sat2數學6套satii level1level2練習題

QuestionQuestion#1:Iff(x)=xandg(x)=√x,x≥0,whatarethesolutionsoff(x)=x=x1=1,x2=-x1=1,x2=x=x=-Question#2:WhatisthelengthofthearcABinthefigurebelow,ifOisthecenterofcircleandtriangleOABisequilateral?Theradiusofthecircleis?2·3·4·?/Question#3:Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6?Eachdicehassidesnumberedfrom1to6.Question#4:AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HefromAtoBataspeedof15miles/hourwhilehisreturnspeedis10miles/hour.Whatisdistancebetweenthe2distancebetweenthe21118151210Question#5:Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeofacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.Whatistheheightofa/?a/?a+Question#6:Howmanyintegersxaretheresuchthat2x<100,andatthesametimethenumber2x+2isanintegerdivisiblebyboth3and2?12345Question#7:sin(x)cos(x)(1+tan2(x))sin(x)+Question#8:If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldbethevalueofx+yexcept:Question#9:Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofthex+9Question#10:Theinequality9Question#10:Theinequality|2x-1|>5mustbetrueinwhichoneofthefollowingx<-x>x>III,IIandIandIIonlyIandIIIIQuestion#1:Iff(x)=xandg(x)=√x,x≥0,whatarethesolutionsoff(x)=(a)x1=1,x2=-(b)x1=1,x2=(c)x=(d)x=(e)x=-oAnswer:x=√x,ifwesquaretheleftandrighttermsoftheequationwegetx2=x·(x-1)=0andx1=1,x2=Question#2:WhatisthelengthofthearcQuestion#2:WhatisthelengthofthearcAB,ifOisthecenterofthecircleandOABisequilateral?Theradiusofthecircleis?(a)(b)2·(c)3·(d)4·(e)oAnswer:OABequilateralsoangleAOBisequaltoTheratiobetweentheAOBangleand360oisequaltotheratiobetweenthelengthofthearcABandthecircumferenceofthecircle.60o/360o=arcAB/(2?·arcAB=3·Question#3:Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6?dicehassidesnumberedfrom1to?(a)(b)(c)(d)(e)oAnswer:Theprobabilitytohavea(5,6)(d)(e)oAnswer:Theprobabilitytohavea(5,6)combinationisequaltotheprobabilitythatdice1is5anddice2is6,plustheprobabilitythatdice2is5anddice1is6.P=1/6·1/6+1/6·1/6=1/36+1/36=(c)isthecorrectQuestion#4:AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HebikesfromAtoBataspeedof15miles/hour,whilehisreturnspeedis10miles/hour.Whatisthedistancebetweenthe2?(a)18(b)15(c)12(d)10(e)11Answer:Thetotaltimet=tAB+tBA=dAB/(15miles/hour)+dAB/(10miles/hour)=dAB/(6miles/hour).dAB=dAB/(6miles/hour)·3hours=18isthecorrectQuestion#5:Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.WhatistheheightofC2??(a)a/(b)a/(c)a/(d)2·a/(e)a+oAnswer:Thevolumeofthe(e)a+oAnswer:Thevolumeofthecubeisa3.ThisisequaltohalfthevolumeofthecylinderC2.a3=?·a2·h/2,wherehistheheightofthecylinder2·a3=?·a2·h,2·a=?