Final Review Semester 1

Transcription

1 -- v 0IQ XK7ujt0ah 7SoafqtqwSaPreet BLGLiCm.p R EAmlslp vreigghittsw VrKesmeerzvNeqdU.z Y MaMdjer jwcitkho ei 7ndfiOnPiwt8e RAclTgLeZbXrFag CT.w Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester Er0hId 0KDu Qt FaR JSobfdtVw8amre9 CLeLaCq.b A baulllu Lrgi egvhwtbst wrkefsaekrhvdekdc.r Graph each equation. ID: Name ) = + ) = Find the value that completes the square and then rewrite as a perfect square. ) + + ) z + 7 z + Solve each equation b completing the square. ) k 0k = 8 Simplif. ) ( i) ( 8i) ( 7i) 7) + i 7i 8) Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) m + m = m + m

2 -- i J0ri WKfultaa SWocfZtAwBalrVej LLLcCc.z n AAlvlm riiguhitmss RrVeasdeurUvAefdM.i F FMaBdien LwfiItiha NIgnNfcientivties AAlZghelbLrdam Ud.R Worksheet b Kuta Software LLC Divide using long division 0) (r + 8r + 8r r 0r 8) (r + ) Divide using snthetic division ) ( ) (7 + ) Identif the domain and range of each. Then sketch the graph. ) = ) = + 8 8

3 -- n 7T0O7W KmugtdaT fs9oqfptkwsasr7ee pluloc8. w talkl LrY iglhgt8sh krreksvenrcvkeedd.b z zmwacdiek AwAitChc ti8nfhignliiteec haklxgfelbyrpae wd.f Worksheet b Kuta Software LLC Solve each equation or state if there is no unique solution. ) 7 X 7 = 7 ) 9 7 = 9 X State the possible rational zeros for each function. Then factor each and find all zeros. ) f () = ) = + + State the possible rational roots for each equation. Then factor each and find all roots. 8) + 8 = 0 Solve each equation b factoring. 9) 7p + 0 = 0 p Solve each equation b taking square roots. 0) 0 = 0 Solve each equation with the quadratic formula. ) n + = n Factor each completel. ) Factor each. ) = 0 ) = 0 Factor each completel. ) + ) v + 7v + 0

4 -- U n0m8z RKputNaD 7Sao0frtSwKarpeq oltlmco.d E LAYlclM MrWimghutvsw kroehssemr0viedb.u K IMcaFdseM Nwtiet8hC 9ICnuf0iznFiJtAeV KA7lzgeekbmrvaa u.k Worksheet b Kuta Software LLC 7) ) a a 0 9) 8r 8r 0 0) m n ) ) 9 ) 7 ) 8u + 7v Sketch the graph of each line. ) = 9 0 Sketch the graph of each linear inequalit. ) + 0 0

5 -- A Yf0mVg FKdutap lsfoqffttwpawrge7 AL8LoCR.X z TAzlElm or 9iWgHhttbs9 rcecsewrjvuendk.i j IMEakdreI Yw itvhr AIAnfBiqnpijtCe AolbgVeLbqr ac TT. Worksheet b Kuta Software LLC Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = ) f () = ( ) ) f () = ( + ) 8 8

6 -- D H0KJu dkluutia wspohftqwvarpep ULLOCs.B O 9AYll0 Xr viwgkhctvsv PrXeBsiefrjvYeldc.t W FMTaudNeC 8wB itphj OIonMfXimnXiStBe EAnlDgXePbKrRaz Cf.v Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = + ) f () = Sketch the graph of each function. ) > + ) > ( + )

7 -7- ui0ly 8KcuAtuat bsiosfstuwxaqrqen LqLvCM.P W RAMllS vrcihgth9tksc JrPeEsBe0rGvfeudR. Z KMDaLdGeM whiltdh kinyfhiqnuitned CAlligzeb7r8aJ LD.i Worksheet b Kuta Software LLC Solve each sstem b graphing. ) = = ) = = 0 0 Sketch the solution to each sstem of inequalities. ) + 7) < + 0 > 0 Write the slope-intercept form of the equation of the line through the given point with the given slope. 8) through: (, ), slope =

8 -8- i uj099 XKkuhtGaR SoftwIadr7ez LALhCr.E aapl8lm rruivgahtesg krwevseprv9eed. Q EMSaYdqe AwCiWtRhw QIFnfQinEi9tPeO XAlOgJeUbdrCad gq.k Worksheet b Kuta Software LLC Write the slope-intercept form of the equation of the line through the given points. 9) through: (, ) and (0, ) Simplif. Write "undefined" for epressions that are undefined. 0) ( ) ) + 0 ) 0 Simplif each epression. ) (n + 8n 7n n ) + (7n + n n + n ) + ( n 7n + 7n ) Describe the end behavior of each function. ) f () = + + ) f () = + Evaluate each function at the given value using snthetic substitution ) f (n) = n n + n + n + 7n n 7 at n = Find each product. 7) ( v + 8v )(v + 8v + 7) Write a polnomial function of least degree with integral coefficients that has the given zeros. 8),, 9), +, +

9 -9- C DR0BSN WKPuOt8aT sskovftjwqarfeu TLDLbCG.b O uazlklc oruivgphuthse pr8erscejrrvseud. X kmpamdez RwZi0tQh IVnVfEignMirtae waaligueqberka ju.9 Worksheet b Kuta Software LLC Solve each sstem of equations. 0) = = 0 ) = 0 + = Simplif. ) 00 ) 7 Solve each sstem. ) + + z = = + + z = 0 ) z = z = 8 + z = ) z = z = z = 0 Solve each sstem b elimination. 7) 0 0 = = Solve each sstem b substitution. 8) + 8 = + = 9) The school that Julio goes to is selling tickets to a spring musical. On the first da of ticket sales the school sold 7 senior citizen tickets and student tickets for a total of $.0. The school took in $7.0 on the second da b selling senior citizen tickets and student tickets. Find the price of a senior citizen ticket and the price of a student ticket. 70) Maria and Jaidee each improved their ards b planting grass sod and ornamental grass. The bought their supplies from the same store. Maria spent $0.0 on 8 ft² of grass sod and 8 bunches of ornamental grass. Jaidee spent $7.0 on 9 ft² of grass sod and bunches of ornamental grass. What is the cost of one ft² of grass sod and the cost of one bunch of ornamental grass?

