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AP Calculus AB Multiple Choice 2012 Questions - Practice Exam (pdf)

AP Calculus AB 2012 MCQ Part B Exam

AP Calculus AB Multiple Choice 2012 Question 1

- If y = x sin x, then dy/dx =

(A) sin x + cos x (B) sin x + x cos x (C) sin x - x cos x (D) x(sin x + cos x) (E) x(sin x - cos x)

AP Calculus AB Multiple Choice 2012 Question 2

2. Let f be the function given by f(x) = 300x - x^{3}. On which of the following intervals is the function f increasing?

AP Calculus AB Multiple Choice 2012 Question 3

3. ∫sec x tan x dx =

AP Calculus AB Multiple Choice 2012 Question 4

4. If f(x) = 7x - 3 + ln x, then f'(1) =

AP Calculus AB Multiple Choice 2012 Question 5

5. The graph of the function f is shown above. Which of the following statements is false?

AP Calculus AB Multiple Choice 2012 Question 6

6. A particle moves along the x-axis. The velocity of the particle at time t is 6t - t^{2}. What is the total distance traveled by the particle from t - 0 to t = 3?

AP Calculus AB Multiple Choice 2012 Question 7

7. If y = (x^{3} - cos x)^{5}, then y' =

AP Calculus AB 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 AB Multiple Choice 2012 Question 9

9. Let f be the function defined above. For what value of k is f continuous at x = 2 ?

AP Calculus AB Multiple Choice 2012 Question 10

10. What is the area of the region in the first quadrant bounded by the graph of y = e^{x/2} and the line x = 2 ?

AP Calculus AB 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 AB Multiple Choice 2012 Question 12

12. Using the substitution u = √x, is equal to which of the following?

AP Calculus AB Multiple Choice 2012 Question 13

13.

AP Calculus AB Multiple Choice 2012 Question 14

14. If (f(x) = √(x^{2} - 4) and g(x) = 3x - 2, then the derivative of f(g(x)) at x = 3 is

AP Calculus AB 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 AB Multiple Choice 2012 Question 16

16. A particle moves along the x-axis with its position at time t given by x(t) = (t - a)(t - b), where a and b are constants and a ≠ b. For which of the following values of t is the particle at rest?

AP Calculus AB Multiple Choice 2012 Question 17

17. The figure above shows the graph of f. If which of the following could be the graph of y = g(x) ?

AP Calculus AB Multiple Choice 2012 Question 18

18.

AP Calculus AB 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 AB Multiple Choice 2012 Question 20

20. Let f(x) = (2x + 1)^{3} and let g be the inverse function of f. Given that f(1) = 0, what is the value of g'(1) ?

AP Calculus AB 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 AB Multiple Choice 2012 Question 22

22. Let f be the function defined by f(x) = (lnx)/x. What is the absolute maximum value of f ?

AP Calculus AB 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 AB Multiple Choice 2012 Question 24

24. Let g be the function given by g(x) = x^{2}e^{kx}, where k is a constant. For what value of k does g have a critical point at x = 2/3.

AP Calculus AB Multiple Choice 2012 Question 25

25. Which of the following is the solution to the differential equation dy/dx = 2 sin x with the initial
condition y(π) = 1 ?

AP Calculus AB Multiple Choice 2012 Question 26

26. Let g be a function with first derivative given by. Which of the following must be true on the interval 0 < x < 2?

AP Calculus AB Multiple Choice 2012 Question 27

27. If (x + 2y)dy/dx = 2x -y, what is the value of d^{2}y/dx^{2} at the point (3,0)?

AP Calculus AB Multiple Choice 2012 Question 28

28. For t ≥ 0, the position of a particle moving along the x-axis is given by x(t) = sin t - cos t. What is the acceleration of the particle at the point where the velocity is first equal to 0 ?

AP Calculus AB Multiple Choice 2012 Practice Exam Questions and Solutions Part B

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