1. AP Exam The Final Hours of Test Prep…

2. Tonight Dont cram – youve spent a month studying for this exam! Spend a little time reviewing –Practice tests –FRQs –Stand and Deliver Relax Calculator check – good batteries, radians Go to bed early – get a good nights rest

3. Tomorrow Morning Get up early Eat a good, healthy breakfast –Avoid sugar or caffeine (its a long test… your blood sugar will spike and drop!) Be confident!

4. During the Test Focus on the problems you know Star and come back to other questions later (esp. on FRQs!) READ carefully! MC – eliminate answers, guessing is ok! FRQs –NEAT and ORGANIZED work! –Use proper notation, ( ), dx, units –Start with the questions you know!

5. GOOD LUCK!! YOU CAN DO IT! Youve studied and worked soooo hard Be confident!

6. When you see… Find equation of the line tangent to f(x) at (a, b) You think…

7. Equation of the tangent line

8. You think… When you see… Find the interval where f(x) is increasing

9. f(x) increasing

10. You think… When you see… Find the interval where the slope of f (x) is increasing

11. Slope of f (x) is increasing

12. You think… When you see… Find the minimum value of a function

13. Minimum value of a function

14. You think… When you see… Find the minimum slope of a function

15. Minimum slope of a function

16. You think… When you see… Find critical numbers

18. You think… When you see… Find inflection points

20. You think… When you see… Show that f(x) is continuous

21. . f(x) is continuous

22. You think… When you see… Find horizontal asymptotes of f(x)

24. You think… When you see… Find the average rate of change of f(x) at [a, b]

25. Average rate of change of f(x) Find f (b) - f ( a) b - a

26. You think… When you see… Find the instantaneous rate of change of f(x) on [a, b]

27. Instantaneous rate of change of f(x) Find f ( a)

28. You think… When you see…

29. Average value of the function

30. You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits

31. Show a piecewise function is differentiable at x=a

32. You think… When you see… Given s(t) (position function), find v(t)

33. Given position s(t), find v(t)

34. You think… When you see… Given v(t), find how far a particle travels on [a, b]

36. You think… When you see… Given v(t) and s(0), find s(t)

37. Given v(t) and s(0), find s(t)

38. You think… When you see… Show that the Mean Value Theorem holds on [a, b]

39. Show that the MVT holds on [a,b]

40. You think… When you see… Find f (x) by definition

42. You think… When you see… y is increasing proportionally to y

43. y is increasing proportionally to y. y is increasing proportionally to y

44. You think… When you see…

45. Fundamental Theorem

46. You think… When you see…

47. Fundamental Theorem, again

48. You think… When you see… The rate of change of population is …

49. Rate of change of a population

50. You think… When you see… The line y = mx + b is tangent to f(x) at (a, b)

51. y = mx+b is tangent to f(x) at (a,b). y = mx+b is tangent to f(x) at (a,b)

52. You think… When you see… Find area using left Riemann sums

53. Area using left Riemann sums

54. You think… When you see… Find area using right Riemann sums

55. Area using right Riemann sums

56. You think… When you see… Find area using midpoint rectangles

57. Area using midpoint rectangles

58. You think… When you see… Find area using trapezoids

59. Area using trapezoids

60. You think… When you see… Solve the differential equation …

61. Solve the differential equation...

62. You think… When you see… Meaning of

63. Meaning of the integral of f(t) from a to x

64. You think… When you see… Given a base, cross sections perpendicular to the x-axis that are squares

65. Semi-circular cross sections perpendicular to the x-axis

66. You think… When you see… Find where the tangent line to f(x) is horizontal

67. Horizontal tangent line

68. You think… When you see… Find where the tangent line to f(x) is vertical

69. Vertical tangent line to f(x)

70. You think… When you see… Find the minimum acceleration given v(t)

71. Given v(t), find minimum acceleration

72. You think… When you see… Approximate the value f(0.1) of by using the tangent line to f at x = 0

73. Approximate f(0.1) using tangent line to f(x) at x = 0

74. You think… When you see… Given the value of F(a) and the fact that the anti-derivative of f is F, find F(b)

75. Given F(a) and the that the anti-derivative of f is F, find F(b)

76. You think… When you see… Given, find

77. Given area under a curve and vertical shift, find the new area under the curve

78. You think… When you see… Given a graph of find where f(x) is increasing

79. Given a graph of f (x), find where f(x) is increasing

80. You think… When you see… Given v(t) and s(0), find the greatest distance from the origin of a particle on [ a, b ]

82. When you see… Given a water tank with g gallons initially being filled at the rate of F(t) gallons/min and emptied at the rate of E(t) gallons/min on, find

83. You think… a)the amount of water in the tank at m minutes

84. Amount of water in the tank at t minutes

85. You think… b) the rate the water amount is changing at m

86. Rate the amount of water is changing at t = m

87. You think… c) the time when the water is at a minimum

88. The time when the water is at a minimum

89. You think… When you see… Given a chart of x and f(x) on selected values between a and b, estimate where c is between a and b.

91. You think… When you see… Given, draw a slope field

92. Draw a slope field of dy/dx

93. You think… When you see… Find the area between curves f(x) and g(x) on [a,b]

94. Area between f(x) and g(x) on [a,b]

95. You think… When you see… Find the volume if the area between the curves f(x) and g(x) is rotated about the x -axis

96. Volume generated by rotating area between f(x) and g(x) about the x-axis