國(guó)外英語(yǔ)考試《SAT Level 1》試題（網(wǎng)友回憶版）三

國(guó)外英語(yǔ)考試《SATLevel1》試題（網(wǎng)友回憶版）三[單選題]1.9sin2x+9cos2x=______.（江南博哥）A.1B.-1C.9D.-9E.0參考答案：C參考解析：9sin2x+9cos2x=9(sin2+cos2x)=9(1)=9[單選題]2.Ifthelinesl1andl2areparallelandareintersectedbyadivansversalt,thenwhatisthesumoftheexterioranglesonthesamesideoft?A.45°B.90°C.180°D.360°E.Cannotbedetermined參考答案：C參考解析：Parallellinescutbyatransversalformeightangles.Theexterioranglesonthesamesideofthetransversalaresupplementary,so180°isthecorrectanswer.[單選題]3.Thediagonalofasquareis12.Whatisthelengthofaside?A.B.14.1C.8.5D.6.9E.17參考答案：C參考解析：Thediagonalofasquaresplitsitintotwo45。-45。-90。righttriangles.Thehypotenuseofeachtriangleis12,soeachlegmeasures[單選題]4.Ifthemeasuresoftheanglesofadiviangleareintheratioof2:3:4,whatisthemeasureofthesmallestangleofthediviangle?A.20B.25C.30D.40E.45參考答案：D參考解析：Let2x，3x，and4xrepresentthemeasuresofthethreeangles.2x+3x+4x=180,x=20.Hence2x=40.[單選題]5.Inthefollowingfigure，ifl1∥l2，thenwhatisthevalueofnintermsofm?A.255-2mB.185-2mC.175-2mD.120-2mE.100-2m參考答案：B參考解析：(m-5)+m+n=180.n=185-2m.[單選題]6.Ifthemeasureofeachexteriorangleofaregularpolygonis20°,howmanysidesdoesthepolygonhave?A.18B.9C.27D.22E.36參考答案：A參考解析：Thesumoftheexterioranglesofanypolygonis360°.Ifeachexterioranglemeasures20°,thepolygonhas360/20=18sides.[單選題]7.IfM=(5,2.5),isthemidpointof,withX=(-4,1)andY=(a,4),whatisthevalueofa?A.6B.8C.10D.12E.14參考答案：E參考解析：Writeanequationforthexcoordinateofthemidpoint,.Solvefora:-4+a=10→a=14.[單選題]8.ThesidesofpentagonABCDEinFigure1areextended.Whatisthesumofthemeasuresofthefivemarkedangles?A.180°B.270°C.360°D.540°E.720°參考答案：C參考解析：ThefivemarkedanglesarethefiveexterioranglesofpentagonABCDE.Thesumoftheexterioranglesofanypolygonis360°,soCisthecorrectanswer.[單選題]9.Ifthelengthofarectangleis7feetmorethanitswidthandifitsareais18squarefeet,thenwhatarethedimensionsoftherectangle?A.-9×-2feetB.1×18feetC.3×6feetD.2×9feetE.1×8feet參考答案：D參考解析：Letw=thewidthoftherectangle.Itslengthisthenw+7.Area=w(w+7)=18,w2+7w-18=0,(w+9)(w-2)=18,w=-9orw=2.Thesolution-9isaroot,however,sincethewidthoftherectanglecannotbenegative.Thedimensionsoftherectangleare2×(2+7)or2×9feet.[單選題]10.sin30°=______.A.cos60°B.sin60°C.cos30°D.tan60°E.csc30°參考答案：A參考解析：sin30°=cos(90°-30°),sin30°=cos60°.[單選題]11.Iff(x)=16/x5andx≠0,thenf(-2)=______.A.-1/2B.1/2C.1/4D.1E.-11參考答案：A參考解析：Sincef(x)=16/x5,f(-2)=16/(-2)5=16/(-32)=-1/2.[單選題]12.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，thetotalnumberofsmallrectanglesisl5×60=900.Case2：ifl=3andW=2，then60÷3=20and60÷2=30.Thetotalnumberofsmallrectanglesis20×30=600.Sothegreatestnumberis900.