国外英语考试《SAT Level 1》试题（网友回忆版）二

国外英语考试《SATLevel1》试题（网友回忆版）二[单选题]1.Whatisthemaximumvalueof（江南博哥）thefunctionf(x)=1/xovertheinterval1/2≤x≤3/2?A.1/2B.3/2C.2D.2/3E.Infinity参考答案：C参考解析：Thegraphofthefunctionf(x)=1/xhasasymptotesofthey-andx-axes.Asxapproacheszero,thevalueofthefunctionapproachesinfinity.Sincethedomainisrestrictedtotheinterval2/1≤x≤3/2themaximumvalueofthefunctionoccurswhenx=1/2,f(x)=1/(1/2)=2.[单选题]2.Whatisthedomainofthefunctionf(x)=x/x+6?A.Allrealnumbers.B.Allrealnumbersexcept0.C.Allrealnumbersexcept6.D.Allrealnumbersexcept-6.E.Allrealnumbersgreaterthanorequalto-6.参考答案：D参考解析：Thefunctionf(x)=x/x+6isundefinedwhenthedenominatoriszero.x+6=0,x=-6.Thefunctionisdefinedforallrealnumbersexceptx=-6.[单选题]3.Whichofthefollowingisequivalenttothestatement：|x-1|<2?A.x<1B.x<3C.-1D.-3E.-1参考答案：E参考解析：Translatewithoutabsolutevalue：-2[单选题]4.Inanopinionpollof50menand40women,70%ofthemenand25%ofthewomensaidthattheypreferredfictiontononfictionbooks.Whatpercentofthenumberofpeoplepolledpreferredtoreadfiction?A.40%B.45%C.50%D.60%E.75%参考答案：C参考解析：Intheopinionpoll,70%ofthe50menor0.70×50=35menpreferredfictiontononfictionbooks.Inthesamepoll,25%ofthe40womenor0.25×40=10womenpreferredfictiontononfictionbooks.Thus,45(=35+10)ofthe90(=50+40)peoplepolledpreferredfictiontononfictionbooks.Since45/90=1/2=50%,50%ofthepeoplepolledpreferredtoreadfiction.[单选题]5.Anumberaincreasedby20%ofaresultsinanumberb.Whenbisdecreasedby33(1/3)%ofb,theresultisc.Thenumberciswhatpercentofa?A.40%B.60%C.80%D.120%E.150%参考答案：C参考解析：Ifaincreasedby20%ofaresultsinb,thena+(20%ofa)=b,a+0.2a=b,1.2a=b.Whenbisdecreasedby33(1/3)%ofb,theresultisc,sob-(1/3)b=(2/3)b=c.Sincec=(2/3)b=(2/3)(1.2a)=0.80a,thencis80%ofa.[单选题]6.Jerry,Will,andAIallworkatthesamecompany.Jerryearns80%ofWill'ssalary,andWillearns75%ofAl'ssalary.WhatpercentofAl'ssalaryisequaltoJerry'ssalary?A.80%B.75%C.70%D.65%E.60%参考答案：E参考解析：J=0.8WandW=0.75A.Substitute0.75AforW.J=0.8×0.75A=0.6A.Therefore,60%ofAl'ssalaryisequaltoJerry'ssalary.[单选题]7.Ifg(x)=x2andh(x)=x+2,thenh(g(x))=______.A.x+4B.x2+2C.x3+2x2D.x+2E.x2+4参考答案：B参考解析：Substituteg(x)forxinthefunctionh(x)=x+2：h(g(x))=g(x)+2.Thensubstitutex2forg(x)：h(g(x))=x2+2[单选题]8.WhichofthefollowingisNOTafunction?A.{(x,y):y=x}B.{(x,y):x=%7cy%7c}C.{(x,y):x2=y}D.{(x,y):}E.{(x,y):y=x3}参考答案：B参考解析：Eachansweriswritteninsetnotationandrepresentsasetoforderedpairs.AnswerA,forexample,isread“thesetofallorderedpairs(x,y)suchthaty＝x.”Ay＝xisalinearequationandpassestheverticallinetest.Bx=isa“V-shaped”graphthatisconcaveleftanddoesnotpasstheverticalline.Whenx＝5,forexample,y=5.Cx2=Visaparabolawhosevertexistheoriginandisconcaveup.Dy=isacurvestartingattheoriginandmovingupwardsinthepositivexdirection.Sinceitisasquarerootequation,itisnotdefinedwhenxisnegative.Therange,y,isrestrictedtopositivevaluesbecauseyequalsasquareroot.Ey＝x3isacubiccurvethatpassesthroughtheorigin.Thedomainisthesetofallrealnumbers,andeachxhasoneyassociatedwithit.