AP Calculus AB Multiple Choice 2013 Questions - Practice Exam (pdf)

- lim (x
^{2}+ x - 6)/(x^{2}- 4) is (A) - 1/4 (B) 0 (C) 1 (D) 5/4 (E) nonexistent - If f(x) = x
^{3}- x^{2}- x + 1, then f'(2) - Which of the following definite integrals has the same value as
- Which of the following is an equation of the line tangent to the graph of x
^{2}- 3xy = 10 at the point (1,-3)? - If g is the function given by
- Let f be the function given by f(x) = x
^{3}- 6x^{2}+ 8x - 2. What is the instantaneous rate of change of f at x = 3? - A particle moves along a straight line. The graph of the particle’s velocity v(t) at time t is shown above for 0 ≤ t ≤ m, where j, k, l, and m are constants. The graph intersects the horizontal axis at t = 0, t = k, and t = m and has horizontal tangents at t = j and t = l. For what values of t is the speed of the particle decreasing?
- Let f be the function given by
- A particle moves along the x-axis with velocity given by v(t) = 3t
^{2}- 4 for time t ≥ 0. If the particle is at position x = -2 at time t, what is the position of the particle at time t = 3? - Let f be the function defined by
- For which of the following does lim f(x) = 0?
- Let f be a differentiable function such that f(0) = -5 and f'(x) ≤ 3 for all x. Of the following, which is not a possible value for f(2)?
- Let f be the function given above. What are all values of a and b for which f is differentiable at x = 1?

- The table above gives values for the functions f and g and their derivatives at x = 3. Let k be the function given by k(x) = f(x)/g(x), where g(x) ≠ 0. What is the value of k'(3)?
- If ln(2x + y) = x + 1, then dy/dx =
- The figure above shows the graph of the function g and the line tangent to the graph of g at x = -1. Let h be the function given by h(x) = e
^{x}· g(x). What is the value of h'(-1)? - The function f is continuous for all real numbers, and the average rate of change of f on the closed interval [6,9] is -3/2. For 6 < c < 9, there is no value of c such that f'(c) = -3/2. Of the following, which must be true?
- Let f be the function defined by f(x) = 2x + e
^{x}. If g(x) = f^{-1}(x) for all x and the point (0,1) is on the graph of f, what is the value of g'(1)? - The function g is given by g(x) = 4x
^{3}- 3x^{2}- 6x + 1. What is the absolute minimum value of g on the closed interval [-2,1]? - Which of the following is the solution to the differential equation dy/dx = e
^{y+x}with the initial condition y(0) = -ln4? - Which of the following is an antiderivative of
- For time t ≥ 0, the height h of an object suspended from a spring is given by h(t) = 16 + 7 cos(πt/4). What is the average height of the object from t = 0 to t = 2?
- The function f is defined by f(x) = sin x + cos x for 0 ≤ x ≤ 2π. What is the x-coordinate of the point of inflection where the graph of f changes from concave down to concave up?

AP Calculus AB Multiple Choice 2013 Practice Exam Questions and Solutions Part B

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