AP Calculus AB and BC – Summer Packet

NAME______

Last Year’s Course ______Last Year’s Teacher :______

This packet is due the first day back in school in the fall. It will be graded for correctness. Spend some quality time on this packet this summer. Work needs to be shown when needed. Also, do not rely on the calculator. Half of your AP exam next year is taken without the calculator, so use paper and pencil techniques only.

If you do not have the skills addressed in this packet, you will find that you will get problems incorrect next year, even though you understand the calculus concepts. It is frustrating for students when they are tripped up by the algebra and not the calculus. This summer packet is intended for you to brush up and possibly relearn these topics.

If you need help on some of these topics, the following websites are good sources for instruction:

The Math Page: http://www.themathpage.com/

Paul’s Online Math Notes: http://tutorial.math.lamar.edu/sitemap.aspx

Virtual Math Lab: http://www.wtamu.edu/academic/anns/mps/math/mathlab//

Khan Academy Teaching Videos: https://www.khanacademy.org/

Also refer to the AP Calculus teachers’ websites for this document and other documents and links.

Section 1: Trigonometry – Know all unit circle values.

Determine the exact value of each without using a calculator:

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. List the Pythagorean Trigonometric Identities: ______

______

______

17. List the Double Angle Trigonometric Identities: ______

______

18. Find all the exact solutions to on the interval .

19. Solve the equation: on the interval .

20. Use Trigonometric Identities to simplify:

21. Graph the following from

a. b.

Section 2: Exponential Functions and Logarithms

Simplify:

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34. 35. 36.

Graph the following:

37. 38.

Section 3: Algebra Review

Simplify the following:

39. 40. 41.

42. 43. 44.

For #’s 45-52, graph each function and state the following:

A. zeros B. y-intercept C. domain and range (interval notation or exclude values)

45. 46.

47. 48.

49. 50.

51. 52.

For #’s 53-56, write the equation of a line in point-slope form:

53. A line containing and 54. A line containing and the origin.

55. A horizontal line with a y-intercept at -3. 56. A vertical line with a root at 5.

57. Expand the binomial 58. Simplify:

59. Use sign analysis to solve:

60. Given , find (the difference quotient).

61. Use your graphing calculator to find the x-values of the point(s) of intersection for: and (Round to 3 decimal places.) Draw a quick sketch and state the intervals where and where .

62. Find the inverse to the following functions. Sketch the function and its inverse on the same graph and state whether the inverse is a function. Support your answer.

a.

b.

63. Find the inverse to and show that