Section Page(s) Problems to Complete Points Section 1 Exercises Section 2 Exercises Section 3 Exercises

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1 To help you prepare for AP Calculus AB, you are required to complete this assignment. These problems will allow you to review and master the prerequisite skills necessary for this rigorous course so that you will be fully prepared in September. I recommend you read Chapter and take notes on vocabulary and theorems. Please epect a test on Chapter during the second cycle and a quiz the first day of school. For both parts, use your graphing calculator to support your answer, where possible. There are many websites/videos available online to teach you how to use the graphing calculator and the links will be shared via Remind. Part : Tetbook Assignment /5 Please answer each question. Please note that the problems with a grey background do not permit the use of a calculator. The assignment will be graded based on effort and accuracy. Work must be shown to support your answer. An attempt must be made to answer problems that you do not know the answers to. Part : Pre-requisite Problems /5 Please answer each question. The assignment will be graded based on effort and accuracy. Work must be shown to support your answer. Please complete on a separate sheet of paper. An attempt must be made to answer problems that you do not know the answers to. Your tetbook and information/videos available online are great resources if you need help. Any resources available online will be shared via Remind. Part : Section Page(s) Problems to Complete Points Section Eercises Section Eercises Section Eercises Pages 9 #s 6 (multiples of ), 7, 4, 47 5, 54, & 57 Pages 9 Pages 6 8 #s -, 5- all, 5 9 (odd), -5, 9, 4, 45, 5, 57 6, 67 & 69. Write the domain and range in interval notation. #s -, 7, 9, -8,, 5, 7, 7, & No calculator permitted for #s - Quick Quiz Page 8 #s 4 Section 5 Eercises Section 6 Eercises Pages 4 44 #s 4 (multiples of ),, 7, 8, 9, 4, 48, & 5 57 Pages 5 5 #s 6, 9, 7, 9,, 7 9,, 4, & Quick Quiz Page 54 #s 4

2 AP Calculus AB Summer Assignment 08 AP Calculus AB Summer Assignment: Part -Prerequisite Review Problems. List the lines in parts d) in order of increasing slope. b) d). Derive Point-Slope Form.. Find the Point-slope form of the line which satisfies the following given conditions: The line parallel to the line y = 4 and passes through the point (, 4). b) The line perpendicular to the line 4y = 7 and passes through the point (, 4). 4. Find the points of intersection for y 5. Find the points of intersection for y and y. e and y. 6. Refer to the graph given on the right on the interval,. Does the graph represent a function? Justify your answer b) Find f (0) and f (), if they eist. 7. Find the standard equation of the circle satisfying the given condition: Center (, ), radius = 4 b) Center (4, 5), passes through (, ) 8. Use the graph of ( ) h given to sketch the following 5 transformations. Do not graph all on the same coordinate plane.

3 AP Calculus AB Summer Assignment Graph the following on a separate sheet of paper using properties of graphs such as translation and reflection. You should be able to quickly sketch the graphs without using a calculator and without making an -y table. Finding the domain, range, end behavior, and intercepts can be helpful. 6 y b) y y 5 d) f ( ) 5 e) y 5 f) y 5 g) y h) y e i) y j) y 0. Sketch the curve defined by the equation given below by first finding two functions y and y whose graphs will combine to give the curve. y 0 b) y 9. Determine whether the graph is symmetric about the y-ais, the origin or neither. y 7 b) 5 y y y sin. Let f 4,, Find f (). b) Solve the equation: f( ) 4.. Determine whether the function is continuous at the point given. 4, 9 f( ) at b) f, at

4 AP Calculus AB Summer Assignment V r h and h r. Epress V as a function of h. 5. Epress the area of a square A as a function of its diagonal, d. 6. Epress the area of an equilateral triangle A as a function of its side length, s. 7. For the following questions, find the end behavior by filling in the blanks. Let f ( ) 7 4. If then f( ) If then f( ) b) Let g( ). If then g ( ) If then g ( ) Let h ( ). If then g ( ) If then g ( ) 8. Which function grows faster as? f ( ) 4 or g ( ) 4 b) f( ) or g ( ) 4 9. If f ( ) 7 find f ( ), f, and f h. 0. If f ( ) 5, find ( ) f h f h and simplify completely.

