# 2008 Test Prepap Calculus

### Questions and Worked Solutions for AP Calculus AB Multiple Choice 2008 (Part B).

Then, with the exception of the addition of slope fields, the 2004, 2005, and 2006 tests were all pretty similar to each other and to the 2003 test. I would not be surprised if the 2008 exam bears some strong resemblance to the 2007 test in some way. Approximately every four years, on a staggered schedule, the AP® Program releases a complete copy of each exam. In addition to providing the multiple-choice questions and answers, the publication describes the process of scoring the free-response questions and includes examples of students' actual responses, the scoring standards,.

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 fincreasing?

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 thefollowing statements are true?

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## 2008 Test Prepa Calculus 1

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. Onwhat interval(s) is f increasing?

AP Calculus AB Multiple Choice 2008 Question 79

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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 ?)

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## 2008 Test Prepa Calculus 3

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?

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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 hashorizontal tangent lines at x = −1, x = 1, and x = 3. At which of the following values of xdoes f have a relative maximum?

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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 theposition, x(t), of the particle for 0 ≤ t ≤ 4?

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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 isx(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 whenthe radius of the sphere is 3 centimeters, what is the rate of change, in square centimeters persecond, 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?

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AP Calculus AB Multiple Choice 2008 Question 90

90. The function f is continuous on the closed interval [2, 4] and twice differentiable on theopen interval (2, 4). If f'(3) = 2 and f'(3) < 0 on the open interval (2, 4), which of thefollowing 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]?

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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. Thepopulation density of the city at any point along a strip x miles from the river’s edge isf(x) persons per square mile. Which of the following expressions gives the population ofthe city?

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