10 -0- Y uq0v hkzuteaw vsqosfetcwtairuew CLaLUCr.D c iawlvlt frilgqhtcss tr0efsedrv0eidf.c v 8MKatdieE OwUitrh lijnvfjirnuiqtfeb eajl9gselbzraae Vp.b Worksheet b Kuta Software LLC 7) Lea and Pranav are selling flower bulbs for a school fundraiser. Customers can bu packages of tulip bulbs and packages of crocus bulbs. Lea sold packages of tulip bulbs and 8 packages of crocus bulbs for a total of $ Pranav sold packages of tulip bulbs and packages of crocus bulbs for a total of $.0. What is the cost each of one package of tulips bulbs and one package of crocus bulbs? 7) Jasmine and Anjali are selling pies for a school fundraiser. Customers can bu apple pies and pumpkin pies. Jasmine sold apple pies and pumpkin pies for a total of $.80. Anjali sold apple pie and pumpkin pies for a total of $98.0. Find the cost each of one apple pie and one pumpkin pie. 7) A boat traveled 7. miles downstream and back. The trip downstream took 7. hours. The trip back took 0.8 hours. Find the speed of the boat in still water and the speed of the current. Solve each question. Round our answer to the nearest hundredth. 7) Working together, Gabriella and Krstal can pick fort bushels of apples in. hours. Had she done it alone it would have taken Krstal. hours. How long would it take Gabriella to do it alone? 7) Working together, Krstal and Ming can pick fort bushels of apples in.8 hours. Had she done it alone it would have taken Ming. hours. Find how long it would take Krstal to do it alone. 7) How much of Brand A fruit punch (0% fruit juice) must be mied with L of Brand B fruit punch (% fruit juice) to create a miture containing % fruit juice? 77) Carlos left the White House three hours before Willie. The drove in opposite directions. Willie drove at 7 km/h for two hours. After this time the were km apart. What was Carlos' speed? 78) Micaela traveled to her cabin on the lake and back. It took one hour longer to go there than it did to come back. The average speed on the trip there was 0 km/h. The average speed on the wa back was 80 km/h. How man hours did the trip there take?

11 -- m Bz0fBi AKhuLtuaD CSmopfitwwaLrreL ILrLLC8.v p HAflqlD Xrei0gWhOtkso rjeshe7rfveldo.c E bmafdleb awrikt8h OIrntfiNneiAtge XAGlg9ePbYriau dm.a Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester 7 E0jj iklumtoab SS0oGfHt 7wKabreI nlpldcw.t f raalhl ZrYipgehctds rraebsearmvkewd K.j Graph each equation. ID: Name ) = + ) = Find the value that completes the square and then rewrite as a perfect square. ) + + ; ( + ) ) z + 7 z + Solve each equation b completing the square. ) k 0k = 8 { , } Simplif. ) ( i) ( 8i) ( 7i) 8) 8 + i ) 9 ( ) ; z + + i 7i + i 7 Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) m + m = m + m 0; two imaginar solutions 8

12 -- g an09f UKLutiaL SPogfftMwraRrweL LLMLCd.z MA9lAlT lrpiqgnhntrsq ArensiewrpvgeCdK.t l umdapdhe8 jwtiftha AIJncfJinliAtSeQ GAGlVgRe8bnrfaR cj.m Worksheet b Kuta Software LLC Divide using long division 0) (r + 8r + 8r r 0r 8) (r + ) r + r + r r r + Divide using snthetic division ) ( ) (7 + ) Identif the domain and range of each. Then sketch the graph. ) = + 8 Domain: Range: 8 ) = + 8 Domain: { All real numbers. } Range: { All real numbers. } 8

13 -- K M0F8j RKeuPtzav msaoffrtzwoakrie mlflpc0.g ZAlVl rixgrhdtnsd trgewsjenrpvwewdb.c c wmqajde8 wwiotlhn PInf0iIn9iWten qalwg7eybarhat Eo. Worksheet b Kuta Software LLC Solve each equation or state if there is no unique solution. ) 7 X 7 = 7 0 State the possible rational zeros for each function. Then factor each and find all zeros. ) ) f () = Possible rational zeros: ±, ±, ±, ±, ± 0, ± 0 Factors to: f () = ( + )( + ) 9 7 = 9 X ) = + + Possible rational zeros: ±, ±, ± State the possible rational Zeros: roots for {i each, i equation., i, i} Then factor each and find all roots. 8) + 8 = 0 Possible rational roots: ±, ±, ±, ± Factors to: ( )( + ) = 0 Roots: {, + i, i} Solve each equation b factoring. 9) 7p + 0 = 0 p {, 7 } Solve each equation b taking square roots. 0) 0 = 0 {i, i } Solve each equation with the quadratic formula. ) n + = n { , } Factor each completel. ) ( + )( + 7) Factor each. Factors to: = ( + ) Zeros: {i mult., i mult. } ) = 0 Factors to: ( + )( + )( + ) )( ) + = 0 = 0 Factors to: ( + )( + )( )( + )( + )( ) = 0 + i Roots: {, + i, i,,, i Roots: {i, i, },, i, i,, } Factor each completel. ) + ( + ) ) v + 7v + 0 (v + )(v + )

14 -- d cq0unp wkuuctsaj isbogfvtqwtarseb LVLC.X saklolh VriIgWhEtest traelsqeprmvnewdq.h I LMFaRdZeV lwyitmhb liunfuinmiqt8ej aa9lygwerberxan Cl.I Worksheet b Kuta Software LLC 7) ( + 8)( ) 8) a a 0 (a 9)(9a + 8) 9) 8r 8r 0 (r )(r + ) ) ( + )( ) ) 7 ( )(9 + + ) 0) m n (m + n)(m n) ) 9 ( + )( ) ) 8u + 7v (u + v)(u uv + 9v ) Sketch the graph of each line. ) = 9 0 Sketch the graph of each linear inequalit. ) + 0 0

15 -- i NL0wnT qkeubtat 0SuofftpwraErVed L9LqCh.r L A8l8lq NrUiIgMhqtUsM lrceks0epr nvnevdq.m 9 wmladkez nwpihtth LIknVf9i9nii9theZ gaklbg7ebtrmaz m. Worksheet b Kuta Software LLC Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = Verte: (, ) Ais of Sm.: = Opens: Up Min value = -int: 8 -int: and 8) f () = ( ) + 8 Verte: (, ) Ais of Sm.: = Opens: Up Min value = -int: -int: None 8 9) f () = ( + ) 8 Verte: (, 0) Ais of Sm.: = Opens: Up Min value = 0 -int: -int: 8

16 -- O KI0Oo QKQuctPaD CSPoFfltBwdacr new VLJLbCA. n faolclg drhibgjhbtsq Dr wetsrebrfv0erdz.r P gmkamdhew cwtitxht ILnofinbistvea falhgecbr9aq H8.B Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = + 8 Real Zeros:.,. Minima: (0, ) Maima: (.8,.) (., ) ) f () = + 8 Real Zeros:.9, 0.8, Minima: ( 0.,.) (.,.) Maima: (.,.) (0., 0.8) 8 8 Sketch the graph of each function. ) > + ) > ( + )

17 -7- p k70kbv LKdumtpa SYoXftmwIaSrGew LnLmCb.o f qarlolq briggrhbtos TrXesreOrrvoerdj.u 7 FMraYdet Ww0ibtfhn BIFnffBi9nniCtte AQlJgDeabkrhaN d.h Worksheet b Kuta Software LLC Solve each sstem b graphing. ) = = ) = = 0 Infinite number of solutions 0 (, ) Sketch the solution to each sstem of inequalities. ) + 7) < + 0 > 0 Write the slope-intercept form of the equation of the line through the given point with the given slope. 8) through: (, ), slope = =

18 -8- U og0wwa wkwuptah HSLotfJtLwPagrveD ololzc.8 K Alil8 8rWiJguhMtFsb JrzeseeNrvfeBdr.O G km8aoder SwoiZtvhE OIUnCfbiInqictleS NAmlggAeZburDa0 Nk. Worksheet b Kuta Software LLC Write the slope-intercept form of the equation of the line through the given points. 9) through: (, ) and (0, ) = Simplif. Write "undefined" for epressions that are undefined. 0) ( ) ) + 0 Undefined Undefined ) 0 0 Simplif each epression. ) (n + 8n 7n n ) + (7n + n n + n ) + ( n 7n + 7n ) n + n 9n + n Describe the end behavior of each function. ) f () = + + f () as f () as + ) f () = + f () as f () + as + Evaluate each function at the given value using snthetic substitution ) f (n) = n n + n + n + 7n n 7 at n = 0 Find each product. 7) ( v + 8v )(v + 8v + 7) 0v 8v 8v + 8v Write a polnomial function of least degree with integral coefficients that has the given zeros. 8),, f () = ), +, + f () =

