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AP Calculus AB Multiple Choice 2008 Part B

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AP Calculus AB Multiple Choice 2008 Questions - Complete Paper (pdf)

AP Calculus AB Multiple Choice 2008 Question 1

AP Calculus AB Multiple Choice 2008 Question 2

AP Calculus AB Multiple Choice 2008 Question 3

3. If f(x) = (x - 1)(x^{2} + 2)^{3} then f'(x) =

AP Calculus AB Multiple Choice 2008 Question 4

AP Calculus AB Multiple Choice 2008 Question 5

AP Calculus AB Multiple Choice 2008 Question 6

6. Let f be the function defined above. Which of the following statements about f are true?

I. f has a limit at x = 2.

II. f is continuous at x = 2.

III. f is differentiable at x = 2.

AP Calculus AB Multiple Choice 2008 Question 7

7. A particle moves along the x-axis with velocity given by v(t) = 3t^{2} + 6t for time t ≥ 0. If the
particle is at position x = 2 at time t = 0, what is the position of the particle at t = 1?

AP Calculus AB Multiple Choice 2008 Question 8

8. If f(x) = cos(3x), then f'(π/9) =

AP Calculus AB Multiple Choice 2008 Question 9

9. The graph of the piecewise linear function f is shown in the figure above. If which of
the following values is greatest?

AP Calculus AB Multiple Choice 2008 Question 10

10. The graph of function f is shown above for 0 3. ≤ ≤x Of the following, which has
the least value?

AP Calculus AB Multiple Choice 2008 Question 11

11. The graph of a function f is shown above. Which of the following could be the graph of f ‘,
the derivative of f ?

AP Calculus AB Multiple Choice 2008 Question 12

12. If f(x) = e^{(2x)} then f’(x) =

AP Calculus AB Multiple Choice 2008 Question 13

13. If f(x) = x^{2} + 2x, then d/dx (f(lnx)) =

AP Calculus AB Multiple Choice 2008 Question 14

14. 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?

AP Calculus AB Multiple Choice 2008 Question 15

15. ∫x/(x^{2} - 4) dx =

AP Calculus AB Multiple Choice 2008 Question 16

16. If sin(xy) = x, then dy/dx =

AP Calculus AB Multiple Choice 2008 Question 17

17. The graph of the function f shown above has horizontal tangents at x = 2 and x = 5. Let g
be the function defined by g(x) = ∫f(t)dt. For what values of x does the graph of g have a point of inflection?

AP Calculus AB Multiple Choice 2008 Question 18

18. In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of
y = x^{2} + 3x + 1. What is the value of k ?

AP Calculus AB Multiple Choice 2008 Question 19

19. What are all horizontal asymptotes of the graph of y = (5 + 2^{x})/(1 - 2^{x}) in the xy-plane?

AP Calculus AB Multiple Choice 2008 Question 20

20. Let f be a function with a second derivative given by f"(x) = x^{2}(x - 3)(x - 6).
What are the x-coordinates of the points of inflection of the graph of f ?

AP Calculus AB Multiple Choice 2008 Question 21

21. 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?

AP Calculus AB Multiple Choice 2008 Question 22

22. A rumor spreads among a population of N people at a rate proportional to the product of the
number of people who have heard the rumor and the number of people who have not heard
the rumor. If p denotes the number of people who have heard the rumor, which of the
following differential equations could be used to model this situation with respect to time t,
where k is a positive constant?

AP Calculus AB Multiple Choice 2008 Question 23

23. Which of the following is the solution to the differential equation dy/dx = x^{2}/y
with the initial condition y(3) = -2?

AP Calculus AB Multiple Choice 2008 Question 24

24. IThe function f is twice differentiable with f(2) = 1, f'(2) = 4 and f"(2) = 3. What is the
value of the approximation of f (1.9) using the line tangent to the graph of f at x = 2?

AP Calculus AB Multiple Choice 2008 Question 25

25. 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 ?

AP Calculus AB Multiple Choice 2008 Question 26

26. What is the slope of the line tangent to the curve y x = arctan(4x) at the point at which x = 1/4?

AP Calculus AB Multiple Choice 2008 Question 27

27. Shown above is a slope field for which of the following differential equations?

AP Calculus AB Multiple Choice 2008 Question 28

28. Let f be a differentiable function such that f(3) = 15, f(6) = 3, f'(3) = -8 and f'(6) = -2.
The function g is differentiable and g(x) = f'(x) for all x . What is the value of g'(3) ?

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