HONORS ALGEBRA 2 FINAL REVIEW Chapters 6, 7, 8, and 10

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1 Name Date Sectios ad Scorig HONORS ALGEBRA FINAL REVIEW 0-8 Chapters 6,, 8, ad 0 Your fial eam will test your kowledge of the topics we studied i the secod half of the school year. There will be two sectios a calculator free sectio ad a calculator active sectio. The eam cosists of a variety of multiple choice ad ope-eded questios. There will be a formula sheet (see last page of this review packet). There will be a maimum possible score of 08 poits. How do I prepare for the Fial Eam? Aswer as may problems as possible from this review packet ad check your aswers. You should oly use a calculator whe absolutely ecessary. Do ot wait util the last miute to begi reviewig for this eam. Review old tests ad quizzes from the rd ad th markig periods. Pay attetio durig class o the review days ad ask questios. Get eough rest the ight before. Wake up early ad eat a healthy breakfast. What do I eed with me o the day of the eam? What are your rules ad epectatios? TEXT BOOK. Brig at least two sharpeed pecils with BIG erasers. You may oly use a calculator that has bee RESET BY ME. Brig thigs that will help you study for your other eams i case you fiish early ad have free time. If you do ot like to study for your other eams, brig a book or school appropriate magazie to read. If you fiish early, you must remai quiet util all eams have bee collected! DO NOT brig hats, ipods, mp players, cellular telephoes, or ay other electroic devices. You are ot permitted to use them at ay poit durig the eam sessio (whether you are fiished or ot). I the past, studets have bee caught usig these thigs to cheat. It is ot wise to place yourself i that situatio. Brig o-electroic forms of etertaimet so that you do ot get ito trouble. NO ONE MAY LEAVE the room uless it is a absolute emergecy. You are required to remai i the eam room the etire time. No oe gets to leave early. Do ot ask for passes to go hag out with other teachers. You will have a break betwee your eams to use the restroom. Eam Schedule Date Sessio Sessio Friday, Jue Moday, Jue 8 Tuesday, Jue 9 Wedesday, Jue 0 9/0 /8 8/9 6/ /6 /

2 INVERSES AND RADICAL FUNCTIONS AND RELATIONS (Chapter 6) Let f 8, g 8, c, m, ad Fid each of the followig. State ay restrictios i the domai, if ecessary. p. ) f g ) g f ) m g ) m g f ) 6) g m a ) g m 8) c p.6 g 9) Fid the iverse of m. Is the iverse a fuctio? 0) Use h ( ) 6 9 to aswer the followig. a) Is h ( ) a fuctio? Why or why ot? b) Graph h ( ) 6 9 ad its iverse o the same coordiate plae without a calculator. c) Fid the equatio of h ( ). Show your steps. ) If f 0, 9,,, 6,6, 8,, fid f ad state whether or ot f is a fuctio. ) Let f ( ) ad g ). a) Fid g b) Fid f ( f. g. c) Are f () ad g () iverses? ) Graph ad provide the requested iformatio for ) Graph y y Domai Rage -it y-it

3 ) Simplify: 0y y 6) Simplify: y 8 y 6 z ) Subtract: 8) Ratioalize the deomiator: 9) Ratioalize the deomiator: 0) Evaluate: 8 q 9 p 6 ) Simplify: ) Solve: ) Solve: ) Solve: ) Simplify: 6) Simplify: ) Simplify: 8 8) Rewrite y as a sigle radical. CPTER 6 ANSWERS ) ) 6 ) ) 06 ) ;, 6) 9a 9 ) 8) 9) 0a) h ( ) is ot a fuctio because h () fails the HLT. 0b) 0c) h ( ) ) 9,0,,, 6,6,,8, Not a fuctio ) a) [ f g]( ) b) [ g f ]( ) c) Yes m, yes

