Download Math 0980 Midterm 1 Objectives Review

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)=