School Year

Transcription

1 AP Calculus AB Assignment School Year In order to ensure that our AP Calculus classes meet the standards required by the College Board, it is strongly recommended that all calculus students complete a summer assignment. This must be submitted by Tuesday Sept. 8 for credit towards etra points on the first quarter grade. Though the summer assignment itself is etra credit, you will be quizzed on this material at the beginning of the year (and will need it throughout the school year) so I strongly suggest that you complete it thoroughly and completely before you arrive to school in August. Your success in Calculus will depend on your knowledge of Algebra, Geometry, Trigonometry and Functions, as well as your effort and work habits. This summer assignment is designed to prepare you for a successful year and to help you meet our objective of giving you the best opportunity to receive college credit while still in high school. If you need help with this assignment, please feel free to contact me online during the summer at harveygl@pwcs.edu. Reminders: SHOW ALL WORK (neatly and completely) You may work with a friend, but be sure you understand how to do all the problems yourself because your friend will not be taking the quiz with you. DO NOT use a calculator unless the problem says you may!!! (Like the AP test, our assessments will include non-calculator and calculator portions so you will have to be able to do many things in your head!) Please share this information with your parents. If you or your parents have any questions, feel free to call or me at Hylton before June 7 th. Good luck and have a great summer! See you net year! Mrs. Harvey

2 AP Calculus AB Assignment Show all work in this packet.. Find all the intercepts: y A. (, 0), (0, -/) B. (, 0) C. (-, 0), (, 0) D. (-, 0), (0, -/) E. none of these. Use fundamental identities to simplify the epression below and then determine which of the following is not equivalent. A) B) C) D) E). Find the equation of the line through (4, ) and perpendicular to the line through (9, 7) and (, 4). A. y B. y C. y 9 7 D. y 4 E. none of these Find the domain of f. A., B., C., D.,, E. none of these 5. Given f 4, find f f. A. + 4 B. + C. + 8 D. 4 E. none of these

3 6. 7. If f and g, find f g. A. these B. C. D. E. none of 8. Given f() = 6 and g() = 4, find f g A. these 6 B. 6 C. 6 D. 6 E. none of 9. Given f() = + and g() =, find f g. A. 7 B. + C. D E. none of these 0. Match the graph to the right with the correct function. A. B. C. D.. Find all vertical asymptotes of f A. = B. = ½, = - C. = - D. = ½

4 . Using the figure to the right, solve for : A. 6 B. 6 C. D. 0º. Solve the equation for 0 : sin sin. A. 0,, B.,, C. 5,, 6 6. A rectangle is bounded by the -ais and the semicircle of the rectangle as a function of. y D., 6 5. Write the area A A. y = B. y = C. y = 8 D. y 5 E. y 5 4. Describe how the graph of f 5 can be obtained from the graph of g. A. reflect over y-ais, shift left, reflect over -ais, vertical stretch by, shift up 5. B. reflect over y-ais, shift right, reflect over -ais, vertical stretch by, shift up 5 C. reflect over y-ais, shift right 5, reflect over -ais, vertical stretch by, shift up D. reflect over -ais, shift left, vertical stretch by, shift down 5 E. reflect over y-ais, shift left, reflect over -ais, vertical stretch by, shift down 5 5. Write a formula for the function graphed on the right A. f C. f 5, 0 5 0, 4 5, 0 5 0, 4 B. f 5 D. f

5 6. Give the equation for the graph after the following transformations have been applied to the graph of y = : vertical stretch by, reflect over the -ais, shift right, shift up. A. y B. y C. y D. y E. y 7. Evaluate the function at and simplify. A) B) C) D) E) 8. Find the value of log8. A. B. 4 C. 5/ D. 5/ 9. Find log 8 + log 50 log 4 A. B. C. log 54 D Find ln /5 e A. e B. /e C. -/e D. - E. e. Solve for : log 9 A. - B. and - C. only D. no solutions. Solve for : log 5 5 log 5 5 A. B. ½ C. - D. 5

6 . The population of mosquitoes follows an eponential growth pattern. If the population of mosquitoes doubles every hour and there are 75 flies initially, approimate how many mosquitoes will be present after 6.5 hours (assuming that none die!). (calculator allowed!) A.,75 B.,97 C. 5,89 D. 8,00 4. Evaluate 9. A. 7 B. 9 C. 9.5 D Evaluate 5 8. A..48 B. C. 6. (calculator) 5 8 D (calculator)

