ALGEBRA'2'HONORS'SUMMER'PACKET'' WELCOME'PROSPECTIVE'ALGEBRA'2'HONORS'STUDENTS:'

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1 ALGEBRA2HONORSSUMMERPACKET WELCOMEPROSPECTIVEALGEBRA2HONORSSTUDENTS: AttachedareAlgebra1problemsthatwillhelpyourbereadyforAlgebraII. A CheatSheet ofselectedformulas,properties,etc.isprovidedtomakeyourlifeeasier. Useit. Showwork.Theanswersareprovided,thereforeitisimportanttoshowstepstoreceive credit.nowork=nocredit. Thisassignmentcountsas3homeworkassignmentsandyouwillbetestedonthis materialwithinthefirstfewdaysofclass.itisnotbeingacceptedlateforanyreason. Beproactive.Comeinpreparedwithquestions. Lastly,Algebra2HonorsisafastKpaced3 rd Kyearmathclassforstudentswhohaveshown anaturalaptitudeformathcombinedwithadedicatedworkethic.ifyoudonotfeelthat youarecapableoffullyunderstandingtheattachedwithlittleornoproblems,consider takingregularalgebra2.

2 Algebra2HonorsSummerPacketCheatSheet Domain: Allowable x-inputs Range: Allowable y-outputs V.L.T. Vertical Line Test iii.

3 Arithmetic sequence: = + ( 1) d = common difference Geometric sequence: = r = common ratio P = principle r = rate (convert to decimal) n = # of times compounded 12 = monthly, 4 = quarterly, etc. t = time (in years)

4 Name: Date: Algebra2HonorsSummerAssignment NOCALCULATORSONTHISPORTIONOFTHESUMMPERPACKET. Whichofthefollowinggraphs,tables,orsetsarefunctions?Whicharenotfunctions?Explain each. Writethepolynomialinstandardform.Identifythedegree,leadingcoefficient,and yointerceptandthenclassifythepolynomialbasedondegreeandnumberofterms. 9) ) 6 + 7

5 Performtheindicatedoperation: 11) ) ) ) Graphthefollowinglinearequations: 15) = )6 3 = 1217) 2 = + 5 Graphthefollowinglinearinequality,absolutevalueinequality,andsystem: 18) < > ) > ) 2

6 CALCULATORSALLOWEDONTHISPORTIONOFTHESUMMERPACKET 21)Writeanequationofalinethatpassesthroughthepoint 2, 3 andisparallel totheline = )Writeanequationofalinethatpassesthroughthepoint 2, 3 andisperpendicular totheline = 2 1. Solvethefollowingequationsforx:++(*hint0there+will+be+one+identity+problem+and+one+no+solution+ problem) 23)5(2 + 3) = ) = ) = )5 7 = Solveandgrapheachinequality: 27) )5 + 6 < 9 18

7 Solveandgrapheachcompoundinequalityorabsolutevalueinequality: 29)4 < )3 + 2 > 17" 3 931) < 15 Solvethesystemsusingsubstitutionorelimination: 32) 2 + = 4 = 5 33) + 3 = = 14 Solveeachequation. 34)4 = 4 35)7 = 49 Determinewhetherthefunctionrepresentsexponentialgrowthordecay. 36) = 5.2(0.9) 37) =.75(3)

8 Simplifyeachexpression: 38) 64 39)8 40) 3 41) " 42) 43) 3 Factorthepolynomial. 44) ) 49 46) ) UseFACTORING+tosolve:+ 48) = 0 49) = 0 UsetheQUADRATIC+FORMULAtosolve: 50) = 0 51) = 0 52)Writethenext3termsofthearithmeticsequence:35,24,13,2,

9 53)Thesurfaceareaofarectangularprismisgivenby = 2" + 2ℎ + 2ℎ.Solvetheliteral equationforh.## 54)Writealinefunctionf+withthegivenvalues: 9 = 10, 15 = 6 55)A)Giventhedata,createascatterplotrememberingtolabelthexKandyKaxis.B)Draw andwritetheequationofalineoffit.c)determineiftherelationhasapositiveor negativecorrelation.d)estimateywhenx=15. Hours,x BatteryLife %,y K5 B) C) D) 56) Evaluate the piecewise function for 3, 1, 5, and = 1 < > 5 57)Given = 3 2 5A)Describethetransformationfromthefunction = 2, B)GraphthefunctionC)Determinethedomain D)Determinetherange A) Transformation: C) Domain: D) Range: Grid Scale = cm

