國外英語考試-SAT Level 2-第1章數及其運算

國外英語考試-SATLevel2-第1章數及其運算[單選題]1.al,a2,a3,a4,as,….,anInthesequenceofpositiveintegersabove,（江南博哥）al=a2=1,a3=2,a4=3,andas=5.Ifeachtermafterthesecondisobtainedbyaddingthetwotermsthatcomebeforeitandifan=55,whatisthevalueofn?A.12B.10C.9D.8E.5正確答案：B參考解析：Followingthegivenruleforobtainingterms,writethetermsofthesequenceuptoandincluding55:1,1,2,3,5,8,13,21,34,55Since10numbersarelisted,n=10.[單選題]2.Whatisthenextterminthesequence:2,8,32,128…?A.512B.510C.452D.324E.550正確答案：A參考解析：Multiplyby4tofindthenextterminthesequence.Therefore,128×4=512.[單選題]3.Thefirstterminageomedivicsequenceis3andthe4thtermis81.Whatisthe10thtermofthesequence?A.177,147B.59,049C.19,683D.6,561E.2,187正確答案：B參考解析：Firstfindthecommonmultiplierneededtogetfrom3to81in3steps.Thisnumberis3.Sixmorestepsgetustothe10thterm.Therefore81×36=59049.[單選題]4.Afterthefirstterminthesequencebelow,eachodd-numberedtermcanbefoundbymultiplyingtheprecedingtermbyfour,andeachevennumberedtermcanbefoundbymultiplyingtheprevioustermby.Whatisthevalueofthe76thterm?240,60,…A.60B.80C.120D.240E.360正確答案：A參考解析：Thepatternalternatesbackandforthbetween240and60.Eacheven-numberedtermis60,sothe76thtermis60.[單選題]5.Thefirsttwotermsofasequenceare243and81.Eachtermafterthefirstisequaltoone-thirdofthepreviousterm.Whatisthevalueoftheeighthterm?A.B.C.D.E.正確答案：B參考解析：Thefirsteighttermsare243,81,27,9,3,1,,.[單選題]6.Whatisthenextterminthesequence:4,9,6,11,8,13?A.18B.16C.10D.9E.8正確答案：C參考解析：Seethepatternbelow.Thesequence4,9,6,11,8,13isformedbyadding5andthensubtracting3.Wecanseethatthenextterminthesequencewillbe10.[單選題]7.Ifthepatternoftheterms3continues,whichofthefollowingwouldbethesixthtermofthesequence?A.B.C.D.E.37正確答案：A參考解析：Thegivensequenceisageometricsequencewhosenthtermis.，=9(3)=27，.Thesixthtermis,therefore,.[單選題]8.Ifaispositiveandbisnegative,whichofthefollowingmustbenegative?A.B.C.D.E.正確答案：E參考解析：AnswersBandDarealwayspositivebecauseoftheabsolutevalue.AnswersAandCcouldresultinapositiveoranegativevalue,soyoucannotsaythattheexpressionsmustresultinanegativevalue.InanswerE,ispositiveandbisnegative.Theproductofapositivenumberandanegativenumberisalwaysnegative.[單選題]9.Ifaandbarebothpositive,aisodd,andbiseven,whichofthefollowingmustbeodd?A.b+2aB.abC.b/aD.abE.ba正確答案：D參考解析：Thinkofthetermsintheexpressionsasbeingoddoreven.Thetablebelowillustrateswhethertheanswersareoddorevenandgivesanumericexampleforeach.[單選題]10.aandbarepositive,aisevenandbisodd.Whichofthefollowingmustalsobeodd?A.abB.a/bC.a+2bD.baE.(ab)a正確答案：D參考解析：Anoddnumberraisedtoanevenpowerequalsanoddnumber.Take32=9,forexample,baisthecorrectanswer.