7 8. Which defined function matches the graph?,, A. f B. f,,, D. f E. none of these, C. f,, 9. Determine which point lies on the graph of the equation. A) (, 9) B) (0, 0) C) (0, 8) D) (, 0) E) (, 8) Use the graph to the right to answer # Which defined function matches the graph? A. f D. f. Find f ( ). B. f C. f A. 0 B. C. DNE D. f and g 5. Let discontinuous.. Find all values of for which A. - B. - and 5 C. 5 D. - and f g is. If, find the value of in degrees without the aid of a calculator. A) B) C) D) E) 4. Describe the rate of change at the indicated point on the graph to the right. A. no slope B. positive C. negative D. zero 5 At which point is the rate of change closest to zero on the graph shown below? A. A B. B C. C B D. D E. E A C D E

8 6. Where is the function f 5 5 discontinuous (has holes or asymptotes)? A. = -5 and = - B. = -5 and = C. = - and = 5 D. = and = 5 E. = and = 5 7. Evaluate tan A. B. - C. D Solve the equation: sin cos for 0.. E. 0 A. 5 7,,, B., 6 C. 5, 4 4 D. 0,,, 9. Use synthetic division to divide by 40. Factor completely: A) 0( + 8)( 7) ( ) B) ( + 8)( 7) (0 0) C) ( + 8)( 7) (5 5) D) ( 7) ( 8)(5 5) 4. Given the equation, determine two solutions such that. A) B) C) D) E) 4. Graph the function: A) B) C) D)

9 4. Write an equation in point-slope form for the line through (4, 6) with slope m =. a. b. c. d. 44. Write the equation of the secant line that passes through (, 5) and (, 7). a. y = ( + ) + 5 b. c. d. y + 5 = ( ) 45. Verify the identity : 46. Multiply. a. b. c. d. 47. A board of length m was cut into two pieces. If one piece is m, epress the length of the other board as a rational epression. a. b. c. d. Evaluate the logarithm. 48. a. 5 b. 5 c. 4 d. 49. log 0.0 a. 0 b. c. d. 0 Solve. Round to the nearest ten-thousandth when necessary (Calculator) a b c d..909

10 5.. a. b. c. d. 5.. (calulator) a b c d a b. 4 c. 50 d (calulator) a b. 0.7 c d (calulator) a..664 b c d Simplify. a. b. c. e d. Write the equation of the piecewise function shown. 57.

11

12 (Do you know how to do this on the calculator??) If, evaluate the following cos 74. cos 75. cos 76. cos If, evaluate the following. 77. sin 78. tan 79. tan 80. sin

13 If, evaluate the following. 8. 4cos 8. tan 8. sin 84. sin 85. The formula to find the average rate of change on f from a to b is:. 86. If h( ), find the equation of the secant line from (, h ()) to (4, h (4)). 87. Using the function below, find the average rate of change on the intervals from: (a) 0 to (b) - to - (c) Write the equation of the secant line from to. In 88 and 89, find the area of the shaded region cm 0 cm 0 cm d = 4 ft 0 cm

14 90. Evaluate the difference quotient, f ( h) f ( ), if h f ( ). 9. Evaluate the difference quotient, f ( ) f ( a), if f ( ) at a. a 9. Use the difference quotient definition f f a a to evaluate f( ) at a. 9. Use f h f h to evaluate the difference quotient for f( ). Given the difference quotient, find f( ) and the value at which it is being evaluated (when applicable). 9. sec h 4 h 9. h h 94. h ln ln 4 e e h

15 For #96-05, use the graph of g. ( ) 96. Find the domain and range of the function. 97. Find g (). 98. Find g (6). 99. For what values of is g ( ) positive? 00. On what intervals is the graph increasing? 0. How many times does the line cross g? ( ) 0. Find g (4). 0. Where does g() have a local min? 04. What is the absolute minimum value of g()? 05. At what value does g() have a local maimum? Answer the following questions about the graph of q. ( ) 06. What kind of function is this? (eponential or logistic) 50 (4, 40) (6, 58) 07. Find q (40) On what intervals is the graph concave down? 09. The point (4, 40) is the inflection point on this graph. What does inflection point mean? 0. Find the average rate of change from 0 to.. Write the equation of the secant line from = 0 to =.

16 Simplify the following epressions y y 6