國外英語考試《SAT Level 2》試題（網(wǎng)友回憶版）三

國外英語考試《SATLevel2》試題（網(wǎng)友回憶版）三[單選題]1.Ifθisanacuteangleandc（江南博哥）otθ=5,thensinθ=______.A.B.C.D.E.參考答案：E參考解析：Becauseθisanacuteangle,thinkoftherighttrianglethatcontainsoneangleofmeasureθ.cotθ=5=adjacent/opposite.Solveforthehypotenuse:.sinθ=opposite/hypotenuse=.[單選題]2.Theareaofarightdiviangleis48squareinches,andthelongerlegis4morethantheshorterleg.Whatisthelengthofthehypotenuseofthisrightdiviangle?A.inchesB.inchesC.inchesD.inchesE.inches參考答案：B參考解析：Drawadiagram.Writeaformulafortheareaandsolveforx.A=1/2(x)(x+4)=48(x)(x+4)=96/2,x2+4x=96,(x+12)(x-8)=0x-8=0x=8.Thelegsofthetrianglearex+4=8+4=12andx=8.c2=122+82:c2=144+64=288.UsethePythagoreanTheoremtofindthehypotenuseoftherighttriangle.c2=208c=.[單選題]3.Inthexy-coordinateplanelinekisareflectionofthelinelabouttheliney=x.iftheslopeoflinelis–3/5whichofthefollowingistheslopeoflinek?A.-3/5B.-5/3C.3/5D.5/3E.-8/3參考答案：B參考解析：WhenlineIisreflectedabouttheliney=x,thexandycoordinatesofeachpointswitch.Thatmeansiftheslopeoflinelis-3/5,thentheslopeoflinekis-5/3.[單選題]4.Arectangularprismhasdimensionsh=3ft,w=5ft,andl=8ft.Theprismiscutintotwoseparaterectangularprismsbyaplaneparalleltooneofthefaces.Whatisthemaximumincreaseinthesurfaceareabetweentheoneprismandthetwoseparateprisms?A.80ft2B.48ft2C.40ft2D.24ft2E.15ft2參考答案：A參考解析：Therearethreepossiblewaystocuttheprismbyaplaneparalleltoaface.Case1：paralleltothe3×5face,theincreaseoftheSAis(2)(3)(5)=30.Case2：paralleltothe3×8face,theincreaseoftheSAis(2)(3)(8)=48.Case3：paralleltothe5×8face,theincreaseoftheSAis(2)(5)(8)=80.Therefore,themaximumincreaseinsurfaceareawouldbe80ft2.[單選題]5.PointsA,B,andCarecollinear.IfandA=(-2,3),B=(2,-4),thenC=______.A.B.(0,-1)C.D.E.參考答案：A參考解析：,andtheyarecolinear.ThatmeansCisthemidpointof.[單選題]6.Intherectangularpyramidbelow,theareaofonediviangularfaceis21ft2.Whatistheheightofthepyramid?A.4B.2C.D.E.參考答案：D參考解析：ThelengthofthebaseB.ofthetriangularfaceisalsoasideofthesquarebaseofthepyramid.Usetheformulafortheareaofatriangle.SubstituteA=21andh=7.A=(1/2)bh2=1/2B.(7)Solveforb.42=b(7)b=6.Constructarighttriangleshownbelowinsidethepyramid.Noticethelengthofthebaseofthetriangle(s)ishalfthelengthofthesquare.Thehypotenuseofthetriangle(7)istheslantheightofthepyramid.UsethePythagoreanTheoremtosolveforh.h3+33=72h2+9=49h2=40h=.[單選題]7.Iftheareaoftherectangleis120,whatistheareaofdiviangleCPD?A.60B.100C.120D.200E.240參考答案：A參考解析：Thebaseandheightforthetriangleandrectangleareequal.Theareaoftherectangleis120.Theareaofthetriangleishalftheareaoftherectangle,(1/2)×120=60.