AP Calculus AB Multiple Choice 2008 Questions and Answers
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Questions and Worked Solutions for AP Calculus AB Multiple Choice 2008.
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)(x2 + 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) = 3t2 + 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) = x2 + 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/(x2 - 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 = x2 + 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 + 2x)/(1 - 2x) 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) = x2(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 = x2/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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