Questions and Worked Solutions for AP Calculus AB Multiple Choice 2012 (Part B).

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AP Calculus AB Multiple Choice 2012 Questions - Complete Paper (pdf)

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

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.

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

82. If f'(x) = √(x

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

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

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

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