19 -9- gy0gl KXutlaD vsjodfutbwaxrked ALkLACQ.9 SAlrlv DrNiCgwhStis Trheseqr8vemdg.E D MOaGdYem withc pizn7fjilnaiptep oadlwgvexbvrfar h9.j Worksheet b Kuta Software LLC Solve each sstem of equations. 0) = = 0 (, ), (, 0) ) = 0 + = (, ) Simplif. ) 00 0 ) 7 7 Solve each sstem. ) + + z = = + + z = 0 Infinitel man solutions (, z, z ) OR (,, ) ) z = z = z = 0 No solution Solve each sstem b elimination. 7) 0 0 = = (, ) Solve each sstem b substitution. 8) + 8 = + = (, 0) ) z = z = 8 + z = (0,, 0) 9) The school that Julio goes to is selling tickets to a spring musical. On the first da of ticket sales the school sold 7 senior citizen tickets and student tickets for a total of $.0. The school took in $7.0 on the second da b selling senior citizen tickets and student tickets. Find the price of a senior citizen ticket and the price of a student ticket. senior citizen ticket: $9.80, student ticket: $9 70) Maria and Jaidee each improved their ards b planting grass sod and ornamental grass. The bought their supplies from the same store. Maria spent $0.0 on 8 ft² of grass sod and 8 bunches of ornamental grass. Jaidee spent $7.0 on 9 ft² of grass sod and bunches of ornamental grass. What is the cost of one ft² of grass sod and the cost of one bunch of ornamental grass? ft² of grass sod: $.0, bunch of ornamental grass: $9.70

20 -0- N SZ0TWc KDuVtaD 7SkoDfCtwwtalrle0 cllzc.w w maltlp Jriegihtt7sQ drlezsqetryv8egdk.z f Mna8dCeG Ew0iBtjh KIFnRfNinwiGtHeH AplwgHeDbKrsad IK.9 Worksheet b Kuta Software LLC 7) Lea and Pranav are selling flower bulbs for a school fundraiser. Customers can bu packages of tulip bulbs and packages of crocus bulbs. Lea sold packages of tulip bulbs and 8 packages of crocus bulbs for a total of $ Pranav sold packages of tulip bulbs and packages of crocus bulbs for a total of $.0. What is the cost each of one package of tulips bulbs and one package of crocus bulbs? package of tulips bulbs: $7.0, package of crocus bulbs: $ 7) Jasmine and Anjali are selling pies for a school fundraiser. Customers can bu apple pies and pumpkin pies. Jasmine sold apple pies and pumpkin pies for a total of $.80. Anjali sold apple pie and pumpkin pies for a total of $98.0. Find the cost each of one apple pie and one pumpkin pie. apple pie: $.0, pumpkin pie: $.0 7) A boat traveled 7. miles downstream and back. The trip downstream took 7. hours. The trip back took 0.8 hours. Find the speed of the boat in still water and the speed of the current. boat: 7. mph, current:. mph Solve each question. Round our answer to the nearest hundredth. 7) Working together, Gabriella and Krstal can pick fort bushels of apples in. hours. Had she done it alone it would have taken Krstal. hours. How long would it take Gabriella to do it alone?.98 hours 7) How much of Brand A fruit punch (0% fruit juice) must be mied with L of Brand B fruit punch (% fruit juice) to create a miture containing % fruit juice? 9 L 7) Working together, Krstal and Ming can pick fort bushels of apples in.8 hours. Had she done it alone it would have taken Ming. hours. Find how long it would take Krstal to do it alone.. hours 77) Carlos left the White House three hours before Willie. The drove in opposite directions. Willie drove at 7 km/h for two hours. After this time the were km apart. What was Carlos' speed? km/h 78) Micaela traveled to her cabin on the lake and back. It took one hour longer to go there than it did to come back. The average speed on the trip there was 0 km/h. The average speed on the wa back was 80 km/h. How man hours did the trip there take? hours

21 -- Wc0WZH wkjuztoav 7SoDfetwpafrueQ LKLtCQ.R X 9AflHlB Brii8gThMtisR ar DelsCeerZv0eodI.v t M9aqdseU qwzith kinqfinqiutbeb aaglzglelbrjam ia.g Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester p c0n c YKmutkaI 8SoVfgtRwfa8rqeg tl9lpci.r h Alpl vrsitghjt ssr aruessveqrrvregdu.b Graph each equation. ID: Name ) = ) = 0 0 Find the value that completes the square and then rewrite as a perfect square. ) p + p + ) + + Solve each equation b completing the square. ) + = 0 Simplif. ) (7 7i) + ( 8i) + ( + i) 7) i 9 + i 8) + + Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) + 7 =

22 -- se0aoe SKuttDak NSEonfPtfwYacrNe TLJLYCQ.n P TACl9lo rzivglhttrs8 frremsxervvoevdm. W fmmaqdze w8i7tphe YIVnOfignaimtNe uarlng8elbtraa ja.d Worksheet b Kuta Software LLC Divide using long division 0) (n + n ) (n + ) Divide using snthetic division ) (a a + a a 9) (a + 8) Identif the domain and range of each. Then sketch the graph. ) = ) = Solve each equation or state if there is no unique solution. ) 0 A + = 0

23 -- a 0t0CNl KIuCtrau lsobfptuwnauroex rltlc.f nalkll Br ibgmhmtsr YrKeFsmearNveNdU.q UM0adgeT nwi7tkhg 7IfnHfOiln7iEt8eX maoltgvekbmrka j.t Worksheet b Kuta Software LLC ) 0 Z 0 = 9 0 State the possible rational zeros for each function. Then factor each and find all zeros. ) f () = 7) = State the possible rational roots for each equation. Then factor each and find all roots. 8) = 0 Solve each equation b factoring. 9) n + n = 0 Solve each equation b taking square roots. 0) 0m + 0 = 0 Solve each equation with the quadratic formula. ) r + r = 0 + 7r Factor each completel. ) Factor each. ) = 0 ) 8 + = 0 Factor each completel. ) 8v + v ) 9k 8k 0k 7) 9n n + 70n 8) k 0k + k

24 -- ZZ0Smo XKCuKta CSdoRfgtwtaVrez SLILNC8.7 aajllh irmitghhbtsb Mrre0sveJrvzegd9.C h vm9acdbex UwciftghV QInNffiOnhiotNed UAtl9gNeHbir FaF RW.H Worksheet b Kuta Software LLC 9) 0v + 0v 0 0) + ) a + b ) 9 ) 9 7 ) a + 0b Sketch the graph of each line. ) = 0 Sketch the graph of each linear inequalit. ) 0

25 Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = ) f () = ( + + ) ) f () = ( )( ) D f0pef HKuqtoa MSosf7tEwacrMeU glelicy.e j AhllV vruiqguhmtqsc briezswefrv9eudx.b V DMhaBdzeC kwkiwt7hm WIAnfniMnoiutcek EAElKg8eRbcrUa ZO.g Worksheet b Kuta Software LLC