·h,soh=2·a/?and(d)isthecorrectQuestion#6:If2x<100andxisaninteger,howmanyofthe2x+2integerswillbeby3andby?(a)(b)(c)(d)(d)oAnswer:26=64and27=128.If2x<100,thenthehighestvalueofxis6.Possiblevaluesforx:0,1,2,3,4,,5,6.2x+2cantakethevalues3,4,6,10,18,34,Outofthesevalues,only6,18and66aredivisibleby3andby2.Thecorrectansweris(c).Question#7:sin(x)cos(x)(1+tan2(x))?tan(x)+sin(x)+oAnswer:sin(x)cos(x)(1+tan2(x))=sin(x)cos(x)(1+sin2(x)/cos2(x))=sin(x)cos(x)[(cos2(x)+sin2(x))/cos2(x)]=sin(x)cos(x)[1/cos2(x)]=sin(x)/cos(x)=Question#8:If5xy=210,andxandyQuestion#8:If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldthevalueofx+y?(a)(b)(c)(d)(e)oAnswer:5xy=210soxy=42=2·3·7.Thefollowingproductsofintegersequalto42:(6·7)or(2·21)(14·3)or(42·6+7=2+21=14+3=42+1=TheonlyanswerthatisNOT43,13,23or17is(d),Question#9:Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofsumx+?(a)(b)(c)(d)(e)oAnswer:Theaverageofthe5numbersis(24+6+12+x+y)/5.(24+6+12+x+y)/5=1124+6+12+x+y=11·24+6+12+x+y=x+y=Question#10:Theinequality|2x-Question#10:Theinequality|2x-1|>5mustbetrueinwhichoneofthefollowingx<-x>x>(a)II(b)I,IIand(c)IandII(d)IandIII(e)IoAnswer:|2x-1|>-5>2x-1or2x-1>-4>2xor2x>-4>2xresultsinx<-22x>6resultsinx>3Iansweristrue,IIanswerisalsotrue,butIIIanswerisfalse,sothecorrectisQuestion#1:50%ofUScollegestudentsliveoncampus.Outofallstudentslivingoncampus,40%aregraduatestudents.WhatpercentageofUSstudentsaregraduatestudentslivingonQuestion#2:IntheQuestion#2:Inthefigurebelow,MNisparallelwithBCandAM/AB=2/3.WhatisthebetweentheareaoftriangleAMNandtheareaoftriangleQuestion#3:Ifa2+3isdivisibleby7,whichofthefollowingvaluescanbe7894Question#4:WhatistheQuestion#4:Whatisthevalueofb,ifx=2isasolutionofequationx2-b·x+1=Question#5:Whichvalueofxsatisfiestheinequality|2x|<x+112Question#6:Ifintegersm>2andn>2,howmany(m,n)pairssatisfytheinequalitymn23457Question#7:TheUSdeerpopulationincreaseis50%every20years.Howmaytimeswillthedeerpopulationbein60yearsQuestion#8:Findthevalueofxifx+Question#8:Findthevalueofxifx+y=13andx-y=23694QuestionThenumberofmedalswonatatrackandfieldchampionshipisshowninthetableabove.WhatthepercentageofbronzemedalswonbyUKoutofallmedalswonbythe2Question#10:Theedgesofacubeareeach4incheslong.Whatisthesurfacearea,squareinches,ofthis321441參考答Question#1:參考答Question#1:50%ofUScollegestudentsliveoncampus.Outofallstudentslivingoncampus,40%aregraduatestudents.WhatpercentageofUSstudentsaregraduatestudentslivingon(a)(b)5%(c)(d)(e)Answer:Ifx=UScollegestudents,y=USgraduatestudents,z=USgraduatestudentslivingoncampus,y=andz=.4·y=.4·(.5x)=ThepercentageofUSstudentsthataregraduatestudentslivingoncampusisQuestion#2:Inthefigurebelow,MNQuestion