 # AP Calculus AB Multiple Choice 2012 Questions and Answers (Part B)

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

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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 = etan 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) = √(x4 + 1) + x3 - 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)/√(t3 + 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 = x2 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?

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