[單選題]11.SetX=evenintegersandSetY=oddintegers.ThereforeX∩Y=______.A.primenumbersB.integersC.emptysetD.compositenumbersE.wholenumbers正確答案：C參考解析：Whentwosetshavenothingincommon,werefertotheirintersectionastheemptyset.Therearetwoappropriatewaystodenotetheemptyset:X∩Y={}orX∩Y=φ.[單選題]12.Ifaandbareintegersandthesumofabandbiseven,whichofthefollowingcouldbedivue?Ⅰ.aandbarebothodd.Ⅱ.aisevenandbisodd.Ⅲ.aisoddandbiseven.A.ⅠonlyB.ⅡonlyC.ⅢonlyD.ⅠandⅡE.ⅠandⅢ正確答案：E參考解析：Plug-in.StatementⅠ：ifaandbarebothodd,saysa=1andb=3,thenab+b=6.Sincethesumiseven,statementⅠistrue.StatementⅡ：1eta=2andb=3,thenab+b=9.Sincethesumisodd,thisstatementisfalse.StatementⅢ：leta=3andb=2,thenab+b=8,whichiseven.SobothstatementⅠandstatementⅢaretrue.[單選題]13.If0>ab3c4,thenwhichofthefollowingmustbedivue?Ⅰ.abispositiveⅡ.abisnegativeⅢ.abcisnegativeA.ⅠonlyB.ⅡonlyC.ⅢonlyD.ⅠandⅢonlyE.ⅡandⅢonly正確答案：B參考解析：Sinceab3c4isnegativeandc4ispositive,theninab3onevariableispositiveandtheothernegative.Henceab<0,ornegative,soⅠisfalseandⅡistrue.Nowlet’slookatⅢ.Youknowabisnegative—butyoudon’tknowathingaboutC.Itcouldbepositiveornegative.SocrossoutE..[單選題]14.x,y,andzarepositiveintegers.Whichofthefollowinglistsallthepossiblewaysforx+y+ztobeanoddnumber?I.Oneofthenumbersisodd.II.Twoofthenumbersareodd.III.Threeofthenumbersareodd.A.IB.IandIIC.IandIIID.IIandIII正確答案：C參考解析：I.Oneofthenumbersisodd.Letxbeodd.Letyandzbeeven.y+ziseven.Anevenplusanoddisodd,sox+y+zisodd.[單選題]15.WhichofthefollowingisNOTanirrationalnumber?A.B.C.eD.1.666...E.正確答案：D參考解析：Irrationalnumbersarenoterminatingandnonrepeating.1.666...isnotirrational,sinceitisarepeatingdecimal.[單選題]16.Ifthegraphofcontainsthepoint(0,1),thenwhichofthefollowingmustbeadivuestatement?A.a=bB.b=0C.b=1D.b=-1E.a=1正確答案：C參考解析：Theequationrepresentsanellipsewithcenter(0,0).Sincethegraphcontainsthepoint(0,1),,,b=1.AnswersAandEmayalsobetrue,butthequestionaskswhichstatementsmustbetrue.AnswerBcanbeimmediatelyeliminated,sinceyoucannotdividebyzero.[單選題]17.Ifand,whichofthefollowingisdivueabouttheirgraphs?A.Theyarethesame.B.Theyaretheline.C.Theyarethesameexceptwhenx=4.D.Theyarethesameexceptwhenx=-4.E.Theydonotshareanypoints.正確答案：C參考解析：Noticethatthefunction.Undefinedwhenx=4,sinceyoucannotdividebyzero.Bothgraphslookliketheline,butf(x)isundefinedatx=4.YoucancheckyouranswerbygraphingthetwofunctionsandcheckingtheTableonyourgraphingcalculatortofindError”forthey-coordinateoff(x)whenx=4.