網(wǎng)絡課堂xdf 08gmat數(shù)學

GMAT數(shù)學講主講：黃歡迎使用新東方在線電子教數(shù)學詞 數(shù)學符GMAT數(shù)學講主講：黃歡迎使用新東方在線電子教數(shù)學詞 數(shù)學符equalto,thesameas,ismorethanlessnomoreaddAtoB,plus,sumofAandB,totalminus,less,difference,subtractAfromBAdividedbyB，AdividedintoB，Aabsolute≡＞＜≥＋－×÷by2XXXsquare3cubeparallel⊥perpendicular2.數(shù)字前1：uni,bi,du,tri,tera,penta,hex,10:dec,3.方程2.數(shù)字前1：uni,bi,du,tri,tera,penta,hex,10:dec,3.方程解4.數(shù)列和集arithmeticgeometric 5.排列組合與概 6.數(shù)common commoncompositeconsecutive位5.排列組合與概 6.數(shù)common commoncompositeconsecutive位divisibleevenly even least naturalnegativeoddpositiveprime primenumber質數(shù) rational有理數(shù)realnumberremainderoddpositiveprime primenumber質數(shù) rational有理數(shù)realnumberremainderwholenumberunits’digittens’digithundreds'2-digitnumber7.單利復利和價compoundinterestcostdiscountdownpaymentinterestratelistpricemarginmarkupmarkdownprofitpurchasingpriceretailvaluesalepricesimplemarginmarkupmarkdownprofitpurchasingpriceretailvaluesalepricesimpleinterest8.其他代additionarithmeticmeanaveragebaseapproximationnotationpointdecreaseddecrease·to··definedenominatordenotedepreciationdistinctexpressionfractiongeometricmeanimproperfractionincreasedindenominatordenotedepreciationdistinctexpressionfractiongeometricmeanimproperfractionincreasedincreased·to··intermsof·leastpossiblemaximumminimummultiplynumeratorpercapitapowerproportionaltoproperfactionratioreciprocalreducedroundedtothenearesttenthsuccessive，inarowtehthtenths’digittietimestworatioreciprocalreducedroundedtothenearesttenthsuccessive，inarowtehthtenths’digittietimestwodigitstwiceasABA是B3/2asmanyasAAis20%BAB9.幾abscissaacuteanglealtitudearcareaanglebisectorbisectcenterchordcirclecircumferencecircumscribeclockwiseconcentriccircleconecongruentcoordinatecubecenterchordcirclecircumferencecircumscribeclockwiseconcentriccircleconecongruentcoordinatecubecylinderdecagondegreediameterdiagonaldimensiondistanceduenorthequilateralfaceheighthexagonhypotenuseisoscelestriangleinscribeintersectlengthmedianofamidheighthexagonhypotenuseisoscelestriangleinscribeintersectlengthmedianofamidpointnumberlinesobtuseangleoctagonordinateoverlapparallelogrampentagonperimeterparallellinesperpendicularlinesplanepolygonquadrantquadrilateralradiusradian（弧長/半徑regularpolygonrectangularsolidrectanglerightanglequadrilateralradiusradian（弧長/半徑regularpolygonrectangularsolidrectanglerightanglerighttrianglesquarespheresidesurfaceareastraightanglesegmenttangenttrianglevertex（vertices）angleverticalanglevolumewidth數(shù)學知識與技引入Ify=5x2－2xandx=3,then數(shù)學知識與技引入Ify=5x2－2xandx=3,thenIfy≠3and3x/yisaprimeintegerbetrue?Ⅰ.x=Ⅱ.yⅢ.xandyareprime2ⅠⅠandIf2x=3y=10,then12xy=?(A)1,200(B)(C)1.