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Chapter 4 TEST – AP Calc BC Name:

Part A No Calculator

1.

2. [pic]

(A) e (B) [pic] (C) [pic] (D) [pic] (E) nonexistent

Part A No Calculator

3. If [pic] , then [pic]=

(A) (B) (C) (D) (E)

4.

12.

Part A No Calculator

6. If [pic], then [pic]

(A) (B) (C) (D) (E)

7. The graph of a twice-differentiable function f is shown in the figure above. Which of the following is true?

(A) [pic] (B) [pic] (C) [pic]

(D) [pic] (E) [pic]

8.

Part A No Calculator

9.

10.

11.

Part A No Calculator

12. What is the slope of the secant line of the function [pic] over the interval [ 0 , ln2 ] ?

(A) (B) (C) (D) (E)

13. What is the instantaneous rate of change of [pic] at x = [pic] ?

(A) (B) (C) (D) (E)

Part A No Calculator

14. If [pic] then [pic] is

(A) ln 2 (B) ln 8 (C) ln 16 (D) 4 (E) nonexistent

15. [pic]

(A) (B) (C) (D) (E)

Part A No Calculator

16. Let [pic] . For what intervals is [pic] decreasing and [pic] is increasing ?

(A) (B) (C) (D) (E)

17. For what value of k will [pic]below be differentiable over its entire domain?

[pic]

(A) 1 only (B) -1 and 1 only (C) [pic] only (D) 0 only (E) all real numbers

Part A No Calculator

18. What is the average rate of change of the function f if the function passes through the point ( 1 , 7 ) and the point ( -2 , -2 ) on [pic] ?

(A) (B) (C) (D) (E)

19. If [pic] , then [pic]=

(A) (B) (C) (D) (E)

Part A No Calculator

20. Suppose a triangular prism has an equilateral triangular base in which the sum of the perimeter of the base and altitude of the prism is 100 cm. Find the perimeter of the base that would maximize the volume of the triangular prism.

(A) [pic]cm (B) [pic]cm (C) 100 cm (D) 150 cm (E) 200 cm

21. If [pic] and [pic] , then [pic]=

(A) (B) (C) (D) (E)

Part A No Calculator

22. If [pic] and [pic] , then [pic]=

(A) (B) (C) (D) (E)

23. Find the largest possible area for a rectangle with its base on the x-axis and upper vertices on the curve [pic].

(A) [pic]

(B) [pic]

(C) [pic]

(D) [pic]

(E) [pic]

Part A No Calculator

24. [pic] is

(A) -9 (B) -6 (C) 0 (D) 6 (E) undefined

25. [pic] =

(A) (B) (C) (D) (E)

Part A No Calculator

26. [pic]

(A) 0 (B) [pic] (C) 1 (D) 2 (E) nonexistent

Part A No Calculator

1.

28. A particle moves along a curve on a plane such that at any time t > 0 its x-coordinate is defined as [pic] and y-coordinate is defined as [pic]. Its acceleration vector at t = 2 is

(A) (B) (C) (D) (E)

Part A No Calculator

29. A particle moves along a curve on a plane such that at any time t > 0 its position is defined by the parametric equations [pic] and [pic]. The acceleration vector of the particle at t = 2 is

(A) (B) (C) (D) (E)

Part A No Calculator

31. [pic]

(A) 0 (B) [pic] (C) 1 (D) 2 (E) 3

32. If f is a vector-valued function defined by [pic], then [pic]

(A) (B) (C) (D) (E)

Part A No Calculator

33. A ladder 13 feet long is leaning against a wall. If the foot of the ladder is pulled away from the wall at the rate of 0.5 feet per second, how fast will the top of the ladder be dropping at the instant when the base is 5 feet from the wall?

(A) [pic] ft/sec

(B) [pic] ft/sec

(C) [pic] ft/sec

(D) [pic] ft/sec

(E) [pic] ft/sec

34. Use the same situation in problem #33. At what rate is the angle created with the ladder and the floor changing at the instant when the base is 5 feet from the wall?

(A) [pic] ft/sec

(B) [pic] ft/sec

(C) [pic] ft/sec

(D) [pic] ft/sec

(E) [pic] ft/sec

Part A No Calculator

35. Use the same situation in problem #29. Consider the area of the triangle created by the ladder and the wall. How fast is this area changing at the instant when the base is 5 feet from the wall?