26 -- n iq0gf KAutMaz usozfctrwbawreh tl0lrcs.e UAZlUlP 7rFiCgjhYts0 br uecsuerkvieidk.p v HMta7deV 8weiatNhe PI nfciuncietle AnlzgebUrnaq a.e Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = + ) f () = Sketch the graph of each function. ) < ) < ( + )

27 -7- r q0bcp 9KJudtoah QSLogfnt7wTaHrNeI zlolfci.p l LAll orkigglhstns rwesjevrvzegdw.a D lmaa0dxek 8wQiStgh7 I7nBfCihnPiDtze hallzgqenbarlam P.J Worksheet b Kuta Software LLC Solve each sstem b graphing. ) 8 = 0 + = ) = + + = Sketch the solution to each sstem of inequalities. ) + < 7) + < 0 0 Write the slope-intercept form of the equation of the line through the given point with the given slope. 8) through: (, ), slope =

28 -8- F md0rhb VKPubtiac OSnoufGtwZaerDed 0LmL9Cj.z p jaclflp IrDiugjhVtlse treeps9ecrjvqeqde. G MCadReb woibtdhs tiendffinnoidteek caulegeeabrrlao Tr.c Worksheet b Kuta Software LLC Write the slope-intercept form of the equation of the line through the given points. 9) through: (, ) and (, ) Simplif. Write "undefined" for epressions that are undefined. 0) ( ) ) 0 ) 0 0 Simplif each epression. ) ( + 7 ) + ( ) ( + 8 ) Describe the end behavior of each function. ) f () = + ) f () = + + Evaluate each function at the given value using snthetic substitution ) f () = at = Find each product. 7) ( 7 7)( 8) Write a polnomial function of least degree with integral coefficients that has the given zeros. 8),, 9),,

29 -9- R Yh08dK KuotCaJ lsqobfqt7wdarrex ullllce.8 O Al8lb KrzibgWhntosP crcevsdetrpvseddh.p z mmakdneo XwBiCthW nipnpfaiknfiutyeo ZA9lfg9eUb7raD Sr.w Worksheet b Kuta Software LLC Solve each sstem of equations. 0) + + = = 0 ) + 0 = = 0 Simplif. ) 9m ) 7n Solve each sstem. ) s t = r s + t = r + t = ) + + z = + z = z = ) r s + t = t = r + s + s t = Solve each sstem b elimination. 7) 7 + = = 0 Solve each sstem b substitution. 8) = + = 9) A boat traveled.0 miles downstream and back. The trip downstream took 8. hours. The trip back took. hours. What is the speed of the boat in still water? What is the speed of the current? 70) A boat traveled 9. miles downstream and back. The trip downstream took. hours. The trip back took 8. hours. What is the speed of the boat in still water? What is the speed of the current? 7) Maria's school is selling tickets to a pla. On the first da of ticket sales the school sold senior citizen tickets and student tickets for a total of $0.0. The school took in $0.0 on the second da b selling senior citizen tickets and student tickets. Find the price of a senior citizen ticket and the price of a student ticket.

30 -0- P Oe0Ez BKmu9tOah wszojfstlwqarrsel UL7LhC.E A AAlilG orfidgzhhtdsh arnegsvewr0vre7ds. W mmlabdhep XwniktWhK liznbffiynkixtler AlRgeMbcrDaY Yo.T Worksheet b Kuta Software LLC 7) The school that Lea goes to is selling tickets to a pla. On the first da of ticket sales the school sold adult tickets and 8 student tickets for a total of $7.0. The school took in $9.0 on the second da b selling adult ticket and student tickets. What is the price each of one adult ticket and one student ticket? 7) A plane traveled 8.8 miles to Rome and back. The trip there was with the wind. It took hours. The trip back was into the wind. The trip back took 7. hours. What is the speed of the plane in still air? What is the speed of the wind? Solve each question. Round our answer to the nearest hundredth. 7) Working alone, it takes Scott.7 minutes to sweep a porch. Kala can sweep the same porch in 0. minutes. If the worked together how long would it take them? 7) Working together, Rob and Norachai can mop a warehouse in.99 hours. Had he done it alone it would have taken Norachai 9. hours. Find how long it would take Rob to do it alone. 7) How man lb. of a metal containing 0% platinum must be combined with 0 lb. of pure platinum to form an allo containing 80% platinum? 77) A cattle train left Bangalore and traveled south at an average speed of 0 mph. Some time later a passenger train left traveling in the opposite direction with an average speed of 0 mph. After the cattle train had traveled for 9 hours the trains were 980 mi. apart. Find the number of hours the passenger train traveled. 78) Carlos left home and drove north at an average speed of mph. Some time later Castel left driving in the same direction but at an average speed of 78 mph. After driving for five hours Castel caught up with Carlos. How long did Carlos drive before Castel caught up?

31 -- b Lc0WqA zkfuvtav ZSfovfAtIwKaTrXev mlzlpcm.s D oaqlflj ruipgmhetasm srnets9enrxv9epdi. c BMUaSdNeu KwRimtOhp LI OnNfiinAiXteZ wanl7gsebprgab P.s Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester Y0HzP 9KButAai nseoafgtwearwey CLfLECj.e c qanlplu NrlicgchGt Qss 0rleKsYehrIvVeTd K. 8 Graph each equation. ID: Name ) = ) = 0 0 Find the value that completes the square and then rewrite as a perfect square. ) p + p + 9 ( ; p + ) ) + + ( ; + ) Solve each equation b completing the square. ) + = 0 {, } Simplif. ) (7 7i) + ( 8i) + ( + i) i 8) ) i 9 + i + i Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) + 7 = ; two imaginar solutions

32 -- W h0vnz ukuu8tva RSSoftgwqaare zllscc.k B caxl9lx rfighetxsa 8rkeXs7eprvre7dh.B n MNaAdjec SwAiEt0hd IMnJfSinizteP 0AlFgegbrRaQ sk.s Worksheet b Kuta Software LLC Divide using long division 0) (n + n ) (n + ) n n + Divide using snthetic division ) (a a + a a 9) (a + 8) a 8a + a a 8 + a + 8 Identif the domain and range of each. Then sketch the graph. ) = Domain: Range: 8 ) = + 8 Domain: { All real numbers. } Range: { All real numbers. } 8 Solve each equation or state if there is no unique solution. ) 0 A + = 0

33 -- N e90ogd MK7uBtMao qsoovfvtkwvaorref zlwlxcf.a T UAblfl8 nrhigehntksa UrRetsoeprDvbedj.X K MaAd8ea owmicthz IIVnfciQnqiAt8eB wal0gnehbirwal gm.m Worksheet b Kuta Software LLC ) 0 Z 0 = State the possible rational zeros for each function. Then factor each and find all zeros. ) f () = Possible rational zeros: ± Factors to: f () = ( + )( + )( )( + + ) 7) = Possible rational zeros: ±, ±, ±, ± Factors to: = ( + )( + )( Zeros: {, + i, i,, + i, i } Zeros: {, + i State the possible rational roots for each equation. Then factor each and find all roots. 8) = 0 Possible rational roots: ±, ±, ±, ± 0 Factors to: ( + )( + )( + ) = 0 Roots: {, i, i, i, i } Solve each equation b factoring. 9) n + n = 0 {, 7 7} Solve each equation b taking square roots. 0) 0m + 0 = 0 {i, i} Solve each equation with the quadratic formula. ) r + r = 0 + 7r { 7 i 7, 7 + i 7 }, i,, Factor each completel. ) ( )(8 + ) Factor each. ) = 0 Factors to: ( + )( + )( )( + + ) = 0 Roots: {, + i Factor each completel., i,, + i ) 8 + = 0 Factors, i to: ( } + ) ( + ) ( ) = 0 Roots: {i mult., i mult., mult., mult. } ) 8v + v (v + 8)(8v ) 7) 9n n + 70n n(n 7)(n 0) ) 9k 8k 0k k(k + )(k 0) 8) k 0k + k k (k )(k )