一元二次方ax2bxcb b2x一般常用因式分解法2x3x(x2x3x(x3)(x1)x13,十字交叉Ifxisanumbersuch 3x2x x20,whatisthevaluexx3X22X8(A)(3X4)(X(B)(3X4)(X(C)(3X2)(X(D)(3X2)(X(E)noneoftheInacertaingame,alargecontainerisfilledwithred,yellow,green,andbluebeadsworth,respectively,7,5,3,and2pointseach.Anumberofbeadsarethenremovedfromthecontainer.Iftheproductofthepointvaluesoftheremovedbeadsis147,000,howmanyredbeadswereremoved?43Ifxandyarepositiveintegersand1xyxy15,whatisthevalueofx界定范圍111 界定范圍111 0.15495Ofthefollowing,whichifclosest4496is3and4and5and6and7and2.二元一次方程3xy2xy（2If2x5y8 3x2y,whatis2xyvalue3xy3xy6x2y3：3xy 6x2y3.二元二次方程a1xb1yby a2xb ay 4.不等若ab>0,a>0,則b>0若a>b，c<0，則ac<bc(注意c的符號的影響)若|x—a|>b,則x—a>b或x—a<—bn=kp(1)n<p(2)n>k1.等差數(shù)a1(nsn(a1an)n/n1.等差數(shù)a1(nsn(a1an)n/na1)/d藍皮本P201第444題Howmanyintegersbetween324,700and458,600havetensdigit1andunitsdigit3?2.等比數(shù)an 1s 11時， 1例：1 1 2Ifthesequencex1,x2,x3,xnisthatx12xn n1,x19(D)220(E)221Thesequencea1,a2,,an,issuchthatan2an1xforallpositiven2a599anda327,whatisthevalueforcertainnumberxxa599anda327,whatisthevalueforcertainnumberxx王小丫的難題：AorB3.集ABAABI=A+B—AB+A1.排列與組m!/(m從mnmm!/n!(mCmC 法完成，則這件事可由m+n種方法來完成。法完成，則這件事可由mxn種方法來完成。2.概第一步：概率基本原理（古典定義P(A)=A所包含的基本事件數(shù)/P(A) /1P(A) /1,P(A) /C21 5只乒乓球，其中三只白色，兩只紅色。現(xiàn)從袋中取球兩次，每次一只，插入練習 藍皮書P208第487Xavier,Yvonne,andZeldaeachtryindependentlytosolveaproblem.Iftheirindividualprobabilitiesforsuccessare1/4,1/2,and5/8,respectively,whatistheprobabilitythatXavierandYvonne,butnotZelda,willsolvetheproblem?牌照號碼中有數(shù)字8的概率？a只白球，bK(1Kab)C1aCC 4 43.條件概CC 4 43.條件概乘法原則 InTownshipK,1/5ofthehousingunitsareequippedwithcabletelevision.If1/10ofthehousingunits,including1/3ofthosethatareequippedwithcabletelevision,areequippedwithvidieocassetterecorders,whatfractionofthehousingunitshaveneithercabletelevisionnorvideocassetterecorders?Acertainjuniorclasshas1,000studentsandacertainseniorclasshas800students.Amongthesestudents,thereare60siblingpairs,eachconsistingof1juniorand1senior.Ifstudentistobeselectedatrandomfromeachclass,whatistheprobabilitythatthe2studentsselectedwillbeasiblingpair?PPP PP p5/5PP p5/5第一，3p 第二，3P 第三，3P8P35 8擋板模型：0102030405C4排列組合題目的四個步驟講義白皮書第28頁31C64． P 5P2P53P5353C9 P 5P2P53P5353C921C952Ck C(2)(2 24 ) ) 22(0.7)24C541 (0.6)4C+5250.7=五、數(shù)論（自然數(shù)的理論五、數(shù)論（自然數(shù)的理論偶數(shù)：能被2整除的整數(shù)（可正可負，零是偶數(shù)。通式：2n。如-4，-2，0，2，4。數(shù)。1不是質數(shù)。如2，3，5，7，11，13。偶數(shù)＝＝若n個連續(xù)的奇數(shù)相加等于零，則n為偶數(shù)。如：(-3)+(-1)+1+3=0兩個質數(shù)之和為奇數(shù)，其中必有一個是2。A.B. C. D. E.綜合例題：若a2b2c2a，b，ca+b+cA.-B.- C. D. E.121.Ifxisaneveninteger,whichofthefollowingisanodd(D)x(E)x57．Ifnisanintegergreaterthan6,whichofthefollowingmustbedivisibleby3?