Questions And Worked Solutions For AP Calculus BC Multiple Choice 2012
AP Calculus BC Multiple Choice 2012 Questions - complete paper (pdf)
AP Calculus BC 2012 MCQ Part B Solutions
AP Calculus BC Multiple Choice 2012 Question 1
- If y = sin3x, then dy/dx =
(A) cos3x (B) 3cos2x (C) 3sin2x (D) -3sin2xcos x (E) 3sin2x cos x
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AP Calculus BC Multiple Choice 2012 Question 2
2. The position of a particle moving in the xy-plane is given by the parametric equations x(t) = t32 and y(t) = 12t - 3t2. At which of the following points (x,y), is the particle at rest?
(A) (-4, 12) (B) (-3, 6) (C) (-2, 9) (D) (0, 0) (E) (3,4)
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AP Calculus BC Multiple Choice 2012 Question 3
3. The graph of f is shown above for 0 ≤ x ≤ 4. What is the value of ?(A) -1 (B) 0 (C) 2 (D) 6 (E) 12
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AP Calculus BC Multiple Choice 2012 Question 4
4. Which of the following integrals gives the length of the curve y = ln x from x = 1 to x = 2 ?
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AP Calculus BC Multiple Choice 2012 Question 5
5. The Maclaurin series for the function f is given by .What is the value of f(3) ?
(A) -3 (B) -3/7 (C) 4/7 (D) 13/16 (E) 4
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AP Calculus BC Multiple Choice 2012 Question 6
6. Using the substitution u = x2 -3, is equal to which of the following?
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AP Calculus BC Multiple Choice 2012 Question 7
7. If arcsin x = ln y then dy/dx =
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AP Calculus BC Multiple Choice 2012 Question 8
8. A tank contains 50 liters of oil at time t = 4 hours. Oil is being pumped into the tank at a rate R(t), where R(t) is measured in liters per hour, and t is measured in hours. Selected values of R(t) are given in the table above. Using a right Riemann sum with three subintervals and data from the table, what is the approximation of the number of liters of oil that are in the tank at time t = 15 hours?
(A) 64.9 (B) 68.2 (C) 114.9 (D) 116.6 (E) 118.2
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AP Calculus BC Multiple Choice 2012 Question 9
9. Which of the following series converge?
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AP Calculus BC Multiple Choice 2012 Question 10
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AP Calculus BC Multiple Choice 2012 Question 11
11. Let f be the function defined by f(x) = √(|x-2|) for all x. Which of the following statements is true?
(A) f is continuous but not differentiable at x = 2.
(B) f is differentiable at x = 2.
(C) f is not continuous at x = 2.
(D) lim f(x) ≠ 0
(E) x = 2 is a vertical asymptote of the graph of f.
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AP Calculus BC Multiple Choice 2012 Question 12
12. The points (-1,-1) and (1,-5) are on the graph of a function y = f(x) that satisfies the differential equationdy/dx = x2 + y. Which of the following must be true?
(A) (1,-5) is a local maximum of f.
(B) (1,-5) is a point of inflection of the graph of f.
(C) (-1,-1) is a local maximum of f.
(D) (-1,-1) is a local minimum of f.
(E) (-1,-1) is a point of inflection of the graph of f.
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AP Calculus BC Multiple Choice 2012 Question 13
13. What is the radius of convergence of the series
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AP Calculus BC Multiple Choice 2012 Question 14
14. Let k be a positive constant. Which of the following is a logistic differential equation?
AP Calculus BC Multiple Choice 2012 Question 15
15. The graph of a differentiable function f is shown above. If h(x) = , which of the following is true?
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AP Calculus BC Multiple Choice 2012 Question 16
16. Let y = f(x) be the solution to the differential equation dy/dx = x - y with initial condition f(1) = 3. What is the approximation for f(2) obtained by using Euler’s method with two steps of equal length starting at x = 1 ?
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AP Calculus BC Multiple Choice 2012 Question 17
17. For x > 0, the power series converges to which of the following?
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AP Calculus BC Multiple Choice 2012 Question 18
18. The graph of f', the derivative of a function f, consists of two line segments and a semicircle, as shown in the figure above. If f(2) = 1, then f(-5) =
(A) 2π - 2
(B) 2π - 3
(C) 2π - 5
(D) 6 - 2π
(E) 4 - 2π
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AP Calculus BC Multiple Choice 2012 Question 19
19. The function f is defined by f(x) = x/(x+2). What points (x,y), on the graph of f have the property that theline tangent to f at (x,y), has slope 1/2?
(A) (0,0) only
(B) (1/2, 1/5) only
(C) (0,0) and (-4,2)
(D) (0,0) and (4,2/3)
(E) There are no such points.
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AP Calculus BC Multiple Choice 2012 Question 20
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AP Calculus BC Multiple Choice 2012 Question 21
21. The line y = 5 is a horizontal asymptote to the graph of which of the following functions?
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AP Calculus BC Multiple Choice 2012 Question 22
22. The power series converges at x = 5. Which of the following must be true?
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AP Calculus BC Multiple Choice 2012 Question 23
23. If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?
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AP Calculus BC Multiple Choice 2012 Question 24
24. Let f be a differentiable function such that. Which of the following could be f(x) ?
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AP Calculus BC Multiple Choice 2012 Question 25
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AP Calculus BC Multiple Choice 2012 Question 26
26. What is the slope of the line tangent to the polar curve r = 1 + 2sinθ at θ = 0?
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AP Calculus BC Multiple Choice 2012 Question 27
27. For what values of p will both series converge?
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AP Calculus BC Multiple Choice 2012 Question 28
28. Let g be a continuously differentiable function with g(1) = 6 and g'(1) = 3.
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