[單選題]18.Theoperationisdefinedas:nm=2n/mIfnandmdonotequalzero,thenforallofthefollowingvaluesnm=mnEXCEPT______.A.n=mB.n=-mC.m=-nD.n=1andm=1E.n=2andm=1/2正確答案：E參考解析：Ifnm=mn,then:2n/m=2m/n,2n2=2m2,n2=m2.AnswersAthroughDarealltruestatements.AnswerEisnottruesince.[單選題]19.Thesymbol☆representsoneofthefundamentalarithmeticoperators：+,-,×,or÷.If(x☆y)÷(y☆x)=1forallpositivevaluesofxandy,then☆canrepresent______.A.+onlyB.÷onlyC.+or×onlyD.-or×onlyE.+,-,×,÷正確答案：C參考解析：(x×y)÷(y×x)=(xy)/(yx)=1and(x+y)÷(y+x)=(x+y)/(y+x)=1.[單選題]20.Let@representoneofthefourbasicarithmeticoperationssuchthat,foranynonzerorealnumbersPandQ,P@0=PandP@Q=Q@P.Whicharithmeticoperation(S)doesthesymbol@represent?A.×onlyB.+onlyC.-onlyD.-and×E.+and÷正確答案：B參考解析：IfP@Q=P,thensymbol@canrepresenteitheradditionorsubtraction,butnotmultiplicationordivision.SinceitisalsogiventhatP@Q=Q@P,theoperation@iscommutative.Sinceadditioniscommutativeandsubtractionisnotcommutative,thesymbol@representsonlyaddition.[單選題]21.Whichofthefollowingmustbedivue?I.aΦb=bΦaII.aΦ(a+1)=a2III.a/2Φb/2=aΦb/2A.IonlyB.IIonlyC.IIIonlyD.IandIIIonlyE.IIandIIIonly正確答案：B參考解析：DeterminewhethereachRomannumeralequationistrueorfalsewhenaΦb=ab-a.~I.SincebΦa=ab－bandab－aisnotnecessarilyequaltoab－b,aΦb=bΦaisnotalwaystrue.EquationIneednotbetrue.~II.ToevaluateaΦ(a+1),letb=a+1:aΦ(a+1)=a(a+1)-a=a2+a－a=a2.Hence,equationIImustbetrue.[單選題]22.Letbedefinedforallrealvaluesofxbytheequation=2x+1,If3-=x,thenx=______.A.2/3B.1C.3/2D.2E.3正確答案：A參考解析：If=2x+1and3-=x,then3-(2x+1)=x,3-2x-1=x,2/3=x[單選題]23.Thelegendinacertainpictographusesrepresentacertainnumberofcomputers.Thepictographbelowrepresents1,750computers.Thereforerepresentshowmanycomputers?A.250B.500C.750D.1,000E.1,250正確答案：B參考解析：3.5symbolsrepresent1,750computers.1.750÷3.5=500.Eachrepresents500computers.[單選題]24.If3x+2=81,thenx=______.A.5B.4C.3D.2E.1正確答案：D參考解析：Usetherulesofexponentstorename81as34.81=34so34=3x+2,Therefore,x+2=4x=2.[單選題]25.Inaclassroomof25students,10ofthestudentsarefemales.Whatistheratioofmalestofemalesintheclassroom?A.5:2B.2:5C.5:3D.2:3E.3:2正確答案：E參考解析：Becausethereareatotalof25students,including10females,theremustbe25-10=15males.Sotheratioofmalestofemalesis.[單選題]26.WhichofthefollowingchoicescouldbeequaltosetZifX={2,5,6,7,9}andY={2,5,7}X∪Y∪Z={1,2,3,4,5,6,7,8,9}X∩Z={2,6}Y∩Z={2}A.Z={1,4,8}B.Z={1,3,8}C.Z={1,3,4,8}D.Z={1,2,3,4,6,8}E.Z={1,2,3,5,6,8}正確答案：D參考解析：Weknowthat:X={2,5,6,7,9}andY={2,5,7},X∪Y∪Z={1,2,3,4,5,6,7,8,9}.ThistellsusthatZmustcontain{1,3,4,8}becausetheseelementsareintheunionofX,Y,andZbutnotinsetXandnotinsetY.Wealsoknowthat:X∩Z={2,6},Y∩Z={2}.ThistellsusthatZmustalsocontain{2,6}.OnlychoiceDcontainsalltheseelements.Z={1,2,3,4,6,8}[單選題]27.Twomovietheaters.TheaterAandTheaterB.sellticketsattwodifferentprices.TheaterAsellsticketsat$6perticket.AndTheaterBsellsticketsat$8perticket.TheaterAsold15.000tickets.HowmanyticketsdoesTheaterBneedtoselltoearnthesameamountofmoney?A.90,000B.45,000C.15,000D.11,250E.7,500正確答案：D參考解析：TheaterA:TheaterAearned$6.15.000=$90.000.TheaterB,Divide$90.000bythe$8ticketpriceforTheaterB:$90.000÷$8=11.250.TheaterBmustsell11250ticketstoearnthesameamountasTheaterA.[單選題]28.Onamapthatisdrawntoscale,twotownsthatarexmilesapartarerepresentedasbeing2inchesapart.Iftwoothertownsarex+4milesapart,howmanyinchesapartwouldtheybeonthesamemap?A.2(x+4)B.6C.2x/(x+4)D.2(x+4)/xE.6/x正確答案：D參考解析：Letyrepresenttheinchesapartbetweenthosetwoothertowns.Sincethemapis“toscale”,thecorrespondingmeasuresareproportional：.Cross-multiply:.Dividebyx:.[單選題]29.Atacollegebasketballgame,theratioofthenumberoffreshmenwhoattendedtothenumberofjuniorswhoattendedis3：4.Theratioofthenumberofjuniorswhoattendedtothenumberofseniorswhoattendedis5：6.Whatistheratioofthenumberoffreshmentothenumberofseniorswhoattendedthebasketballgame?A.5：8B.3：4C.3：5D.2：3E.1：3正確答案：A參考解析：FreshmentoJuniorsis3：4.andJuniorstoSeniorsis5：6.Sincetheleastcommonmultipleof4and5is20.multiplythetermsofthefirstratioby5andthesecondoneby4.Thentheratiooffreshmentojuniorstoseniorsisl5:20:24.Therefore,15:24istheratiooffreshmentoseniors.15:24=15/24=5/8[單選題]30.TheratioofDan'sheighttoPhil'sheightisproportionaltotheratioofJim'sheighttoMike'sheight.IfDanis76inchestallPhilis80inchestallandMikeis74inchestall.HowtallisJim?A.70.3in.B.77.9in.C.79.3in.D.82.2in.E.84.5in.正確答案：A參考解析：D=Dan'sheight.P=Phil'sheight.M=Mike'sheight.J=Jim'sheight.Writeaproportion..SolveforJ.80J=5.624J=70.3inches.[單選題]31.Billcaninspectacaseofcellphonesin6hours.JackcaninspectthesamecaseofcellPhonesin4hours.Afterworkingaloneforlhour,Billstopsforlunch.Aftertakinga30-minutelunchbreak.BillandJackworktogethertoinspecttheremainingcellphones.HowlongdoBillandJackworktogethertocompletethejob?A.1hr.andl2minB.1hr.and24minC.2hrsD.2hrsandlominE.2hrsand20min正確答案：C參考解析：IfxrepresentsthenumberofhoursBillandJackworktogether,thenthetotalnumberofBill’sworkinghoursisx+1.Bill’srateofworkis1/6ofthejobperhour,andtheJack’srateofworkis1/4ofthejobperhour.Hence,(x+1)/6+x/4=1.x=2.[單選題]32.Ittook12men4hourstobuildasdivucture.Workingatthesamerate,howmanyadditionalmencouldhavebeenhiredinorderforthejobtohavetaken1hourless?A.twoB.threeC.fourD.six.E.eight正確答案：C參考解析：Thenumberofmenworkingandthehoursneededforthementocompletethejobareinverselyrelated.Ifxrepresentsthenumberofadditionalmenneededtocompletethejobin3hours,then4×12=3(12+x),x=4.