(A)n(n+1)(n-4)(B)n(n+2)(n-(C)n(n+3)(n-(D)n(n+4)(n-(E)n(n+5)(n-8n能被abn8n能被abn一定能夠被[a,b]（其中[a,b]a和b的最小公倍數(shù)，另外{a,b}a和b的最大公約數(shù)n812整除，n24258．Theproductofthefirsttwelvepositiveintegersisdivisiblebyallofthefollowing521．Ifnandkareintegerswhoseproductsis400.whichofthefollowingstatementsmustbetrue?n+EithernorkisamultipleofIfniseven,thenkisIfnisodd,thenkis于是p=7(2q+1)+3=14q+1010。顯然答案為A。14除余幾，則必然結果唯一，任意代入一個數(shù)即推論：一個數(shù)是否能夠被5整除，只要看它的最后一位。練習：求265的個位數(shù)是多少？求3365=8116×a1×(1+100×第一階段：先看條件(1)，只要(1)充分，答案不A就是D再看條件(2)，只要(2)充分，答案不是B就是D如果(1)(2)都充分，則答案一定是D如果一個充分一個不充分，答案就是A或者B(只要(1)不充分，答案肯定不是A或者D)第二階段：C是好的，EBB×（2）降低后的價格一美元三個。例：WwW=a+w=a-××x2（2）x>0唯一性?！獭痢獭粒?）x2=(1)Thereare20peoplebehindPamand20peopleinfrontof×(2)Thereare5peoplebetweenPamand×例 （1）x2>（2）x3<n>k2（1）k2－4k+4=（1）k2－4k+4=（1）k－1=k1k=2(1+ （2）x-y=-（2）x2y+xy2=106.Isthepositiveintegernequaltothesquareofan(1)Foreveryprimenumberp,ifpisadivisorofn,thensop2× nisan√111．Ifxandyarepositiveintegersandxisamultipleofy,isy(1)(2)x+2isamultipleof113.Ifxandyareintegersbetween10and99,inclusive,an 9(1)xandyhavethesametwo113.Ifxandyareintegersbetween10and99,inclusive,an 9(1)xandyhavethesametwodigits,butinreverse√(2)thetens’digitofxis2morethantheunitsdigit,andthetensdigitofyis2lessthanunits 122.If⊙denotesamathematicaloperation,doesx⊙y=y⊙xforallxandy?(1)allxandy,x⊙y=2(x2y2)(2)ally,0⊙y=2yn124.Ifnaninteger,aninteger?isan×isan√134.Atotalof774doctoratesinmathematicsweregrantedtoUnitedStatescitizensbyAmericanuniversitiesinthe1972-1973schoolyear,andWofthesedoctoratesweregrantedtowomen.Thetotalofsuchdoctoratesinthe1986-1987schoolyearwas362,andwoftheseweregrantedtowomen.IfthenumberofdoctoratesinmathematicsgrantedtofemalecitizensoftheUnitedStatesbyAmericanuniversitiesdecreasedfromthe1972-1973schoolyeartothe1986-1987schoolwasthedecreaselessthan10percent? W<< (2)習題講Aparkinggaragerentsparkingspacesfor$10perweekor$30permonth.Howmuchdoesapersonsaveinayearbyrentingbythemonthratherthanbytheweek?In1979approximately1/3ofthe37.3millionairlinepassengerstravelingtoorfromtheUnitedStatesusedKennedyAirport.In1979approximately1/3ofthe37.3millionairlinepassengerstravelingtoorfromtheUnitedStatesusedKennedyAirport.IfthenumberofsuchpassengersthatusedMiamiAirportwas1/2thenumberthatusedKennedyAirportand4timesthenumberthatusedLoganAirport,approximatelyhowmanymillionsofthesepassengersusedLoganAirportthatyear?BenandAnnareamong7contestantsfromwhich4semifinalistsaretobeselected.Ofthedifferentpossibleselections,howmanycontainneitherBennorAnn?567Howmanypositiveintegerskaretheresuchthat100kisafactorofEachoftheintegersform0to9,inclusive,iswrittenonaseparateslipofblandpaperandthetenslipsaredroppedintoahat.Iftheslipsarethendrawnoneatatimewithoutreplacement,howmanymustbedrawntoensurethatthenumbersontwooftheslipsdrawnwillhaveasumof10?Inacertainformula,pisdirectlyproportionaltosandinverselyproportionaltor.Ifp=1whenr=0.5ands=2,whatisthevalueofpintermsofr,ands?