[單選題]8.Howmanydifferentdivianglesarethereforwhichthelengthsofthesidesare3,8,andn,wherenisanintegerand3A.TwoB.ThreeC.FourD.FiveE.Six參考答案：A參考解析：Sincenisanintegerand3~Ifn=4,then4<3+8and3<4+8,but8isnotlessthan3+4,son≠4.~Ifn=5,then5<3+8and3<5+8,but8isnotlessthan3+5,son≠5.~Ifn=6,then6<3+8,3<6+8,and8<3+6,sonmaybeequalto6.~Ifn=7,then7<3+8,3<7+8,and8<3+7,sonmaybeequalto:7.Hence,twodifferenttrianglesarepossible.[單選題]9.InthefigurebelowBC∥DEandpointBisthemid-pointofAD.IftheareaofdiviangleABCis12,whatistheareaofdiviangleADE?A.4B.12C.24D.48E.72參考答案：D參考解析：Notice△ABCand△ADEaresimilartriangles.WeknowfromthequestionthatBisthemidpointofAD.ThatmeansADistwicethelengthofAB.Itfollowsthatthereisa2to1ratiobetweenthelengthsatcorrespondingpartsof△ADEand△ABC.22=4,sotheareaof△ADEisfourtimestheareaof△ABC.Areaof△ABC=12;Areaof△ADEis4×12=48.[單選題]10.Theperimeterofarectangleis72.Thelengthoftherectangleisthreetimesthewidth.Whatistheareaoftherectangle?A.3B.9C.27D.81E.243參考答案：E參考解析：Usetheperimetertofindthewidth.2(w)+2(3w)=722w+6w=728w=72w=9.Thewidthoftherectangleis9,andthelengthoftherectangleis27.Multiplytofindthearea.A=9×27=243.[單選題]11.Adiagonalofarectangleformsa30°anglewitheachofthelongersidesoftherectangle.Ifthelengthoftheshortersideis3,whatisthelengthofthediagonal?A.B.C.4D.5E.6參考答案：E參考解析：Ifadiagonalofarectangleformsa30oanglewitheachofthelongersidesoftherectangle,theshortersideisthelegofarighttrianglethatisoppositethe30oangle.Sincethelengthoftheshortersideis3,thelengthofthediagonal,orhypotenuseoftherighttriangle,is2x3or6.[單選題]12.Inthexy-plane,lineqandlinerareparallel.Lineqpassesthroughthepoint(3.7),andlinerpassesthroughthepoint(3.2).Ifthey-interceptforlineris-2,whatistheequationofalineperpendiculartolineq,whichintersectslineqonthey-axis?A.y=(-4/3)x+3B.y=(-3/4)x+3C.y=(-4/3)x+11D.y=(-4/3)x+11E.y=(-3/4)x+11參考答案：B參考解析：Findtheslopeofliner.Linerpassesthroughthepoints(3,2)and(0,-2)[y-interceptof-2].Theslopeoflineris.Findtheequationoflineq.Linerandlineqareparallel,sotheslopelineqisalso4/3.Lineqpassesthroughthepoint(3,7).y=(4/3)x+b,7=4+b,3=b.Theequationoflineqisy=(4/3)x+3.y=4/3x+3istheequationofthelinewiththesamey-interceptaslineqandperpendiculartolineq.[單選題]13.Thelengthsofthesidesof△ABCareconsecutiveintegers.If△ABChasthesameperimeterasanequilateraldivianglewithasidelengthof9,whatisthelengthoftheshortestsideof△ABC?A.4B.6C.8D.10E.12參考答案：C參考解析：Sincethelengthsofthesidesof△ABCareconsecutiveintegers,letx,x+1,andx+2representthelengthsofthethreesides.Sincetheperimeterof△ABChasthesameperimeterasanequilateraltrianglewithasidelengthof9,x+(x+1)+(x+2)=9+9+9,3x+3=27.3x=24Thenx,thelengthoftheshortestsideof△ABC,is24/3or8.12BDrawDE⊥ABBC,is24/3or8.