Directions: Please read questions carefully. It is recommended that you do the Short Answer Section prior to doing the Multiple Choice.

Transcription

1 AP Calculus AB SUMMER ASSIGNMENT Multiple Choice Section Directions: Please read questions carefully It is recommended that you do the Short Answer Section prior to doing the Multiple Choice Show all work on this packet If no work is required, EXPLAIN how you arrived at your answer Follow calculator instructions as given in each section * A choice of none is short for none of these A choice of DNE means does not eist These problems are due the first day of class On the first day of class you will have a short amount of time to ask questions before turning these packets in Do not epect there to be time in class for ALL questions to be resolved There will be classwork assignments on the material starting with the third week of school NO CALCULATOR Lines and functions ) Determine the slope of the line that passes through the points (-, 6) and (, -6) ) Find the equation of the line that passes through the point (, -) and has a slope of - y = - y = - + y = - y = of these ) Determine which points lie on the vertical line that contains the point (5, ) (5, 0) (0, ) (, 5) all of these of these 4) What is the slope of the line parallel to the line 7 - y =? ) Find an equation of the line that passes through (-, -) parallel to the line + y = 9 y = - y = - 5 y = 7 y none of these

2 6) Find an equation of the line that passes through (8, 7) and is perpendicular to the line + y = 7) Given A = {,, } and B = {-, -, 0, }, determine which of the sets of ordered pairs represents a function from A to B {(, -), (, -), (, -), (, 0), (, )} {(, -), (, -), (, 0), (, )} {(, -), (, -), (, 0), (, )} all of these of these 8) Which of the following does not represent y as a function of? y 0 4y 8 y 0 4y 8 e) y 6 9) Given f ( ) 6, find ( ) f ) Given, 4 f( ) 6 7, 4 find f ( ) ) Given f( ) 6 and g ( ), find f ( ) g( ) ) Given f ( ) and g( ) 5, find g( f ( )) ) Given f ( ) and g ( ) 7, find f() g ()

3 4) Given f ( ) and g( ), find f ( g( )) of these 5) Given f ( ) and g( ) 6, find f( g( )) 6) If f ( h) f ( ) f ( ), find h h h 7) Is the function f ( ) even, odd, or neither? Show why 8) If f is a one-to-one function on its domain, the graph with respect to: f ( ) is a reflection of the graph of f( ) the -ais the y-ais y = y = - 9) In which graph does y not represent a one-to-one function of? All of these are one-to-one functions of e) None of these are one-to-one function of 0) Given f ( ), find f ( ) ( )

4 CALCULATOR Lines and functions ) Use your calculator to determine the interval(s) on the real ais for which f( ) 0 where f ( ) 9, 9, 9, 9, ) Find the relative ma/min of f ( ) relative maimum at (-058, -08) relative maimum at (-058, 08) relative minimum at (058, -08) relative maimum at (058, -08) no relative minimum or relative maimum relative minimum at (-058, 08) of these ) Find the minimum point on the graph of f ( ) 4 4 (, 8) (-, 8) (-, 6) (, 0) Solving equations NO CALCULATOR 4) Solve for ) Solve for and

5 6) Solve for ) Solve for p: g 4 p r 8) Solve for ) Solve for 5 4, -, -, 4 0) Solve for 4 0 7, -7, - 0,, 7 0, -, -7 ) Solve for , 58-46, 46 -, ) Solve for 4 5 7, 5 7, 5 5, 5

6 ) Solve by factoring ,, ) Solve by completing the square ) Solve for 4 -,, 6) Solve for 6 0 5, 7) Solve for , 5, 5 9, 6 8) Solve the inequality algebraically 9,,,, 9) Find all the real zeros of the polynomial function f ( ) 6 0 0, 0,, -

7 CALCULATOR Solving equations 40) Approimate the solution(s) of using your graphing calculator -7, 00 -, 0-7, -0 no solution 4) Use your graphing calculator to approimate the solution(s) of no solution 4) Approimate the points of intersection of the graphs of y 5 4 and y 6 (, -9) (, -4) (, -5) no solution 4) Approimate the solution(s) of 0 -, -767,, ) Evaluate y when t t e Factoring and division NO CALCULATOR 45) Use synthetic division to factor the polynomial 0 8 completely if - is a zero 4 -, -4, of these

8 46) Which polynomial function has zeros of 0, - and? f ( ) f ( ) f ( ) f ( ) 47) Use long division to find the quotient ( ) 5 5 ( ) 5 5 ( ) 9 / 4 7 ( ) 48) Use synthetic division to find the quotient Graphs NO CALCULATOR 49) Find the domain of the relation shown at the right,,,, of these 50) Find the range of the function shown at the right, 8,,, 5 of these

