much like Jacob Barnett did or others like him).
The point is, that you have to figure out whether skipping is best for you, how much you want to try to skip, how well you actually know the content, and why you want to skip. I wanted to skip for very specific reasons, my classes next year will still be miserably easy, but that wasn't my reason for skipping ahead. Also, you have to be positive you know the content, not just the main ideas. When I learn something new, I go through at least two different materials, often many more (e.g. I took 3 classes, read 2 books and used 2 Internet sites on topology), because you need to be sure you know the content well, and can solve the problems not just understand concepts.
Now, if you have all that figured out, talk to your teachers, and show off a bit to let them know your ability. There is typically no precedent to skip a class or grade, so the teachers will have to talk about it, probably go to the principal and local board of education as well. I warn you though, have good grades and scores in your current classes! I had a 120% in Algebra II last year, but even that wasn't quite enough, because I fell asleep during the final exam, and had to complete the whole thing in about 5 minutes, so I got more like an 80. The board didn't like this, but because of the other circumstances and a demonstration of proficiency in algebra, trig/pre-cal and calculus to my teachers, they approved me to skip and take calculus instead.
So, be sure you know whether this choice is best and why you want to do it, then go talk to your teachers and show them your abilities, while also continuing to put forth some effort (even if it only requires minuscule amounts) to get good grades. Good luck! I hope this helped and conveyed my message accurately, I know you probably aren't so nerdy that you're doing chaos theory and stuff like I have enjoyed doing for a couple years now. Nevertheless, you seem to be very capable and intelligent, so good luck with everything!