10 58)Youdeposit$1200intoanaccountthatearns3 %interestquarterly.howmuchmoneyis intheaccountafter8years? 59)Solve49 = )Writeapolynomialinstandardformthathasonenegativerootandtwopositiveroots. 61)Solve7 + 2 = 15 62)Solve = 63)In an auditorium, the first row of seats has 36 seats. Each row behind the first row has 4 more seats than the row in front of it. A) Write an explicit rule to represent the number of seats for any given row. B) How many seats are in the 23 rd row? C) Which row has 156 seats? 64)Eachtestisworthtwiceasmanypointsastheprevioustest.A)Ifthefirsttestwasworth 6points,whatequationmodelsthenumberofpointsthenthtestisworth?B)Howmany pointsisthe6 th testworth? 65) Arectangularcourtyardcontainsasquarefountain,asshownbelow.Thecourtyardhasa lengthof feetandawidthof2 + 3feet.Thefountainhasalength 1feet.Writean expressionfortheareaoftheshadedregionasapolynomialinstandardform.

Algebra2HonorsSummerPacketAnswerSheet 1)

PassesV.L.T.(x snotrepeated) 3) Function.PassesV.L.T.(x snotrepeated) 4) Notafunction.

PassesV.L.T. 7) Notafunction.FailsV.L.T. 8) Function.

9) 3 + 5 + 71,4thdegree,leadingcoefficient

CubicBinomial 11) 5 4 + 4 12) 5 12 + 10 13) + 2

11 Algebra2HonorsSummerPacketAnswerSheet 1) Notafunction.FailsV.L.T.5 0and5 10 2) Function.PassesV.L.T.(x snotrepeated) 3) Function.PassesV.L.T.(x snotrepeated) 4) Notafunction.FailsV.L.T. 2, 0, and 4 5) Function.PassesV.L.T. 6) Function.PassesV.L.T. 7) Notafunction.FailsV.L.T. 8) Function.PassesV.L.T. 9) ,4thdegree,leadingcoefficient 5,yKintercept 71.QuarticTrinomial. 10) 7 6,3rddegree,leadingcoefficient 7,yKintercept 0.CubicBinomial 11) ) ) ) ) 16) 17) 18) 19) 20) 21) 3 = " = ) 3 = + 2 " = ) = 3 24) = 23/2" = 11.5

12 25) ""#$%&"(45 2) 26) "#$%&% "#$"$%&"#$"#$%"&( 7 = 7) 27) ) > ) 2 < 630) 3" > 531) 9 < < ) 33) 34) 35) 36) 37) 38) 39) 40) 41) , 2 4, 1 = 3 = 2 "#$% "#$%ℎ ) 43) 44) 45) 46) 47) 48) = 5, = 2 49) = 5, = 50) = ± " 51) = ± " 52) 9, 20, 31 53) ℎ = 54) = + 4" 10 = + 9 " + 6 = 15 55) Answersmayvaryslightly B) = C)NegativeCorrelationD) 15 = 25 "

56) 3 = 6; 1 = 1; 5 = 125; 7 = 10 57) A) = 2 hasaverticalstretchof3andismovedleft4unitsanddown5units C)Domain:"""#$"#$%&, RD)Range: > 5 58) $1585.

13 56) 3 = 6; 1 = 1; 5 = 125; 7 = 10 57) A) = 2 hasaverticalstretchof3andismovedleft4unitsanddown5units C)Domain:"""#$"#$%&, RD)Range: > 5 58) $ ) = 9 60) Answerswillvary 61) = ) = 4 63) A) = B) " = seatsinthe23 rd row. C) = 31 The31 st rowhas156seats. 64) A) = 6 2 B) = pointsforthe6 th test. 65) Areaoftheshadedregion: "