AP Calculus AB Multiple Choice 1998 Part B Questions and Answers

Questions and Worked Solutions for AP Calculus AB Multiple Choice 1998 (Part B).

AP Calculus AB Multiple Choice 1969 - 1998 Questions - Complete Paper (pdf)

AP Calculus AB Multiple Choice 1998 Questions 76 - 80
76. The graph of a function f is shown above. Which of the following statements about f is false?

77. Let f be the function given by f(x) = 3e^2x and let g be the function given by g(x) = 6x³. At what value of x do the graphs of f and g have parallel tangent lines?

78. The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

79. The graphs of the derivatives of the functions f, g, and h are shown above. Which of the functions f, g, or h have a relative maximum on the open interval a < x < b ?

80. The first derivative of the function f is given by f'(x) = (cos² x)/x = 1/5. How many critical values does f have on the open interval (0,10) ?

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AP Calculus AB Multiple Choice 1998 Questions 81 - 85
81. Let f be the function given by f(x) = |x|. Which of the following statements about f are true?
I. f is continuous at x = 0.
II. f is differentiable at x = 0.
III. f has an absolute minimum at x = 0.

82. If f is a continuous function and if F'(x) = f(x) for all real numbers x, then
    

83. Population y grows according to the equation dy/dt = ky, where k is a constant and t is measured in years. If the population doubles every 10 years, then the value of k is

84. The function f is continuous on the closed interval [2,8] and has values that are given in the table above. Using the subintervals [2,5], [5,7] and [7,8], what is the trapezoidal approximation of

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AP Calculus AB Multiple Choice 1998 Questions 86 - 92
86. The base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line x + 2y = 8, as shown in the figure above. If cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?

87. Which of the following is an equation of the line tangent to the graph of f(x) = x⁴ + 2x² at the point where f'(x) = 1?

88. Let F(x) be an antiderivative of (lnx)³/x. If F(1) 0, = then F(9) =

89. If g is a differentiable function such that g(x) < 0 for all real numbers x and if f'(x) = (x² - 4), which of the following is true?

90. If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?

91. Let f be a function that is differentiable on the open interval (1,10). If f(2) = -5, f(5) = 5, and f(9) = -5, which of the following must be true?
    I. f has at least 2 zeros.
    II. The graph of f has at least one horizontal tangent.
    III. For some c, 2 < c < 5, f(c) = 3.

92. If 0 ≤ k < π/2 and the area under the curve y = cos x from x = π/2, then k =

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