AP Multiple Choice Released Questions

  1. If
  1. b. c. d. e.
  1. For the horizontal line is an asymptote for the graph of the function f. Which of the following statements must be true?
  1. is undefined
  1. If
  1. b. c. d. e.
  1. b. 1 c. d. e.
  1. If
  1. b. c. d. e. nonexistent
  1. If , then
  1. b. c. d. e.

The graph of , the derivative of the function f, is shown above. Which of the following statements is true about f?

  1. is decreasing for
  2. is increasing for
  3. is increasing for
  4. has a local minimum at
  5. is not differentiable at and
  1. The graph of a function is shown below. At which value of is continuous, but not differentiable?
  1. a b. b c. c d. d e. e
  1. Let be the function with derivative given by . On which of the following intervals is decreasing?
  1. only b. c. only d. e.
  1. If the line tangent to the graph of the function at the point (1,7) passes through the point (-2,-2), then is
  1. b. c. d. e. undefined
  1. The function f has the property that and are negative for all real values of x. Which of the following could be the graph of f?
  1. Let be the function given by The graph of is concave down when
  1. b. c. d. e.
  1. The derivative of a function is continuous and has exactly two zeros. Selected values of are given in the table below. If the domain of is the set of all real numbers, then is decreasing on which of the following intervals?
  1. only
  2. only
  3. only
  4. or
  1. Let be the function given below. Which of the following statements are true about
  1. exists
  2. is continuous at
  3. is differentiable at
  1. None b. I only C. II only d. I and II only e. I, II, and III
  1. The second derivative of the function is given by The graph of is shown below. For what values of does the graph of have a point of inflection?
  1. 0 and a only b. 0 and m only c. b and j only d. 0,a, and b e. b,j, and k
  1. Let be the function defined by . Which of the following is an equation of the line tangent to the graph of at the point where
  1. b. c. d. e.
  1. A particle moves along the x-axis so that at time its position is given by At what time t is the particle at rest?
  1. only b. only c. only d. and e. and
  1. What is the slope of the line tangent to the curve at the point (3,2)?
  1. 0 b. c. d. e.
  1. Let be the function defined by . If and , what is the value of
  1. b. c. d. 4 e. 13
  1. Let be a twice-differentiable function with and for all real numbers , such that and Of the following, which is a possible value for
  1. 15 b. 18 c. 21 d. 24 e. 27
  1. b. c. d. e.
  1. 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?
  1. b. c. d. e.
  1. A curve has slope at each point on the curve. Which of the following is an equation for this curve if it passes through the point ?
  1. b. c. d. e.
  1. The graph of , the derivative of f, is the line shown in the figure below. If , then
  1. 0 b. 3 c. 6 d. 8 e. 11