(E)SetS(E)SetSconsistsofndistinctpositiveintegers,noneofwhichisgreaterthan12.WhatisthegreatestpossiblevalueofnifnotwointegersinShaveacommonfactorgreaterthan1?4567Inacertaincontest,Fredmustselectany3of5differentgiftsofferedbythesponsor.Fromhowmanydifferentcombinationsof3giftscanFredmakehisselection?IfthenumberofsquareunitsintheareaofcircleCistwicethenumberoflinearunitsinthecircumferenceofC,whatisthenumberofsquareunitsinthearea?48Ifw,x,y,andnon-negativeintegers,eachlessthan3,andw(33)+x(32)+y(3)+z=34,then01234Inthefigureabove,ifAB∥CE,CE=DE,andy=45,then(C)67.5(D)(E)BCADENote:figurenotdrawnto藍皮書：P200—Thetableaboveshowsthecost,indollars,oftravelingtoandfromcitiesA,B,C,D,E,andE.(D)(E)BCADENote:figurenotdrawnto藍皮書：P200—Thetableaboveshowsthecost,indollars,oftravelingtoandfromcitiesA,B,C,D,E,andE.AsalesrepresentativewantstoleavefromA,traveltoC,E,andF,andreturntoA.IfthefirstcitythatthesalesrepresentativetravelstomustbeE,whatistheminimumpossiblecostfortheentiretrip?(A)(B)(C)(D)(E)藍皮書：P204—Ifitis6:27intheeveningonacertainday,whattimeinthemorningwasitexactly2,880,717minutesearlier?(Assumestandardtimeinonelocation.)(A)(B)(C)(D)(E)藍皮書：P204—Ifnisaninteger,whichofthefollowingCANNOTbeafactorofCityA33273City33455City33124City2455City7556City35456456783.1平面幾a,b,c：面積456783.1平面幾a,b,c：面積=1/2absinγ（γa,b兩邊之夾角1ab2對于直角三角形34對于等邊三角形，γ=60°，S等邊三角形。周長面積面積周長面積周長面積周長面積周長3.2立體幾周長面積周長3.2立體幾體積表面積2．正方體（立方體（體積表面積體積表面積3.3解析幾②x/a+y/b（截距式，a為x軸上截距，b為y軸上截距)/()=(④(y-y1)/(x-x1)例：請寫出x軸與y2030x,y≥0 算術平均數(shù)（arithmeticmeann1na ababa22122 aa2 算術平均數(shù)（arithmeticmeann1na ababa22122 aa22調和平均，1122 Whatistheaverage(arithmeticmean)ofthenumbers15,16,17,17,18,andAstudent'saverage(arithmeticmean)testscoreon4testsis78.Whatstudent'sscoreona5thtsetforthestudent'saveragescoreonthe580期望偏差 方差1nnaiE期望偏差 方差1nnaiE2 標準差（standardσ=中間數(shù)}，然后取中為Forthepositivenumbersandn+8,themeanishowmuchthemedian眾數(shù)求下圖的medianscore0Amarketingfirmdeterminedthat,of200householdssurveyed,80used求下圖的medianscore0Amarketingfirmdeterminedthat,of200householdssurveyed,80usedAnorBrandBsoap,60usedonlyBrandAsoap.andforeveryhouseholdthatbothbrandsofsoap,3usedonlyBrandBsoap.Howmanyofthe200usedbothbrandsof范圍人人Raffleticketsnumberedconsecutivelyfrom101through350areRaffleticketsnumberedconsecutivelyfrom101through350areplacedinabox.Whatisprobabilitythataticketselectedatrandomwillhaveanumberwithahundredsdigitof2527Ifxandyareprimenumbers,whichofthefollowingCANNOTbethesumofxandy59Ifeachoffollowingfractionswerewrittenasarepeatingdecimal,whichwouldhavethelongestsequenceofdifferentdigits?