(A) [pic] ft²/sec (B) [pic] ft²/sec (C) [pic] ft²/sec (D) [pic] ft²/sec (E) [pic] ft²/sec

36. [pic]

(A) [pic], where [pic]

(B) [pic], where [pic]

(C) [pic], where [pic]

(D) [pic], where [pic]

(E) [pic], where [pic]

Stop! You may use your graphing calculator for the remainder of the test.

Part B Graphing Calculator Required

37. Bacteria is decaying in such a way where after 2 days, its size was 30 cm³. After 10 days, its size was 25 cm³. The half life of the bacteria is

(A) (B) (C) (D) (E)

38. Which of the following satisfy the hypotheses of Rolle’s Theorem on the interval [ 0 , 2 ] ?

I. [pic]

II. [pic]

III. [pic]

IV. [pic]

(A) I only (B) II only (C) III only (D) IV only (E) I and II

Part B Graphing Calculator Required

39. Let [pic] represent the position of a particle moving horizontally , [pic]. The acceleration of the particle at t = [pic] is

(A) (B) (C) (D) (E)

40. A curve described by the parametric equations [pic] and [pic] is concave up over what interval(s)?

(A) (B) (C) (D) (E)

Part B Graphing Calculator Required

41. Find [pic] for [pic] and [pic] .

(A) (B) (C) (D) (E)

42. If [pic], then [pic] for what interval(s)?

(A) (B) (C) (D) (E)

Part B Graphing Calculator Required

43. The equation of the tangent line for the parametric equations [pic] and [pic] at t = 2.

(A) (B) (C) (D) (E)

44. The equation of the tangent line for the parametric equations [pic] and [pic]

at ( 2 , 3 ) is

(A) (B) (C) (D) (E)

45. A particle moves along a curve on the xy-plane such that at any time t > 0 its position vector is defined as [pic]. Find it's velocity vector at t = [pic] .

(A) (B) (C) (D) (E)

Part B Graphing Calculator Required

Peterson 2 #45B

46.

47. A particle moves along the x-axis so that at time [pic], its position is given by [pic]. At what time t is the particle at rest?

(A) [pic] only

(B) [pic] only

(C) [pic] only

(D) [pic] and [pic]

(E) [pic] and [pic]

48. The position function of an object moving horizontally is given by [pic]. How many times on the interval [pic], where t is time in seconds, does the object change direction from moving right to moving left?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

Part B Graphing Calculator Required

49. The table above shows selected values of [pic] and [pic]. If f and [pic] (the inverse of f ) exist, are continuous and differentiable for x > 0, then [pic] at x = 1 is

(A) -4 (B) -2 (C) [pic] (D) [pic] (E) 2

50. The maximum acceleration attained on the interval [pic] by the particle whose velocity is given by [pic] is

(A) 8 (B) 20 (C) 35 (D) 50 (E) 62

Part B Graphing Calculator Required

51. [pic] =

(A) [pic] (B) [pic] (C) [pic] (D) 0 (E) nonexistent

Part B Graphing Calculator Required

53.

54. A rectangle of perimeter 18 inches is rotated about one of its sides to generate a right circular cylinder. The rectangle which generates the cylinder of largest volume has an area in square inches of

(A) 10 (B) 12 (C) 15 (D) 16 (E) 18

AP Free Response No Calculator

1. Sketch [pic]and[pic].

AP Free Response No Calculator

2.

AP Free Response No Calculator

3. At time t , the position of a particle moving on a curve is given by [pic] and [pic].

a) Find [pic].

b) Find all values of t at which the curve has

i) a horizontal tangent

ii) a vertical tangent

c) Find [pic].

d) Find the speed of the particle at t = 3 .

AP Free Response No Calculator

4. The function f is continuous for [pic] and differentiable for [pic].

[pic] contains both ( -2 , 6 ) and ( 2 , -4 )

a) What does the Intermediate Value Theorem guarantee?

b) What does the Mean Value Theorem guarantee?

b) What does the Rolle's Theorem guarantee?

Also study 4.9 Worksheet!

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PT

[pic]

[pic]

[pic]

[pic]

5.

y

x

O

1

[pic]

[pic]

[pic]

[pic]

[pic]

( x , y )

[pic]

Hint: The base of the rectangle is not x . The base is 2x .

[pic]

27.

[pic]

30.

13

y

x

[pic]

|x |[pic] |[pic] |

|1 |2 |1/2 |

|2 |3 |1/3 |

|3 |1 |-2 |

[pic]

52.

[pic]

[pic]

y

x

[pic]

[pic]

[pic]

[pic]

[pic]

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