AP CALCULUS. Summer Assignment. Name:

Transcription

1 AP CALCULUS Summer Assignment Name: 08/09

2 North Point High School AP Calculus AB Summer Assignment 08 Congratulations on making it to AP Calculus! In order to complete the curriculum before the AP Eam in Ma, it is necessar to do some preparator work this summer. This packet will help ou focus on the mathematical skills and content ou will need to use in solving Calculus problems. These problems deal with skills and content that ou studied in Pre-Calculus. Use our Pre-Calculus notes, as well as online resources to help ou solve the review problems. You are responsible for completing this summer assignment b the first Frida of the new school ear (Frida September 7, 08). The assignment will be collected and counted as a process grade for quarter. In order to receive full credit, complete work must be shown to justif our answers and graphs must be carefull drawn and labeled. If ou use a calculator, then ou must show the set up that ou entered into the calculator and what the calculator produced for ou on our paper. There ma also be a quiz on this summer assignment the second week of school for a product grade. At this level, doing homework is more than just getting the problems done. The problems should be a learning eperience. It is strongl recommended that ou do a few problems each da throughout the summer. Do not leave the entire assignment for the night before school starts. If ou are having trouble with some of the problems, ou can contact me at jburton@ccboe.com. I usuall check m on a weekl basis throughout the summer. Additionall, if ou would like to join a Remind to send me questions ou can b to the number 800. Best of luck on the assignment! I look forward to seeing ou in September! Mr. Burton Mrs. Cockerham

3 Name: AP CALCULUS AB SUMMER ASSIGNMENT Solve each of the following problems, showing all work. Do NOT just write the answer. Be sure all answers are in simplified form. Bo in and/or highlight our answers. The assignment is due on the first da of class. The first unit test of the semester will include topics from this assignment following a brief review of these topics. Write each of the following absolute value equations in piecewise form. Show work leading to our answers. E: f ( ). Determine where the absolute value epression is positive and where it is negative b setting 0 and solving to get. Since 0 for an, the epression remains positive when the absolute value is dropped. Since 0 for an, the epression, becomes negative when the absolute value is dropped. f ( ),. f ( ) 5. f ( ) 4. f ( ) Find each of the following for f ( ) and g ( ). Simplif our answers f ( g( )) 5. f ( h) 6. g ( ) Find each of the following values in eact form 7. 4 sin 8. 7 cos 9. 4 tan sin 5. cos. csc. sec 4. cot 5. csc 6 Find each of the following for the piecewise function form. Show our work!!, 0 f ( ). Be sure answers are in eact, 0 6. f ( ) 7. f (5) 8. f ( 9)

4 Solve each of the following for in terms of. Show all work = Sketch the graph of each function.. f ( ) ( ) 4. f ( ) 4 5. f ( ) ( ) 6. f ( ) 5 7. f ( ) 8. f ( ) ( ) 9. f ( ) ( ) 4 0. f ( ) sin( ). f ( ) cos( ). f ( ) e. f ( ) ln( ) 4. f ( ) tan Find an asmptotes (vertical, horizontal, or slant) for the following functions and an -intercepts. Do Not Graph. 5. f ( ) 6. f ( ) 6 Solve each of the following equations for. Use algebra and show our work. For trigonometric equations, give all eact solutions on the interval [ 0, ) ln( 5) ln( 5 7) e e 0e 0 5. ln( 5) ln( ) 0

5 Solve each trigonometric equation for. Give all eact solutions on the interval [ 0, ). 5. sin sin 0 5. cos cos sin cos tan( ) sin cos cos 57. sec sec 58. sin cos cos 60. tan 0 Sketch a graph of each piecewise function { { < - 6. f () - 6. f () e sin 6. Given the graph of f() below, identif the 64. Find the area of the region between the lines intervals where f is increasing and decreasing. and the -ais using formulas from Then identif where the values of f go from Geometr. Show our work!! negative to positive and positive to negative.

6 LIMITS The limit of a function is the -value that ou are getting close to as gets close to some number in the domain. In the limit process ou never get to the limit, ecept for the limit of a constant function. We write lim f ( ), which is read the limit of f() as approaches a domain value of a. The limit must be the same as approaches a from both the left and the right. To find the limit, substitute in values ver close to a on both left and right and see if the -value is approaching a single value. The limit does eist at a hole in a graph, but does not eist at a vertical asmptote or a jump in the graph. a Limit eist at No limit at No limit at The graphs of some functions are pictured below. Do ou think that lim f ( ) eists? If ou think the limit does eits, state its value. If not, then state wh.. f f

7 State the value of each of the following: 5. lim lim 7. 8 lim 8. lim sin lim 0 0. lim DERIVATIVES Find the derivative using the definition of derivative. f '( ) lim 0 f ( ) f ( ). f() =. f() =. f Find the derivatives using the power rule. 4. f() = 5. f 6. 4 f f 8. 4 f 5 9. f

8 CALCULUS SUMMER FLASH CARDS Based on those prepared b Gertrude R. Battal ( with her gracious permission. Instructions for Using the Flash Cards:. Cut along the horizontal lines onl.. Fold along the vertical lines. This will result in flash cards with the term on one side and the definition or equivalent epression on the other. You ma choose to tape or glue this paper card to a 5 card.. Use the flash cards a few times a week. If ou know the content of a card, put it awa for this session. If ou don t know it, put it at the back of the stack and do it again. 4. Work alone or with a partner. 5. There will be a quiz on this information during the first week of school. Be read to ace it!

9 sin 0 0 sin 6 sin 4 sin sin

10 sin π 0 sin sin π 0 cos 0 cos 6

11 cos 4 cos cos 0 cos π cos 0

12 cos π tan (in terms of sine and/or cosine) sin cos cot (in terms of sine and/or cosine) cos sin csc (in terms of sine and/or cosine) sin sec (in terms of sine and/or cosine) cos

13 Graph of = Graph of = Graph of = Graph of = Graph of =

14 Graph of = Graph of = sin Graph of = cos Graph of = tan Graph of = sec

15 Graph of = Graph of = Graph of = Graph of = e Graph of = ln

16 Definition: An even function is Definition: An odd function is smmetric with respect to the -ais, like =, = cos, or =. f ( ) = f () smmetric with respect to the origin, like =, = sin, or = tan. f ( ) = f () Point-slope form of a linear equation = m( ) Sine is positive in quadrants I and II, where > 0 Cosine is positive in quadrants I and IV, where > 0