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MIT tuition doesn't depend on how many courses you take, so unless you want to graduate in three years, it doesn't matter financially what you take before you get there.
I took BC in a little under three months, over the summer. However, this is not really normal... CTY gave me a six-month schedule that I went through at double the intended rate, and the instructor was often a bit surprised and confused at the rate I was turning things in.
How it worked: There were video lectures and course notes online. The lectures were good, but I mostly just ignored them and learned from the notes. Then there were a *lot* of practice problems... I filled up like three or four notebooks. Each chapter has a mandatory homework assignment and a test. You're assigned to an online tutor that you correspond with by e-mail or online whiteboard who can explain anything you need, and the videos essentially "teach" you. (That's how it's supposed to work, anyway, but I didn't really have any trouble with the material so I mostly just used the notes and practice problems.)
Side note: My school has a very rigorous BC course that only about 10 of 300 people take, and I learned a lot more than they did. I went to an "integration bee" during campus preview weekend and found that I felt very very well-prepared in calculus despite that my school's math department didn't teach me a lot.
Other side note: CTY Online is a little pricey and the benefits of doing an online course are obviously debatable, but I loved the course. It was challenging but not impossible, and it was so rigorous I came out of it feeling stronger than ever in algebra and trig... if you love learning, it's an awesome option.
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