AP Calculus AB-McDermott
AP Review – Multiple Choice 3.1
(Non-Calculator)
Complete all of the following multiple choice problems.
1) If f (x)  x 3/2 , then f (4) 
A. 6
B. 3
C. 3
D. 6
E. 8
2) Which of the following represents the area of the shaded region in the figure above?
d
D. b  a  f (b)  f (a)
A.  f (y)dy
E. d  c  f (b)  f (a)
c
b
B.
 d  f (x)dx
a
C.
f (b)  f (a)
3n3 - 5n
3) lim 3
n®¥ n - 2n 2 +1 is
A. –5
B. –2
C. 1
4) If x 3  3xy  2y 3  17, then in terms of x and y,
x2  y
x  2y 2
x2  y
B. 
x  y2
x2  y
C. 
x  2y
A. 
D. 3
E. nonexistent
dy

dx
x2  y
2y 2
x2
E. 
1 2y2
D. 
AP Calculus AB-McDermott
5) If the function f is continuous for all real numbers and if f (x) 
A. – 4
B. –2
C. –1
D. 0
E. 2
6) The area of the region enclosed by the curve y 
A.
x2  4
when x ≠ –2, then f (–2) =
x2
5
36
B. ln
2
3
1
, the x-axis, and the lines x = 3 and x = 4 is
x 1
4
3
C. ln
D. ln
E. ln 6
3
2
7) An equation of the line tangent to the graph of y 
A. 13x  y  8
B. 13x  y  18
C. x 13y  64
8) If y  tan x  cot x, , then
2x  3
at the point (1, 5) is
3x  2
D. x 13y  66
E. 2x  3y  13
dy

dx
D. sec2 x  csc2 x
E. sec2 x  csc2 x
A. sec x csc x
B. sec x  csc x
C. sec x  csc x
9) If h is the function given by h(x)  f g(x), where f x   3x 2  1 and g(x)  x , then h(x) =
B. 3x 2 1
A. 3x 3  x
10) If f (x)  x 1 sin x, then f (0) 
A. 2
B. 1
C. 0
C. 3x 2 x  1
D. 3 x  1
2
D. 1
E. 2
E. 3x 2 1
AP Calculus AB-McDermott
11) The acceleration of a particle moving along the x-axis at time t is given by a(t) = 6t  2. If the
velocity is 25 when t = 3 and the position is 10 when t = 1, then the position x(t) =
A. 9t 2 1
D. t 3  t 2  9t  20
B. 3t 2  2t  4
E. 36t 3  4t 2  77t  55
C. t 3  t 2  4t  6
12) If f and g are continuous functions, and if f (x) ≥ 0 for all real numbers x, which of the following
must be true?
b
b
 b

I.  f (x)g(x)dx    f (x)dx    g(x)dx 
a
 a

a
b
II.
a
b
III.
b
b
a
a
  f (x)  g(x)dx   f (x)dx   g(x)dx
b

f (x) dx 
a
 f (x)dx
a
A. I only
B. II only
C. III only
13) The fundamental period of 2 cos(3x) is
2
A.
3
D. II and III only
E. I, II, and III
D. 2
E. 3
B. 2
C. 6
14)

3x 2
x3  1
dx 
A. 2 x 3  1  C
3 3
x 1  C
B.
2
C.
D. ln x 3  1  C
E. ln x 3  1 C
x3  1  C
15) For what value of x does the function f (x)  x  2 x  3 have a relative maximum?
A. –3
7
D.
7
3
B. 
3
5
E.
5
2
C. 
2
2
AP Calculus AB-McDermott
16) The slope of the line normal to the graph of y = 2 ln(sec x) at x 
 x
A.
B.
2
4
is
D. 2
E. nonexistent
A. –2
1
B. 
2
1
C.
2
17)

1 dx 
2
x
x
2
3
2
 C
1
 C
1
6x
3
D.
3

 C
2x x 2 1
3
3
x
2x 3

 xC
5
3
5
E.
2
C.
 x3

 3  x   C

3
 x
18) If f (x)  sin   , then there exists a number c in the interval  x 
that satisfies the
 2
2
2
conclusion of the Mean Value Theorem. Which of the following could be c ?
D. π
2
A.
3
3
E.
2
3
B.
4
5
C.
6
 x 3 for x  0,
19) Let f be the function defined by f (x)  
Which of the following statements about f is
 x for x  0.
true?
A. f is an odd function.
D. f (0)  0
B. f is discontinuous at x = 0.
E. f (x)  0 for x ≠ 0.
C. f has a relative maximum.
AP Calculus AB-McDermott
20) Let R be the region in the first quadrant enclosed by the graph of y  x 1 , the line x = 7, the xaxis, and the y-axis. The volume of the solid generated when R is revolved about the y-axis is given
by
1/3
7
2
A.   x  1 dx
D. 2  x x  1 dx
2/3
0
7
B.
0
7
2  x x  1 dx
1/3
E.
0
2
1/3
  y 3  1 dy
2
0
C.   x  1 dx
2/3
0
21) At what value of x does the graph of y 
A. 0
B. 1
C. 2
1
is
x  2x  2
22) An antiderivative for
B.

ln x
C.
ln

 2x  2 
A.  x 2  2x  2
2
1 1

have a point of inflection?
x2 x3
D. 3
E. At no value of x
2
D. arcsec x 1
E. arctan x 1
2
x2
x 1
23) How many critical points does the function f (x)  x  2  x  3 have?
A. One
D. Five
B. Two
E. Nine
C. Three
5
4
24) If f ( x)   x 2  2 x  1 , then f (0) is
2/3
4
3
B. 0
C.

4
3
E. 2
D. 
A.
2
3
AP Calculus AB-McDermott
25)
d x
2 
dx
A. 2 x1
B.  2 x 1  x
C.
 2  ln 2
x
D.
 2  ln 2
E.
2x
ln 2
x1
26) The function f given by f (x)  x 3 12x  24 is
A. Increasing for x < 2, decreasing for –2 < x < 2, increasing for x > 2
B. decreasing for x < 0, increasing for x > 0
C. increasing for all x
D. decreasing for all x
E. decreasing for x < –2, increasing for –2 < x < 2, decreasing for x > 2
27) The region enclosed by the x-axis, the line x = 3, and the curve y  x is rotated about the x-axis.
What is the volume of the solid generated?
A. 3π
D. 9
B. 2 3
36 3

E.
9
5
C.

2
  , then f ( x) 
3ln x2
28) If f ( x)  e
 
3ln x 2
A. e
3 3lnx 2 
B.
e
x2
C.
6 ln x e
D. 5x 4
E. 6x 5
 
3ln x 2