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is given by
(A) π ∫ 7
0 (D) 2π ∫ 2
( x + 1) 3 dx 2
0 (B) 2π ∫ 1
x( x + 1) 3 dx (D) x3 have a point of inflection?
(D) 3 (E) At no value of x is arcsec( x − 1) (E) 1 ln( x 2 − 2 x + 2) ln x2 − −( x 2 − 2 x + 2) −2 (C) 1 (C) 2 x2 − 2x + 2 (B) 0 2
( x + 1) 3 dx 0 1 (A) (C) π ∫ 2 7 (B) 1 22. An antiderivative for 0 1
x( x + 1) 3 dx (E) π ∫ ( y 3 − 1) 2 dy 21. At what value of x does the graph of y =
(A) 0 7 arctan( x − 1) x−2
x +1 23. How many critical points does the function f ( x) = ( x + 2)5 ( x − 3) 4 have?
(A) One (B) Two (C) Three (D) Five (E) Nine (E) –2 2 24. If f ( x) = ( x 2 − 2 x − 1) 3 , then f ′(0) is
(A) 4
3 (B) 0 (C) − 2
3 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) − 4
3 83 1993 AP Calculus AB: Section I
25. () dx
2=
dx
2 x −1 (A) (B) (2 x −1 ) x (C) (2 x ) ln 2 (D) (2 x −1 ) ln 2 (E) 2x
ln 2 26. A particle moves along a line so that at time t, where 0 ≤ t ≤ π , its position is given by
t2
s (t ) = −4 cos t − + 10 . What is the velocity of the particle when its acceleration is zero?
2
(A) –5.19 (B) 0.74 (C) 1.32 (D) 2.55 (E) 8.13 (D) 46.000 (E) 136.364 (D) 1 (E) nonexistent 27. The function f given by f ( x) = x3 + 12 x − 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
28. 500 ∫1 (13x − 11x ) dx + ∫ 2500 (11x − 13x ) dx = (A) 0.000
29. lim θ→0 1 − cos θ
2sin 2 θ (A) 0 (B) 14.946 (C) 34.415 is
(B) 1
8 (C) 1
4 30. The region enclosed by the xaxis, the line x = 3 , and the curve y = x is rotated about the
xaxis. What is the volume of the solid generated?
(A) 3π (B) 2 3π (C) 9
π
2 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 9 π (E) 36 3
π
5 84 1993 AP Calculus AB: Section I
2 31. If f ( x) = e3ln( x ) , then f ′( x) =
(A) 32. 2 ) dx 3 ∫0 4 − x2 (A) 33. If e3ln( x (B) 3
x 2 ) (C) 6(ln x) e3ln( x (C) e3ln( x
2 π
6 2 ) (D) 5 x 4 (E) 6 x5 (D) 1
ln 2
2 (E) − ln 2 (D) 1
3 (E) 2
3 = π
3 (B) π
4 dy
= 2 y 2 and if y = −1 when x = 1, then when x = 2, y =
dx (A) − 2
3 (B) − 1
3 (C) 0 34. The top of a 25foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute.
When the top of the ladder is 7 feet from the ground, what is the rate of change of the distance
between the bottom of the ladder and the wall?
(A) − 7
feet per minute
8 (B) − 7
feet per minute
24 (C) 7
feet per minute
24 (D) 7
feet per minute
8 (E) 21
feet per minute
25 35. If the graph of y =
then a + c =
(A) –5 ax + b
has a horizontal asymptote y = 2 and a vertical asymptote x = −3 ,
x+c
(B) –1 (C) 0 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 1 (E) 5
85 1993 AP Calculus AB: Section I
36. If the definite integral 2 x2 ∫0 e dx is first approximated by using two inscribed rectangles of equal width and then approximated by using the trapezoidal rule with n = 2 , the difference between the
two approximations is
(A) 53.60 (B) 30.51 (C) 27.80 (D) 26.80 (E) 12.78 37. If f is a differentiable function, then f ′(a ) is given by which of the following?
I.
II.
III. lim f ( a + h) − f ( a )
h lim f ( x) − f (a)
x−a lim f ( x + h) − f ( x )
h h →0 x →a x →a (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III 38. If the second derivative of f is given by f ′′( x) = 2 x − cos x , which of the following could be f ( x) ?
(A) x3
+ cos x − x + 1
3 (B) x3
− cos x − x + 1
3 (C) x3 + cos x − x + 1 (D) x 2 − sin x + 1 (E) x 2 + sin x + 1 39. The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in
the area of the circle is numerically equal to the rate of increase in its circumference. At this
instant, the radius of the circle is
(A) 1
π (B) 1
2 (C) 2
π AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 1 (E) 2 86 1993 AP Calculus AB: Section I 40. The graph of y = f ( x) is shown in the figure above. Which of the following could be the graph
of y = f 41. ( x )? dx
cos(2π u ) du is
dx ∫ 0
(A) 0 (B) 1
sin x
2π (C) 1
cos(2πx)
2π (D) cos(2πx) (E) 2π cos(2πx) 42. A puppy weighs 2.0 pounds at birth and 3.5 pounds two months later. If the weight of the puppy
during its first 6 months is increasing at a rate proportional to its weight, then how much will the
puppy weigh when it is 3 months old?
(A) 4.2 pounds (B) 4.6 pounds (C) 4.8 pounds AP Calculus MultipleChoice Question Collection
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This note was uploaded on 12/29/2010 for the course MATH 214 taught by Professor Smith during the Fall '10 term at Oregon Tech.
 Fall '10
 smith
 Calculus

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