[單選題]13.Iftwosidesofadiviangleare4and5，thenthethirdsidecannotbe______.A.2B.3C.7D.8E.10參考答案：E參考解析：Thethirdsidecannotbe10becausethesumofanytwosidesofatrianglemustbegreaterthanthethirdside.[單選題]14.Ifthesidesofacubearedoubled,thenitsvolumeisincreasedbywhatfactor?A.2B.3C.4D.8E.16參考答案：D參考解析：Iftheoriginalcubehassidesoflengthe,itsvolumeise3.Doublingthesidesofthecuberesultsinavolumeof(2e)3=8e3.Thevolumeisincreasedbyafactorof23or8.[單選題]15.Acubewhosevolumeis1/8cubicfootisplacedontopofacubewhosevolumeis1cubicfoot.Thetwocubesarethenplacedontopofathirdcube,whosevolumeis8cubicfeet.Whatistheheight,ininches,ofthestackedcubes?A.30B.40C.42D.44E.64參考答案：C參考解析：Theheightofthestackedcubeswillbethesumoftheedgelengthsofthethreecubes.~Ifthevolumeofthefirstcubeis1/8cubicfeet,itsedgelengthis1/2ofafootor6inches.~Ifthevolumeofthesecondcubeis1cubicfoot,itsedgelengthis1footor12inches.~Ifthevolumeofthethirdcubeis8cubicfeet,itsedgelengthis2feetor2×12or24inches.Theheightofthestackedcubes,ininches,is6+12+24or42.[單選題]16.WhatistheperimeteroftheregularhexagonshowninFigure1iftheapothem,XO,measures2units?A.12B.12C.24D.24E.36參考答案：C參考解析：Eachangleofaregularhexagonmeasures120°.UsingXOasoneleg,sketcha30°-60°-90°righttriangleasshown:Thesideoppositethe30°anglemeasures2units.Theregularhexagoncanbebrokeninto12righttrianglesthatarecongruenttotheoneshowninthediagram.Theperimeterofthehexagonis,therefore,12(2)or24units.[單選題]17.Whichofthefollowingistheequationofacirclewithcenter(-1,7)andaradiusoflength3?A.(x+1)2-(y+7)2=9B.(x+1)2+(y-7)2=3C.(x-1)2+(y+7)2=3D.(x+1)2+(y-7)2=9E.(x-1)2+(y+7)2=9參考答案：D參考解析：Thegeneralequationofacircleis(x-h)2+(y-k)2=r2where(h,k)isthecenterandristhelengthoftheradius.Theequationofacirclewithcenter(-1,7)andaradiusoflength3is(x-1)2+(y-7)2=32(x+1)2+(y-7)2=9[單選題]18.Whatisthelengthoftheedgeofacubehavingthesametotalsurfaceareaasarectangularprismmeasuring3cmby4cmby8cm?A.22.7cmB.4.8cmC.136cmD.5.8cmE.11.7cm參考答案：B參考解析：ThesurfaceareaoftheprismisSA=2(3)(4)+2(3)(8)+2(4)(8)=136cm2.ThesurfaceareaofthecubeisgivenbytheformulaSA=6e2,wheree=thelengthofanedgeofthecube.136=6e2,22.67=e2,e=4.8cm.[單選題]19.Whatisthelateralsurfaceareaofarightcircularconewhoseradiusis3cmandwhoseslantheightis12cm?A.36cm2B.18cm2C.18cm2D.36cm2E.72cm2參考答案：D參考解析：TheformulaforthelateralsurfaceareaofaconeisgivenintheReferenceInformation.LateralArea=1/2cl,LateralArea=cm2.[單選題]20.Twocircles,PandQ,lieinthesameplane.IfthecenterofcircleQliesoncircleP,theninhowmanypointscouldcirclePandcircleQintersect?Ⅰ.0Ⅱ.1Ⅲ.2A.ⅠonlyB.ⅡonlyC.ⅢonlyD.Ⅰ,ⅡandⅢE.