Questions and Worked Solutions for AP Calculus AB Multiple Choice 2008.

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

AP Calculus AB Multiple Choice 2008 Question 2

AP Calculus AB Multiple Choice 2008 Question 3

3. If f(x) = (x - 1)(x

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

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

AP Calculus AB Multiple Choice 2008 Question 13

13. If f(x) = x

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

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

19. What are all horizontal asymptotes of the graph of y = (5 + 2

20. Let f be a function with a second derivative given by f"(x) = x

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

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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