[High School - Calculus] Preparing for the AP Exam

[Relambrien]

So, I'm taking the AP Calc exam (Calc AB or whatever the first one is) on the seventh. I need to know what sort of things I'm going to have to be good at, what tips or tricks I could use, etc. If anyone could provide any help on this, it would be great.

The reason I'm asking here instead of in class is because my math teacher...is a terrible teacher. I know because he's exactly like me: he can understand things well, but can't explain them at all. Still, I understand the material better than anyone else in the class, and I'm the only one that really has a shot at passing. Considering no one in my school's five-year history has passed the AP Calc exam before, I'm taking this very seriously.

Now, I know the basic tenets of the exam. Limits, differentiation, integration. I'll need to know common derivatives and derivative properties, like these:

Sum and difference rule for differentiation/integration
Product/division rule for differentiation
Power rule for differentiation/integration
Chain rule for differentiation

Derivatives of the six trigonometric functions and their inverses
Derivative of the natural log function
Derivatives of functions involving e

I assume I'll also need to know l'Hopital's Rule, for 0/0, inf^0, 1^inf, inf/inf, etc.

Are there any other topics I missed?

Now, the integration is where I get a little bit confused. How much of the exam involves u-substitution, or the Fundamental Theorem? What antiderivatives do I need to know? What sorts of integration will be allowed with a calculator?

Speaking of calculators, I have a TI-89 Titanium. I know -how- to use it, and I can use it well, but what I don't know is what sort of strategies I can use with it. The solve, differentiate, and integrate commands are awesome, but is there anything else I could apply in obscure ways to help bring about the answer?

And then, just general exam tips. How many questions, how many sections, etc. How many multiple-choice, how many grid-in? Does it work like the SAT in which an incorrect answer takes points away? Which sections will allow the use of a calculator?

If anyone could help me out, I'd really appreciate it. I need to do everything I can to prepare for this exam. Like I said, I'm the first person in my school's history to be likely to pass, and beyond that, I need a 5 for the colleges I want to attend to give me credit for the course. I just want to do the best I can.