AP CALCULUS AB Summer Work. The following are guidelines for completing the summer work packet

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1 Name: Perio: AP CALCULUS AB Summer Work For stuents to successfully complete the objectives of the AP Calculus curriculum, the stuent must emonstrate a high level of inepenence, capability, eication, an effort. This summer packet is not intene to scare you, but is intene to help you maintain/improve your skills. This packet is a requirement for those entering the AP Calculus course an is ue on the first ay of class. If it is not complete on the first ay of class, you shoul consier yourself behin not only on your class grae (00 points), but also on the concepts necessary for success in Calculus. Complete as much of this packet on your own as you can, then get together with a frien, me, or google the topic. You may also check out your book for the summer. Everything shoul be covere in the Pre-reqs chapter an Chapter One for the limit problems. SHOW YOUR BEST WORK. Requirements The following are guielines for completing the summer work packet There are 48 questions you must complete. You must show all of your work on the packet. I woul epect that you unerstan at least 80% to be reay for the class. Be sure all problems are neatly organize an all writing is legible. In the event that you are unsure how to perform functions on your calculator, you may nee to rea through your calculator manual to unerstan the necessary synta or keystrokes. You must be familiar with certain built-in calculator functions such as fining values, intersection points, using tables, an fining zeros of a function. I epect you to come in with certain unerstanings that are prerequisite to Calculus. A list of these topical unerstanings is below. Topical unerstanings within summer work Factoring Zeros/roots/-intercepts of rational an polynomial functions Polynomial Long Division Completing the square Write the equation of a line Quaratic formula Unit Circle Composite function an notation Solving trigonometric equations Domain/Range Interpreting an comprehening wor problems Graphing, simplifying, an solving equations of the following types: trigonometric, rational, piecewise, logarithmic, eponential, polynomial/power, an raical. Limits Finally, I suggest not waiting until the last two weeks of summer to begin on this packet. If you sprea it out, you will most likely retain the information much better. Once again this is ue, complete with quality, on the first ay of class. It is your ticket into the class. Best of luck an if you have any questions, feel free to contact me at steven.becker@orecity.k.or.us An etra copy of the work can be foun by going to my webpage through the istrict website.

2 AP CALCULUS SUMMER PACKET ) Simplify Epress your answer using a single raical. ). Factor completely ) Determine the range an the zeros of: f( ) ) Fin the equation of the line through (,7) an (3,5) in point slope form. 5) Solve the equation both algebraically an graphically ) Rewrite the epression log 5( + 3) into an equivalent epression using only natural logarithms 7) Solve the following Logarithmic Equation: log4 56

3 8) Three sies of a fence an an eisting wall form a rectangular enclosure. The total length of a fence use for the three sies is 40 ft. Let be the length of two sies perpenicular 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. Then fin value(s) of for which the area is 5500? ft Eisting wall 9) Let f( ) 3 an g ( ) +. Compute ( g f)( ), state its omain. 0) Let f( ). Fin f ( ), the inverse of f( ) ) Fin an equation for the parabola whose verte is (, 5) an passes through (4,7). Epress your answer in the stanar form for a quaratic.

4 ) Which of the following coul represent a complete graph of number? f ( ) a 3, where a is a real A. B. C. D. 3) Fin a egree 3 polynomial with zeros -,, an 5. 4) The graph of y a + 3 for a > is best represente by which graph? A. B. C. D. 5) Describe the transformations that can be use to transform the graph of ln( ) to a graph of f( ) 4ln( + ) 3. 6) The number of elk after t years in a state park is moele by the function 6 Pt (). 0.03t + 75e a) What was the initial population of elk? b) When will the number of elk be 750? c) Use your calculator to etermine the maimum number of elk possible in the park?

