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Algebra I

KCSatHomeLearningPacket

April2020AlgebraI

ThispacketisalignedtothefollowingTennesseeMathematicsStandardsandKCSCurriculummodules.

ModuleOneA1.F.BF.A.1aDetermineanexplicitexpression,arecursiveprocess,orstepsforcalculationfromacontext.A1.F.LE.A.2Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,atable,adescriptionofarelationship,orinput-outputpairs.A1.S.ID.B.4aFitafunctiontothedata;usefunctionsfittedtodatatosolveproblemsinthecontextofthedata.Usegivenfunctionsorchooseafunctionsuggestedbythecontext.�

ModuleTwoA1.F.LE.A.1aRecognizethatlinearfunctionsgrowbyequaldifferencesoverequalintervalsandthatexponentialfunctionsgrowbyequalfactorsoverequalintervals.��A1.F.LE.A.1bRecognizesituationsinwhichonequantitychangesataconstantrateperunitintervalrelativetoanother.��A1.A.CED.A.1Createequationsandinequalitiesinonevariableandusethemtosolveproblems.A1.A.CED.A.2Createequationsintwoormorevariablestorepresentrelationshipsbetweenquantities;graphequationswithtwovariablesoncoordinateaxeswithlabelsandscales.A1.A.CED.A.3Representconstraintsbyequationsorinequalitiesandbysystemsofequationsand/orinequalities,andinterpretsolutionsasviableornonviableoptionsinamodelingcontext.A1.A.REI.B.2Solvelinearequationsandinequalitiesinonevariable,includingequationswithcoefficientsrepresentedbyletters.A1.A.REI.C.4Writeandsolveasystemoflinearequationsincontext.A1.A.REI.D.7Graphthesolutionstoalinearinequalityintwovariablesasahalf-plane(excludingtheboundaryinthecaseofastrictinequality),andgraphthesolutionsettoasystemoflinearinequalitiesintwovariablesastheintersectionofthecorrespondinghalf-planes.A1.F.BF.B.2Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative);findthevalueofkgiventhegraphs.

ModuleThreeA1.F.LE.A.1aRecognizethatlinearfunctionsgrowbyequaldifferencesoverequalintervalsandthatexponentialfunctionsgrowbyequalfactorsoverequalintervals.A1.F.LE.A.1bRecognizesituationsinwhichonequantitychangesataconstantrateperunitintervalrelativetoanother.��A1.F.LE.A.1cRecognizesituationsinwhichaquantitygrowsordecaysbyaconstantfactorperunitintervalrelativetoanother.A1.F.BF.B.2Identifytheeffectonthegraphofreplacingf(x)byf(x)+k,kf(x),f(kx),andf(x+k)forspecificvaluesofk(bothpositiveandnegative0;findthevalueofkgiventhegraphs.

Carnegie Algebra 1 Skills Practice

Module1:SearchingforPatterns[1]Usetheexplicitformulatodeterminethefollowingsequence(geometricorarithmetic)

andfindthe10thterm;3,6,12,…

[2]Kyleiscollectingcannedgoodsforafooddrive.Onthefirstday,hecollects1can.Onethe

secondday,hecollects2cans.Onthethirdday,hecollects4cans.Oneachsuccessiveday,hecollectstwiceasmanycansashecollectedthepreviousday.RepresentthetotalnumberofcansKylehascollectedbytheendofeachofthefirst7daysofthefooddrivewithanumericsequence.

[3]Graphtheorderedpairsforthesequencegivenbytheformulagn=2 ∗3n-1

[4]Thelinearregressionequationforadatasetisy=-1.2x+23.5,whereyrepresentsthe

numberofballoonssoldbyapartystoreeachweekandxrepresentstheweeknumber.Usetheequationtopredictthenumberofballoonsthestorewillsellduringweek8.Roundtothenearestwholenumber.

a. 14 b.33 c.73 d.96

[5]ThetableshowsSavannah’ssalaryfordifferentyears.

Carnegie Algebra 1 Skills Practice

Whichlinearregressionequationbestrepresentsthelineofbestforthedataifxrepresentsthenumberofyearssince2000?

a. Y=39,625x+4375b. Y=4375x+39,625c. Y=1750x+40,500d. Y=40,500x+1750

Module2:ExploringConstantChange[6]Afaucetleakswaterataconstantrate.Andreaplacesameasuringcupundertheleakto

catchthewater.Thetableshowsthenumberofmillilitersofwaterinthecupatdifferenttimes.

a. Determinetheaveragerateofchangefortheproblemsituation.Besuretoinclude

units.

b. Writeafunctiontomodelthetableofvalues.

c. Determinetheamountofwaterinthecupafterthefaucetleaksataconstantratefor11hours.

