Questions and Worked Solutions for AP Calculus BC Multiple Choice 2012.

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1. If y = sin^{3}x, then dy/dx =

(A) cos^{3}x (B) 3cos^{2}x (C) 3sin^{2}x (D) -3sin^{2}xcos x (E) 3sin^{2}x cosx

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) = t^{3}2 and y(t) = 12t - 3t^{2}. 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)

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

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 ?

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 AP Calculus BC Multiple Choice 2012 Question 6

6. Using the substitution u = x^{2} -3, is equal to which of the following?
AP Calculus BC Multiple Choice 2012 Question 7

7. If arcsin x = ln y = then dy/dx = 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

AP Calculus BC Multiple Choice 2012 Question 9

9. Which of the following series converge? AP Calculus BC Multiple Choice 2012 Question 10

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. 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 equation dy/dx = x^{2} + 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.

AP Calculus BC Multiple Choice 2012 Question 13

13. What is the radius of convergence of the series 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? 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 ? AP Calculus BC Multiple Choice 2012 Question 17

17. For x > 0, the power series converges to which of the following? 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 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 the line 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. AP Calculus BC Multiple Choice 2012 Question 20

20. 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?

AP Calculus BC Multiple Choice 2012 Question 22

22. The power series converges at x = 5. Which of the following must be true? 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? 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) ? AP Calculus BC Multiple Choice 2012 Question 25

25. 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? AP Calculus BC Multiple Choice 2012 Question 27

27. For what values of p will both series converge? 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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AP Calculus BC Multiple Choice 2012 Questions - Complete Paper (pdf)

AP Calculus BC Multiple Choice 2012 Question 11. If y = sin

(A) cos

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) = t

(A) (-4, 12) (B) (-3, 6) (C) (-2, 9) (D) (0, 0) (E) (3,4)

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

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 ?

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 AP Calculus BC Multiple Choice 2012 Question 6

6. Using the substitution u = x

7. If arcsin x = ln y = then dy/dx = 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

AP Calculus BC Multiple Choice 2012 Question 9

9. Which of the following series converge? AP Calculus BC Multiple Choice 2012 Question 10

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. 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 equation dy/dx = x

(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.

AP Calculus BC Multiple Choice 2012 Question 13

13. What is the radius of convergence of the series 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? 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 ? AP Calculus BC Multiple Choice 2012 Question 17

17. For x > 0, the power series converges to which of the following? 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 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 the line 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. AP Calculus BC Multiple Choice 2012 Question 20

20. 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?

AP Calculus BC Multiple Choice 2012 Question 22

22. The power series converges at x = 5. Which of the following must be true? 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? 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) ? AP Calculus BC Multiple Choice 2012 Question 25

25. 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? AP Calculus BC Multiple Choice 2012 Question 27

27. For what values of p will both series converge? 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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