5 7) Hannah invests $700 in a savings account that pay 9% interest, compoune quarterly. If there are no other transactions, when will his balance reach $4550? 8) Simplify ( ) csc( ) tan( ) sin( )cos( ) A. C. sin( ) cos ( ) B. sin ( ) cos( ) + D. cos( ) sin ( ) cos ( ) sin( ) 9) Without using a calculator, fin the eact value of 7π cos cos 5. Justify your answer. 0) Solve the inequality > 0. A. (, 4) an(3, ) B. 4, 3 C. ( 3, 4) D. (, 3) an(4, ) ) Fin the perimeter of a 30 slice of cheesecake if the raius of the cheesecake is 8 inches. ) Use polynomial long ivision to rewrite the epression ) Transform y to verte form.

6 4) Solve the system of equations graphically, accurate to the nearest thousanth. Please sketch an label your solution on the graph provie. y + 5 y 3 5) Two stuents are 80 feet apart on opposite sies of a telephone pole. The angles of elevation from the stuents to the top of the pole are 35 an 3. Fin the height of the telephone pole. 6) Graph the piecewise function. < f( ) 3+ 5 < 3 7) Solve the equation sin ( )cos( ) cos( ) algebraically on [0, π ). 8) Fin all the eact solutions to sin ( ) 3sin( ) 0 0, π. + on the interval [ )

7 9) For the function f( ) graphe answer the following (assume a scale of ) A. ( 3) f B. f ( ) 0 C. f (0) D. f ( ) E. lim f ( ) 3 F. lim f ( ) 30) Use a graphing calculator to solve the following for. e 3 3) Fin the omain of f( ) Epress your answer in interval notation. 3) Give that function. f( ) 5 9. Fin the vertical asymptotes. Also state the Domain of the 33) Use a graphing calculator to approimate all of the function s real zeros. Roun your results to 4 ecimal places. f ( ) ) Factor to solve the inequality. Write your answer in interval notation

8 35) Simplify the epression as much as possible 3( + h) 3 h ) Simplify the epression as much as possible. 0 (3 4) 6 + (3 4) ) Use your calculator to etermine where the two lines intersect. + 5y an 7 y 9 38) Simplify the epression an etermine where the epression is positive. ( + ) ) Use the quaratic formula to fin the eact solutions to Show all work.

9 40) lim ) + 4 lim+ ( 3)( 3 8) 3π + 4) lim sin ) lim 4cos( ) + 44) (3 )(6 ) lim ) lim 0 tan() ) lim h ( ), whereh ( ) + 5 > 47) lim cos 48) lim 0

10 Create flashcars for ALL of the following using the left sie for one sie of the car an the right sie for the other (These MUST be one prior to the first ay yes, I know you on t know what these mean, but you will shortly after the class starts an throughout the year. You will eventually nee to know ALL these by heart) Basic Differentiation Formulas. ( n ) n n. ( fg) fg + gf 3. f gf fg g g 4. f ( g( )) f ( g( )) g ( ) 5. (sin f ( ) ) f '( ) cos f ( ) 6. (cos f ( ) ) f '( ) sin f ( ) 7. (tan f ( ) ) f '( ) sec f ( ) 8. (cot f ( ) ) f '( ) csc f ( ) 9. f ( ) f ( ) f ( ) f (sec ) ' sec( ) tan ( ( )) 6. ( tan ( )) f '( ) ( ( )) f '( ) Arc f + f Arc f ( ) 7. sec ( ) f f ( ) ( ) ( ) 0. (csc f ( ) ) f '( ) csc( f ( ) ) cot ( f ( ) ).. 3. f ( ) ( ) '( ) f ( e f e ) f ( ) f ( ) ( a ) f '( ) a ln a (ln ) f '( ) ( ln f ) f 4. ( ) Arc f ( ) 5. sin ( ) ( ) '( ) ( f ( ) ) f

11 Basic Integration Formulas. a a + C. n+ n + C, n + n 3. ln + C 4. e e + C 5. a a + C ln a 6. ln ln + C 7. sin cos + C 8. cos sin + C 9. tan ln sec + C or ln cos + C 0. cot ln sin + C. sec ln sec + tan + C. csc ln csc cot + C ln csc + cot + C 3. sec tan + C 4. sec tan sec + C 5. csc cot + C 6. csc cot csc + C 7. tan tan + C 8. Arc tan + C a + a a 9. Arcsin + C a a a 0. Arcsec + C Arc cos + C a a a a