34 -- H E00EM rkxuctoag nsofhtlwpatrqeq LhLECA.W p APllf drnivgohttsb wr8evsbewrgv9eqdp.p W VMOadVev AwXi9tShj IIn7fifnb it7en harlgejbtrlaq 7.Q Worksheet b Kuta Software LLC 9) 0v + 0v 0 (v )(v + ) 0) + Not factorable ) a + b Not factorable ) 9 7 ( )( ) ) 9 ( + )( ) ) a + 0b (a + b)(a ab + b ) Sketch the graph of each line. ) = 0 Sketch the graph of each linear inequalit. ) 0

35 -- Lk0mfg fkiuzthan SjokfmtswJare ELwLgCr.W carlrl UrvigKhJtQsb LrSeAskeFrveezds.W w MnadieT KwJiftIhq OIInafiipniMtner 8AnlXgsetbr Ua m.9 Worksheet b Kuta Software LLC Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = Verte: ( 9, ) Ais of Sm.: = 9 Opens: Up 8) f () = ( + + ) 8 Verte: (, ) 8 Min value = -int: 0 -int: and 8 Ais of Sm.: = Opens: Down Ma value = -int: -int: and 9) f () = ( )( ) 8 Verte: (, ) Ais of Sm.: = Opens: Down Ma value = -int: -int: and 8

36 -- X a70bn cku0ttaf ts0odfftfw9ar8e0 MLGL8Cz.U N MAMlulh Zrimg8hPtBsY Ar0eNsGeFrDvkeedY.M f wmsadeq uwithk BInAfginIiZtse7 da0lige0borda t. Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = + 8 Real Zeros:., 0,. Minima: (.7,.) (0.9, ) Maima: (0, 0) ) f () = Real Zeros:.7,.,.9 Minima: (., 0.9) (0.,.) Maima: ( 0.,.) (.,.9) 8 8 Sketch the graph of each function. ) < ) < ( + )

37 -7- f Nk0rUi gkdustvab NSDo0fgtWwOaarCez VLfLnCb.c U gaclhlm 9rWijgOhLtse rnersgeor9vhewdj. l UMfaldbeI WwsiptKht SI7nfriYni0tXeT KAslWg9eQbzrvaH Tr. Worksheet b Kuta Software LLC Solve each sstem b graphing. ) 8 = 0 + = ) = + + = 0 0 No solution 0 (, ) Sketch the solution to each sstem of inequalities. ) + < 7) + < 0 0 Write the slope-intercept form of the equation of the line through the given point with the given slope. 8) through: (, ), slope = =

38 -8- A I0vIP tkvuhttah lsmoyftzwsacre8 clblck.9 t VAllBlz rvikgfhqtcs9 prfezszezrgvqeadd.z A KMVatdTe Vwit9h8 bikn8f7inzittved eawlbgjekbqr8az L.m Worksheet b Kuta Software LLC Write the slope-intercept form of the equation of the line through the given points. 9) through: (, ) and (, ) = Simplif. Write "undefined" for epressions that are undefined. 0) ( ) 0 0 ) 0 0 ) 0 0 Simplif each epression. ) ( + 7 ) + ( ) ( + 8 ) + + Describe the end behavior of each function. ) f () = + f () + as f () as + ) f () = + + f () + as f () as + Evaluate each function at the given value using snthetic substitution ) f () = at = Find each product. 7) ( 7 7)( 8) Write a polnomial function of least degree with integral coefficients that has the given zeros. 8),, f () = ),, f () = 0 9 0

39 -9- z h80 ckkuxtzav ksopfutdw9amrren WLLLOCY.q 7 AIlFlI 9rFigRhtYsh 9rgeshevrJv7eqdF.c N zmda9dfe0 EwjimtzhE UInmfNi0nWiWte AljgNeKbrEav DY. Worksheet b Kuta Software LLC Solve each sstem of equations. 0) + + = = 0 (, ), (, ) ) + 0 = = 0 No solution. Simplif. ) 9m 0m ) 7n 0 n Solve each sstem. ) s t = r s + t = r + t = (,, ) ) + + z = + z = z = (,, ) ) r s + t = t = r + s + s t = Infinitel man solutions Solve each sstem b elimination. 7) 7 + = = 0 (, ) Solve each sstem b substitution. 8) = + = (, ) 9) A boat traveled.0 miles downstream and back. The trip downstream took 8. hours. The trip back took. hours. What is the speed of the boat in still water? What is the speed of the current? boat: 8. mph, current: 9. mph 70) A boat traveled 9. miles downstream and back. The trip downstream took. hours. The trip back took 8. hours. What is the speed of the boat in still water? What is the speed of the current? boat:. mph, current:. mph 7) Maria's school is selling tickets to a pla. On the first da of ticket sales the school sold senior citizen tickets and student tickets for a total of $0.0. The school took in $0.0 on the second da b selling senior citizen tickets and student tickets. Find the price of a senior citizen ticket and the price of a student ticket. senior citizen ticket: $.0, student ticket: $7.0

40 -0- c b0kq KqurttaL lsgoafntwwsavrkex jlxlqcy.i 9 qallbld GrpikgZhitOs8 trzekseorbvcexdz.n M8avdHeH 8wzidtQhZ niznzftifnciotaee lauligkeqbsrfaf k.8 Worksheet b Kuta Software LLC 7) The school that Lea goes to is selling tickets to a pla. On the first da of ticket sales the school sold adult tickets and 8 student tickets for a total of $7.0. The school took in $9.0 on the second da b selling adult ticket and student tickets. What is the price each of one adult ticket and one student ticket? adult ticket: $0.90, student ticket: $.80 7) A plane traveled 8.8 miles to Rome and back. The trip there was with the wind. It took hours. The trip back was into the wind. The trip back took 7. hours. What is the speed of the plane in still air? What is the speed of the wind? plane:. mph, wind:. mph Solve each question. Round our answer to the nearest hundredth. 7) Working alone, it takes Scott.7 minutes to sweep a porch. Kala can sweep the same porch in 0. minutes. If the worked together how long would it take them?.9 minutes 7) How man lb. of a metal containing 0% platinum must be combined with 0 lb. of pure platinum to form an allo containing 80% platinum? lb. 7) Working together, Rob and Norachai can mop a warehouse in.99 hours. Had he done it alone it would have taken Norachai 9. hours. Find how long it would take Rob to do it alone. 0.9 hours 77) A cattle train left Bangalore and traveled south at an average speed of 0 mph. Some time later a passenger train left traveling in the opposite direction with an average speed of 0 mph. After the cattle train had traveled for 9 hours the trains were 980 mi. apart. Find the number of hours the passenger train traveled. hours 78) Carlos left home and drove north at an average speed of mph. Some time later Castel left driving in the same direction but at an average speed of 78 mph. After driving for five hours Castel caught up with Carlos. How long did Carlos drive before Castel caught up? hours

