Preparation for Advanced Placement Calculus

Transcription

1 Tappan Zee High School Mathematics Department June 07 Preparation for Advanced Placement Calculus Dear Advanced Placement Calculus Student, We hope that you have had a successful year! Before you leave for the summer, we would like to give you some information about the Calculus class you will be taking net year. Your AP Calculus class will require a combination of homework and problem sets, class participation, projects, and eams. You should epect to spend a significant amount of time each night reviewing the day s notes and completing homework assignments. Problem sets will be comprehensive homework assignments that will take several days to complete and may be worked on cooperatively. We are looking forward to an eciting Calculus Eperience net year. To enable us to make a smooth transition into the new material, you are required to complete a problem set comprised of problems from Algebra II/Trigonometry and Pre-Calculus. Since this is a review assignment, we epect that you will complete the problem set over the summer and you will be tested on this material during the first week of school. We will be available for last minute questions during the first week of classes. This problem set can be found on the district website ( Your work will be collected on Friday September 8, 07. You should complete the summer assignment without using a calculator. Please do not wait until the last minute to complete this assignment. year! We hope you enjoy your summer and we look forward to working with you net Sincerely, Mrs. Braunagel and Mrs. Corcoran

2 Problem Set #: All work must be neatly shown. Do NOT use a calculator. Read the attached Prerequisites Complete the attached packet From the College Board:

3 Trigonometry Practice Name: **Please note that you are prohibited from using a calculator on half of the AP Eam and in half of this course. Therefore, give eact answers without using a calculator. Part I: Evaluate each of the following. Eact values only. Calculators should NOT be used unless indicated net to the question.. sin π. csc π. cos π. sec π. sin π 6. tan π 7. cos π 8. π cot π 9. sin( ) 0. 6 π π tan + csc 6 π π. (sin )(cos ). π π sin + cosπ + cos Part II: Determine which quadrant angle is located in:. sin < 0 and cos < 0. csc > 0 and cot < 0. sin < 0 and sec > 0

4 Part III: Find the value of the specified trigonometric function. Eact values only. Do NOT use a calculator. 6. If cos = and is in quadrant IV, find sin. 7. If sin = and is in quadrant III, find cos. 8. If csc = and is in quadrant IV, find cot. Part IV: State the amplitude, frequency, and period of each of the following: 9. y = sin 0. y = cos. y = sin. A building s temperature, T, varies with time of day, t, during the course of one day as follows: T = 8 cost The air-conditioning operates when T 80 F. Graph this function for 6 t 7 and determine, to the nearest tenth of an hour, the amount of time in one day that the air-conditioner operates. (calculator allowed)

5 Logarithm Practice Name: Part I: Evaluate each epression. DO NOT use a calculator.. log 6. log 6 6. log 8. log 8. log 6. 7 ln 6 e 7. ln e 8. log 9. log. + log80 0. log 08 log. log8 6 log8 + log8 Part II: Epress the given quantity as a single logarithm:. log + log ( + ) + log ( ). ln ln( + )

6 Part III: Match the equivalent epressions.. ln. ln e 6. ln e 7. ln 8. ln 9. ln a. b. ln c. 0 d. ln e. -ln f. - Part IV: Solve the given equation for. 0. log =. e = 6. e =. ln = ln + ln8. ln = ln ln. ln( e ) = 6. e e = 0

7 Algebra Practice Name: **Please note that you are prohibited from using a calculator on half of the AP Eam and in half of this course. Therefore, give eact answers without using a calculator. Complete each of the following. Show all work.. Given f ( ) =, find f(-8).. Find the point(s) of intersection of the following graphs: f ( ) = 6 g ( ) =. Solve: e e = 0. Solve for z: z y = yz +. Solve for all values of, 0 < π : sin cos = 0

8 6. The two branches of the following piece-wise function meet when =. +, f ( ) = m, > Find m. 7. Given f ( ) = sec, find f ( π ). 8. Find the y-coordinate of the graph of y = at = Simplify each of the following: a) + 8 d) b) e) 7 c) 6 7 8