[单选题]9.Adivuckrentalcompanycharges$20foradivuckrentalplus$0.15foreverymileover100milesWhichofthefollowinggraphsbestrepresentsthecostforrentingadivuck?A.B.C.D.E.参考答案：C参考解析：Thetruckrentalcosts$20forthefirst100miles.Therefore,forthefirst100miles,therewillbenochangeinthecostofrentingthetruckwhichismodeledbyahorizontalline.Afterthefirst100milesthechargewillbe$0.15permileaconstantincreaseof$0.15permile,whichismodeledbyalinewithapositiveslope[单选题]10.Iff(x)=x4-2x3+6x-1,thenf(-2)=______.A.-13B.19C.32D.11E.43参考答案：B参考解析：f(-2)=(-2)4-2(-2)3+6(-2)-1=16+16-12-1=19[单选题]11.If,thenf(f(4))=______.A.B.20C.D.8E.16参考答案：A参考解析：Since[单选题]12.Whatisthemaximumvalueoff(x)=4-(x+1)2?A.-1B.4C.1D.-4E.-5参考答案：B参考解析：Themaximumvalueofthefunctionisthey-coordinateoftheparabola’svertex.Forthefunctionf(x)=4-(x+1)2,thevertexis(-1,4).(Youcancheckthisbygraphingtheparabolaonyourgraphingcalculator.)Themaximumvalueis,therefore,4.Analternatewayofsolvingforthemaximumistofindtheyvaluewhenx=-b/2A.Inthiscase,x=(-2)/[2(-10]=-1,soy=4-(-1+1)2=4.[单选题]13.If4x3=-64,thenx=______.A.-1B.1C.D.E.4参考答案：C参考解析：4x3=-64,x3=-16,.[单选题]14.Ify/6+6=y/3,whatisthevalueofy?A.2B.4C.18D.24E.36参考答案：E参考解析：Multiplyby6toclearfractions,y+36=2y,y=36.[单选题]15.Forhowmanyorderedpairsofpositiveintegers(m,n)is2m+3n<9?A.NoneB.OneC.TwoD.ThreeE.Morethanfour参考答案：D参考解析：Ifm=1,then3n<7,ncouldbeeitherlor2.Sotherearetwoorderedpairsthatwork：(1,1)and(1,2).Ifm=2,then3n<5,ncouldonlyequalto1.So(2,1)isthethirdorderedpair.Ifm=3,then3n<3.Therearenointegervaluesofnthatsatisfytheinequality.Therefore,therearethreeorderedpairsthatsatisfytheinequality.[单选题]16.Threeyearsfromnow,Susan'sagewillbe3x+1.Representheragethreeyearsago.A.3x-6B.3x+4C.3x-5D.3x-2E.2x+1参考答案：C参考解析：Susan'sagenowcanbefoundbysubtracting3fromherage3yearsfromnow.Herpresentageis3x-2.Tofindherage3yearsago,subtractanother3.[单选题]17.If3/4=6/x=9/y,thenx+y=______.A.4B.8C.12D.16E.20参考答案：E参考解析：Writetheequation3/4=6/x=9/yastwoequations:3/4=6/xand3/4=9/y.Solvethefirstequationforx:3/4=6/x,3x=24,x=24/3=8.Solvethesecondequationfory:3/4=9/y,3y=36,y=36/3=12.Hence,x+y=8+12=20.[单选题]18.Forwhatvalueofpis(x-2)(x+2)=x(x-p)?A.-4B.0C.2/xD.4/4E.-x/4参考答案：D参考解析：Multiplyoneachsideofthegivenequation,(x-2)(x+2)=x(x-p).Theresultis:x2-4=x2-xp,so4=xpandp=4/x.[单选题]19.If(x+7)(x-3)=0,thenx=______.A.7or3B.7or-3C.-7or3D.-7or-3E.-4or-3参考答案：C参考解析：If(x+7)(x-3)=0,theneitherorbothfactorsmaybeequalto0.Ifx+7=0,thenx=-7.Also,ifx-3=0,thenx=3.Hence,xmaybeequalto-7or3.[单选题]20.Forx≠-1andx≠1/3,iff(x)=1-3xandg(x)=3x2+2x-1,then(x)=______.A.B.C.D.E.3x2+5x-2参考答案：B参考解析：[单选题]21.Iff(x)=x2+5and,thenf(g(7))=______.A.7.6B.-2C.54D.9E.12参考答案：E参考解析：Applytheinsidefunction,g(7),first..[单选题]22.Iff(x)=5x+3andg(x)=(x+1)/2,thenwhatisg(f(4))?A.12B.11C.23D.15.5E.23.5参考答案：A参考解析：f(4)=5(4)+3=23,g(23)=(23+1)/2=24/2=12.[单选题]23.Asalesmanearnsabasesalaryof$120perweekplusa5％commissiononallsalesover$600.Findhistotalearningsinaweekinwhichhesellsmdollarsworthofmerchandise,withmbeinggreaterthan600.A.150+0.05mB.150mC.120+0.05mD.120-0.05mE.90+0.05m参考答案：E参考解析：Commissionispaidon(m-600)dollars.Hiscommissionis0.05(m-600)or0.05m-30.Sohistotalearningswillbe：120+0.05(m-600)=90+0.05m.