9 5) Find the domain of the function f ( ) 5,5,5 5, 5, e)none 5) Describe the transformation of the graph of f ( ) which yields the graph of g( ) 0 vertical shift 0 units up vertical shift 0 units down horizontal shift 0 units right horizontal shift 0 units left 5) Graph g( ) ( ) using a transformation of the graph of f ( ) 54) Which sequence of transformations will yield the graph of of f ( )? g ( ) ( ) 0 horizontal shift 0 units right horizontal shift unit left vertical shift unit up vertical shift 0 units up horizontal shift unit right horizontal shift 0 units left vertical shirt 0 units up vertical shift unit up from the graph 55) Find the -intercept(s) of y 4y 0, 0 6, 0 (4, 0) (6, 0)

10 56) Find the intercepts of the graph of 7y -int: (0, 7) -int: (0, ) -int: (, 0) y-int: (, 0) y-int: (7, 0) y-int: (0, 7) -int: (7, 0) y-int: (0, ) 57) Find the and y-intercepts: y 5 4 (0, -4), (0, ), (4, 0) (0, 4), (4, 0), (, 0) (0, -4), (-4, 0), (-, 0) (0, 4), (-4, 0), (-, 0) of these 58) Determine the left and right behaviors of the graph of 5 f ( ) up to the left, down to the right down to the left, up to the right up to the left, up to the right down to the left, down to the right of these 59) Determine the left and right behaviors of the graph of f ( ) 5 4 up to the left, down to the right down to the left, up to the right up to the left, up to the right down to the left, down to the right of these 60) Which function is graphed? f ( ) 6 f ( ) 6 f ( ) 6 4 f ( ) 6 of these

11 6) Graph the following:, 0 f( ), 0 6) Find the domain of the function f( ),,,,,,,,,,,,,, of these 6) Find the domain of f( ) all real numbers ecept -,, and all real numbers ecept - all real numbers ecept and all real numbers 64) Find the domain of f( ) 9 all real numbers all real numbers ecept all real numbers ecept all real numbers ecept, 65) Find the vertical asymptote(s) of the graph of f( ) ( )( 5) y =, y = -5, y = - =, = -5, = -, = = =, = -5 66) Find the horizontal asymptote(s) of the graph of f( ) y = 0 = - y =

12 67) Find the horizontal asymptote(s) of the graph of f( ) y = y 7 y = 0 68) Find all intercepts of the graph of f( ) 4 7 (0, -), (4, 0) (-4, 0), (, 0) (4, 0), (0, ) 7 (4, 0), (0, ) 69) Match the rational function with the correct graph f( ) 70) Match the graph with the correct function f( ) f( ) f ( ) f( ) e) None of these 7) What is the domain of f ( ) e?, 0,,,

13 7) Without using a graphing utility, sketch the graph of f( ) Trigonometry NO CALCULATOR 7) Give the eact value of cos 4 74) Find all solutions to cos 0 in the interval 0,, 6 6 5, , 4, 75) Give the eact value of csc undefined - of these 76) Find all solutions to sec sec 0, in the interval 4,,, 5,, 4,,, ) Find the eact value of 5 tan 6 -

14 78) Evaluate sec 79) Find all solutions of sin cos cos 0 in the interval 0, 5,,, 6 6 7,,, 6 6 5, 6 6 0, of these CALCULATOR Trigonometry 80) Given tan 67, find ) Find two values of ( 0 ) that satisfy sec and and and and 4909 of these 8) Evaluate arc cos( 04777)

15 NO CALCULATOR Logarithms and natural logarithms 8) Solve for ) Evaluate ln e e e ln ( ) 85) Simplify ln e 5 e ln e ln ln ln ) Simplify ln e ln ln 87) Solve for ln e 9 ln ln e 88) Simplify 5 7 ln e 5 ln ln 7 5 5

16 89) Solve for ln ln 6 ln ln ln ln 90) Solve for ln(7 ) ln( 5) ln(4 ) 6 7 7, 5 6,5 9) Find the domain of the function f ( ) ln( ), 0,,, Limits NO CALCULATOR 9) Use the graph to estimate lim f( ) DNE 0-9) Use the graph to find lim f( ), if it eists - DNE - e) -

17 94) Find lim ( ) ) Find lim ) Find lim f( ) if 4, f( ), 97) If lim f( ) and c lim g ( ) c, find lim f ( ) g( ) c 98) Find lim ) Find lim e) DNE 00) Find the limit lim 0 ( ) ( ) ( ) 4 - DNE