I apologize for the late answer. This is the first notification I have gotten, and when I first posted this, I was unable to view the post for some reason.
In regards to how I study math:
I borrow textbooks on the topics, read them, and do every other problem. I use StackExchange and reddit for proof verification whenever the answer isn’t obviously correct.
In regards to whether or not MIT would be a good fit:
I wanted to go to MIT in part because everyone I knew was calling it a ‘math school’. I was thinking less about whether or not it was a good fit for me, because I care very little for anything outside of my studies, and (perhaps wrongly) see most schools as the same in what they teach. I just want to be able to study and hopefully conduct research. If I care about anything, it’s to have a quiet, organized workplace with minimal interaction with other people.
In regards to CLEPing out of classes:
I actually have the official big purple book that has a test for each of the CLEP subjects in it. In that book, I tried and passed the mathematics, humanities, and literature courses.
In regards to showing passion for math:
I first thought that just sending TeX copies of my notebooks and schedules would suffice to show passion, since math takes up at least 30 hours of my week, and leaves little time for anything else. I’m currently studying for the PRIMES entrance exam, and if I get in, I would suppose the actual math research I would do there would suffice to show passion.
Misc.
Nearly all of my bad grades were freshman year, or more accurately, worse than this one. I now have a B+ average (3.3 GPA). I recently learned I can test out of high school classes, so I’ll only have to go through 1-2 hours of hell next year, rather than 6.
I think that this will help to improve my GPA, both directly, by taking higher-weighted advanced classes, and indirectly, by not taking boring classes. That being said, I can only attempt to test out once, so this is becoming a gigantic object of stress for me. Every test I don’t pass is 200 hours of my life wasted per year of high school.
I just hate high school. It’s so boring, and the more I learn about a subject, the more distorted and evil the high school interpretation of it seems. I hope that college will be better.