ⅡandⅢonly參考答案：D參考解析：IftheradiusofcircleQisgreaterthanthediameterofcircleP，thereisnointersectionpoint.IftheradiusofcircleQisequaltothediameterofcircleP，thereisoneintersectionpoint.IftheradiusofcircleQislessthanthediameterofcircleP，therearetwointersectionpoints.[單選題]21.Acylinderwithradiusrandheighthisclosedonthetopandbottom.Whichofthefollowingexpressionsrepresentsthetotalsurfaceareaofthiscylinder?A.2πr(r+h)B.πr(r+2h)C.πr(2r+h)D.πr2+2hE.2πr2+h參考答案：A參考解析：Ifacylinderwithradiusrandheighthisclosedonthetopandbottom,thenthesumoftheareasofthecirculartopandbottomisπr2+πr2or2πr2.Theareaofthecurvedsurfaceistheheighthtimesthedistancearoundthecurvedsurface,2πr.Hence,thetotalsurfaceareais2πr2+2πrhor2πr(r+h).[單選題]22.WhatistheareaofthequadrilateralinFigure2?A.2units2B.8units2C.16/2units2D.16units2E.8units2參考答案：E參考解析：Thediagonaldividesthesquareinto2congruentrighttriangles.Sincethetrianglesareisoscelesrighttrianglesandthehypotenusemeasures4units,eachlegmeasuresunits,TheareaofthesquareunitsA=bh=squareunits.[單選題]23.WhatistheperimeterofthedivianglewithverticesL=(1,5),M=(-3,-3),andN=(3,1)?A.B.C.D.E.參考答案：B參考解析：Findthelengthsofeachsideofthetriangle.,Theperimeteris[單選題]24.Eachsideofthecubebelowhasalengthof5in.AF=______.A.B.C.10D.E.參考答案：B參考解析：ArighttrianglecanbeformedwithlegsAGandGFandhypotenuseAF.AGisoneofthesidesofthecube,so,AG=5.GFisthehypotenuseofa45o-45o-90~righttrianglewhoselegsarethesidesofthecube,soGF=5.Now,usethePythagoreanTheorem,tosolveforAF.SubstituteAG=5andGF=5~/2.(AF)2=(AG)2+(GF)2=(5)2+(5)2=25+50=75,(AF)2=75,AF=5.[單選題]25.Whatisthedistancebetweenthepointswithcoordinates(-2,6)and(2,-3)?A.9.85B.97C.65D.8.06E.3參考答案：A參考解析：,,.Hence.[單選題]26.Howmanysidesdoesaregularpolygonhaveifeachinterioranglemeasures140°?A.6B.7C.8D.9E.10參考答案：D參考解析：Letn=thenumberofsidesofthepolygon.180(n-2)/n=140,180(n-2)=140n.40n=360,thereforen=9.[單選題]27.InFigure3,andareparallel.Themeasureof∠ZXYis75°andthemeasureof∠ZYXis25°.Whatisthemeasureof∠VZY?A.75°B.80°C.155°D.165°E.105°參考答案：C參考解析：∠VZXand∠ZXYarealternateinterioranglesandare,therefore,congruent,m∠VZX=75°.Sincem∠ZYX=25°andm∠VZX=75°,theremainingangleinZYXmustmeasure180-(75+25)=80°.m∠VZY=75+80=155°.[單選題]28.Whatisthecircumferenceofacircleinwhicha3by4rectangleisinscribed?A.7π+1B.7πC.7π-1D.5πE.4π參考答案：D參考解析：Ifarectangleisinscribedinacircle，thediagonalsoftherectanglearediametersofthecircle.Thediagonalequalsto.Sothecircumferenceequalsto5π.