AP Calculus BC Multiple Choice 2003 Questions And Answers

Questions And Worked Solutions For AP Calculus BC Multiple Choice 2003, Practice Exam

AP Calculus BC Multiple Choice 2003 Questions - Practice Exam (pdf)

Part A, Q1 - 28

Part B, Q76 - 92

• Show Video for Q76 - 92

1. If y = sin(3x) then dy/dx =
2. Limits
3. Antiderivative
4. For 0 ≤ t ≤ 13 an object travels along an elliptical path given by the parametric equations x = 3cos t and y = 4sin t. At the point where t =13, the object leaves the path and travels along the line tangent to the path at that point. What is the slope of the line on which the object travels?
5. Let y = f(x) be the solution to the differential equation dy/dx = x + y with the initial condition f(1) = 2. What is the approximation for f(2) if Euler’s method is used, starting at x =1 with a step size of 0.5 ?
6. What are all values of p for which
7. The position of a particle moving in the xy-plane is given by the parametric equations
10. What is the value of
11. The Maclaurin series for
12. The rate of change of the volume, V, of water in a tank with respect to time, t, is directly proportional to the square root of the volume. Which of the following is a differential equation that describes this relationship?
13. The graph of a function f is shown above. At which value of x is f continuous, but not differentiable?
14. Shown above is a slope field for which of the following differential equations?
15. The length of a curve from x =1 to x = 4 is given by
16. If the line tangent to the graph of the function f at the point (1,7) passes through the point (-2,-2), then f′(1) is
17. A curve C is defined by the parametric equations
18. The graph of the function f shown in the figure above has horizontal tangents at x = 3 and x = 6.
19. A curve has slope 2x + 3 at each point (x,y) on the curve. Which of the following is an equation for this curve if it passes through the point (1,2)?
20. A function f has Maclaurin series given by
21. The number of moose in a national park is modeled by the function M that satisfies the logistic differential equation
22. What are all values of p for which the infinite series
24. Which of the following series diverge?
25. The function f is continuous on the closed interval [2,14] and has values as shown in the table above. Using the subintervals [2,5], [5,10], and [10,14], what is the approximation of
26. 
    

27.
28. What is the coefficient of x² in the Taylor series for
 
76. The graph of the function f is shown above. Which of the following statements must be false?
77. Let P(x)
78. The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?
79. The table above gives values of
80. Insects destroyed a crop at the rate of
81. The graph of the function f is shown in the figure above.
82. The rate of change of the altitude of a hot-air balloon is given by
83. The function f is continuous and differentiable on the closed interval [0,4]. The table above gives selected values of f on this interval. Which of the following statements must be true?
84. A particle moves in the xy-plane so that its position at any time t is given by
85. If a trapezoidal sum overapproximates
86. Let f be the function with derivative defined by
87. A particle moves along the x-axis so that at any time t ≥ 0, its velocity is given by v(t) = cos(2 - t²) The position of the particle is 3 at time t = 0. What is the position of the particle when its velocity is first equal to 0?
88. On the closed interval [2,4], which of the following could be the graph of a function f with the property that
89. The region bounded by the graph of y = 2x - x² and the x-axis is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is an equilateral triangle. What is the volume of this solid?
90. The graph of f ‘, the derivative of the function f , is shown above. If f (0) = 0, which of the following must be true?
91. The height h, in meters, of an object at time t is given by
92. Let f be the function defined by f(x) = x + ln x. What is the value of c for which the instantaneous rate of change of f at x = c is the same as the average rate of change of f over [1,4] ?

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