[7]Solvethefollowing.

a. Writetheyinterceptfortheequation:8x+3y=-24

b. Writetheequationinstandardform:y=#$x–4

c. Solveforx

½(16x+5)–3=19–5x

Carnegie Algebra 1 Skills Practice

[8]Foreachofthefollowing,afunctionhasbeengivenalongwithitsgraph.Performthe

specifiedtransformationonthefunctionandgraph.

[9]Solvethecompoundinequalityandrepresentthesolutiononthenumberlineshown.

[10]Aphonecompanyhastwolongdistancecallingplans.Thefirstplanis$25permonthforunlimitedlong-distancecalling.Thesecondplanis$10permonthplus$0.05perminuteoflongdistancecalling.Afterhowmanyminutesoflongdistancecallswillbecheaperforacustomertopurchasethefirstplan?

[11]Samuelpays$59.99plus$0.25foreachminuteover450minutesforhiscellphoneplan.

Monicapays$64.99plus$0.10foreachminuteover450minutesforhercellphoneplan.Whichsystemofequationsrepresentsthissituation?Letxrepresentthenumberofminutesover450.

Carnegie Algebra 1 Skills Practice

[12]Graphthesystemofequations.Determinethesolution.

[13]Howmanysolutionsdoeseachsystemofequationshave?

[14]Alfonsowantstopurchaseapoolmembershipforthesummer.Hehasnomorethany

dollarstospend.TheAquaticsClubchargesaninitialfeeof$75plus$20permonth.TheSwimmingHolechargesaninitialfeeof$15plus$65permonth.Writeasystemofinequalitiesthatcanbeusedtodeterminewhichcompanyoffersthebetterdeal.Letxrepresentthenumberofmonths.

[15]Alexsaved$65.Hehasalreadyspent$25.Heplanstospend$8onamovieticketeach

month.Writeaninequalitytorepresentsthenumberofmovieticketshecanbuy.ThendeterminethemaximumamountofmonthsAlexcangotothemovies.

Carnegie Algebra 1 Skills Practice

[16]Writeasystemoflinearinequalitiesthatrepresentsthegraph.

[17]Yourunbyareststationhalfwaythrougharoadrace.Youarerunningatarateof1/10

mileperminute.a. Completethetabletoshowyourdistance

fromthereststationovertime.Considerthetimebeforeyoupassthereststationtobenegative.

c.Writeafunctiontorepresentthegraph.

b.Plotthepointsfromthetableonthecoordinateplane.

Carnegie Algebra 1 Skills Practice

[18]Theequation,% = '(#givethearea,A,ofacirclewithradius,r.Solvethefunctionfor'.[19]Givenf(x)= ) Describethetransformationsperformedonthegraphoff(x)togetg(x)=3f(x)+4.

Module3:InvestigatingGrowthandDecay[20]Taylorearnedthefollowingamounteachday.• onedollarofthefirstday• threedollarsonthesecondday• ninedollarsonthethirdday• twenty-sevendollarsonthefourthdayWhichfunctionrepresentsTaylor’sdailyearningsasafunctionofthenumberofdays,t?

[21]Claytonplaced$1500intoasavingsaccountwith2.8%interest,compoundedannually.He

alsohas$200inasafeathomethathedoesnottouchoraddto.WriteClayton’stotalsavingsS(t)asafunctionoftimeinyears,t.

[22]Completethetabletodeterminethecorrespondingpointsonc(x),givenreferencepointsonf(x).Thengraphc(x)onthesamecoordinateplaneasf(x)andstatethedomainandrange.

Carnegie Algebra 1 Skills Practice

Module1:SearchingforPatternsAnswerKey[1]gn=∗g1×rn-1g10=∗3×210-1g10=1536

[2]1,3,7,15,31,63,127

[4]A.14

[5]C.Y=1750x+40,500

Module2:ExploringConstantChangeAnswerKey[6]A.Theaveragerateofchangeis5millilitersperhour.B.f(t)=5tC.f(11)=55;Thecupwillhave55millilitersofwaterinitafter11hours.

[7]A.(0,-8)(yintercept)

B.2x–3y=12(standardform)C.x=3/2

[8]A. B.

[3]

Carnegie Algebra 1 Skills Practice

[9]

[10]300minutes [11]

[12]

[14] [15]

[16]

17]a b.

c.

[13]a.infinitesolutionsb.nosolutions

Carnegie Algebra 1 Skills Practice

[18] [19]b.

Module3:InvestigatingGrowthandDecayAnswerKey

[20] [21]

[22]