AP Calculus AB - Mrs. Mora. Summer packet 2010

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Darrell Mason
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1 AP Calculus AB - Mrs. Mora Summer packet 010 These eercises represent some of the more fundamental concepts needed upon entering AP Calculus AB This "packet is epected to be completed and brought to class on the first full day of school. As you work through these problems, you most likely will come across topics that require a little review...you might even find some that you have completely forgotten! Requirements The following are guidelines for completing the summer work packet There are questions you must complete. You must show all of your work on the packet. Be sure all problems are neatly organized and all writing is legible. You must be familiar with certain built-in calculator functions such as finding values, intersection points, using tables, and zeros of a function. I epect you to come in with certain understandings that are prerequisite to Calculus. A list of these topical understandings is below. Topical understandings within summer work Factoring Zeros/roots/-intercepts of rational and polynomial functions Polynomial Long Division Completing the square Write the equation of a line Quadratic formula Unit Circle Composite function and notation Solving trigonometric equations Domain/Range Interpreting and comprehending word problems Graphing, simplifying epressions, and solving equations of the following types: trigonometric, rational, piecewise, logarithmic, eponential, polynomial/power Finally, I suggest not waiting until the last two weeks of summer to begin on this packet. If you spread it out, you will most likely retain the information much better. Once again this is due, completed with quality, on the first day of class. Best of luck and if you have any questions, feel free to contact me at Moramary@dadeschools.net

2 AP Calculus AB - Mrs. Mora Summer packet 010 1) Simplify Epress your answer using a single radical. ). Factor completely ) Determine the range and the zeros of: f ( ) ) Find the equation of the line through (,7) and (,5) in point slope form. 5) Solve the equation both algebraically and graphically ) Rewrite the epression log 5( ) into an equivalent epression using only natural logarithms

3 7) Three sides of a fence and an eisting wall form a rectangular enclosure. The total length of a fence used for the three sides is 40 ft. Let be the length of two side s perpendicular to the wall as shown. Write an equation of area A of the enclosure as a function of the length of the rectangular area as shown in the above figure. The find value(s) of for which the area is 5500? ft Eisting wall 8) Let f ( ) and g( ) 1. Compute ( g f )( ), state its domain in interval notation. 9) Let 7 f( ). Find f 1 ( ), the inverse of f( ) 10) Find an equation for the parabola whose verte is (, 5) and passes through (4,7). Epress your answer in the standard form for a quadratic. 11) Which of the following could represent a complete graph of f ( ) a, where a is a real number?

4 A. B. C. D. 1) Find a degree polynomial with zeros -, 1, and 5 and going through the point (0, ). 1) The graph of y a for 1 a is best represented by which graph? A. B. C. D. 14) Describe the transformations that can be used to transform the graph of log( ) to a graph of f ( ) 4log( ). 15) Arturo invests $700 in a savings account that pay 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $4550? 16) Solve the inequality 1 0. A. (, 4) (, ) B. 4, C. (,4) D. (, ) (4, )

5 17) Find the perimeter of a 0 slice of cheesecake if the radius of the cheesecake is 8 inches. 18) Use polynomial long division to rewrite the epression ) Transform y = to verte form by completing the square. 0) Solve the system of equations graphically, accurate to the nearest thousandth. Please sketch and label your solution on the graph provided. y 5 1 y 1 1) Two students are 180 feet apart on opposite sides of a telephone pole. The angles of elevation from the students to the top of the pole are 5 and. Find the height of the telephone pole.

6 ) Graph the piecewise function. 1 f ( ) ) Find the points of intersection of y 4 And y y ) For the function f( ) graphed answer the following A. f () B. f ( ) 0 C. f (0) D. f ( ) 1 5) Use a graphing calculator to solve the following for. e 6) Find the domain of f( ) 5. Epress your answer in interval notation. 7) Give that f( ) 5 9. Find the vertical asymptotes. Also state the Domain of the function.

7 8) Use a graphing calculator to approimate all of the function s real zeros. Round your results to 4 decimal places. f 6 5 ( ) ) Factor to solve the inequality. Write your answer in interval notation ) Simplify the epression as much as possible. 10 ( 4) 6 ( 4) ) Use your calculator to determine where the two lines intersect. +5y = and 7 y = 19. ) Simplify the epression and determine where the epression is positive. ( 1) 6 ) Use the quadratic formula to find the eact solution to = 0. Show all work.

AP CALCULUS AB & BC ~ er Work and List of Topical Understandings~

AP CALCULUS AB & BC ~ er Work and List of Topical Understandings~ AP CALCULUS AB & BC ~er Work and List of Topical Understandings~ As instructors of AP Calculus, we have etremely high epectations of students taking our courses. As stated in the district program planning