AP Calculus AB Mrs. Mills Carlmont High School

Transcription

1 AP Calculus AB Mrs. Mills Carlmont High School AP CALCULUS AB SUMMER ASSIGNMENT NAME: READ THE FOLLOWING DIRECTIONS CAREFULLY! Read through the notes & eamples for each page and then solve all problems. Show all steps and be neat & organized & draw graphs or tables when necessary and label everything. If you get stuck, search the internet and see if you can teach yourself how to do it, or ask your friends (I encourage you to form study groups), but do not copy anyone for any reason! Be sure to complete the reflection at the very end of the packet. This summer assignment will be the last grade recorded for the class for 1 st semester. It s worth 100 points (the same as a chapter test) and is due on the first day of school, Tuesday August 18 th, 015. At the end of the semester when you are tempted to ask if there is anything you can do to improve your grade, this is what you can do! Don t forget that you never get another chance to make a first impression, so do your best!

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4 POINTS OF INTERSECTION To find where functions intersect, set the functions equal to each other and solve. Then sketch the functions on the same coordinate plane to make sure your answer(s) is (are) reasonable. Remember: You are finding a POINT OF INTERSECTION so your answer is an ordered pair. Eample: f g( ) 4 ( ) ) f ( ) 3 17) f ( ) 5 g( ) 4 g( ) 18) f( ) 3 g( )

5 Find the domain & range of each function. Write your answer in INTERVAL notation. 19) f ( ) 5 0) f ( ) 3 1) f ( ) 3sin ) f( ) 1

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8 LOGARITHMS & NATURAL LOGARITHMS We will only use natural logs in calculus ln( y) ln ln y ln ln ln y y ln e ln e 36. a) ln e = 37. a) b) ln1= b) 3 ln e = 1 ln e = 38. a) 9ln e = 39. a) 0 e = b) 10ln e = b) l e = 40. a) ln 4 ln 6 = c) b) ln 4 ln6 = ln8 e =

9 State whether the following graphs are even, odd or neither. 44. f ( ) 45. f ( ) 46. f ( ) f ( ) f ( ) sin( ) 49. f ( ) cos( ) 50. f ( ) sin( ) f ( ) cos( ) FACTORING Factor completely and write the type of factoring required for each problem. (difference of two squares or cubes, general trinomial, grouping, etc ) ) a b 53) a ab b 54) a b 55) a a b ab 56) a b 57) 3 3 a ab ab b 58) a 5a 1 59) 1a 6a 1

10 SOLVING EQUATIONS Solve for the given variable. Show all steps & check your answer(s). 60) a a 0 61) a a 8 6) a a 8 63) a 8 64) a 8 65) 3 a a a ) 3 a 7 67) a 5 68) 5a 5 69) a 5 70) e ( 3) 0 71) ) ln( ) 5 73) e 5 74) 75) 3 y 6 0 8y 9 4y 9y

11 Geometry 76) These are all of the formulas you should have memorized, fill them in! Square Rectangle y Trapezoid h 1 h Perimeter = Area = Perimeter = Area = b Area = Circle Triangle Cube r Circumference = Area = a Pythagorean Theorem (only good for right triangles) = b c Volume = Surface Area = Area (of any triangle) = Sphere Washer R Cylinder r r r h Volume = Area of the shaded region = Volume =

12 Geometry Applications Find the area between the -ais and f( ) from = 0 to = 5. Sketch and show all work. Eample: f ( ) Find the area between the -ais and f( ) from = 0 to = 5. Sketch and show all work. 77) f ( ) 78) f( ) 3 79) f ( ) 3 80) 1 f( ) 5

13 Trigonometry Unit Circle (0, 1) (-1,0) (1,0) (cos,sin) (0, -1) 3 Special Right Triangles 1 Important Identities csc 1 1 sec Which trig function is positive? cot 1 Students All 1 1 tan Take Calculus Converting Angle Measurement replace with sin cos 81. You must know how to calculate these values without the use of a calculator! or 0 or or or or or 3 Sin Cos Tan 8) 5 sin 6 83) sin 3 84) sin 85) cos 3 Multiple Choice 4 86) cos is equivalent to 3 A) cos 3 B) cos C) cos30 D) cos30 E) None of these ) sin is equivalent to 6 A) sin 6 B) sin C) sin 60 D) sin 60 E) None of these 6

14 Calculus relies heavily on Algebra and a clear understanding of how different functions behave. These 10 problems are known as the parent functions and you should be comfortable filling in all questions, without a calculator. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 88) f ( ) Name of function = Graph Table f() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Decreasing intervals Horizontal Asymptotes Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim f( ) lim f( ) Inverse

15 89) q( ) Name of function = Graph Table q() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim q ( ) lim q ( ) Inverse

16 90) c( ) 3 Name of function = Graph Table c() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim c ( ) lim c ( ) Inverse

17 91) a( ) Name of function = Graph Table a() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim a ( ) lim a ( ) Inverse

18 9) s( ) Name of function = Graph Table s() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior Inverse lim s ( ) lim f( ) 0

19 93) r ( ) 1 Name of function = Graph Table r() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim r ( ) lim r ( ) Inverse

20 94) s( ) sin( ) Name of function = Graph Table s() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim s ( ) lim s ( ) Inverse

21 95) c( ) cos( ) Name of function = Graph Table c() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim c ( ) lim c ( ) Inverse

22 96) n( ) ln( ) Name of function = Graph Table n() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior Inverse lim n ( ) lim n ( ) 0

23 97) f ( ) e Name of function = Graph Table f() Domain Range - intercept(s) (roots) y intercept Vertical Asymptotes Horizontal Asymptotes Decreasing intervals Increasing intervals Relative minimums Relative maimums Continuous? Even, odd or neither End behavior lim f( ) lim f( ) Inverse

24 98) When you finish, please reflect on this summer assignment. Some things to include: How long did it take you to complete? Who did you work with and in what capacity? What are the areas you feel the most comfortable with and what areas do you feel are your weakest? What did you learn as a result of doing this summer assignment?