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AP Calculus AB Multiple Choice 2008

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AP Calculus AB Multiple Choice 2008 Questions - Complete Paper (pdf)

AP Calculus AB Multiple Choice 2008 Question 76

76. The graph of f', the derivative f, is shown above for -2 ≤ x ≤ 5. On what intervals is f
increasing?

AP Calculus AB Multiple Choice 2008 Question 77

77. The figure above shows the graph of a function f with domain 0 ≤ x ≤ 4. Which of the
following statements are true?

AP Calculus AB Multiple Choice 2008 Question 78

78. The first derivative of the function f is defined by f'(x) = sin(x^{3} - x) for 0 ≤ x ≤ 2. On
what interval(s) is f increasing?

AP Calculus AB Multiple Choice 2008 Question 79

AP Calculus AB Multiple Choice 2008 Question 80

80. The derivative of the function f is given by f'(x) = x^{2}cos(x^{2}). How many points of inflection does the graph of f have on the open interval (−2, 2 ?)

AP Calculus AB Multiple Choice 2008 Question 81

81. If G(x) is an antiderivative for f(x) and G(2) = -7, then G(4) =

AP Calculus AB Multiple Choice 2008 Question 82

82. A particle moves along a straight line with velocity given by v(t) = 7 - (1.01)^{-t2} at time t ≥ 0. What is the acceleration of the particle at time t = 3?

AP Calculus AB Multiple Choice 2008 Question 83

83. What is the area enclosed by the curves y = x^{3} - 8x^{2} + 18x - 5 and y = x + 5?

AP Calculus AB Multiple Choice 2008 Question 84

84. The graph of the derivative of a function f is shown in the figure above. The graph has
horizontal tangent lines at x = −1, x = 1, and x = 3. At which of the following values of x
does f have a relative maximum?

AP Calculus AB Multiple Choice 2008 Question 85

85. The table above gives values of a function f and its derivative at selected values of x. If f '
is continuous on the interval [-4, -1], what is the value of ∫f'(x)dx?

AP Calculus AB Multiple Choice 2008 Question 86

86. The table gives selected values of the velocity, v(t), of a particle moving along the x-axis.
At time t = 0, the particle is at the origin. Which of the following could be the graph of the
position, x(t), of the particle for 0 ≤ t ≤ 4?

AP Calculus AB Multiple Choice 2008 Question 87

87. An object traveling in a straight line has position x(t) at time t. If the initial position is
x(0) = 2 and the velocity of the object is v(t) = 3√(1 + t^{2}), what is the position of the object at time t = 3?

AP Calculus AB Multiple Choice 2008 Question 88

88. The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when
the radius of the sphere is 3 centimeters, what is the rate of change, in square centimeters per
second, of the surface area of the sphere? (The surface area S of a sphere with radius r is S = 4πr^{2})

AP Calculus AB Multiple Choice 2008 Question 89

89. The function f is continuous for -2 ≤ x ≤ 2 and f(-2) = f(2) = 0. If there is no c, where
-2 < c < 2, for which f'(c) = 0, which of the following statements must be true?

AP Calculus AB Multiple Choice 2008 Question 90

90. The function f is continuous on the closed interval [2, 4] and twice differentiable on the
open interval (2, 4). If f'(3) = 2 and f"(3) < 0 on the open interval (2, 4), which of the
following could be a table of values for f?

AP Calculus AB Multiple Choice 2008 Question 91

91. What is the average value of y = cos x/(x^{2} + x + 2) on the closed interval [1, 3]?

AP Calculus AB Multiple Choice 2008 Question 92

92. A city located beside a river has a rectangular boundary as shown in the figure above. The
population density of the city at any point along a strip x miles from the river’s edge is
f(x) persons per square mile. Which of the following expressions gives the population of
the city?

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