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AP Calculus AB 2012 Exam

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AP Calculus AB Multiple Choice 2012 Questions - complete paper (pdf)

AP Calculus AB 2012 MCQ Part A Exam

AP Calculus AB Multiple Choice 2012 Question 76

76. The graph of the function f is shown in the figure above. For which of the following values of x is f'(x)
positive and increasing?

AP Calculus AB Multiple Choice 2012 Question 77

77. Let f be a function that is continuous on the closed interval [2, 4] with f(2) = 10 and f(4) = 20. Which of the following is guaranteed by the Intermediate Value Theorem?

AP Calculus AB Multiple Choice 2012 Question 78

78. The graph of y = e^{tan x} - 2 crosses the x-axis at one point in the interval [0,1] What is the slope of the graph?

AP Calculus AB Multiple Choice 2012 Question 79

79. A particle moves along the x-axis. The velocity of the particle at time t is given by v(t), and the acceleration of the particle at time t is given by a(t). Which of the following gives the average velocity of the particle from time t = 0 to time t = 8.

AP Calculus AB Multiple Choice 2012 Question 80

80. The graph of f', the derivative of the function f, is shown above. Which of the following statements must be
true?

AP Calculus AB Multiple Choice 2012 Question 81

81. Water is pumped into a tank at a rate of (r(t) = 30(1 - e^{-0.16t}) gallons per minute, where t is the number of minutes since the pump was turned on. If the tank contained 800 gallons of water when the pump was turned on, how much water, to the nearest gallon, is in the tank after 20 minutes?

AP Calculus AB Multiple Choice 2012 Question 82

82. If f'(x) = √(x^{4} + 1) + x^{3} - 3x, then f has a local maximum at x =

AP Calculus AB Multiple Choice 2012 Question 83

83. The graph above gives the velocity, v, in ft/sec, of a car for 0 ≤ t ≤ 8, where t is the time in seconds. Of the following, which is the best estimate of the distance traveled by the car from t = 0 until the car comes to a complete stop?

AP Calculus AB Multiple Choice 2012 Question 84

84. For -1.5 < x < 1.5, let f be a function with first derivative given by f'(x) = e^{(x4-2x2 + 1)} - 2. Which of the following are all intervals on which the graph of f is concave down?

AP Calculus AB Multiple Choice 2012 Question 85

85. The graph of f(c), the derivative of f, is shown in the figure above. The function f has a local maximum at x =

AP Calculus AB Multiple Choice 2012 Question 86

86. If f'(x) > 0 for all real numbers x and ∫f(t)dt = 0, which of the following could be a table of values for the function f?

AP Calculus AB Multiple Choice 2012 Question 87

87. The graph of f'', the second derivative of f, is shown above for -2 ≤ x ≤ 4. What are all intervals on which the graph of the function f is concave down?

AP Calculus AB Multiple Choice 2012 Question 88

88. A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of the streetlight is 15 feet, what is the rate at which the person’s shadow is lengthening?

AP Calculus AB Multiple Choice 2012 Question 89

89. A particle moves along a line so that its acceleration for t ≥ 0 is given by a(t) = (t + 3)/√(t^{3} + 1). If the particle’s velocity at t = 0 is 5, what is the velocity of the particle at t = 3 ?

AP Calculus AB Multiple Choice 2012 Question 91

91. Let f be a polynomial function with values f'(x) at selected values of x given in the table above. Which of the following would be true for -2 < x <6?

AP Calculus AB Multiple Choice 2012 Question 92

92. Let R be the region in the first quadrant bounded below by the graph of y = x^{2} and above by the graph of y = √x. R is the base of a solid whose cross sections perpendicular to the x-axis are squares. What is the volume of the solid?

AP Calculus AB Multiple Choice 2012 Practice Exam Questions and Solutions Part A

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