GMAT数学讲义.pptx

有关数学的运算Add,plusSubtractDifferenceMultiply,timesProductdivide有关数学的运算Add,plusSubtractDifferenceMultiply,timesProductdivide加减差乘积除有关数学的运算DivisibleDividedevenlyDividentDivisorQuotientRemainder有关数学的运算DivisibleDividedevenlyDividentDivisorQuotientRemainder可被整除的被整除被除数，红利因子，除数商余数Whichofthefollowingcouldbetheremainderwhenfourconsecutivepositiveintegersareeachdividedby3?A.1,2,3,1B.1,2,3,4C.0,1,2,3D.0,1,2,0E.0,2,3,0PowerRadicalsign,rootsignfactorial乘方方根阶乘N!=1*2*3*.(N-2)*(N-1)*N且规定0!=1例如8!=1*2*3*4*5*6*7*8PowerRadicalsign,rootsignfactorial1、根号8除以2倍根号2IfUnitedStatesimportsincreased20percentandexportdecreased10percentduringacertainyear,theratioofimportstoexportsattheendoftheyearwashowmanytimestheratioatthebeginningoftheyear?A.12/11B.4/3C.11/8D.3/2E.2有关数学的运算RoundoffRoundto熟悉：sqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236有关数学的运算RoundoffRoundto四舍五入四舍五入熟悉：sqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236有关集合SetSubsetPropersubsetSolutionsetComplementarysetintersection有关集合SetSubsetPropersubsetSolutionsetComplementarysetintersection集合子集真子集解集补集交集最近演了3部电影。调查了100个人，其中20人看了所有3部，10人什么都没看。看了每部电影的人数分别为：47，48，55。问：只看了2部的人数？A20，B30，C40，D70，E90。代数式方程不等式AlgebraicLiketerms,similartermsInequalityTriangleinequality代数式方程不等式AlgebraicLiketerms,similartermsInequalityTriangleinequality代数项同类项不等式三角不等式OriginalequationEquivalentequationLinearequationQuadraticequationOriginalequationEquivalentequationLinearequationQuadraticequation原方程同解方程，等价方程一次方程二次方程1.00001*0.99999+1.00002*0.99998=?分数fractionimproperfractionproperfractiondenominatornumeratorMixednumber分数分数假分数真分数分母分子带分数fractionimproperfractionproperfractiondenominatornumeratorMixednumber小数DecimalInfinitedecimalRecurringdecimaltenthsdigittenthunitsdigit3-digitnumber小数DecimalInfinitedecimalRecurringdecimaltenthsdigittenthunitsdigit3-digitnumber小数无穷小数循环小数十位十分位个位三位数基本数论integerIrrationalRealnumber,rationalnumbermultipliermultiplenaturalnumberreciprocal基本数论整数无理数有理数乘数倍数自然数倒数integerIrrationalRealnumber,rationalnumbermultipliermultiplenaturalnumberreciprocalPositivenumberNegativenumberOddnumberEvennumberCompositenumberPrimenumberPositivenumberNegativenumberOddnumberEvennumberCompositenumberPrimenumber正数负数奇数偶数合数质数MultipleFactorGreatestcommonfactorLeastcommonmultipleMultipleFactorGreatestcommonfactorLeastcommonmultiple倍数约数最大公约数最小公倍数Domainrange定义域值域Domainrangemeanarithmaticmeangeometricmean平均数算术平均数几何平均数（几何平均数）n个数之积的n次方根meanarithmaticmeangeometricmeanmedianmedian（中数）将一堆数排序之后，正中间的一个数（奇数个数字），或者中间两个数的平均数（偶数个数字）e.g.medianof1,7,4,9,2,2,2,2,2,5,8is2medianof1,7,4,9,2,5is(5+7)/2=6modemode众数一堆数中出现次数最多的数Eg.1、2、3、2、4、21、1、2、3、3三角形余玄定理两线垂直的条件为K1K2=(-1)三的倍数的特点：所有位数之和可被3整除Inthexy-plane,pointR(2,3)andpointS(5,6)aretwoverticesoftriangleRST.ifthesumoftheslopesofthesidesofthetriangleis1,whichofthefollowinganglescouldbearightangle?1.R2.S3.TA.noneB.1onlyC.3onlyD.1and3onlyE.1,2and3.2/3asmanyAasB.twiceasmany.AasBA=2/3*BA=2*BSequencearithmeticprogressiongeometricprogressionSequencearithmeticprogressiongeometricprogression数列等差数列等比数列一个电影院，第一排有16个位置，每后一排多两个，最后一排64，问总共多少？