Loudoun County Public Schools



AP Calculus AB Assignment Name:_______________

Due Date: The beginning of class on the first class day of the second week of school.

The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Calculus AB. All of the skills covered in this packet are skills from Algebra 2 and Pre-Calculus. If you need to, you may use reference materials to assist you and refresh your memory (old notes, textbooks, online resources, etc.). While the graphing calculators will be used in class, there are no calculators allowed on this packet. You should be able to do everything without a calculator.

AP Calculus AB is a fast paced course that is taught at the college level. There is a lot of material in the curriculum that must be covered before the AP exam in May. Therefore, we cannot spend a lot of class time re-teaching prerequisite skills. This is why you have this packet. Spend some time with it and make sure you are clear on everything covered in the packet so that you will be successful in Calculus. Of course, you are always encouraged to seek help from your teacher if necessary.

This assignment will be collected and graded for accuracy the first day of the second week of school. Be sure to show all appropriate work to support your answers. In addition, there may be a quiz on this material during the first quarter.

If you have any questions, please contact me.

Mrs. McFadden

lmcfadde@

Name:

This assignment is intended to be done without a calculator. Appropriate work must be shown to receive credit. Show all work with each problem. Do not use a separate sheet of paper.

Section I: Algebra Review

Identify the following statements as true or false.

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

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

Identify the following statements as true or false over the set of real numbers. Give a counter example for any false statement.

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

10. [pic] 11. [pic] 12. [pic]

13. [pic] 14. [pic] 15. [pic]

16. Solve [pic] for [pic]. 17.Solve [pic] for [pic].

Factor each of the following expression completely.

18. [pic] 19. [pic]

20. [pic] 21. [pic]

22. [pic] 23. [pic]

Rewrite each expression as a single quantity or variable to a power.

For example [pic]

24. [pic] 25. [pic]

26. [pic] ________________ 27. [pic] _____________

Simplify each expression. Do not leave any in compound fraction form.

28. [pic] 29. [pic] ______________

30. [pic] ______________ 31. [pic] ______________

32. [pic]______________ 33. [pic] ______________

Expand each expression using the Binomial Theorem or Pascal’s Triangle.

34. [pic] 35. [pic] ______________

What is the coefficient for the x4 term in the following binomial expansion?

35. [pic] ______________ 36. [pic] ______________

Simplify, using factoring of binomial expressions. Leave answers in factored form.

Example:

[pic]

37. [pic]

38. [pic] ___________________________

39. [pic]________________________

Simplify by rationalizing the numerator.

Example:

[pic]

40. [pic]______________ 41. [pic] _______________

Solve each equation or inequality for x over the set of real numbers.

42. [pic] __________ 43. [pic] ___________

44. [pic]____________ 45. [pic] ___________

46. [pic] ___________ 47. [pic] _________

Solve each of the systems.

48. [pic] _________ 49. [pic] ___________

Section II: Pre-Calculus Review

Evaluate each of the following using your knowledge of the unit circle. Do not use a calculator! Leave your answers in radical form.

50. [pic] 51. [pic] 52. [pic]

53. [pic] 54. [pic] 55. [pic]

56. [pic] 57. [pic] 58. [pic]

59. [pic] 60. [pic] 61. [pic]

Solve each trigonometric equation for [pic].

62. [pic] ___________ 63. [pic] ____________

64. [pic]___________ 65. [pic] _____________

Complete each of the following using trigonometric identities and formulas.

66. [pic] 67. [pic] 68. [pic] __________

69. [pic] 70. [pic] 71. [pic]_________

Solve each exponential or logarithmic equation.

72. [pic] 73. [pic] 74. [pic]________

75. [pic] 76. [pic] 77. [pic]______

78. [pic] 79. [pic] ____________

Expand each of the following using the laws of logs.

80. [pic] 81. [pic]

82. On the coordinate planes provided sketch the graph of each of the following types of functions. Label each graphs axis appropriately.

|a. [pic] Linear | |i. [pic] |Rational |

|B [pic] Quadratic | |j. [pic] |Sine |

|c. [pic] Cubic | |k. [pic] |Cosine |

|d. [pic] Quartic | |l. [pic] |Tangent |

|e. [pic] Exponential | |m. [pic] |Secant |

|f. [pic] Constant | |n. [pic] |Cosecant |

|g. [pic] Absolute Value | |o. [pic] |Cotangent |

| | | | |

|h. [pic] Radical | |p. [pic] |Logarithmic |

a. [pic] b. [pic]

c. [pic] d. [pic]

e. [pic] f. [pic]

g. [pic] h. [pic]

i. [pic] j. [pic]

k. [pic] l. [pic]

m. [pic] n. [pic]

o. [pic] p. [pic]

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