(A)(B)1/3(D)(E)whatisthelowestwhatisthelowestpositiveintegerthatisdivisiblebyeachoftheintegers1through7,(A)(B)840(C)1,260(E)Ifapositiveintegernisdivisiblebyboth5and7,thennmustalsobedivisiblebywhichof(1)(1)(2)(D)(1)and(E)(2)and(2)(3)Inacertainpopulation,thereare3timesasmanypeopleaged21orunderastherearepeople21.Theratioofthose21orundertothetotalpopulation1to1to1to2to3toFermatprimesareprimenumbersthatcanbewrittenintheform 1,wherekisanintegerandpowerof2,whichofthefollowingisNOTaFermatprime?35(E)AcomputerchipmanufacturerexpectstheratioofthenumberofdefectivechiptothetotalnumberofchipsinallfutureshipmentstoequalthecorrespondingratioforshipmentsS1,S2,S3,andS4of60,000chips?Numberofdefectivechipsinthe2Numberofdefectivechipsinthe2564Totalnumberofchipsinthe Twointegerswillberandomlyselectedfromthesetsabove,oneintegersetAandoneintegerfromsetB.Whatistheprobabilitythatthesunofthetwointegerswillequal9?(A)(B)(C)(D)(E)Inthelistabove,ifnisanintegerbetween1and10,inclusive,thenthemedianmusteither4oreither5oreither6or(E)Agymclasscabbedividedinto8teamswithanequalnumberofplayersoneachteamorinto12teamswithanequalnumberofplayersoneachteam.Whatisthelowestpossiblenumberofstudentsintheclass?(A)InInaincreasingsequenceof10consecutiveintegers,thesumofthefirst5integersis560.Whatisthesumofthelast5integersinthesequence?Ifthemedianofthenumbersinlist1aboveisequaltothemedianofthenumbersinthelist2above,whatisthevalueofx?78Acertaincompanyretirementplanhasa“ruleof70”provisionthatallowsanemployeetoretirewhentheemployee’sageplusyearsofemploymentwiththecompanytotalatleast70.Inwhatyearcouldafemaleemployeehiredin1986onher32ndbirthdayfirstbeeligibletoretireunderthis(A)(B)(C)(D)(E)Onascalethatmeasurestheintensityofacertainphenomenon,areadingofn+1correspondstoanintensitythatis10timestheintensitycorrespondingtoareadingofn.Onthatscale,theintensitycorrespondingtoareadingof8ishowmanytimesasgreatastheintensitycorrespondingtoareadingof3?5(C)810Ifxandyaredifferentprimenumbers,eachgreaterthan2,,whichofthefollowingmust(C)810Ifxandyaredifferentprimenumbers,eachgreaterthan2,,whichofthefollowingmustbe doesn’tequalx-yisanevenx/yisnotan(2)(1)and(2)(1)and(3)(E)(1)(2)and(3)Each*inthemileagetableaboverepresentsanentryindicatingthedistancebetweenapairofthefivecities.Ifthetablewereextendedtorepresentthedistancesbetweenallpairsof30citiesandeachdistanceweretoberepresentedbyonlyoneentry,howmanyentrieswouldthetablethenhave?(A)(B)(C)(D)(E)Thereare8teamsinacertainleagueandeachteamplayseachoftheotherteamsexactlyonce.Ifeachgameisplayedby2teams,whatisthetotalnumberofgamesplayed?