AP Calculus AB Summer Assignment Name:_______________ Welcome to AP Calculus. While you are enjoying your summer, you need to take time to complete the attached assignment. These problems are designed to help you make the transition into this challenging course as smooth as possible. 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.). I would recommend you spend some time with the Algebra & Trigonometry review available at http://tutorial.math.lamar.edu/pdf/AlgebraTrig.pdf. While the graphing calculators will be used in class for some topics, there are no calculators allowed on this packet except where noted. You should be able to do almost all the problems below without a calculator. Where you cannot use the calculator, leave your answer in the simplest terms possible. If it is obvious to me that you used a calculator to compute your answer, it will be marked incorrect. You should know that a surprising amount of AP Calculus and about 60% of the AP exam is completed with no calculator. Your summer assignment consists of problems that cover the following areas: I. Algebra II. Logarithms III. Trigonometry IV. Graphing V. Problem Solving 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 AUGUST 21, 2017 @ 2:00. The test on Chapter P (which consists of this material) will be during the first week we meet. Any updates or schedule changes will be posted at tmorrismath.weebly.com. You should check the website at least once a week starting in August. Please make sure you complete this summer work with care. If you fail the first test, your grade in AP Calculus is in serious jeopardy! The test and packet together will account for about 25% of your first quarter grade. I look forward to our year together! Mr. Morris
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AP Calculus AB Summer Assignment Name:_______________
Welcome to AP Calculus. While you are enjoying your summer, you need to take time to
complete the attached assignment. These problems are designed to help you make the transition into this challenging course as smooth as possible. 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.). I would recommend you spend some time with the Algebra & Trigonometry review available at http://tutorial.math.lamar.edu/pdf/AlgebraTrig.pdf. While the graphing calculators will be used in class for some topics, there are no calculators allowed on this packet except where noted. You should be able to do almost all the problems below without a calculator. Where you cannot use the calculator, leave your answer in the simplest terms possible. If it is obvious to me that you used a calculator to compute your answer, it will be marked incorrect. You should know that a surprising amount of AP Calculus and about 60% of the AP exam is completed with no calculator. Your summer assignment consists of problems that cover the following areas: I. Algebra II. Logarithms III. Trigonometry IV. Graphing V. Problem Solving
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 AUGUST 21, 2017 @ 2:00. The test on Chapter P (which consists of this material) will be during the first week we meet. Any updates or schedule changes will be posted at tmorrismath.weebly.com. You should check the website at least once a week starting in August. Please make sure you complete this summer work with care. If you fail the first test, your grade in AP Calculus is in serious jeopardy! The test and packet together will account for about 25% of your first quarter grade. I look forward to our year together! Mr. Morris
Name: ________________________________________________ Show all work – no credit will be awarded for answers missing appropriate work. You may use another sheet of paper if there is insufficient room provided. No calculators except where noted! Section I: Algebra Review Identify the following statements as true or false.
_____.6_____3
3.5_____3
3.4
_____2
2.3_____
111.2_____
222.1
22 babac
ba
c
ba
b
a
b
a
hx
k
hx
k
qpqp
yxyx
••
Identify the following statements as true or false over the set of real numbers. Give a counter example for any false statement.
3 3 3 3 2
2
7. 1 _____ 8. _____ 9. 0 _____
10. _____ 11. 2 _____ 12. 0 _____
113. 0 _____ 14. _____ 15. _____
x x x x x x
x x x x x
x x x xx
16. Solve '' 1 yyxy for 'y . 17.Solve kty ln for y . 16._____________
Section II: 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 (this is harder to master than you think). Although I only provided three examples in this review, you have a lot to remember!! examples
3a. tan ____________ . arcsin ____________ . csc ____________
6 2 4b c
Complete each of the following using trigonometric identities and formulas.
2 2 2 235. sin cos _________ 36. 1 cot ____________ 37. 1 tan ____________x x x x
Solve each trigonometric equation for 20 x .
2338. sin ____________ 39. tan 1 ___________
2x x
2240. cos ____________ 41. 2sin sin 1 0 ____________
2 2
xx x
Section III: Logarithm Review Solve each exponential or logarithmic equation.
3
1 442. 5 125 __________ 43. 8 16 __________ 44. 81 _________x x x x
Expand each of the following using the laws of logs. 2
3
2
50. log 5 ________________________
551. ln _______________________
x
x
y
Section IV: 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.