#2:Inthefigurebelow,MNisparallelwithBCandAM/AB=2/3.WhatisthebetweentheareaoftriangleAMNandtheareaoftriangle(a)(b)(c)(d)(e)?Answer:TrianglesABCandAMNaresimilar,sothelengthsoftheircorrespondingsidesareproportional.ThismeansMN/BC=2/3andtheratiobetweentheiraltitudesisalso2/3.TheareaoftriangleABCis(BC·H)/2whereHisthealtitudeofABC.TheareaoftriangleAMNis(MN·h)/2wherehisthealtitudeofAreaAMN/AreaABC=(2/3)·(2/3)=Question#3:Ifa2+3isdivisibleQuestion#3:Ifa2+3isdivisibleby7,whichofthefollowingvaluescanbe?(a)(b)(c)(d)(e)o72+3=52=2·2·82+3=92+3=84=2·2·3·112+3=124=2·2·42+3=Thecorrectanswerisa=Question#4:Whatisthevalueofb,ifx=2isasolutionofequationx2-b·x+1=?(a)(b)-(c)(d)-(e)oAnswer:x=(d)-(e)oAnswer:x=2isasolutionoftheequation,so22-b·2+1=0.4-2·b+1=0,b=Question#5:Whichvalueofxsatisfiestheinequality|2x|<x+1(a)-(b)(c)(d)-(e)oAnswer:Wecanwritetheinequalityas-(x+1)<2xOR2x<x+-x-1<2x;3x+1>0x>-2x<x+1x<1Outof2x<x+1x<1Outofthegivenanswers,theonlyxthatsatisfiestheinequalityisx=Question#6:Ifintegersm>2andn>2,howmany(m,n)pairssatisfytheinequalitymn<2(b)(c)(d)(e)Answer:Thelowestmnpossibleisform=3andn=3.mn=27.Thispairsatisfiestheinequality.m=3andn=4thenmn=81.Thisisalsolessthan100.Thispairalsosatisfiesthem=3andn=5thenmn=243.Foralln>5,mn>100.m=4andn=3thenmn=64.Thisisalsolessthan100.Thispairsatisfiesthem=4andn=4thenmn=256.Foralln>4,mn>100.Inconclusionthereareonly3combinationsthatsatisfytheoQuestion#7:TheUSdeerpopulationincreaseisQuestion#7:TheUSdeerpopulationincreaseis50%every20years.Howmaytimeslargerwillthedeerpopulationbein60years?(a)?(b)(c)(d)(e)oAnswer:xbeingthepresentnumberofdeer,in20years,thenumberwillbe+In40yearsthenumberwillbe(1+.5)·(1+.5)·xandin60years(1+.5)·(1+.5)·+.5)x=(1+Theanswerwillbe(1+.5)3=Question#8:Findthevalueofxifx+y=13andx-y=(a)?(b)(c)(d)(e)oAnswer:Wenoticethatifweaddthe2equationsweget2x=18,oAnswer:Wenoticethatifweaddthe2equationsweget2x=18,thenx=9iscorrectQuestion?ThenumberofmedalswonatatrackandfieldchampionshipisshowninthetableWhatisthepercentageofbronzemedalswonbyUKoutofallmedalswonbythe2????????????(a)(b)(c)(d)(e)oAnswer:Thenumbersofmedalswonbythe2teamsis3+2+1+4+4+1=ThenumberofbronzemedalswonbyUKis1.Thepercentagewillbe1/15·100=Question#10:Theedgesofacubeareeach4incheslong.Whatisthesurfacearea,squareinches,ofthis?321441oAnswer:EachfaceoftheoAnswer:Eachfaceofthecubehasanareaof4×4=16squareThetotalsurfaceareaofthecubeis(6faces)x(16squareinches)=96squareQuestion#1:Thesumofthetwosolutionsofthequadraticequationf(x)=0isequalto1andtheproductofthesolutionsisequalto-20.Whatarethesolutionsoftheequationf(x)=16-x?x1=3andx2=-x1=6andx2=-x1=5andx2=-x1=-5andx2=x1=6andx2=?Ifa,barethesolutionsoftheequationf(x)=0,ab=-20a+b=oWesolvethissystemofequations,anda=5,b=-4.Thenf(x)=(x-f(x)=x2-x-f(x)=16-x2-x-20=16-x2=x1=6andx2=-??Question#2:Inthe(x,y)coordinateplane,threelineshavetheequations:l1:y=ax+1l2:y=bx+l3:y=cx+WhichofthefollowingmaybevaluesWhichofthefollowingmaybevaluesofa,bandc,iflinel3isperpendiculartobothlinesand(a)a=-2,b=-2,c=(b)a=-2,b=-2,c=(c)a=-2,b=-2,c=-(d)a=-2,b=2,c=(e)a=2,b=-2,c=oIflinel3isperpendiculartobothlinesl1andl2,thenl1mustbeparalleltol2.slopesofl1andl2shouldbeequal,slopel1=slopel2,andtheslopel3=-1/slopel1.a=-2,b=-2,c=.5istheonlyanswerthatsatisfiestheseconditions.Question#3:Themanagementteamofacompanyhas250menand125women.If200ofthemanagershaveamasterdegree,and100ofthemanagerswiththemasterdegreewomen,howmanyofthemanagersaremenwithoutamaster?(a)(b)(c)(d)(e)oAnswer:If200ofthemanagershaveamasterdegree,and100ofthemanagerswithamasterdegreearewomen,then100ofthemanagerswithamasterdegreearemen.Thecompanyhas250menmanagersand100ofthemanagerswithamasterdegreearemen,sothenumberofmanagersthataremenwithoutamasterdegreeis250-100=Question#4:Inthefigurebelow,theareaofsquareABCDisequaltothesumoftheoftrianglesABEandDCE.IfAB=6,thenCE?56234AreaABCD56234AreaABCD=AreaABE=AreaDCE=DC·CE/2=oTheproblemstatesthattheareaofsquareABCDisequaltothesumoftheareasoftrianglesABEandDCE.AB2=AB·BE/2+AB·CE/2AB=BE/2+CE/2BE=CE+AB=CE/2+AB/2+CE/2AB/2=CE/2+CE/2CE=CE=?Ifαandβare?Ifαandβaretheanglesoftherighttriangleshowninthefigureabove,thensin2α+sin2βequal1osin2α+sin2β=sin2α+sin2(90o-α)=sin2α+cos2α=Question#6:Theaverageofnumbers(a+9)and(a-1)isequaltob,whereaandbintegers.Theproductofthesametwointegersisequalto(b-1)2.Whatisthevalueof?a=a=a=a=a=o1/2(a+9+a-1)=b(a+9)(a-1)=(b-1)2Weneedtosolvethissystemofequations.1/2(2a+8)=ba+4=(a+9)(a-1)=(a+a2+9a-a-9=a2+a2+9a-a-9=a2+6a+92a=18a=轉載請注明來自天道Question1:Whatistheclosestapproximationofthesolutionoftheequation2x-1=3x+?(a)-(b)-(c)-(d)(e)olog(2x-1)=log(3x+(x-1)log2=(x+1)log3x(log2-log3)=log3+log2x=(log3+log2)/(log2-xisaprox.=-Question#2:Whatistherangeof(x-y)if3<x<4and-2<y<-?(a)4<x-y(b)1<x-y(c)1<x-y(d)4<x-y(e)3<x-yoAnswer:Wecandeterminetherangeof-1<-y<Wedeterminetherangeofx-ybyaddingtherangesWedeterminetherangeofx-ybyaddingtherangesofxand-Therefore,4<x-yQuestion#3:AbustravelsthedistancedfromNewYorktoBoston.t1hoursafterthebusleftNewYork,acarstartstotravelthesamedistancedfromNewYorktoBoston.BothvehiclesreachBostonatthesametime.Findanexpressionfordasafunctionoft1,thespeedofthebusv1andthespeedofthecar?