AP Calculus AB
WS – Ch 5 AP Practice A
Assn #10
d2y

dx 2
3
1. If y  ln 3x  5 , then
a.
3
3x  5
b.
Name
Date
3x  5 
2
c.
9
3x  5 
2
9
d.
3x  5 
2
e.
Period
3
3x  5 2
2. For x  1, the derivative of y  ln 1  x 2 is
a.
x
1  x2
3. If y  ln
a.
x
x2  1
1
2
x 1
b.
x
x 1
2
, then
b.
c.
x
x 1
d.
c.
2x 2  1
x x2  1
d.
2
1
2 1  x2


1
e.
1  x2
dy
is
dx

1

x x2  1
4. If v t   ln t 2  t  1, then a 1 =
1
2
a.
b.
c. 1
3
3


1
x x2  1
4
3
d.
e.
1  x2
x x2  1


e. 3
5. The slope of the line tangent to the graph of 3x 2  5 ln y  12 at 2,1 is
12
12
5
a. 
b.
c.
d. 12
e. -7
5
5
12
6. Let f be the function defined by f x   ln 3x  2 for some positive constant k. If f ' 2   3, what is
the value of k?
ln 3
a.
b. ln 8
c. 4
d. 8
e. 16
ln 8
k
7. A relative maximum value of the function y 
a. 1
8.

b. e
1
ln ln x  C
6
1
e. ln x  C
3
3
x
1
2
3
0
x
x  16
a. 1
2
e2
11.
e. none of these
c.
1 2
ln x  C
3
x
dx 
1
a. ln 5

b.
1 2
ln x  C
6
d.
10.
2
e
ln x
dx =
3x
a. 6 ln 2 x  C
9.
c.
ln x
is
x
1
d.
e
1
ln 5
2
 5
e. ln  
 2
b. ln 10
c. 2 ln 2
d.
b. 2
c. 3
d. 4
e. 5
1
2
c. 1
d. 1
e. e
dx 
dx
 x ln x 
e
a. ln 2
2
12.
x
dx =
1
2
a. ln
5
x
1
b.
2
b. 0
c.
1 5
ln
2 2
d.
1
ln 3
2
e. undefined
13.
cos x
 4  2 sin x dx 
a.
4  2sin x  C
d. 2 ln 4  2sin x  C
b. 
e.
1
C
2 4  sin x 
c. ln 4  2sin x  C
1
1
sin x  csc 2 x  C
4
2
14. The average value of f x   ln 2 x on the interval [2, 4] is
a. -1.204
b. 1.204
c. 2.159
d. 2.408
e. 8.636
15. Let f x   x 5  1 and let g be the inverse function of f. What is the value of g’(0)?
1
a. -1
b.
c. 1
d. g’(0) does not exist
5
e. It cannot be determined from the given information
16. If f is a function which is everywhere increasing and concave upwards, which statement is true about
f 1 , the inverse of f?
a. f 1 is not a function.
b. f 1 is increasing and concave upwards.
c. f 1 is increasing and concave downwards
d. f 1 is decreasing and concave upwards.
e. f 1 is decreasing and concave downwards.
17. For the given figure, the area of the shaded region is ln 4 when k is
a. 4
b. 8
c. e
1
d. e2
y
x
e. e3
2
k
7
18. If
 ln x dx is approximated by 3 circumscribed rectangles of equal width on the x-axis, then the
1
approximation is
1
a. ln 3  ln 5  ln 7 
2
c. 2 ln 3  ln 5  ln 7 
e. ln1  2 ln 3  2 ln 5  ln 7
1
ln1  ln 3  ln 5 
2
d. 2 ln 3  ln 5 
b.