41 -- Z 8b0rIj ekjuptsam LSoXfgtiwbaorMeZ PLnL9Cf.C faqlln 7rgigwhGtss hrteestewrovpevdz. O dmaideg 8wiStVhv tisnrfjindiuteek WAIlzgdeebEr8ao ju.n Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester S XS0Owl KNuItWaa Soofft 7waazraef XLuL9C7.S I faslglg TrliDgShVtOsZ rdevsreqrevetd G. l Graph each equation. ID: Name ) = + + ) = Find the value that completes the square and then rewrite as a perfect square. ) + ) + + Solve each equation b completing the square. ) n + = 8n Simplif. ) ( i) + ( + i) + ( + 8i) 7) + i + 8i 8) Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) 0 =

42 -- m 8t0K7k UKhuJttab XShohfYtCwvaYrJer LNLoCV.Q QAUll croicg7hptpsv br aeksleerbvceadz.b K MGaNdHeO 0waictlh7 ii LnzfPiLnliKtea TAUlkgBe9bsrqak F.c Worksheet b Kuta Software LLC Divide using long division 0) (8a + a + a 9a 7a + 8) (8a 7) Divide using snthetic division ) (k + 7 7k k + k 8k ) ( 0 + k) Identif the domain and range of each. Then sketch the graph. ) = ) = 8 8

43 -- D sr0hwi okauetnav ISsoOftwa8rveN GLBLCT.n a AzlUlk arcirgrhfts roenssekrmvfeds.e H YMSatde Ywziqt0ho bimnffriyn7iqtset AIlcg8eBbWrYa S.7 Worksheet b Kuta Software LLC Solve each equation or state if there is no unique solution. ) 7 0 X + = ) + Y = 9 State the possible rational zeros for each function. Then factor each and find all zeros. ) f () = ) = State the possible rational roots for each equation. Then factor each and find all roots. 8) + + = 0 Solve each equation b factoring. 9) 9b = 7b Solve each equation b taking square roots. 0) v + = Solve each equation with the quadratic formula. ) + 9 = 8 Factor each completel. ) 0mn m n 0n Factor each. ) = 0 ) + + = 0 Factor each completel. ) n 8n ) b 8b + 8b

44 -- z uo0h8e KeuStRai ws0omfvtxwaxried 0LXLqCX.A q TAdlElX IrmiMg7hot9sR sr7eosersveeadr.m H jmfaldxef MwoiwtZhQ liwnrfaibnlitdes FAlgDecbRraaf IY.k Worksheet b Kuta Software LLC 7) 0 0 8) 8n + n 9) 0r r r 0) m n ) ) m + 0m n + n ) a b ) + 8 Sketch the graph of each line. ) = 0 0 Sketch the graph of each linear inequalit. ) + 0

45 -- L DJ0XXW KDuQtkae isfolfet7wiamrgeu mlalrca.g d nallhlh DrBilgzhAt0sj XrAeise0rTve7d9.X z omwakdveg owqiwtkhh ginmfpivnimtek FAAlOgIebbraP jd.p Worksheet b Kuta Software LLC Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = ) f () = ( ) ) f () = ( )( 7) 8 8

46 -- A wh00hw qkfustaam TSsoJfItwZaIrkew zllrci.a Q 9AllG QrEi7gNhrtmsv orpeisxe8r Mvsed7.w u qmamdqed pwfigtrhy uidnifbiinnictje AhlRgYe9bYrTac T.V Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = + + ) f () = Sketch the graph of each function. ) ) > ( )

47 -7- p SC0rgF ik0ujtab TSbopfitYwka8rDe ZLtLWCM.i AHlVlv tr9ipgbhites SreLsceYrTvepdq.T AMsa8dOeM tweiptzhp MI7nZf0iwnMitTeb eallqgtepbprxai 8v.Y Worksheet b Kuta Software LLC Solve each sstem b graphing. ) = = 0 ) = + 9 = + 0 Sketch the solution to each sstem of inequalities. ) < + 7) 0 < + 0 Write the slope-intercept form of the equation of the line through the given point with the given slope. 8) through: (, ), slope =

48 -8- m U80qS KluGtral qsomfwtvw0aer aec VLQLLCu.e XARlzlP jriigghvtse brzeasewrvdesdc.v q 0MZaBd7eD gwwittghf 8InifiLnriGtfe AAlpgSedbzrTaV 7C.9 Worksheet b Kuta Software LLC Write the slope-intercept form of the equation of the line through the given points. 9) through: (, ) and (0, ) Simplif. Write "undefined" for epressions that are undefined. 0) ( ) ) ) 0 Simplif each epression. ) (r + 7r r + r ) (r + r r) (r r) Describe the end behavior of each function. ) f () = + ) f () = + Evaluate each function at the given value using snthetic substitution ) f () = at = Find each product. 7) ( n n + )( n n 8) Write a polnomial function of least degree with integral coefficients that has the given zeros. 8),, 9), + 0

49 -9- c so0s8d SKruttzao msiocfntkwpafrgev qlulocn.z Alvl riigdhatvsk kreexsuedrevee8di.t m imhasdqed swjijtuh 9InnIfWiAnmiTt8eB AABlhgrebwr8aV K.D Worksheet b Kuta Software LLC Solve each sstem of equations. 0) = = 0 ) = = 0 Simplif. ) 7 7b ) 7 r Solve each sstem. ) r s t = r t = t = s ) a c = a = b c a + b c = 8 ) z = 0 = z z = 9 Solve each sstem b elimination. 7) 7 = = Solve each sstem b substitution. 8) + = + = 9) Jack and Kali each improved their ards b planting rose bushes and geraniums. The bought their supplies from the same store. Jack spent $8.0 on rose bushes and 7 geraniums. Kali spent $.0 on 8 rose bushes and geraniums. Find the cost of one rose bush and the cost of one geranium. 70) Kim and Stefan are selling fruit for a school fundraiser. Customers can bu small boes of oranges and large boes of oranges. Kim sold small boes of oranges and large bo of oranges for a total of $7.90. Stefan sold small boes of oranges and large boes of oranges for a total of $.0. Find the cost each of one small bo of oranges and one large bo of oranges.

50 -0- R Wa077m 0K7uZtLaE esjoifmtowtahrfey CLXLdCw.G FAjlTlj YriUghdtEsq HrHeEsKer9vejdV.I GMardHen kwhittehv IZnsfAiznCictdeO ua lghehb7rrad B.F Worksheet b Kuta Software LLC 7) Maria's school is selling tickets to a spring musical. On the first da of ticket sales the school sold adult tickets and student tickets for a total of $9.90. The school took in $.70 on the second da b selling 8 adult tickets and student tickets. What is the price each of one adult ticket and one student ticket? 7) The school that Julio goes to is selling tickets to a spring musical. On the first da of ticket sales the school sold senior citizen tickets and 7 child tickets for a total of $.. The school took in $. on the second da b selling 7 senior citizen tickets and child tickets. What is the price each of one senior citizen ticket and one child ticket? 7) A boat traveled 8.8 miles downstream and back. The trip downstream took 8.8 hours. The trip back took hours. What is the speed of the boat in still water? What is the speed of the current? Solve each question. Round our answer to the nearest hundredth. 7) Working together, James and Julia can clean an attic in.97 hours. Had she done it alone it would have taken Julia. hours. How long would it take James to do it alone? 7) Jacob can harvest a field in 9. hours. One da his friend Daniel helped him and it onl took.09 hours. Find how long it would take Daniel to do it alone. 7) How man oz of copper which costs $/oz must be added to oz of tin which costs $0/oz to make bronze which costs $/oz? 77) Daniel left home and drove south at an average speed of km/h. Carlos left at the same time and drove in the opposite direction with an average speed of 70 km/h. Find the number of hours Carlos needs to drive before the are 7 km apart. 78) A cruise ship left Hawaii two hours before a container ship. The ships traveled in opposite directions. The container ship traveled at 7 km/h for four hours. After this time the ships were 88 km apart. What was the cruise ship's speed?

