Incidentally, I am a high school sophomore educated in a way that is not quite home-schooling but very similar to it. It’s called home-bound education. The difference between this and home-schooling: You get a tutor which the school district pays for, you generally get less work than other at-home kids, it is temporary (usually only for a couple of months) and you only qualify if you have a very serious, serious problem (kids usually get home-bound if they have a medical condition, depression most commonly. I got it because I have an ill family member). I know this isn’t what your looking for, but I’ve been through similar paper work and procedure the at-home kids have, and I possess first hand experience on the general subject.
First off, you should know that school’s are(or at least my school district is) very much against home schooling, and there going to give you a hellish time about it . Also, this sort of thing takes time, and you’re not going to be able to switch back and forth when you feel like it.
If you still really want to go through with this, the first place you need to go is to your guidance counselor. They have, or will get you, all the info you’ll need. If your still determined, you’ll see an administrator who will give you a thick packet of papers you’re supposed to read over with your parents. After your parents sign them and some other documents, and make out arrangements for borrowing books and materials, you’ll be set (it’ll take some serious time for it to go through, probably). If I recall, they asked a lot of questions about my parents level of education and willingness to commit. Keep this in mind.
I’m not an expert on the subject, but I strongly doubt the school district will allow you to completely tutor yourself (I know over a thousand high school kids, and I say this would be a wise policy). If you can’t find a dedicated parent, guardian, or teacher to go in with you, your chances of being abdicated from the public school life are very slim. Even worse, those subjects you mentioned are fundamental to getting your diploma, and the school’s not going to let you get by without knowing them. I hate to be concrete on this matter, partly because most of the replies have been positive regarding your idea, and the Straight Doper’s are very bright people, but I think you’re going to get a resounding ‘hell no’ when you tell the school about your plan. Honestly, I almost laughed when I read about your ambitions and your circumstance. If your hearts set, though, I’d recommend giving it a try. I’m sure the standards differ form state to state.
On a more superficial, but equally important, level, there are some serious cons to not going to school. Namely, having a social life. I am well connected, am fairly popular, somewhat anti-social, have a great girl friend, but I feel lonely a lot. Staying home 24/7 isn’t the utopia you might think it is (my one home-schooled friend works his ass off). Besides, where else do you get to see, everyday, hundreds of busty teenager girls in slutty tank tops and mini-skirts? (Still love you Alexa:) ) Obviously, if you have a functioning set of balls, you’re gonna be missing out.
Someone else mentioned going to college right now. Trust me on this and Don’t Do It. If you want reasons, or any more info, tell me. It’s late, and I’m tired.
As a peer, I wish you much luck.