AP Calculus AB Summer Assignment



Welcome to AP Calculus!! You have finally reached the pinnacle of high school mathematics. It will be a challenging time, but one that will pay off if you keep your nose to the grindstone.

While you are enjoying your summer, I would like to ask you to take time to complete the attached assignments. They are designed to help you make the transition into this challenging course as smooth as possible. One thing is for sure – the more you do over the summer, the easier it will be when school starts and the more comfortable you will feel with the pace of the class.

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 for some things, there are no calculators allowed on this packet. You should be able to do everything without a calculator.

Your summer assignment consists of problems that cover the following 5 areas:

I. Survey (This will count for a grade and can be done TODAY!) Email me and I will respond with a link to the survey.

II. Algebra

III. Logarithms

IV. Trigonometry

V. Graphing

It is very important that you complete the summer work and have a firm understanding of the prerequisite skills, as we will be building on these concepts throughout the course. This assignment is DUE ON THE FIRST DAY OF SCHOOL. All work must be neatly shown for each problem. Use graph paper for the problems that require you to graph.

*There will be a test over the summer packet material on the first ‘normal’ day of school.

Thursday, August 14th

IMPORTANT NOTE: NO RETAKES!!!! This means if you fail this test your grade in AP Calculus is in serious jeopardy! This test and the packet will account for about 33% of your first quarter grade. It matters A LOT!

Give us your best work while giving yourself the opportunity to get off to a great start!

Mr. Gray

Name:

Show all work – no credit will be awarded for answers missing appropriate work.

No calculators!

Section II: Algebra Review

Identify the following statements as true or false.

[pic]

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

[pic]

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

17._____________

18. Factor: [pic] 19. Factor: [pic]

18._____________

19._____________

Simplify each expression.

[pic]

[pic]

Simplify by rationalizing the numerator.

Example:

[pic]

[pic]

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

[pic]

[pic]

Section III: Trigonometry Review

34. You must have the first quadrant of the unit circle (all 6 functions and arc-functions) memorized to the point where you can answer any question within 10 seconds. This part of the test will be a slide show with 10 seconds per slide. I suggest creating flash cards and using them MANY times over several weeks (this is harder to master than you think).

examples

[pic]

Complete each of the following using trigonometric identities and formulas.

[pic]

Solve each trigonometric equation for [pic].

[pic]

[pic]

Section IV: Logarithm Review

Solve each exponential or logarithmic equation.

[pic]

[pic]

Expand each of the following using the laws of logs.

[pic]

Section V: Graphing Review

This section will also be timed to 10 seconds per problem. You must be able to go both ways (draw a rough graph given the function and write the function when shown a rough graph).

Sketch the following functions. Draw and label your own axes.

52. [pic] 53. [pic]

54. [pic] 55. [pic]

56. [pic] 57. [pic]

58. [pic] 59. [pic]

60. [pic] 61. [pic]

62. [pic] 63. [pic]

64. [pic] 65. [pic]

66. [pic] 67. [pic]

68. [pic] 69. [pic]

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