[單選題]29.Acube-shapedboxwhosevolumeislcubicfootisplacedontopofasimilarboxwhosevolumeis8cubicfoot.Thetwoboxesarethenplacedontopofathirdcubeshapedbox，whosevolumeis27cubicfeet.Whatistheheight,ininches,ofthestackedboxes?A.35B.40C.54D.64E.72參考答案：E參考解析：Theheightofthestackedboxeswillbethesumoftheedgelengthsofthethreeboxes.Theedgelengthofthefirstbox：1ft,or12inches.Theedgelengthofthesecondbox:ft,or24inches.Theedgelengthofthethirdbox:ft,or36inches.Sotheheight：12+24+36=72[單選題]30.Thebaseareaofacylinderis16nm2.Aplanecutsthecylinderinhalfformingtherectanglebelow.Ifthevolumeofthecylinderis240nm3,whatistheareaoftherectangle?A.110B.115C.120D.125參考答案：C參考解析：Thebaseareaofthecylinderisacircle.B=r2.Substitute16=Bandsolveforr.16r=4.ThevolumeofthecylinderisV=240=Bh.SubstituteB=16andsolveforh.240=16h15=h.Theplanecutsthecylinderinhalf,sothewidthoftherectangleisthediameterofthecircularbasew=8andtheheightoftherectangleish=15.Therefore,theareaoftherectangleisA=wh=815=120m2.[單選題]31.Whatistheslopeofthelinecontainingthepoints(6,0)and(6,7)?A.7B.0C.UndefinedD.1/6E.-7參考答案：C參考解析：Slope=,m=(7-0)/(6-6)undefined[單選題]32.Whichofthefollowingisanequationofthelinethatisparalleltotheliney=4x=0andhasthesamey-interceptastheliney+3=-x+1?A.y=4x-2B.y=4x+1C.y=-(1/4)x+1D.y=-(1/4)x-2E.y=-4x+2參考答案：A參考解析：Lety=mx+brepresenttheequationofthedesiredline.~Ify-4x=0,theny=4x,sotheslopeofthislineis4.Sinceparallellineshaveequalslopes,m=4.~Ify+3=-x+1,theny=-x-2,soitsy-interceptis-2.Sincethedesiredlinehasthesamey-intercept,b=-2.~Theequationofthedesiredlineisy=4x-2.[單選題]33.InthediviangleshowninFigure4,whatisthevalueofc?A.B.C.D.E.參考答案：C參考解析：Thetriangleisa30°-60°-90°specialrighttriangle.Sincethesideoppositethe60°anglemeasures9,,therefore,.[單選題]34.Whatistheradiusofthecirclerepresentedbytheequationx2-2x+y2+6y+6=0?A.2B.4C.1D.3E.16參考答案：A參考解析：Writetheequationofthecircleinstandardformbycompletingthesquareforxandy.x2-2x+y2+6y+6=0.(x2-2x)+(y2+6y)=-6.(x2-x+1)+(y22+6y+9)=-6+1+9.(x-1)2+(y+3)2=4.Thecenterofthecircleis(1,-3),anditsradiushasalengthofunits.[單選題]35.Ifthedegreemeasuresoftheanglesofaquadrilateralare4x,7x,9x,and10x,whatisthesumofthemeasuresofthesmallestangleandthelargestangle?A.140.B.150C.168D.180E.192參考答案：C參考解析：Thesumofthemeasuresofthefouranglesofaquadrilateralis360.Ifthedegreemeasuresoftheanglesofaquadrilateralare4x,7x,9x,and10x,then4x+7x+9x+10x=360.30x=360,x=360/30=12.Thedegreemeasureofthesmallestangleis4x=4(12)=48,andthedegreemeasureofthelargestangleis10x=10(2)=120.Hence,thesumofthedegreemeasuresofthesmallestandlargestanglesofthequadrilateralis48+120or168.[單選題]36.If,inthefigureabove,CD=1,AB=2,andAD=6,thenBC=______.A.5B.9C.D.E.參考答案：D參考解析：RighttrianglesCDEandBAEaresimilar,sothelengthsofcorrespondingsidesareinproportion.SinceCD=1andAB=2,eachsideofABAEis2timesthelengthofthecorrespondingsideofACDE.SinceAD=6,itmustbethecasethatAE=4andDE=2.SinceBC=CE+BE,usethePythagoreanTheoremtofindthelengthsofCEandBE.~InrighttriangleCDE,(CE)2=12+22=1+4=5,soC