# AP Calculus BC Test: Applications of Integration


6.103
3.124
4.223
2.498
5.126

There is no minimum value for ‘a’
e
1

1/12
-1/12
0
1
Undefined

0
1
n – 1
n
n + 1
Which of the following represents the graph of the polar curve r = 2 sec(?

2(e – 1)
4(e – 1)

17/2
5
15/2
nonexistent


None of the above

28
20
16
24
32

None of the above

None of the above
The number of bacteria in a culture is growing at a rate of 6000e3t/4 per unit of time t. At t = 0, the number of bacteria present was 8000. Find the number present at t = 4.
7500e2
2000e2
6000e5
1400 e2
8000e3


1/4
3/4
1/2
-3/4
-1/4
Consider the curve in the xy-plane represented by x = et and y = te-t for t ( 0. The slope of the line tangent to the curve at the point where x = 3 is
2.075
0.482
–0. 037
–0.066
–0. 005
A point moves in a straight line so that its distance at time t from a fixed point of the line is 4t2 -5t. What is the total distance covered by the point between 3rd and 6th seconds?
13
43
53
23
93
The length of the curve determined by the equations x = t2 and y = t from t = 0 to t = 4 is
( x sec2 x dx =
x tan x + C
sec2x + 2 sec2 x tan x + C
x tan x – ln |cos x| + C
x tan x + ln |cos x| + C

2
1.16
1.28
1.12
1.04
Description:

This test contains twenty questions on Derivatives and Applications of derivatives, Vector valued functions, 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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