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Unformatted text preview: t h is given by V = π r 2 h . If the radius and the height
3
1
both increase at a constant rate of centimeter per second, at what rate, in cubic centimeters per
2
second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?
(A) 32. ∫ π
3
0 (A) 1
π
2 (B) 10 π (C) 24 π (D) 54 π (E) 108 π sin ( 3 x ) dx = −2 (B) − 2
3 (C) 0 (D) 2
3 (E) 2 33. The graph of the derivative of f is shown in the figure above. Which of the following could be the
graph of f ? AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 43 1985 AP Calculus AB: Section I
34. The area of the region in the first quadrant that is enclosed by the graphs of y = x3 + 8 and
y = x + 8 is
(A) 1
4 (B) 1
2 (C) 3
4 (D) 1 (E) 65
4 35. The figure above shows the graph of a sine function for one complete period. Which of the
following is an equation for the graph?
(A) ⎛π ⎞
y = 2 sin ⎜ x ⎟
⎝2 ⎠ (B) y = sin ( π x ) (D) y = 2sin ( π x ) (E) y = sin ( 2 x ) (C) y = 2sin ( 2 x ) 36. If f is a continuous function defined for all real numbers x and if the maximum value of f ( x) is 5
and the minimum value of f ( x) is −7 , then which of the following must be true?
I. The maximum value of f ( x ) is 5. II. The maximum value of f ( x) is 7. III. The minimum value of f ( x ) is 0. (A) I only
37. (B) II only (C) I and II only (D) II and III only (E) I, II, and III (D) 1 ∞ lim ( x csc x ) is x →0 (A) −∞ (B) –1 (C) 0 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (E) 44 1985 AP Calculus AB: Section I
38. Let f and g have continuous first and second derivatives everywhere. If f ( x ) ≤ g ( x ) for all real
x, which of the following must be true?
f ′( x) ≤ g ′( x) for all real x
f ′′( x) ≤ g ′′( x) for all real x I.
II. 1 ∫0 III. f ( x) dx ≤ (A) None
39. If f ( x) =
(A)
(B)
(C)
(D)
(E) f
f
f
f
f 1 ∫ 0 g ( x) dx (B) I only (C) III only (D) I and II only (E) I, II, and III ln x
, for all x > 0, which of the following is true?
x is increasing for all x greater than 0.
is increasing for all x greater than 1.
is decreasing for all x between 0 and 1.
is decreasing for all x between 1 and e.
is decreasing for all x greater than e. 40. Let f be a continuous function on the closed interval [ 0, 2] . If 2 ≤ f ( x) ≤ 4, then the greatest
possible value of
(A) 0 2 ∫0 f ( x) dx is (B) 2 (C) 4 (D) 8 (E) 16 41. If lim f ( x) = L, where L is a real number, which of the following must be true?
x →a (A) f ′(a ) exists. (B) f ( x) is continuous at x = a. (C) f ( x) is defined at x = a. (D) f (a) = L (E) None of the above AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 45 1985 AP Calculus AB: Section I
42. d
dx
(A) (D) x ∫2 1 + t 2 dt =
x
1+ x (B) 2 x
1 + x2 − 1
5 (E) 1 + x2 − 5
1
2 1 + x2 − (C) 1 + x2 1
25 43. An equation of the line tangent to y = x3 + 3 x 2 + 2 at its point of inflection is
(A) y = −6 x − 6 (B) y = −3x + 1 (D) y = 3x − 1 (C) y = 2 x + 10 (E) y = 4 x + 1 44. The average value of f ( x) = x 2 x3 + 1 on the closed interval [ 0, 2] is
(A) 26
9 (B) 13
3 (C) 26
3 (D) 13 (E) 26 45. The region enclosed by the graph of y = x 2 , the line x = 2, and the xaxis is revolved about the
y axis. The volume of the solid generated is
(A) 8π (B) 32
π
5 (C) 16
π
3 (D) AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 4π (E) 8
π
3 46 1985 AP Calculus BC: Section I
90 Minutes—No Calculator Notes: (1) In this examination, ln x denotes the natural logarithm of x (that is, logarithm to the base e).
(2) 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.
1. The area of the region between the graph of y = 4 x3 + 2 and the xaxis from x = 1 to x = 2 is
(A) 36 2. (B) 23 2 ∫1 (A) 4. (D) 17 (E) 9 At what values of x does f ( x) = 3 x5 − 5 x3 + 15 have a relative maximum?
(A) –1 only 3. (C) 20 x +1
x2 + 2 x (B) 0 only (C) 1 only (D) –1 and 1 only (E) –1, 0 and 1 dx = ln 8 − ln 3 (B) ln 8 − ln 3
2 (C) ln 8 (D) 3 ln 2
2 (E) 3 ln 2 + 2
2 A particle moves in the xyplane so that at any time t its coordinates are x = t 2 − 1 and y = t 4 − 2t 3 .
At t = 1, its acceleration vector is
(A) ( 0, − 1) (B) ( 0,12 ) (C) ( 2, − 2 ) AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) ( 2, 0 ) (E) ( 2,8) 47 1985 AP Calculus BC: Section I 5. The curves y = f ( x) and y = g ( x) shown in the figure above intersect at the point ( a , b ) . The
area of the shaded region enclosed by these curves and the line x = −1 is given by
0 a (A)
(B) ∫...
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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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