(a)d=v1t1/(v2-(b)d=v1v2t1/(v2-(c)d=v1t1/(v2+(d)d=v1v2t1/(v2+(e)d=oAnswer:Iftisthedurationofthetravelofthebus,d=v1td=v2(t-Therefore,v1t=v2(t-t1)t=v2t1/(v2-v1)d=v1v2t1/(v2-?Findthevalueofxif:x+y+z=5x+y-z=x-y=(a)-(b)-(c)(d)(e)oAnswer:Wenoticethatifweaddequations(e)oAnswer:Wenoticethatifweaddequations1and2wecaneliminatez:x+y+z++y-z=5+x+y=4Atthispointwehaveasystemof2linearequationswith2variables,xandy:x-y=2x+y=Ifweaddthese2equations,weget2·x=6andx=Question#5:Acamerahasapriceof300dollars.Itspriceislowered10%andincreased10%.Whatisthefinalsellingpriceofthe?(a)(b)(c)(d)(e)oAfteritisloweredby10%,thepriceis$300-$30=A10%increaseofa$270priceis$27,sothefinalpriceis$270+$27=Question#6:Theequation2x2-2x-60=0hasthefollowing2?(a){-5,(b){5,-(c){-5,-(d){-5,(e){5,oAnswer:2x2-2x-60=0x2-x-30=0TheoAnswer:2x2-2x-60=0x2-x-30=0Thesumofthesolutionsis1andtheproductis-30sothesolutionsare{-5,Question#7:Thesideofacubeistwotimestheradiusofasphere.Whatistheratioofvolumeofthecubetothevolumeofthe?(a)(b)(c)(d)(e)oAnswer:Iflisthesideofthecube,thevolumeofthecubeis:Vcube=l3.ThevolumeofthesphereisVsphere=4?r3/3=4?(l/2)3/3=(?/6)l3Vcube/Vsphere=Question#8:Iftan(2x)=2,tan(x)isequivalenttowhichofthefollowing?(a)(b)1+(c)1-(d)(1-tan(x))(1+(e)(1-oAnswer:tan(2x)=2tan(x)/(1-tan2(x))2=2tan(x)/(1-tan2(x))tan(x)=1-tan(x)=(1-tan(x))(1+Question#9:WhatistheclosestapproximationofQuestion#9:Whatistheclosestapproximationofthevalueofangleainthefigurebelow,AB=7,BC=11andCA=?(a)(b)(c)(d)(e)oBC2=AB2+CA2-112=52+72-121=25+49-cos(a)=-a=arccos(-47/70)=Question#10:Forsomepositiverealnumber‘a’,thefirst3termsofaprogressionarea-1,a+3and3a+1.Whatisthenumericalvalueofthefourth?(a)(b)(c)(d)(e)oa+3=k(a-1)3a+1=k(a+(c)(d)(e)oa+3=k(a-1)3a+1=k(a+3)(a+3)(a+3)=(3a+1)(a-1)a2+6a+9=3a2-2a-12a2-8a-10=a2-4a-5=thesolutionsofthisequationare5and-1.Theonlypositivesolutionis5,sotheprogressionis4,8,16.Thefourthtermwillbe16·2=32轉載請注明來自天道Question#1:Iff(x)=(2x+5)/(4x-7),whatvaluedoesf(x)approachxgetsinfinitelylarger??1oAnswer:Asxgetsinfinitelylim[(2x+5)/(4x-7)]=lim[(2+5/x)/(4-7/x)]=(2+0)/(4-0)=2/4=1/2Question#2:Inthefigurebelow,whatisthelengthofthearcAB,ifisthecenterofthecircleandtriangleOABisequilateral?Theofthe?2·?3·?4·?meanstheAOBangleisoOABofthe?2·?3·?4·?meanstheAOBangleisoOABthelengthofthearcABandthecircumferenceofthecircle60o/360o/(2?·=3·CD.WhatistheareaoftriangleABD??34689oAnswer:Theareaof34689oAnswer:TheareaoftriangleABDisthealtitudefromDtoAB.=(1/2)4·3=Question#4:Whatisthedistancespacebetweenthepoints?coordinates(-1,5,3)and(2,6,-5(d)(e)oAnswer:Thecoordinatesofthe2points=-= == = =-Thedistanceinspacebetweenwithcoordinates(-1,3)and6,-1)squared2222=(d)(e)oAnswer:Thecoordinatesofthe2points=-= == = =-Thedistanceinspacebetweenwithcoordinates(-1,3)and6,-1)squared2222=x)+(y-y)+z)[(-1+(-2))2+(5---d12 122+(3-(- ]=9+1+16=d=Question#5:Inthestandard(x,y)coordinateplane,thegraphof(x–2)2+(y+2)2=16isacircle.Whatistheareaenclosedbythiscircle,expressedinsquarecoordinateunits??4·8··?