[單選題]33.Whichofthefollowingdescribesonepossiblerelationshipbetweenthevaluesofxandyshowninthefollowingdiv?A.yvariesdirectlyasxB.yvariesinverselyasxC.yvariesdirectlyasthesquareofxD.yvariesinverselyasthesquareofxE.yvariesdirectlyasthesquarerootofx正確答案：D參考解析：Sincexincreases,ydecreases.Therefore,onlychoicesB.andD.arepossibilities.Ifyvariedinverselyasx,thenthetwovariableswouldalwayshavethesameproduct,butthisisnotthecase：1×8=8,2×2=4,and4×0.5=2.However,y×x2wouldalwayshavethesameproduct.Therefore,thecorrectanswerisD..[單選題]34.Ifrlifeboatscancarryppassengers,howmanylifeboatsareneededtocarrympassengers?A.rm/pB.pr/mC.prmD.pm/rE.m/rp正確答案：A參考解析：Letnbethenumberoflifeboatsneededtocarrympassengers.Youcancomparelifeboatstopassengers.r/p=n/mCrossmultiply.Dividebyp，n=rm/p.[單選題]35.Twoteenagerscanpaintagaragein6hours.Howmanyhourswouldittake3teenagerstopaintthesamegarage?A.3/2B.5/2C.8/3D.3E.4正確答案：E參考解析：Letxrepresentthetimethreeteenagerstaketopaintagarage,then.3x=2×6.x=12/3,x=4.[單選題]36.Inthecorrectlyworkedoutadditionexamplebelow,whatisthegreatestpossiblevalueofdigitB?A.9B.8C.6D.5E.4正確答案：C參考解析：Since2iscarriedoverfromaddingthedigitsinthefirstcolumn,inthesecondcolumnA+B+B+1=14,soA+2B=13.SinceBmustbeaninteger,Acannotbe0.Hence,thegreatestpossiblevalueofdigitBoccurswhenA=1andB=6.[單選題]37.Alocalnewspapercompanyprints520pagesofthenewspaperevery30minutes.Howmanypageswillitprintin5hours?A.2,600pagesB.86.7pagesC.5,200pagesD.10,400pagesE.1,300pages正確答案：C參考解析：Letp=thenumberofpagesprintedin5hours.Setupaproportiontosolveforp,rememberingtouseconsistentunitsfortime(eitherminutesorhours).Let’schange30minutesto0.5hours.520/0.5=p/5,p=5.200pages.[單選題]38.Philhasxquarters,ydimes,andznickelsandnothingelse.WhichofthefollowingexpressionsrepresentstheamountofmoneythatPhilhas,indollars?A.0.25x+0.10y+0.05zB.2.5x+1.0y+0.5zC.25x+10y+5zD.0.25x+0.10y+0.5zE.25x+10y+50z正確答案：A參考解析：Multiplythevalueofeachcoinbythenumberofcoinsandadd.0.25x+0.10y+0.05z.[單選題]39.Juliedrinks4bottlesofwatereveryday.Howmanybottlesofwaterdoesshedrinkinaweek?A.20B.22C.24D.26E.28正確答案：E參考解析：Justthink,4×7=28.Oryoucanwriteaproportion.B=28.[單選題]40.Onacertainmap,10milesisrepresentedby1.5centimeters.Whatisthedistanceonthemapthatrepresents40miles?A.4centimetersB.5centimetersC.6centimetersD.7centimetersE.8centimeters正確答案：C參考解析：Justthink,eachmileis1.5centimeters.4×1.5=6.Orwriteaproportion.10D=60D=6centimeters.[單選題]41.Intheexpressionan,nisanevenpower.Whichofthefollowingexpressionsdoesnothaveevenpower?A.an