一个球落下弹回原高度75%，到第三次落地共旅程为2146CM，问最初高度？FunctionInversefunctionExponentLogarithmComplementaryfunctionLinearfunctionQuadraticfunctionFunctionInversefunctionExponentLogarithmComplementaryfunctionLinearfunctionQuadraticfunction函数反函数指数对数余函数一次函数二次函数Forallpositivevaluesofx,thefunctionfisdefinedby.ofthefollowing,whichisthebestapproximationoff(x)forvalueofxgreaterthan1000?AbscissaordinateQuadrantCoordinateSlopeintercedeAbscissaordinateQuadrantCoordinateSlopeintercede横坐标纵坐标象限坐标斜率截距排列(permutation)组合(combination)有两个老师三个学生排队，老师只能在最前或最后，有多少种排法？6本书其中paperbook4本,hardbook2本.求取3本至少1本hardbook,有多少种取法(2次)w概率(probability)tOnMonday,AndersonHighSchoolsbasketballteamwillplaytheteamfromBakerHighSchool.OnWednesday,BakersteamwillplaytheteamfromColeHighSchool.OnFriday,ColewillplayAnderson.ineachgame,eitherteamhasa50percentchanceofwinning.(a)whatistheprobabilitythatAndersonwillwinbothitsgame?(b)whatistheprobabilitythatBakerwilllosebothitsgame?(c)whatistheprobabilitythatAndersonwillwinbothitsgameandBakerwilllosebothitsgame?抛三次硬币，相同的面朝上的概率onthedeskshowabove,aplayerspinsthearrowtwice.thefractionisformed,whereaisthenumberofthesectorwherethearrowstopsafterthefirstspinandbisthenumberisthesectorwherethearrowstopsafterthesecondspin.oneveryspin,eachofthenumberedsectorshasanequalprobabilityofbeingthesectoronwhichthearrowstops.whatistheprobabilitythatthefractionisgreaterthan1?A.B.C.D.E.IncludedangleInteriorangleExteriorangleAjacentangleIncludedangleInteriorangleExteriorangleAjacentangle夹角内角外角邻角StraightangleSupplementaryanglescomplementaryanglesStraightangleSupplementaryanglescomplementaryangles平角补角余角AcuteangleObtuseangleRightangleAcuteangleObtuseangleRightangle锐角钝角直角CentralangleRoundangleCentralangleRoundangle圆心角圆周角TriangleEquilateraltrianglesIsoscelestrianglesPythagoreantheoremTriangleEquilateraltrianglesIsoscelestrianglesPythagoreantheorem三角形等边三角形等腰三角形毕达哥拉斯定理CongruenttrianglesSimilartrianglesCongruenttrianglesSimilartriangles全等三角形相似三角形一个三角形，一个角60度，另一个45度，45度角对应的边长10，问60度对应的边长。InPQRabove,and.whatisthevalueofthefractionInthefigureabove,arcSBTisonequarterofacirclewithcenterRandradius6.ifthelengthplusthewidthofrectangleABCRis8,thentheperimeteroftheshadedregionisA.B.C.D.E.QuadrilateralsParallelogramsRectanglesSquaresTrapezoidrhombusQuadrilateralsParallelogramsRectanglesSquaresTrapezoidrhombus四边形平行四边形矩形正方形梯形菱形Inthefigureshowabove,lengthsAB,BD,andCDareallunits.anglesAandCareboth.whatistheperimeterofABCD?WhatistheareaofABCD?diagonalsegmentlengthwidthperimeterareadiagonalsegmentlengthwidthperimeterarea对角线线段长宽周长面积PolygonPentagonHexagonheptagonPolygonPentagonHexagonheptagon多边形五边形六边形七边形Octagonenneagon=nonagondecagonOctagonenneagon=nonagondecagon八边形九边形十边形CirclesDiameterRadiusArcchordCirclesDiameterRadiusArcchord圆直径半径弧弦TangentcircumferenceTangentcircumference切线周长Inthefigureshowabove,Aiscenterofacirclewhoseareais25.BandCarepointsonthecircle.themeasureofangleABCis.whatisthelengthoflinesegmentBC?CubesRectangularsolidsPrismsCylindersConeSpherespyramidsCubesRectangularsolidsPrismsCylindersConeSpherespyramids立方体长方体棱柱圆柱圆锥球棱锥increasebyincreasetointermsof.increasebyincreasetointermsof.增加了增加到用表达Inthexy-planeabove,pointQandSarethecentersoftheciecles,whicharetangenttothex-axis.whatistheslopoflineQS?A.1/8B.1/4C.1/2D.7/8E.1Awheelhasanouterdiameterof11inchs,asshownabove.therimis1inchwideandthediameterofthehubis2inches.ifeachspokeextendinchintothehubandinchintotherim,whatisthesumofthelengthofthe5spokes,ininches?Thefigureaboveshowstheremainingpiecesofapaperchainfromwhichasectionhasbeenremoved.thefirstlinkoftheoriginalchainwasredandthecolorsofthelinksformedtherepeatingpatternofred(R),yellow(Y),green(G),white(W)andblue(B)fromlefttoright.whichofthefollowingcouldbethenumberoflinksinthesectionthatwasremoved?A.60B.61C.62D.63E.64Inaplane,tworegions,SandT,arecalled“unlinked”if(1)ShasnopointsincommonwithT.(2)anylinesegmentthatcanbedrawnwithbothendpointsinShasnopointsincommonwithanylinesegmentthatcanbedrawwithbothendpointsinT.Whichofthefollowingshowsapairofregionsthatareunlinked?3,5,-5,Thefirstterminthesequenceofnumbersshowaboveis3.eacheven-numberedtermis2morethantheprevioustermandeachodd-numberedterm,afterthefirst,is-1timesthepreviousterm.forexample,thesecondtermis3+2,andthethirdtermis.whatisthe55thtermofthesequence?A.-5B.-3C.-1D.3E.55.101001000100001Thedecimalnumberaboveconsistsofonly1sand0stotherightofthedecimalpoint.thefirst1isfollowedbyone0,thesecond1isfollowedbytwo0s,thethird1isfollowedbythree0s,andsoon.whatisthetotalnumberof0sbetween98thandthe101st1inthisdecimalnumber?A.288B.291C.294D.297E.300Ifthe5cardsshowaboveareplacedinarowsothatisneverateitherend,howmanydifferentarrangementsarepossible?Ifthe5cardsshowaboveareplacedinarowsothatisneverateitherend,howmanydifferentarrangementsarepossible?79EllipsehyperbolaparabolaEllipsehyperbolaparabola椭圆双曲线抛物线Thefigureaboveshowsthegraphsofy=x2andy=a-x2forsomeconstanta.ifthelengthofPQisequalto6,whatisthevalueofa?A.6B.9C.12D.15E.18Thequadraticfunctiongisgivenby,whereaandcarenegativeconstants.whichofthefollowingcouldbethegraphofg?Thefigureaboveshowsthegraphofaquadraticfunctionfthathasaminimumatthepoint(1,1).iff(b)=f(3),whichofthefollowingcouldbethevalueofb?A.-3B.-2C.-1D.1E.5Inthefigureabove,ABCDisarectangle.pointsAandClieonthegraphof,wherepisaconstant.iftheareaofABCDis4,whatisthevalueofp?PointOhascoordinates(0,0),pointPliesonthegraphof,andpointBhascoordinates.ifOP=BP,theareaoftriangleOPBisA.1.7B.3.0C.3.5D.4.7E.5.2Lilyslockcombinationconsistsof3two-digitnumber.thecombinationsatisfiesthethreeconditionsbelow.Onenumberisodd.Onenumberisamultipleof5.Onenumberisthedayofthemonthoflilysbirthday.Ifeachnumbersatisfiesexactlyoneoftheconditions,whichofthefollowingcouldbethecombinationtothelock?A.14-20-13B.14-25-13C.15-18-16D.20-15-20E.34-30-21N,_,2n,_Thefirstnumberinthesequenceaboveisn,andeachnumberafterthefirstispunitsgreaterthanthepreviousnumber.intermsofp,whatisthesixthnumberinthesequenceA.3pB.4pC.5pD.6pE.7p1/x=0.0N1/y=0.00PThefractions1/xand1/ycanbewrittenasdecimalsasshowabove,whereNandPrepresentdifferentdigits.whichofthefollowingisequalto1/xyisSequalsNtimesPandSisadigit?A.0.0000SB.0.000SC.0.00SD.0.0SE.0.SThefigureaboveshowsacylinderwithradius2andhight5.ifpointsAandBlieonthecircumferenceorthetopandbottomofthecylinder,respectively,whatisthegreatestpossiblestraight-linedistancebetweenAandB?A.3B.5C.7D.E.1,234,1,920,21,484,490Theintegeraboveisformedbywritingtheintegersfrom1to50,inolder,nexttoeachother.iftheintegerisreadfromlefttoright,whatisthe50thdigitfromtheleft?A.0B.1C.2D.3E.9Acircleofradiusrollstotherightalongthelineshownabovewithoutslipping.inthestartingposition,pointAonthecircletouchesthelineforthefirsttimeatpoint0ontheline.AtwhatpointonthelinewillpointAtouchthelineforthefourthtime?A.12B.10C.8D.6E.4Whichofthefollowinghasthesamevolumeasthecylindershownabovewithradiusxandheight2x?A.acylinderwithradius2xandheightxB.AcylinderwithradiusandheightxC.Acubewithedge2xD.AcubewithedgeE.Arectangularsolidwithdimensionsx,2x,Inthescheduleabove,eachsessionistobe1.5hourslong,eachbreakistobehourlong,andlunchistobe1hourlong.ifsession4istoendat4:30P.M,atwhattimeshouldsession1begin?A.8:15A.MB.8:30A.MC.8:45A.MD.9:00A.ME.9:15A.MEventBeginningTimeEndingTimeSession1BreakSession2LunchSession3BreakSession44:30P.MAmerchantsellsthreetypesofclocksthatchimeasindicatedbythecheckmarksinthetableabove.whatisthetotalnumberofchimesoftheinventoryofclocksinthe90-minuteperiodfrom7:15to8:45?Number0fclocksChimesntimesonthenthHourChimesonceonthehourChimesonceonthehalfhourTypeA10TypeB5TypeC3a,3a,Thefirstterminthesequenceaboveisa,andeachtermafterthefirstis3timestheprecedingterm.ifthesumofthefirst5termis605.whatisthevalueofa?Inthefigureabove,ABCDisarectanglewithBC=4andAB=6PointsP,Q,andRaredifferentpointsonaline(notshown)thatisparalleltoAD.pointsPandQaresymmetricaboutlineABandpointsQandRaresymmetricaboutlineCD.whatisthelengthofPR?A.6B.8C.10D.12E.20NumberofsiblingsperstudentinapreschoolclassThetableaboveshowshowmanystudentsinaclassof12preschoolershad0,1,2,or3siblings.later,anewstudentjoinedtheclass,andtheaverage(arithmeticmean)numberofsiblingsperstudentsbecameequaltothemediannumberofsiblingsperstudent.howmanysiblingsdidthenewstudentshave?A.0B.1C.2D.3E.4NumberofSiblingsNumberofStudents03162231Ifp,r,andsarethreedifferentprimenumbersgreaterthan2,andn=prs,howmanypositivefactors,including1andn,doesnhave?Howmanyintegersgreaterthan20andlessthan30areeachthepreductofexactlytwodifferentnumbers,bothofwhichareprime?A.zeroB.oneC.twoD.threeE.fourIfi=,forwhichofthefolloeingvaluesofndoeshaveapositivevalue?A.23B.24C.25D.26E.27Twoidenticalspheresofradius6intersectsothatthedistancebetweentheircentersis10.thepointsofintersectionofthetwospheresfromacircle.whatistheareaofthiscircle?A.B.C.D.E.Eachofthe3circlesistangenttotheother2,andeachsideoftheequilateraltriangleistangentto2ofthecircles.ifthelengthofonesideofthetriangleisx,whatistheradius,intermsofx,ofoneofthecircles?A.B.C.D.E.Inaremainderof4isobtainedwhenisdividedbyx-2,whatisthevalueofk?A.4B.6C.10D.12E.14Inthestopsignshowninthefigureabove,allsideshaveequallengthandallangleshaveequalmeasure.ifthefigurecouldberotated225degreesinaclockwisedirection,pointGwouldbeinthepositionofpointA.IB.JC.KD.LE.MAschoolbushas10doubleseatsineachof2rows.twostudentscansitineachdoubleseat.ifanemptybusstartsoutandmakestwostops,pickingupthreetimesthenumberofstudentsatthesecondstopasatthefirststop,andifthebusisthenfilledtoseatingcapacity,howmanystudentsgotonthebusatthesecondstop?A.5B.10C.15D.20E.30KNKNKNKN+_232IfKandNaredigitsinthetwodigitnumbersinthesumabove,thenK+N=Inthefigureabove,thecircleinscribedinPQRShasradius3.whatistheperimeterofsquarePQRS?A.9B.24C.36D.54E.81Inalistofnumbers,thefirstnumberis3.thesecondis4.andeachsubsequentnumberisthesumofalltheproceedingnumbersinthelist.ifthe20thnumberinthelistisx.whatisthe25thnumberinthelist?A.7XB.16XC.32XD.35XE.161XInthefigureaboveiftheareaoftheinscribedrectangularregionis32,thenthecircumferenceofthecircleisA.B.C.D.E.Acertainintegernisamultipleofboth5and9.whichofthefollowingmustbetrue?.nisanoddinteger.nisequalto45.nisamultipleof15A.onlyB.andonlyC.andonlyD.andonlyE.,andInthefigureabove,thecircleisinscribedinthesquare.ifthesquarehassideoflength100,thentheperimeterofthesquareisapproximatelyhowmuchgreaterthanthecircumferenceofthecircle?A.9686B.2150C.243D.100E.86Asecretarytyped6letters,eachofwhichhadeither1or2pages.ifthesecretarytyped10pagesinall,howmanyofthelettershad2pages?A.1B.2C.3D.4E.5At9:00a.m.trainTleftthetrainstationandtwohourslatertrainSleftthesamestationonaparalleltrack.iftrainTaveraged60kilometersperhourandtrainSaveraged75kilometersperhouruntilSpassedT,atwhattimedidSpassT?A.2:00p.mB.5:00p.mC.6:00p.mD.7:00p.mE.9:00p.mThevolumeofthecubeinthefigureaboveis64.iftheverticesofPQRaremidpointsofthecubesedges,whatistheperimeterofPQR?A.6B.C.D.12E.ThefigureaboveshowsthepathtracedbytheendofapendulumasitmovesfrompointXtopointY.howmanycentimetersdoestheendofthependulumtravelalongthearcfromXtoY?A.B.C.D.E.Threeindividualscontributed$800eachtowardthepurchaseofacomputer.iftheyboughtthecomputeronsalefor$1950plus10percentsalestax,howmuchmoneyshouldberefundedtoeachindividual?A.$65B.$85C.$150D.$195E.$255Inthefigureabove,arcsPRandQSaresemicircleswithcentersatQandRrespectively.ifPQ=5,whatistheperimeteroftheshadedregion?A.B.C.D.E.Whichofthefollowingstatementsmustbetrueaboutthecubeabove?.planeFEHisparalleltoplaneGDC.BGisperpendiculartoplaneFED.FEisparalleltoBC.A.onlyB.omlyC.onlyD.andE.,andIfPQRandPRSaboveareequilateral,whatfractionofPQRSisshaded?A.1/3B.1/4C.1/6D.1/9E.1/12Inthefigureabove,OisthecenterofthecircleandarcSRThaslength,ifthecircumferenceofthecircleis,whatisthevalueofx+y?A.60B.90C.120D.150E.itcannotbedeterminedfromtheinformationgiven.IfBandDarecentersofthecirclesshowninthefigureaboveandifBD=12,BC=2,andDE=3,thenAB=A.12B.14C.21D.22E.24Intherectangularcoordinatesystemabove,theareaoftheshadedregionisA.1.5B.2C.2.5D.3E.4Inthefigureabove,theproductofanytwonumbersinadjacentcirclesisequaltotheproductofthetwonumbersthatareoppositethosecircles.forexample.3f=46.whatisthevalueofj?A.3B.4C.6D.12E.20Thefigureaboveshowsthelengthsofthesidesofanequiangularpolygon,whatisthear