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Math980Midterm1ObjectivesReview Pleasestudythefollowingobjectivesfrommodulesoneandtwobeforetakingyourfirstmidterm.This reviewprovidesyouwithsampleproblemsthatcorrespondtotheobjectivesgiven,however,the problemsonyourmidtermwillnotbeexactlyliketheproblemsonthisreview.Youshouldgoback andstudyyournotesandlookatallofthedifferenttypesofproblemsthatreinforcetheobjectives below. Module1-LinearEquationsinOneVariable 1.1SolveOne-StepLinearEquations 1.)Solve:–x=7 2.)Solve: ! !! = −3 1.2SolveTwo-StepLinearEquations 1.)Solve:8–2y=–2 2.)Solve:10–4x=20 1.3SolveLinearEquationsbyCombiningLikeTermsandtheDistributiveProperty 1.)Solve:–9x–1+8x=2+9 2.)Solve:2(b–6)–3b=8–7 1.4SolveLinearEquationswithVariablesonBothSidesoftheEquation 1.)Solve:5z+8=–4z+5 2.)Solve:6+3x–2=7x–2(2x–8) 1.5SolveLinearEquationsContainingFractions ! 1.)Solve:! 𝑦 − 3 = ! ! ! ! 2.)Solve:! + 𝑥 = !" 𝑦 1.6SolveLinearEquationsContainingDecimals 1.)Solve:0.6x–0.27=0.5x–2.25 2.)Solve:0.25(x+50)–0.03(x–40)=15.9 1.7SolveApplicationsUsingLinearEquations 1.)Thesumoffivetimesanumberandeightis12.Findthenumber. 2.)ThedifferenceoftwotimesanumberandsixIsninemorethanthenumber.Findthenumber. 3.)Thesumofthreeconsecutiveintegersis33.Listthenumbersfromsmallesttolargest. 4.)Thesumoftwoconsecutiveoddintegersis92.Listthenumbersfromsmallesttolargest. 5.)Thesumofthreeconsecutiveevenintegersis–198.Listthenumbersfromsmallesttolargest. 6.)Arectangularroomis3meterslongerthanitiswide,anditsperimeteris30meters.Findthe dimensionsoftheroom. 7.)Abagisfilledwithyellowandorangemarbles.Thereare97marblesinthebag.Ifthereare25more yellowmarblesthanorangemarbles,findthenumberofyellowmarblesandthenumberoforange marblesinthebag. 8.)Aboardthatis16incheslongiscutintotwopieces.Thelongerpieceis3timeslongerthantheother piece.Howlongarethepieces? 9.)yvariesdirectlyasx.Ifx=7theny=35.Findywhenx=3. 10.)yvariesinverselyasx.Ifx=2theny=6.Findywhenx=8. 11.)Whatnumberis7.8%of114?Roundanswertotwodecimalplacesasneeded. 12.)120iswhatpercentof350?Roundanswertoonedecimalplaceasneeded. 1.8EvaluateFormulas 1.)Determinethesurfaceareaofaboxwithlengthof6cm,widthof3cm,andheightof10cm.Usethe formula:A=2LH+2WH+LW 2.)Findthevolumeofaboxwithlengthof6cm,widthof3cm,andheightof10cm.Usethe formula:V=LWH 1.8SolveaFormulaforaGivenVariable 1.)Solvefora. ! 2= ax ! 2.)Solvefory. ax+by=c Module2–LinearInequalitiesandAbsoluteValue 2.1Solve,Graph,andGiveIntervalNotationforLinearInequalitieswithOneVariable 1.)Solve,graph,andgiveintervalnotationfortheinequality: –7+4x<1 ←____________________________________→ 2.)Solve,graph,andgiveintervalnotationfortheinequality: –3x+9<0 ←____________________________________→ 2.2SolveApplicationsUsingLinearInequalities 1.)Sarah’sgoalistofindajobthatprovidesanincomeofatleast$65,000ayear.Acompanyoffersher ajobpayingabasesalaryof$17,000ayear,plusacommissionof4%ofhersales.Determinethe amountSarah’stotalsaleswillneedtobeforhertohaveayearlyincomegreaterthanorequalto $65,000. 2.)Astudenthasscoresof80,68,and75onhisfirstthreetests.Heneedsanaverageofatleast73to earnaCintheclass.WhatistheminimumscorethatastudentneedsonthefourthtesttoensureaC? 2.3FindtheIntersectionandUnionofSets 1.)GivenSetA={1,5,7,11,14,16,17,18,20)andSetB={7,8,15,16,18,19,20} Listtheelementsintheset(AUB) Listtheelementsintheset(A∩B) 2.3Solve,Graph,andGiveIntervalNotationforCompoundInequalities 1.)Solve,graph,andgiveintervalnotationforthecompoundinequality: 3x–2<–11OR4x–4>–8 ←____________________________________→ 2.)Solve,graph,andgiveintervalnotationforthecompoundinequality: ! – x+2>5OR5x>–5 ! ←____________________________________→ 3.)Solve,graph,andgiveintervalnotationforthecompoundinequality: 4(2x–3)<12AND–8x–7<–5x–8 ←____________________________________→ 4.)Solve,graph,andgiveintervalnotationforthecompoundinequality: –4x–1>–13AND2(x+1)<10 ←____________________________________→ 5.)Solve,graph,andgiveintervalnotationforthecompoundinequality: –13<4x–1<7 ←____________________________________→ 6.)Solve,graph,andgiveintervalnotationforthecompoundinequality: 2<3x+2<11 ←____________________________________→ 2.4SolveAbsoluteValueEquations 1.)Solvetheabsolutevalue. |x+5|=10 2.)Solvetheabsolutevalue. |2n+3|=8 2.5Solve,Graph,andGiveIntervalNotationforAbsoluteValueInequalities 1.)Solve,graph,andgiveintervalnotationfortheinequality: |2x–1|>–5 ←____________________________________→ 2.)Solve,graph,andgiveintervalnotationfortheinequality: |4x–9|>4 ←____________________________________→ 3.)Solve,graph,andgiveintervalnotationfortheinequality: 6+4|3x–4|<14 ←____________________________________→ 2.6IdentifytheDomain,Range,andDetermineWhethertheRelationisaFunction 1.)Findthedomainandrangeoftherelation:{(–6,7),(–6,6),(–6,5),(–6,4)}. Thedomainis: Therangeis: Istherelationafunction? Why? 2.)Findthedomainandrangeoftherelation:{(8,2),(7,2),(6,2),(5,2)}. Thedomainis: Therangeis: Istherelationafunction? Why? 2.6FindtheDomainofFunctions 1.)Findthedomainofh(x)= ! !!! Writeyouranswerinintervalnotation. 2.)Findthedomainoff(x)= 2𝑥 − 1 Writeyouranswerinintervalnotation. 2.6EvaluateFunctions 1.)Giventhefunctionf(x)=3x2+3x–8.Calculatethefollowingvalues: f(2)= f(-2)=