51 -- W IC0PjA ckmuvtaq oshoffithwzalroel RLwLuC.O t FAn llg ArNi8gihNtWsu 9rceLsNearvGefd8.q o kmzadel pwkiztfhf niuncfinniltoel PAglbge8bGrPaN eh.r Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester O0SH QKu stcak 0SHoYfQtdwka0rVeM zlaltck. P 9 0A0lol irti qgwh JtVsQ rryecsre9rlvfede.v Graph each equation. ID: Name ) = + + ) = Find the value that completes the square and then rewrite as a perfect square. ) + ( ; ) Solve each equation b completing the square. ) ( ; + ) ) n + = 8n {, } Simplif. ) ( i) + ( + i) + ( + 8i) 8) 9 + 7i ) + i + 8i 9i Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) 0 = ; two imaginar solutions 0

52 -- J t80ne rkudtaar usbozfvtlwajroem elvlcu.f EAlBln jrbighjthst rrgeszedrvcetdf.f u NMmaMdmeR lwkigtqhh VIqnnfUiPnsit7eN raflngze0bbrjas s9.s Worksheet b Kuta Software LLC Divide using long division 0) (8a + a + a 9a 7a + 8) (8a 7) a + a + 9a 7a 7 8a 7 Divide using snthetic division ) (k + 7 7k k + k 8k ) ( 0 + k) k + k + k 7k k Identif the domain and range of each. Then sketch the graph. ) = + 8 Domain: Range: 8 ) = 8 Domain: { All real numbers. } Range: { All real numbers. } 8

53 -- m Vb0nmZ UKquitVaK DSo7fktWw8azrAee elclic. C CAClJlt YrniqgohBtnsK ZrYeZseeHrqvbebdO.M H EMjaUdLeE weiwtsh9 WI8nmfhiXnniftJeI zavlgfehbzr0az Vz.p Worksheet b Kuta Software LLC Solve each equation or state if there is no unique solution. ) 7 0 X + = 7 9 State the possible rational zeros for each function. Then factor each and find all zeros. ) + Y = 9 ) f () = Possible rational 7) zeros: = ±, ±, ±, Possible ± 8 rational zeros: ±, ±, ± Factors to: f () = ( )( + )(Factors + ) to: = ( + )( )( + ) Zeros: {, i, i, i, i} Zeros: {,, i, i} State the possible rational roots for each equation. Then factor each and find all roots. 8) + + = 0 Possible rational roots: ±, ±, ±, ±, ±, ± 9, ±, ± 8, ± Factors to: ( + ) = 0 Roots: {i mult., i mult. } Solve each equation b factoring. 9) 9b = 7b {, 7} Solve each equation b taking square roots. 0) v + = {, } Solve each equation with the quadratic formula. ) + 9 = 8 { + i, i 0 0 } Factor each completel. ) 0mn m n 0n n (m n)(n 8m) Factor each. ) = 0 Factors to: ( + )( + )( )( + ) + ) + = 0 + = 0 Factors to: ( + )( + )( + )( Roots: {, + i Factor each completel., i,, + i, i } Roots: {, + i, i,, + ) n 8n n (n 7) ) b 8b + 8b b(b )(b 7)

54 -- w nx0o wknu7tga nsgofntewdaqriej olnlgc.e AZlelD rhioghitesp 7r8ehsKebrfvfeMdG. t DMbaRdFeO Twithl IkncfkifnMigtXe SAUlFgHeLberNa JT.F Worksheet b Kuta Software LLC 7) 0 0 8) 8n + n 0 ( ) (n + )(n 9) 9) 0r r r r(r )(r + ) ) ( + )( ) ) a b (a b)(a + ab + b ) 0) m n (m + n)(m n) ) m + 0m n + n (m + n ) ) + 8 ( + )( + ) Sketch the graph of each line. ) = 0 0 Sketch the graph of each linear inequalit. ) + 0

55 -- t 0Enl UKYuTta7 TSOojfGtawiarXet alalsc7.q E daflqlm vrmirgnhutsc ZrTe7soesrXvIefdf.h 8MKaodFek wwirtha pinefkihnwiltlea AljgdebYrdaM lq. Worksheet b Kuta Software LLC Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = Verte: (, ) Ais of Sm.: = Opens: Up Min value = -int: 8 -int: and 8) f () = ( ) 8 Verte: (, ) Ais of Sm.: = Opens: Down Ma value = -int: -int: None 8 9) f () = ( )( 7) 8 Verte: (, ) Ais of Sm.: = Opens: Down Ma value = -int: -int: and 7 8

56 -- l 70uVs lkvuqtuaa SocfAtNwearteH vlylic.7 h XAUljlJ rlitgrhttesz LrDeOsseLr vvpehd9.q MOaHdHeo LwriftAhl I0nNfkipnBitLeR ZAulUgKeUbTraaK U.O Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = Real Zeros: 0.,. Minima: ( 0.,.) Maima: (., 0.7) (.,.9) ) f () = + 8 Real Zeros: 0.,., Minima: ( 0.7,.) (., 0.) Maima: (.,.9) (0.7, 0.) 8 8 Sketch the graph of each function. ) ) > ( )

57 -7- S0nOt YKuAtIaT BSVoNfZtZwAarbee LLLnCK.p I VAUlql8 bridgfhqts urterscerv8evdo.9 FMPaPddeA Hwiutshn pirnzfqirn8ihtse lalgteqbvrmao 9I.L Worksheet b Kuta Software LLC Solve each sstem b graphing. ) = = 0 ) = + 9 = + 0 (, ) Sketch the solution to each sstem of inequalities. ) < + (, ) 7) < Write the slope-intercept form of the equation of the line through the given point with the given slope. 8) through: (, ), slope = =

58 -8- Qq0k7l akduetmat 0SoEfhtwfaRrle0 LLsLKCl.b d AAalVl RraiXgwhMtrsw or cesuernvkehdw.v R 9MVakdweB OwzihthW EIZnufEinIiJtmef 8AdlUgeeIbEr7a8 Ej. Worksheet b Kuta Software LLC Write the slope-intercept form of the equation of the line through the given points. 9) through: (, ) and (0, ) = + Simplif. Write "undefined" for epressions that are undefined. 0) ( ) 9 8 ) ) Simplif each epression. ) (r + 7r r + r ) (r + r r) (r r) r 7r + r + r + Describe the end behavior of each function. ) f () = + f () as f () as + ) f () = + f () as f () + as + Evaluate each function at the given value using snthetic substitution ) f () = at = Find each product. 7) ( n n + )( n n 8) n + n + n + n Write a polnomial function of least degree with integral coefficients that has the given zeros. 8),, f () = ), + 0 f () = +

