Cracking The Ap Calculus ab Exam 2018

13.∫ sec u tan u du = sec u + C

14.∫ csc u cot u du = − csc u + C

15.∫ + C; |u| < a

16. =

17. 
    

    +   C;  |u| >   a

    
    

PREREQUISITE MATHEMATICS

One of the biggest problems that students have with calculus is that their algebra, geometry, and
trigonometry are not solid enough. In calculus, you’ll be expected to do a lot of graphing. This requires
more than just graphing equations with your calculator. You’ll be expected to look at an equation and have
a “feel” for what the graph looks like. You’ll be expected to factor, combine, simplify, and otherwise
rearrange algebraic expressions. You’ll be expected to know your formulas for the volume and area of
various shapes. You’ll be expected to remember trigonometric ratios, their values at special angles, and
various identities. You’ll be expected to be comfortable with logarithms. And so on. Throughout this
book, we spend a lot of time reminding you of these things as they come up, but we thought we should
summarize them here at the end.

Powers

When you multiply exponential expressions with like bases, you add the powers.

xa  •   xb  =   xa  +   b

When you divide exponentiated expressions with like bases, you subtract the powers.

    =   xa−b

When you raise an exponentiated expression to a power, you multiply the powers.

    =   xab

When you raise an expression to a fractional power, the denominator of the fraction is the root of the
expression, and the numerator is the power.