4 ) ) Domai Rage,, -it y-it ) y 6) z z y ) 0 q p 8) p ) ) 6 ) ) Solutio : 8 Etraeous root : 9) 6 9 0) )., ) 6) 8) 8 y 0 I ve had a great time appearig o your math papers this year! The Deer EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Chapter ) Graph each fuctio. State the domai, rage, ad equatio of ay asymptotes. ) y ) y log

5 ) Determie whether ) Simplify without usig a calculator: y 0. represets epoetial growth or epoetial decay. ) Describe how to trasform the graph of f ) l Solve each equatio without usig a calculator. 9 0 ( ito the graph of ) l g. ( 6) ) 9 8) Write 6 i logarithmic form. 9) Write log 6 i epoetial form. 0) Write l. 609 i epoetial form. 6 Evaluate without usig a calculator. ) log 9 ) ) log log ) log log l e 6) l e ) l 8) Solve each equatio or iequality without a calculator. 9) log 9 0) log ) log 9 ) log 8 log 8 ) log log ) log log log 9 log ) log 6) log log ) log 8 log log 0 ) Evaluate log. i terms of commo logarithms. The approimate to four decimal places. 8) Rewrite as a sigle logarithm: l A l B l C 9) Without usig a calculator, determie which logarithm is greater i value: log or log ) Write the equatio i y ab form that passes through,,. Solve each equatio or iequality. Roud to four decimal places. ) ).. ) l ) e ad ) Suppose Ms. Walsh fids a accout that will allow her to ivest her $00 at a.% iterest rate compouded quarterly. If there are o other deposits or withdrawals, what will Ms. Walsh s accout balace be after 0 years? Roud to the earest cet. 6) How log will it take a ivestmet to double at.% compouded cotiuously? ) The Reidy family bought a ew car for $6,00 i 0. If the aual rate of depreciatio is.% t for that particular car, i what year would you epect the car to be worth $000? Use y a( r). 8) How old is a fossil that lost % of its Carbo-? Use k

6 CPTER ANSWERS ) ) Domai:, Rage:, Rage:, : y :, Domai: ) Growth ) ) Reflect over the y-ais, epad horizotally by a factor of, traslate oe uit dow 6), ) 8) log 6 6 9) 6 0).609 e ) ) ) ) ) 6) ) 0 8) 9) 0) ) ) ) ) ) log. A 6) 00 or 00 ) log 0. 8) l C B 9) log log 80 0) y ) ) 0. 6 ). 89 ) Ø ) $698. 6) about. years ) the year 0 8) about, years old Study Tip Studyig for 0-0 miutes at a time (with 0 miute breaks i betwee) is the most effective way to retai iformatio.

7 RATIONAL EXPRESSIONS AND EQUATIONS (Chapter 8) ) For what value(s) of m is Simplify each epressio. 6m m m m 0m udefied? The, simplify the epressio. ) 8 9 ) 6 8 ) 9 ) y 6a b 6) abc y ) 8 6 8) 8 6 State the ecluded value(s). State the LCD. Solve each equatio or iequality. 9) 9 6 0) ) 8 ) Last year, it took Miss Heidor hours ad 0 miutes to stai her deck. This year, she asked Mr. Stramaglia for some assistace ad together it took them hour. How log would it have take Mr. Stramaglia to stai the deck by himself? The fuctio below is a trasformatio of ) f ) ( f ) (. Complete the chart ad sketch the graph. Equatio of Equatio of Domai Rage ) State the domai ad rage of f ( ). f ) ) g ( ) is a trasformatio of (. Describe the trasformatios. 6) Is the graph of f ( ) the same as the graph of ( ) g? Eplai.

