SAT2数学习题6套

SATII数学Level1&Level2练习题满分网（）SAT2数学Level1习题1Question#1:Iff(x)=xandg(x)=√x,x≥0,whatarethesolutionsoff(x)=g(x)?x=1x1=1,x2=-1x1=1,x2=0x=0x=-1Question#2:WhatisthelengthofthearcABinthefigurebelow,ifOisthecenterofthecircleandtriangleOABisequilateral?Theradiusofthecircleis9.¶2·¶3·¶4·¶¶/2Question#3:Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6?Eachdicehassidesnumberedfrom1to6.1/21/61/121/181/36Question#4:AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HebikesfromAtoBataspeedof15miles/hourwhilehisreturnspeedis10miles/hour.Whatisthe满分网（）distancebetweenthe2towns?11miles18miles15miles12miles10milesQuestion#5:Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeofacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.WhatistheheightofC2?2·a/¶a/¶a/(2·¶)a/¶a+¶Question#6:Howmanyintegersxaretheresuchthat2x100,andatthesametimethenumber2x+2isanintegerdivisiblebyboth3and2?12345Question#7:sin(x)cos(x)(1+tan2(x))=tan(x)+1cos(x)sin(x)tan(x)sin(x)+cos(x)Question#8:If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldbethevalueofx+yexcept:1317231543Question#9:Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofthesumx+y?满分网（）111713159Question#10:Theinequality|2x-1|5mustbetrueinwhichoneofthefollowingcases?I.x-5II.x7III.x0IIonlyI,IIandIIIandIIonlyIandIIIonlyIonlyQuestion#1:Iff(x)=xandg(x)=√x,x≥0,whatarethesolutionsoff(x)=g(x)?(a)x1=1,x2=-1(b)x1=1,x2=0(c)x=1(d)x=0(e)x=-1oAnswer:x=√x,ifwesquaretheleftandrighttermsoftheequationwegetx2=x.x·(x-1)=0andx1=1,x2=0满分网（）Question#2:WhatisthelengthofthearcAB,ifOisthecenterofthecircleandtriangleOABisequilateral?Theradiusofthecircleis9.(a)¶(b)2·¶(c)3·¶(d)4·¶(e)¶/2oAnswer:OABequilateralsoangleAOBisequalto60o.TheratiobetweentheAOBangleand360oisequaltotheratiobetweenthelengthofthearcABandthecircumferenceofthecircle.60o/360o=arcAB/(2¶·9)arcAB=3·¶Question#3:Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6?Eachdicehassidesnumberedfrom1to6.(a)1/6(b)1/12(c)1/18满分网（）(d)1/36(e)1/2oAnswer:Theprobabilitytohavea(5,6)combinationisequaltotheprobabilitythatdice1is5anddice2is6,plustheprobabilitythatdice2is5anddice1is6.P=1/6·1/6+1/6·1/6=1/36+1/36=1/18.(c)isthecorrectanswer.Question#4:AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HebikesfromAtoBataspeedof15miles/hour,whilehisreturnspeedis10miles/hour.Whatisthedistancebetweenthe2towns?(a)18miles(b)15miles(c)12miles(d)10miles(e)11milesoAnswer:Thetotaltimet=tAB+tBA=dAB/(15miles/hour)+dAB/(10miles/hour)=dAB/(6miles/hour).dAB=dAB/(6miles/hour)·3hours=18miles.(a)isthecorrectanswer.Question#5:Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeofacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.WhatistheheightofC2?(a)a/¶(b)a/(2·¶)(c)a/¶(d)2·a/¶满分网（）(e)a+¶oAnswer:Thevolumeofthecubeisa3.ThisisequaltohalfthevolumeofthecylinderC2.a3=¶·a2·h/2,wherehistheheightofthecylinder2·a3=¶·a2·h,2·a=¶·h,soh=2·a/¶and(d)isthecorrectanswer.Question#6:If2x100andxisaninteger,howmanyofthe2x+2integerswillbedivisibleby3andby2?(a)1(b)2(c)3(d)4(d)5oAnswer:26=64and27=128.If2x100,thenthehighestvalueofxis6.Possiblevaluesforx:0,1,2,3,4,,5,6.2x+2cantakethevalues3,4,6,10,18,34,66.Outofthesevalues,only6,18and66aredivisibleby3andby2.Thecorrectansweris(c).Question#7:sin(x)cos(x)(1+tan2(x))=(a)tan(x)+1(b)cos(x)(c)sin(x)(d)tan(x)(e)sin(x)+cos(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)=tan(x)满分网（）Question#8:If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldbethevalueofx+yexcept:(a)13(b)17(c)23(d)15(e)43oAnswer:5xy=210soxy=42.42=2·3·7.Thefollowingproductsofintegersequalto42:(6·7)or(2·21)or(14·3)or(42·1).6+7=13,2+21=23,14+3=1742+1=43TheonlyanswerthatisNOT43,13,23or17is(d),15.Question#9:Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofthesumx+y?(a)11(b)17(c)13(d)15(e)9oAnswer:Theaverageofthe5numbersis(24+6+12+x+y)/5.(24+6+12+x+y)/5=1124+6+12+x+y=11·524+6+12+x+y=55x+y=13满分网（）Question#10:Theinequality|2x-1|5mustbetrueinwhichoneofthefollowingcases?I.x-5II.x7III.x0(a)IIonly(b)I,IIandII(c)IandIIonly(d)IandIIIonly(e)IonlyoAnswer:|2x-1|5,-52x-1or2x-15-42xor2x6-42xresultsinx-22x6resultsinx3Iansweristrue,IIanswerisalsotrue,butIIIanswerisfalse,sothecorrectansweris(c)SAT2数学Level1习题2Question#1:50%ofUScollegestudentsliveoncampus.Outofallstudentslivingoncampus,40%aregraduatestudents.WhatpercentageofUSstudentsaregraduatestudentslivingoncampus?90%5%40%20%25%满分网（）Question#2:Inthefigurebelow,MNisparallelwithBCandAM/AB=2/3.WhatistheratiobetweentheareaoftriangleAMNandtheareaoftriangleABC?5/92/34/91/22/9Question#3:Ifa2+3isdivisibleby7,whichofthefollowingvaluescanbea?789114满分网（）Question#4:Whatisthevalueofb,ifx=2isasolutionofequationx2-b·x+1=0?1/2-1/25/2-5/22Question#5:Whichvalueofxsatisfiestheinequality|2x|x+1?-1/21/21-12Question#6:Ifintegersm2andn2,howmany(m,n)pairssatisfytheinequal