[單選題]14.WhatisthegreatestnumberofrectangleswithintegersidelengthsandPerimeter10thatcanbecutfromasquarepieceofpaperwithasidelengthof60?A.900B.600C.360D.240E.180參考答案：A參考解析：Theperimeteris2(l+W)=10,thusl+W=5.Casel：ifl=4andW=1,then60÷4=15and60÷1=60,thetotalnumberofsmallrectanglesis15×60=900.Case2：ifl=3andW=2,then60÷3=20and60÷2=30.Thetotalnumberofsmallrectanglesis20×30=600.Sothegreatestnumberis900.[單選題]15.Iftheratiooftheareaofasectortotheareaofthecircleis2:3.whatistheratioofthelengthofthearcinthesectortothecircumferenceofthecircle?A.3/2B.2/3C.4/9D.1/4E.9/4參考答案：B參考解析：Theratioofsectorareatocircleareaisproportionaltotheratioofsectorarclengthtocircumference.[單選題]16.Inthefollowingfigure,whichofthefollowingstatementsmustbedivue?(Note：Figurenotdrawntoscale)Ⅰ.A+B<180Ⅱ.A+D=180Ⅲ.A+D>180A.ⅠonlyB.ⅡonlyC.ⅠandⅡonlyD.ⅡandⅢonlyE.None參考答案：E參考解析：Areanyoftheselinesparallel?Youdon’tknow.Soyoucan’tdrawanyconclusionsatall.[單選題]17.Ifsinx=7/25,thentanx=______.A.7/20B.24/25C.7/24D.24/7E.8/24參考答案：C參考解析：Thinkofarighttrianglewithahypotenuseoflength25andalegoflength7.Thesineofoneoftheacuteanglesofthetrianglewould,therefore,be7/25.UsethePythagoreanTheoremtofindthelengthoftheotherleg.72+b2=252.b=24,tanx=opposite/adjacent=7/24.[單選題]18.InquadrilateralABCD,∠A+∠Cis2times∠B+∠D.If∠A=40,then∠B=______.A.60B.80C.120D.240E.Itcannotbedeterminedfromtheinformationgiven.參考答案：E參考解析：Youaregiventhat,inquadrilateralABCD,∠A+∠Cis2times∠XB+∠D,and∠A=40,so40+∠C=2(∠B+∠D..Sincethesumofthedegreemeasuresofthefouranglesofaquadrilateralis360,40+∠C+(∠B+∠D.=360.Substituting2(∠B+∠D.for40+∠Cgives2(∠B+∠D.+(∠B+∠D.=360.Sincethelastequationcontainstwounknowns,themeasuresofanglesBandD,itisnotpossibletofindthemeasureof∠B(or∠D..[單選題]19.CylinderAhasavolumeof256πandaheightof4.CylinderBhasthesamevolumeasCylinderAandaheightequaltotheradiusofCylinderA.WhatistheradiusofCylinderB?A.8B.C.4D.E.2參考答案：D參考解析：CylinderA:UsethevolumeformulatofindtheradiusofCylinderA.h=4,..CylinderB:TheradiusofCylinderAis8,soh=8.UsethevolumeformulatofindtheradiusofCylinderB...[單選題]20.Whatisthelengthofinthegraphbelow?A.B.C.D.E.參考答案：C參考解析：Usethedistanceformulatofindthelengthof..[單選題]21.Aconehasaradiustwicetheheight.Theheightoftheconeisequaltotheradiusofasphere.Whichofthestatementsisdivueabouttheratiobetweenthevolumeoftheconeandthevolumeofthesphere?A.2:1B.1:2C.4:1D.1:4E.1:1參考答案：E參考解析：-Volumeofaconeis1/3r2h.Substituter=2h.V=1/3(4h2)h=4/3h3.Volumeofasphereis4/3h3.Theradiusofthesphereandtheheightoftheconeareequal.Theratiois1:1.