8 ) g is a trasformatio of ( ) f. Determie the equatio of ad a horizotal asymptote at y. 6 8) For the fuctio f ( ), as, f ( ). p( ) 9) Write f ) i f ( ) q( ) form. ( Complete the chart ad the draw the graph. g if it has a vertical asymptote at 0) f ( ) 0 Hole y-itercept ) f ( ) Hole y-itercept Complete the chart for each give fuctio. Do ot draw the graph. ) f ( ) ) f ( ) Hole Hole y-itercept y-itercept

9 CPTER 8 ANSWERS ) The epressio is udefied whe m, or 0. Simplified epressio:, m m(m ) ) 6 9 ) ( ) ) ) 6 ( )( ) bc 6) 8y ) 8 8) ( )( )( ) 9) Ecluded Values:, 0) Ecluded Values:, ) Ecluded Values: 0 ) hour ad 0 miutes ) f ) ( LCD: Solutio: LCD: Solutio: LCD: 8 Solutio:, 0., Equatio of Equatio of Domai Rage y,,,, ) Domai:, 00, Rage: 0, ) Reflectio i the y-ais, epaded vertically by, traslatio of uits to the right ad uits up 6) ( ) g is the same lie as f ( ), but it has a poit discotiuity at,. Therefore, they are ot the same graph. ) g ) 8) 9) ( f ( ) 0) oe Hole, oe oe y-itercept

10 ) Hole, 6 y oe 0 y-itercept 0 ) f ( ) ) f ( ) Hole oe Hole oe y 0 oe oe y oe y-itercept y-itercept SEQUENCES AND SERIES (Chapter 0) ) a) List the first 6 terms i the sequece of perfect cubes. b) Write a formula for the th term ad fid a. c) Is this sequece arithmetic, geometric, or either? Eplai. ) Fid a for the arithmetic sequece,,,... ) I the arithmetic sequece,, 0,,..., which term has a value of 0? ) Fid the sum of the arithmetic series ) Fid the sum of the arithmetic series: p 0 p 6) Fid the et two terms i the geometric sequece:.,.,.8,... ) Fid the geometric meas i the sequece:,,,,, 6 8) Fid the sum of the geometric series to terms ) Fid the first term i the geometric series described: S 6; r ; a 8 0) Fid the sum of the ifiite geometric series, if it eists:

11 ) Cotagious diseases ca spread very quickly. Suppose five people are ill durig the first week of a epidemic ad that each perso who is ill spreads the disease to four people by the ed of the et week. By the ed of the teth week of the epidemic, how may people have bee ifected by the illess? ) Fid the value of that makes,, 9,... a arithmetic sequece. The fid the first terms. ) If a ad a a, fid the first five terms of the sequece. ) Fid the first three iterates of f ( ) for a iitial value of. ) Mr. Geist loves geometry! He is plaig o buildig a brick patio that approimates the shape of a trapezoid. The shorter base of the trapezoid eeds to start with a row of bricks, ad each row must icrease by two bricks o each ed util there are rows. How may bricks does Mr. Geist eed to buy? 6) Evaluate: P ) Evaluate: y 9) Epad the biomial: 0) Fid the th term i the epasio of i 8 ) Factor usig the Biomial Theorem: 0 C 8) Simplify:!!, where i is the pure imagiary uit y 80 y 0 y 0y y CPTER 0 ANSWERS a), 8,, 6,, 6 b) a c) Neither, o commo differece or ratio a ; ) ) 00 th term ) 60 ) 0 6).6,. 9 ) 6, 8,, 08 8) 6 9) 0) ),, 6 ) ;,6, ),,,, ), 0, 0 ), bricks 6) 0 ) 8) 9) 6 y 000 y 600 y 60 y y 6 0) i y ) Study Tip Break the study guide problems up i to sectios, ad do a sectio each day. If you have ay questios, come to etra help ad get them aswered!

12 HONORS ALGEBRA FINAL EXAM 0-08 FORMULA SHEET Epoetial Growth ad Decay Formulas t t y a r Epoetial growth, where r is the growth factor y a r Epoetial decay, where r is the decay factor A P t r rt Pe Iterest, compouded times a year A Iterest, compouded cotiuously kt y ae Epoetial growth, where k is the rate of cotiuous growth y kt ae Epoetial decay, where k is the rate of cotiuous decay Variatio Formulas Direct Variatio: Iverse Variatio: Joit Variatio: y k k y y kz Sequece ad Series Formulas a d S a a a S a r r S a ar r a a a S r r

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