·?·?Answer:Wecomparetheequationofthecircle,(x–+(y+o22x1)+(y-y1)=16withthegeneralequationofacircle:(x–whereRistheradiusoftheWenoticethattheradiusTheareaofthecircleofourcircleis√16=?·42=16·Question#6:|3-5|-|2-1|+|-5|5679(d)2oAnswer:|3-5|=|-2||2|-|31|=5||1|=|2-1|+|-5|=2-1+(d)2oAnswer:|3-5|=|-2||2|-|31|=5||1|=|2-1|+|-5|=2-1+5=Question#7:a,bandcarethesidesofanytriangle,whichof?followinginequalitiesisnota·b>a+bca+b+ca(a+b)·(b+c)>Answer:Thefirstansweristrue,sincetheproductof2positiverealswillbepositive.Thesecondandthefourthanswerswillalsobetrue,sincethesumof2sidesofatriangleisalwayshigherthanthethirdside.Thefifthanswersisalsotruebecauseitisjustamultiplicationofthesecondandfourthinequalitiesofpositiveterms.Answerthreeshouldbetheonethatisnottrue,andwecanverifythisresultwithanexample:anisoscelestrianglewitha=3,c=3,b=10willsatisfytheinequality.oQuestion#8:Foranyxsuchthat0<x<?/2,theexpression(1-+(1-cos2x)/sin(x)isequivalent?sin(x)-sin(x)+cos(x)o(1-sin2x)/cos(x)+(1-cos2x)/sin(x)=cos2x/cos(x)+sin2x/sin(x)=sin(x)+cos(x).Question#9:Alinehasparametricequationsx=t+3andy=t+9.?oftheline39145Answer:Fromthefirstequation,x=Question#9:Alinehasparametricequationsx=t+3andy=t+9.?oftheline39145Answer:Fromthefirstequation,x=t+3,t=x-Wesubstitutetinthesecondequation:y=t+9=x-3+9=+mistheslopeandntheoffsetandtheslopeofy=x+6isoQuestion?Whichofthefollowingequationsbestmodelsthedatainthetable??????-2=====4·5·5·5·-1ofthe5answersforx=0:o5·y=-2=4·y==45·y==55·y=-1=x- 37y5(e)y=5·1.30+1=and(c)mustbethecorrectanswer.Wecanverifyatthispointtheresultsofy=5·1.3xforx=-5,x=3andx=7(e)y=5·1.30+1=and(c)mustbethecorrectanswer.Wecanverifyatthispointtheresultsofy=5·1.3xforx=-5,x=3andx=7轉載請注明來自天道Question1:Ifthevalueoftan(-2a)is2,whatisthe?-2-43oWeknowthattan(θ)=-tan(-θ),anyθ,sotan(2a)=-2Question#2:Whatissec(a)sin(a)+csc(a)cos(a),ifa=?21-osec(a)sin(a)+csc(a)cos(a)=[1/cos(a)]sin(a)+=sin(a)/cos(a)+cos(a)/sin(a)=(√2/2)/(√2/2)+=1+1=Question#3:Whatissin2(a)·cos2(a)·[1+?(a)(b)(c)(d)(e)oAnswer:sin2(a)·cos2(a)·[1+tan2(a)]=sin2(a)·cosQuestion#3:Whatissin2(a)·cos2(a)·[1+?(a)(b)(c)(d)(e)oAnswer:sin2(a)·cos2(a)·[1+tan2(a)]=sin2(a)·cos2(a)·[1+sin2(a)/cos2(a)]=sin2(a)·cos2(a)·[(cos2(a)+sin2(a))/cos2(a)]=sin2(a)·cos2(a)·[1/cos2(a)]=sin2(a).thepointwith(-Question#4:Whatarethepolarcoordinatesofrectangularcoordinates??(5√2,(5,(5,(5√2,(-5,2or2=+=5-r==tan(θ)=-andthevolumeofthegeometricsolidproducedQuestion#5:What?thefigurebelowwhen