[單選題]22.WhichofthefollowingCANNOTrepresentthedegreemeasureofanequiangularpolygon?A.165B.162C.140D.125E.90A.:Themeasureofanexteriorangleis180-165or15and360/15=24,sothepolygonhas24sides.B.:Themeasureofanexteriorangleis180-162or18and360/18=20,sothepolygonhas20sides.C.:Themeasureofanexteriorangleis180-140or40and360/40=9,sothepolygonhas9sides.D.:Themeasureofanexteriorangleis180-125or55,but360/55doesnotgiveanintegeranswer.Hence,apolygoninwhicheachinterioranglemeasures125isnotpossible.參考答案：D參考解析：Ateachvertexofapolygon,aninteriorangleissupplementarytoanexteriorangledrawnatthatvertex.Inanequiangularpolygon,alltheexteriorangleshavethesamemeasures.Dividing360,thesumofthedegreemeasuresoftheexterioranglesofapolygon,bythemeasureofanexterioranglegivesthenumberofsidesofthatpolygon.Testeachanswerchoiceuntilyoufindanexterioranglethatdoesnotdivideevenlyinto360.[單選題]23.Ifapolygonhasnsides,thenthesum,S,ofthedegreemeasuresoftheinterioranglesisgivenbytheformulaS=(n-2)180.IfS=540t,whatisnintermsoft?A.3t+2B.2t-3C.(t+2)/3D.(t-3)/2E.(t-2)/180參考答案：A參考解析：IfS=540tandS=(n-2)180,then(n-2)180=540t.Dividingbothsidesoftheequationby180gives.n-2=540t/180=3t.Sincen-2=3t,thenn=3t+2.[單選題]24.Ifonepairofoppositesidesofasquareareincreasedinlengthby20%andtheotherpairofsidesareincreasedinlengthby50%,bywhatpercentistheareaoftherectanglethatresultsgreaterthantheareaoftheoriginalsquare?A.10%B.50%C.70%D.75%E.80%參考答案：E參考解析：Supposethelengthofasideoftheoriginalsquareis10;thentheareaofthatsquareis10x10or100.Sinceonepairofoppositesidesofthesquareareincreasedinlengthby20%,and20%of10is2,thelengthofthatpairofoppositesidesofthenewrectangleis10+2or12.Sincetheotherpairofsidesareincreasedinlengthby50%,and50%of10is5,thelengthoftheotherpairofoppositesidesofthenewrectangleis10+5or15.Theareaofthenewrectangleformedis12×15or180,whichis80%greaterthan100,theareaoftheoriginalsquare.[單選題]25.TheheightofdiviangleABCistwicetheheightofparallelogramADEC.IftheareaofdiviangleABCis14,whatistheareaofparallelogramADEC?A.12B.2C.7D.14E.28參考答案：D參考解析：Thebasesofthisparticularparallelogramandthisparticulartriangleareequal.Ifaparallelogramandatrianglehavethesamebaseandheight,theareaoftheparallelogramistwicetheareaofthetriangle.Theheightofthisparallelogramishalfthisheightofthetriangle.Thatmeanstheareaofeachfigureisthesame.Theareaoftheparallelogramis14.[單選題]26.Whatisthevolumeoftherightdiviangularprisminfollowingfigure?A.650cm3B.600cm3C.300cm3D.325cm3E.780cm3參考答案：C參考解析：VolumeisgivenbytheformulaV=Bh,whereBistheareaofthebase.TheareaofthebaseoftherighttriangularprismisB=1/2(12)5=30cm2.ThevolumeoftheprismisthenV=Bh=30(10)=300cm3.