[单选题]24.Atthebeginningoftheday,thepricesofstocksXandYarethesame.Attheendoftheday,thepriceofstockXhasincreasedby1/20ofitsoriginalpriceandthepriceofstockYhasdecreasedby1/20ofitsoriginalprice.ThenewpriceofstockXiswhatfractionofthenewpriceofstockY?A.2/20B.19/21C.21/19D.18/20E.20/18参考答案：C参考解析：Pluggingin.SupposethepricesofstocksXandYwereeach$100atthebeginningoftheday.Then：ThenewpriceofstockXis$105.ThenewpriceofstockYis$95.stockX/stockY=105/95=21/19.[单选题]25.Ifxpercentof80is12,thenxpercentofwhatnumberis18?A.112B.115C.117D.118E.120参考答案：E参考解析：Percent==15%,18=0.15xWhole120=Whole,xpercentof120is18.[单选题]26.Ifx2-16>0,whatarethepossiblevaluesofx?A.x>4B.x<4C.x>-4D.-4E.x<-4orx>4参考答案：E参考解析：.Therefore,x<-4orx>4whenisgreaterthan16.[单选题]27.(3x-4)(2x-5)-(x+3)(4x-7)=______.A.B.C.D.E.参考答案：B参考解析：Simplifythepolynomial(3x-4)(2x-5)-(x+3)(4x-7)=(6x2-15x-8x+20)-(4x2-7x+12x-21)=(6x2-23x+20)-(4x2+5x-21)=(6x2-4x2)+(-23x-5x)+[20-(-21)]=2x2-28x+41[单选题]28.3(x-10)=5(x+20),x=______.A.-65B.-50C.-35D.-20E.-15参考答案：A参考解析：Theproblemstates3(x-10)=5(x+20).Multiply3x-30=5x+100,therefore-130=2x,and-65=x.[单选题]29.Iff(x)=16/x5andx≠0,thenf(-2)=______.A.-1/2B.1/2C.1/4D.1E.-1参考答案：A参考解析：Sincef(x)=16/x5,f(-2)=16/(-2)5=16/(-32)=-1/2.[单选题]30.Iff(x)=x2+3x,thenf(3x)=______.A.3(x2+3x)B.9(x+1)C.9x2+9xD.3x2+9xE.9x2+6x参考答案：C参考解析：Givenf(x)=x2+3x,f(3x)=(3x)2+3(3x),f(3x)=9x2+9x.[单选题]31.Ataxiridecost5dollarsforthefirst3milesplus85centsforeachadditionalmile.Iftheridewasxmilesindistanceandxwasanintegergreaterthan3,whichofthefollowingcouldexpressthecostoftheride,indollars?A.5+0.85(x-3)B.5(3)+0.85xC.5(3)+0.85(x+3)D.5+0.85(3-x)E.5+0.85x参考答案：A参考解析：Thefirst3milesoftheridecost$5.Iftheentireridecoveredadistanceofxmiles,therestoftheridecost$0.85(x-3).Sothecostoftheentirerideis5+0.85(x-3)[单选题]32.If(px+q)2=4x2+kx+25,whatisthevalueofk?A.50B.20C.10D.5E.2参考答案：B参考解析：Since(px+q)2=p2x2+2pqx+q2=4x2+kx+25.ThenP2=4andq2=25.Sop=±2andq=±5.Sincetheanswerchoicescontainonlypositivenumbers,sok=2pq=2·2·5=20.[单选题]33.If2y/7=y+3/4,theny=______.A.5B.9C.13D.17E.21参考答案：E参考解析：If2y/7=y+3/4,setthecross-productsequalandthensolvetheresultingequation.2y/7=y+3/4,4(2y)=7(y+3),8y=7y+21,y=21.[单选题]34.(4a+a-3)(4b-2b-b)=______.A.2a-bB.2ab-2bC.5ab–bD.5ab-3bE.3ab参考答案：D参考解析：Beforemultiplying,simplifyeachexpressioninsidetheparentheses:(4a+a-3)(4b-2b-b)=(5a-3)(4b-3b)=(5a-3)B.=5ab-3b.[单选题]35.If(x-1)2-(x-1)=0,then,______.A.x=0orx=2B.x=0orx=1C.x=-1orx=2D.x=1orx=2E.x=0orx=-1参考答案：D参考解析：Solution1:If(x-1)2-(x-1)=0,thenfactoringtheleftsideoftheequationgives(x-1)[(x-1)-1]=0whichsimplifiesto(x-1)(x-2)=0.Hence,xmaybeequalto1or2.Solution2:Substitutethepairofvaluesineachoftheanswerchoicesintothegivenequation,(x-1)2-(x-1)=0,untilyoufindapair,x=1orx=2,thatworks.[单选题]36.Inadramaclub,xstudentseachcondivibutedydollarstobuya$60giftfortheiradviser.Iffourmorestudentshadcondivibuted,each