CALCULUS BC - Shelby County Schools



TO: Next Year’s BC Calculus Students

FROM: Printup, BC Calculus Teacher

Attached is a summer homework packet, which will be due the first day of Calculus class in August. The material in the packet should be material you learned in Algebra II and Precalculus.

You will turn in the packet the first day of Calculus class, and it will count as a TEST grade. During the first week of school, you will take a test on the material in the packet.

My recommendation is that you look over the problems in this packet and determine what you do NOT know how to do. You may look up help online or you may ask a question in the group chat.

Certain topics may include:

• Limits

• Derivatives (power rule, product rule, quotient rule)

We will be using the TI-89 graphing calculator in Calculus. A TI-89 costs around $150. The price varies some so you should compare the prices at various places before purchasing one. You can buy a TI-89 at stores such as Target, Walmart, Best Buy, Office Depot, as well as from online sites like Amazon.

I do have TI-89’s to loan during the school year, at a replacement cost of $150 if lost, damaged, or stolen.

The problems in this packet do NOT require the use of a TI-89,

I am looking forward to seeing you in Calculus in August.

CALCULUS

SUMMER HOMEWORK

This homework packet is due the first day of school. It will be turned in the first day of Calculus class and will count as a daily grade.

Work these problems on notebook paper. All work must be shown.

Use your graphing calculator only on problems 40 - 50.

Find the x- and y-intercepts and the domain. No calculator.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic] 9. [pic]

10. [pic] 11. [pic]

[pic] [pic]

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Find the asymptotes (horizontal, vertical, and slant), symmetry, and intercepts.

No calculator.

14. [pic] 15. [pic] 16. [pic] 17. [pic]

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Solve. No calculator.

18. [pic] 19. [pic] 20. [pic] 21. [pic]

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Evaluate. No calculator.

22. [pic] 23. [pic] 24. [pic]

25. [pic] 26. [pic] 27. [pic]

28. [pic] 29. [pic] 30. [pic]

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Solve. Give exact answers in radians, [pic] No calculator.

31. [pic] 32. [pic] 33. [pic]

34. [pic] 35. [pic] 36. [pic]

37. [pic] 38. [pic] 39. [pic]

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Solve. Show all steps. Use your calculator, and give decimal answers correct to three decimal places.

40. [pic] 41. [pic] 42. [pic]

43. [pic] 44. [pic] 45. [pic]

46. [pic] 47. [pic]

48. [pic] 49.[pic]

50. The number of students in a school infected with the flu t days after exposure is modeled by the

function [pic].

(a) How many students were infected after three days?

(b) When will 100 students be infected?

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Use the figure to find the limit. No calculator.

51. [pic] 52. [pic]

53. [pic] 54. [pic]

55. [pic] 56. [pic]

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Evaluate. Show supporting work for each problem (algebraic steps or sketch). No calculator.

57. [pic] 58. [pic] 59. [pic]

60. [pic] 61. [pic] 62. [pic]

Evaluate. Show supporting work for each problem (algebraic steps or sketch). No calculator.

63. [pic] 64. [pic] 65. [pic]

66. [pic]

TURN->>>

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Use the definition of the derivative to find the derivative. No calculator.

| [pic]. (You must know this formula.) |

67. [pic] 68. [pic]

69. [pic] 70. [pic]

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Use the differentiation rules (power rule, product rule, quotient rule) to find the derivative. Do not leave negative exponents or complex fractions in your answers. No calculator.

71. [pic] 72. [pic]

73. [pic] 74. [pic]

75. [pic]

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76. Given the function [pic].

(a) Use the differentiation rules to find [pic].

(b) Write the equation of the tangent line to f at (1, 5). Leave your equation in point-slope form.

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