[單選題]27.Whatistheareaofaparallelogramwhoseverticesare(-4,-2),(-2,6),(10,6),and(8,-2)?A.32B.48C.72D.96E.104參考答案：D參考解析：Sketchtheparallelogramwhoseverticesare(-4,-2),(-2,6),(10,6),and(8,-2).Sinceb=8-(-4)=8+4=12,andh=6-(-2)=6+2=8,thenAreaofparallelogram=b×h=12×8=96.[單選題]28.InFigure5,whichofthefollowingmustbedivue?I.cotx=3/4II.cosx=sinyIII.tanx=tanyA.IonlyB.IIonlyC.IIandIIIonlyD.IandIIonlyE.I,II,andIII參考答案：D參考解析：Thefirststatementistruebecausecotx=adjacent/opposite=3/4.Thesecondstatementisalsotrue,sincecosx=3/5andsiny=3/5.Thethirdstatementisnottrue,sincetanx=4/3andtany=3/4.AnswerDisthecorrectchoice.[單選題]29.Whatistheareaofaregularhexagonwithaperimeterof12?A.B.C.D.E.參考答案：E參考解析：Aregularhexagoniscomposedof6equilateraltriangleswiththesidemeasureof2.Ifyoudrawaheightofthetriangle,theintroductionoftheheightcreates2congruent30-60-90triangles.Sincethesideopposite30degreesisl,thesideopposite60degreesis.Sotheareaoftheentireequilateraltriangleis.Theareaofthehexagonis.[單選題]30.WhichofthefollowingsetsofnumbersCANNOTrepresentthelengthsofthesidesofadiviangle?A.9,40,41B.7,7,3C.4,5,1D.1.6,1.4,2.9E.6,6,6參考答案：C參考解析：Foreachchoice,checkthateachofthethreegivennumbersislessthanthesumoftheothertwonumbers.InchoiceC.,4<5+1and1<4+5,but5isnotlessthan1+4.[單選題]31.Whatisthevolumeofaregularhexagonalprismwithheight13ftandbase-edgelengthof10ft?A.1950B.750C.150D.25E.5參考答案：A參考解析：Firstfindtheareaofthehexagonalbase.Weknowthelengthofeachsideofthehexagonis10.Wecanfindtheareaofoneofthecentralequilateraltrianglesandmultiplythatareaby6.Usetherulesofa30°-60°-90°righttriangle,tofindtheheightofthetriangleis.Theareaofthetriangleis:A=.Areaofhexagonisft2.SubstituteB=andh=3.ThevolumeoftheprismisV=Bh=ft3.[單選題]32.Whatistheradiusofarightconewithheight15cmandvolume90gcm3?A.3cmB.2cmC.6cmD.9cmE.18cm參考答案：A參考解析：SubstituteV=90andh=15.V=1/3r2hl/3r2(15)=905r2=90.Solveforr.r2=18r=.[單選題]33.Whatistheperimeterofasquarethathasanareaof25?A.15B.20C.25D.20E.25參考答案：B參考解析：Iftheareaofasquareis25,thenthelengthofasideofthatsquareis4or5.Theperimeterofthesquareis4×5or20.[單選題]34.Thebaseofarectangleisthreetimesaslongastheheight.Iftheperimeteris64,whatistheareaoftherectangle?A.24B.64C.96D.192E.216參考答案：D參考解析：Drawapicture.Theperimeteris64so8x=64°,x=8.So,h=8andb=3×8=24.Substituteh=8andb=24intheareaformula.A=b×h=8×24=192.[單選題]35.Theanglesofapentagonareinratio9:10:12:14:15.Whatisthesumofmeasuresofthesmallestandlargestangles?A.54°B.81°C.135°D.216°E.270°參考答案：D參考解析：Theanglesumoftheanglesinapentagon=(5-2)×180°=3°180°=540°.Usetheratiofromtheproblemtowriteanequationsolveforx.9x+10x+12x+14x+15x=540,x=9.Thesmallestangleis9×9=81°andthelargestangleis15×9=135°.Therefore,thesumofthesmallestangleandthelargestangleis81+135=216°.[單選題]36.Ifsinx=7/2