AP Calculus BC Multiple Choice 2008 Questions - Practice Exam (pdf)

Part A, Q1 - 28

Part B, Q76 - 92

- At time t ≥ 0, a particle moving in the xy-plane has velocity vector given by
- Antiderivative
- Limits
- Consider the series
- Which of the following gives the length of the path described by the parametric equations
- Let f be the function defined above. Which of the following statements about f are true?
- Given that y(1) = 3
- The function f is continuous on the closed interval [2, 13] and has values as shown in the table above. Using the intervals [2, 3], [3, 5], [5, 8], and [8, 13], what is the approximation of
- The graph of the piecewise linear function f is shown in the figure above.
- In the xy-plane, what is the slope of the line tangent to the graph of
- Let R be the region between the graph of
- Which of the following series converges for all real numbers x?
- Antiderivative
- The polynomial function f has selected values of its second derivative f" given in the table above. Which of the following statements must be true?
- If f(x) = (ln x)
^{2} - What are all values of x for which the series
- Let h be a differentiable function, and let f be the function defined by
- In the xy-plane, the line x y k + = , where k is a constant, is tangent to the graph of
- Antiderivative
- What is the sum of the series
- A particle moves along a straight line. The graph of the particle’s position x t( ) at time t is shown above for 0 < t < 6. The graph has horizontal tangents at t = 1 and t = 5 and a point of inflection at t = 2. For what values of t is the velocity of the particle increasing?
- The table above gives values of f , f', g and g' for selected values of x
- If f(x) = x sin(2x) which of the following is the Taylor series for f about x = 0?
- Which of the following differential equations for a population P could model the logistic growth shown in the figure above?
- Let f be the function defined above, where c and d are constants. If f is differentiable at x = 2, what is the value of c + d?
- Which of the following expressions gives the total area enclosed by the polar curve
r = sin
^{2}θ shown in the figure above? - Which of the following could be the slope field for the differential equation
- In the xy-plane, a particle moves along the parabola y = x
^{2}− x with a constant speed of

76. The graph of f', the derivative of a function f , is shown above. The domain of f is the open interval 0 < x < d. Which of the following statements is true?

77. Water is pumped out of a lake at the rate

78. The graph of a function f is shown above. For which of the following values of c

79. Let f be a positive, continuous, decreasing function such that

80. The derivative of the function f is given by

81. Let f and g be continuous functions for a ≤ x ≤ b.

82. Diverge

83. What is the area enclosed by the curves

84. Let f be a function with

85. A particle moves on the x-axis with velocity given by

86. On the graph of y = f(x), the slope at any point (x, y) is twice the value of x

87. An object traveling in a straight line has position x(t) at time t.

88. For all values of x, the continuous function f is positive and decreasing.

89. The function f is continuous for −2 ≤ x ≤ 2 and f(-2) = f(2) = 0.

90. The table above gives values of the differentiable functions f and g and of their derivatives f' and g', at selected values of x. If h(x) = f(g(x)), what is the slope of the graph of h at x = 2?

91. Let f be the function given by

92. The figure above shows the graphs of the functions f and g. The graphs of the lines tangent to the graph of g at x = −3 and x = 1 are also shown.

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