5 AP Calculus AB Summer Assignment 08. If f ( ) and g( ), find f g.. Determine functions f and g such that h( ) f ( g( )). (Do not choose f ( ) or g( ) ). h ( ) 4 b) h( ) 4 e h( ) sin. Solve for ': y y y ' y ' y 4. Solve for c : a c ab 4a b 5. A rock breaks loose from the top of a tall cliff, where ( t) 6t represents the height of the object in feet with time measured in seconds. Find the average velocity of the rock during the first seconds. 6. If a ball is thrown straight up with an initial velocity of feet per second, then after t seconds, the distance s above its starting height, in feet, is given by s t 6t. Use the graph of st () to find what time the ball will reach its highest point and how high will it rise. 7. A rectangular field is to be enclosed with 500 ft. of fencing along three sides and by a straight stream on the fourth side. Let be the length of each side perpendicular to the stream, and let y be the length of the side parallel to the stream. Draw a figure representing the situation modeled above. b) Epress y in terms of. Find a formula for the area A of the field in terms of. d) What is the largest area that can be enclosed?

6 AP Calculus AB Summer Assignment Solve the equations given below where 0. Do not use a calculator. sin b) sec cos cos sin 0 9. Solve the equation given below where 0 0 cos The angle is an acute angle of a right triangle. Solve the following problems by drawing an appropriate right triangle. Do not use a calculator. Findsin and tan, given that the hypotenuse has length 5 and the side adjacent to has length. b) Find tan and csc, given that 5 sec.. Evaluate each of the following: arcsin0 b) cos cos arctan. Simplify the following sin sin t t b) cos(arcsin ). Sketch the following graphs on and give the amplitude and period of each. = cos b) y sin 4 d) y cos 4 e) y cos f) y cos

7 AP Calculus AB Summer Assignment Rewrite the following functions as a power function or sum/difference of a power function. a (Note a power function is f ( ), where a is a constant). 7 g ( ) b) g ( ) 4 4 g ( ) d) g ( ) 5. Simplify the following by factoring completely. 5 b) Simplify y y y b) ( y ) ( y ) h d) y y e) y 5 f) 7. Simply the following epressions tan ln e 7 b) ln e r ln5 e log 5 d) 5 8. Solve the following eponential equations. b) log 8 9 8

8 AP Calculus AB Summer Assignment Graph the following: y y log 5 b) Solve for y terms of. Simplify your answer completely. ln y b) ln y ln5 4. Use the properties of logarithms to rewrite ln ln ln in condensed form. 4. Find the domain of the following functions in interval notation. y b) y y d) y e yln( 5) f y g y e i) y h y 4. Given the following conditional, if a function is differentiable, then it s continuous. Write the converse of the conditional. b) Write the contrapositive of the conditional. If the conditional is true, decide which also must be true, the converse, the contrapositive, or cannot be determined.

9 AP Calculus AB Summer Assignment Solve the equations algebraically. Justify your answer by graphing the function using your calculator. 0 b) e d) 4 5 e) 4 4 4e 6e Use the graph below to answer the following questions. Write your answer in interval notation where needed. On which interval(s) is the function decreasing? b) For which -value(s) does the function change signs? On which interval(s) is the function positive? 46. Use the graph given to state the -value(s) where the function changes signs. 47. Use algebraic methods by creating a sign chart to state the -value(s) where the function changes signs. f ( ) 4 b) f ( ) cos on [0,4] f( ) 4

10 AP Calculus AB Summer Assignment Solve the non-linear inequalities graphically. Write your answer using interval notation. 4 0 b) ln Solve the non-linear inequalities algebraically by using a sign chart. Write your answer using interval notation. 0 b) e e 0 cos 0 6 for Evaluate the limit given below. If it does not eist, write DNE. 0 lim 4

11 AP Calculus AB Summer Assignment