59 -9- j HQ0uOg SKwuht7aI SSbofctEwraPrber LtLbC7.M i 7AHlClS 8rSiJg9hctds rhepserxvoexdl.t E qmna8dtev waiptfhn VIMnlfYitnsiBt7e DA lgvetbyrxa Zi.a Worksheet b Kuta Software LLC Solve each sstem of equations. 0) = = 0 (, 7), (, 9) ) = = 0 (, ) Simplif. ) 7 7b b ) 7 r r Solve each sstem. ) r s t = r t = t = s (, 0, 0) ) a c = a = b c a + b c = 8 (,, ) ) z = 0 = z z = 9 No solution Solve each sstem b elimination. 7) 7 = = (, 0) Solve each sstem b substitution. 8) + = + = (, 0) 9) Jack and Kali each improved their ards b planting rose bushes and geraniums. The bought their supplies from the same store. Jack spent $8.0 on rose bushes and 7 geraniums. Kali spent $.0 on 8 rose bushes and geraniums. Find the cost of one rose bush and the cost of one geranium. rose bush: $.80, geranium: $ ) Kim and Stefan are selling fruit for a school fundraiser. Customers can bu small boes of oranges and large boes of oranges. Kim sold small boes of oranges and large bo of oranges for a total of $7.90. Stefan sold small boes of oranges and large boes of oranges for a total of $.0. Find the cost each of one small bo of oranges and one large bo of oranges. small bo of oranges: $.0, large bo of oranges: $8.0

60 -0- d pr0btl BK8u9tUaa MS9okftWwiaRr ees OLiLhCB.I Z XA8lTl8 grqi0guhttvs rqewsvetrrvierdo. V WMVakdtej bwtiqtrhk SIbnIfTiunpiXtheT JALlegfeSbZrBa H.B Worksheet b Kuta Software LLC 7) Maria's school is selling tickets to a spring musical. On the first da of ticket sales the school sold adult tickets and student tickets for a total of $9.90. The school took in $.70 on the second da b selling 8 adult tickets and student tickets. What is the price each of one adult ticket and one student ticket? adult ticket: $9.90, student ticket: $.0 7) The school that Julio goes to is selling tickets to a spring musical. On the first da of ticket sales the school sold senior citizen tickets and 7 child tickets for a total of $.. The school took in $. on the second da b selling 7 senior citizen tickets and child tickets. What is the price each of one senior citizen ticket and one child ticket? senior citizen ticket: $0., child ticket: $.98 7) A boat traveled 8.8 miles downstream and back. The trip downstream took 8.8 hours. The trip back took hours. What is the speed of the boat in still water? What is the speed of the current? boat: 8.9 mph, current:. mph Solve each question. Round our answer to the nearest hundredth. 7) Working together, James and Julia can clean an attic in.97 hours. Had she done it alone it would have taken Julia. hours. How long would it take James to do it alone?.9 hours 7) How man oz of copper which costs $/oz must be added to oz of tin which costs $0/oz to make bronze which costs $/oz? ozs 7) Jacob can harvest a field in 9. hours. One da his friend Daniel helped him and it onl took.09 hours. Find how long it would take Daniel to do it alone.. hours 77) Daniel left home and drove south at an average speed of km/h. Carlos left at the same time and drove in the opposite direction with an average speed of 70 km/h. Find the number of hours Carlos needs to drive before the are 7 km apart. hours 78) A cruise ship left Hawaii two hours before a container ship. The ships traveled in opposite directions. The container ship traveled at 7 km/h for four hours. After this time the ships were 88 km apart. What was the cruise ship's speed? 0 km/h

61 -- g DT0GrS skduktrag ESVofntmwLa8rYeV FLILCG.t o aalol ZrviUgOhYtPs LrFeMsieUr 8vMefdX.K 7 MPaJdTea gwgintdhy 0IdnEfwiDnkictPeg iazlkgnejbfraf Kn.v Worksheet b Kuta Software LLC Algebra /Trig Final Review Semester a bt0mbt IKu Tt nam gsqoifft wwfaprweb LHLCb.0 R AXllP brigvhtjsa DrZeisneHrwvnegd. b Graph each equation. ID: Name ) = ) = 0 0 Find the value that completes the square and then rewrite as a perfect square. ) + ) z + 9z + Solve each equation b completing the square. ) 8a a = Simplif. ) (7i) ( + i) + ( 7 + i) 7) + 0i + i 8) 8 9 Find the discriminant of each quadratic equation then state the number and tpe of solutions. 9) n + n = 8n + + n

62 -- o Ib0qaZ TKLuitao WSToMfqttwwajrel tlrlc.i F YAlClD CrsijgthtAs prtegsbewrvhezdr.d W NMjaCdNeH hwfiutbhh SInjfBibnsiftAew kawlrgreqbarcat KR.g Worksheet b Kuta Software LLC Divide using long division 0) (m m 8m + ) (m ) Divide using snthetic division ) ( p + p + p + p ) (p ) Identif the domain and range of each. Then sketch the graph. ) = ) = 8 8

63 -- Dk0 EKRuvtpat asoifstvwjaxrek alclecu.t w ZAklgl9 Gr hivghqtqse SreSsmeirHvSeAd.g nmbaidget wiht8ho EIlnufWignhi9teV pailggpesbkrcaz qv.0 Worksheet b Kuta Software LLC Solve each equation or state if there is no unique solution. ) 0 C 7 = 0 7 ) 0 9 = X + 0 State the possible rational zeros for each function. Then factor each and find all zeros. ) f () = + + 7) = 8 State the possible rational roots for each equation. Then factor each and find all roots. 8) = 0 Solve each equation b factoring. 9) v = v + Solve each equation b taking square roots. 0) + 7 = Solve each equation with the quadratic formula. ) + 9 = + 9 Factor each completel. ) uv u + 8v v Factor each. ) = 0 ) + 7 = 0 Factor each completel. ) v 7v + 0 ) 0m 9m +

64 -- D0Xuz qkrumtal PSoMfatJwraQrFel VLuLrC.T a naglnls MrGiXgXhctXsV crqevs7e7rrveqdd.l I amlaedbe bwqibtehj 7IEncfLinnqi7tYeb XAdlggPeibUruaT WA.H Worksheet b Kuta Software LLC 7) 0n + n 8) 0a a 9) ) ) 9 ) a + 80a b + 00b ) ) 0m + n Sketch the graph of each line. ) + = 0 Sketch the graph of each linear inequalit. ) 0

65 Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Then sketch the graph. 7) f () = 8) f () = ( 9 ) ) f () = ( + )( ) G hr0dtq lkxutpat ESAoqfEtGwFaarneT ql9lqca.u najlle AriihgXhmtjsb urbersceerivnedg.j e wm0aadde8 FwiWtEhb cibn7frindirtse UAlRggeqbargaV E9. Worksheet b Kuta Software LLC

66 -- i 0J0FeF 8KvuYtBa XSHoCfWt7wtaQrnej nlklzc7. J uahlhln trivg8httsp MrezseTrQvweHdR.z R GMwaldfe GwniVthj IanfaiXnsiQtfeG uawlpgbeab0r aai BH.D Worksheet b Kuta Software LLC Sketch the graph of each function. Use our graphing calculator to approimate the relative minima and relative maima to the nearest tenth. 0) f () = ) f () = Sketch the graph of each function. ) > + 7 ) ( )