Let F Be the Function Defined Above For What Values of B is F Continuous at X 2

Questions And Worked Solutions For AP Calculus AB Multiple Choice 2012 (Part A), Practice Exam, Questions 1 to 28

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

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)

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AP Calculus AB Multiple Choice 2012 Question 2
2. Let f be the function given by f(x) = 300x - x³. On which of the following intervals is the function f increasing?

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AP Calculus AB Multiple Choice 2012 Question 3
3. ∫sec x tan x dx =

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AP Calculus AB Multiple Choice 2012 Question 4
4. If f(x) = 7x - 3 + ln x, then f'(1) =

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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?

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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 - t². What is the total distance traveled by the particle from t - 0 to t = 3?

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AP Calculus AB Multiple Choice 2012 Question 7
7. If y = (x³ - cos x)⁵, then y' =

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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

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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 ?

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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 ?

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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.

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AP Calculus AB Multiple Choice 2012 Question 12
12. Using the substitution u = √x, is equal to which of the following?

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AP Calculus AB Multiple Choice 2012 Question 13
13.

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AP Calculus AB Multiple Choice 2012 Question 14
14. If (f(x) = √(x² - 4) and g(x) = 3x - 2, then the derivative of f(g(x)) at x = 3 is

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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?

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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?

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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) ?

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AP Calculus AB Multiple Choice 2012 Question 18
18.

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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.

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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) ?

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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?

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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 ?

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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?

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AP Calculus AB Multiple Choice 2012 Question 24
24. Let g be the function given by g(x) = x²e^kx, where k is a constant. For what value of k does g have a critical point at x = 2/3.

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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 ?

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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?

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AP Calculus AB Multiple Choice 2012 Question 27
27. If (x + 2y)dy/dx = 2x -y, what is the value of d²y/dx² at the point (3,0)?

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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 ?

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

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