(A)CityCityCityCityCityCity****City***City**City*CityItwouldtakeonemachine4hourstocompletealargeproductionorderandanothermachine3hourstocompletethesameorder.Howmanyhourswouldittakebothmachines,workingsimultaneouslyattheirrespectiveconstantrates,tocompletetheorder?(A)121732Itwouldtakeonemachine4hourstocompletealargeproductionorderandanothermachine3hourstocompletethesameorder.Howmanyhourswouldittakebothmachines,workingsimultaneouslyattheirrespectiveconstantrates,tocompletetheorder?(A)121732(E)Onarecenttrip,Cindydrovehercar290miles,roundedtothenearest10mails,andused12gallonsofgasoline,roundedtothenearestgallon.TheactualnumberofmilespergallonthatCindy’scargotonthistripmusthavebeenbetween(A)290/12.5and290/11.4(B)295/12and284/11.4(C)284/12and295/12(D)284/12.5and(E)295/12.5andIftheoperationQisdefinedbyxQy xyforallpositivenumbersxandy,then(5Q45)(D)30(E)60Inthefigureabove,VrepresentsanobservationpointatoneInthefigureabove,Vrepresentsanobservationpointatoneendofapool.FromV,anobjectthatisactuallylocatedonthebottomofthepoolatpointRappearstobeatpointS.IfVR=10feet,whatisthedistanceRS,infeet,betweentheactualpositionandtheperceivedpositionofthe(A)103(B)10(C)222(E)VRS黃皮書官方指P172—Atoystoreregularlysellsallstockatadiscountof20percentto40percent.Ifanadditional25percentweredeductedfromthediscountpriceduringaspecialsale,whatwouldbethelowestpossiblepriceofatoycosting$16beforeanydiscount?(A)(B)(C)(D)$9.60(E)黃皮書官方指南P172--Jackisnow14yearsolderthanBill.Ifin10yearsJackwillbetwiceasoldasBill,howoldwillJackbein5years?(E)Ifthe(E)Iftheproductoftheintegersw,x,yandzis770,andif1wxyz,whatisthevalueof(E)Theprobabilityis1/2thatacertaincoinwillturnupheadsonanygiventoss.Ifthecoinistobetossedthreetimes,whatistheprobabilitythatonatleastoneofthetossesthecoinwillturnuptails?(B)(C)3/4ThetableaboveshowsthenumberofstudentsinthreeclubsatMcAuliffeschool.Althoughnostudentisinallthreeclubs,,10studentsareinbothChessandDrama,5studentsareinbothChessandMath,and6studentsareinbothDandM.Howmanydifferentstudentsareinthethreeclubs?Inanationwidepoll,Npeoplewereinterviewed,If1/4ofthemanswered“yes”toquestion1,andofthose,1/3answered“yes”toquestion2,whichofthefollowingexpressionsrepresentsthenumberofpeopleinterviewedwhodidnotanswer“yes”tobothquestions?(C)(D)7N/12(E)Theratiooftwoquantiyiesis3to4.Ifeachofthequantitiesisincreasedby5,whatistheratioofthesetwonewquantities?(B)8/9(C)18/19(D)(E)ItcannotbedeterminedfromtheinformationIfp(B)8/9(C)18/19(D)(E)ItcannotbedeterminedfromtheinformationIfpisanevenintegerandqisanoddinteger,whichofthefollowingmustbeanoddinteger?PatwalkfromintersectionXtointersectionYalongaroutethatisconfinedtothesquaregridoffourstreetsandthreeavenuesshowninthemapabove.HowmanyroutesfromXtoYcanPa