AP Calculus AB Test : Derivatives & Integrals


e2
1
½
0
Non- existent
Let f(x) = |sin x – ½ |. The maximum value attained by f is
½
1
3/2
p/2
3 p/2

-1/2
ln 2- 2
ln 2
2
ln 2+ 2

2
4
8
16
32

Suppose that f is an odd function; i.e., f (-x) = - f (x) for all x. Suppose that f (x0) exists. Which of the following must necessarily be equal to f (-x0)?
f’ (x0 )
-f’ (x0 )
None of the above
The region in the first quadrant bounded by the graph of y = secx, x= p/4, and the axes is rotated about the x-axis. What is the volume of the solid generated?
If tan(x/y) = x , then dy /dx =

If the solutions of f (x) = 0 are –1 and 2, then the solutions of f (x/2 ) =0 are
- 1 and 2
-1/2 and 5/2
-3/2 and 3/2
-1/2 and 1
-2 and 4



None of the above.




1
e
e-1
There is no maximum value for v

II only
III only
I only
I and III only
I and II only

None of the above

12
None of the above
Description:

This test contains twenty questions on Derivatives and Applications of derivatives, Integrals, Application of Integrals. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Wherever appeared, lnx represents the natural logarithm of x with base e. Sometimes, the options may not contain exact numerical value of an answer. In that case, select best approximation to the numerical value you got. After examining the form of the choices, decide the best of the choices given.

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