套餐全部-网络课堂.xdf08gmat数学

GMAT数学讲等于 equalto,thesameas,不等于 more less nomore加 addAtoB,plus,sumofAandB,—minus,less,difference,subtractAB×除 AdividedbyB，AdividedintoB，AdivisiblebyX绝对值： absoluteX

X

X 开平方 square3开立方 cube3parallel⊥perpendicular1：uni,mono,2:bi,du,di3:tri,ter4:tera,5:penta,6:hex,7:8:9:10:dec, 方 arithmeticprogression等差数列geometricprogression等比数列set集合 inclusive common common composite consecutive divisibleby evenlydivisible evennumber leastcommon naturalnumber negativenumber oddnumber positivenumber primefactor primenumber质数 rational有理数realnumber实数remainder余数wholenumber整数units’digittens’digit十位数hundreds' 2-digitnumbercompoundinterestcost成本discountdownpayment预付款，现付款 抵押mortinterestrate利率listpricemargin利润markup涨价markdownmarkupprofit利润purchasingprice价retailvalue零售价saleprice销售价simpleinterest单利additionarithmeticmeanaveragebaseclosestapproximationdecimaldecimalnotationdecimalpoint小数点decreased下降后的decrease·to··by·define定义denominator分母denotedepreciationdistinct不同的expressionfraction分数geometricmeanimproperfraction假分数increased增加后的increased·to··increaseby·增加了intermsofleastpossibleum最大值minimum最小值multiply乘multipliernumerator分子percapitapower质数proportionaltoproperfactionratio比率reciprocalreduced降低后roundedtothenearesttenthsuccessive，inarowtehth十分位tenths’digittie平局timestwodigitstwiceasmanyAasBAB3/2asmanyAasBAB3/2Ais20%morethan A比B多 abscissaacuteanglealtitudearcareaanglebisectorbisectcenterchord弦circle圆circumference圆周长circumscribe外切，外接clockwise顺时针concentriccirclecone圆锥congruent全等的coordinate坐标counterclockwisecube正方体cylinder圆柱decagon十边形degree角度diameter直径diagonal对角线dimensiondistance距离duenorthequilateraltrianglefaceheight高hexagon六边形hypotenuseisoscelestriangleinscribe内接，内切intersect相交lengthmedianofatrianglemidpoint中点numberlinesobtuseangleoctagon八边形ordinate纵坐标overlap交叠parallelogrampentagon五边形perimeter周长parallellines平行线perpendicularlinesplane平面polygonquadrantquadrilateralradiusradian（弧长/半径）regularpolygonrectangularsolidrectangle长方形rightanglerighttrianglesquaresphere球side边surfaceareastraightanglesegment线段tangent切线triangle三角形vertex（vertices）angleverticalanglevolumewidth1P133Ify=5x2－2xandx=3,then2P13620Ify≠3and3x/yisaprimeintegergreaterthan2,whichofthefollowingmustbetrue?x=yxandyareprimeⅠⅡⅢⅠand3P13624If2x=3y=10,thenax2bxcb b2b b2x22x30(x3)(x1)0x13,x211P14050Ifxisanumbersuchthat

x23x2

x2x20,whatisthevalueofx2P1732643X22X8(A)(3X4)(X(B)(3X4)(X(C)(3X2)(X(D)(3X2)(X(E)noneofthe3P210499Inacertaingame,alargecontainerisfilledwithred,yellow,green,andbluebeadsworth,respectively,7,5,3,and2pointseach.Anumberofbeadsarethenremovedfromthecontainer.Iftheproductofthepointvaluesoftheremovedbeadsis147,000,howmanyredbeadswereremoved?4P155148Ifxandyarepositiveintegers

1xyxy15,whatisthevalue

x351P143691

2P14898Ofthefollowing,whichifclosestto3P14476443and4and5and6and7and1：

0.15?3xy

2xy

（2P14792If2x5y

3x2y,whatis value

2xy2：3xy

6x2y

3：3xy

6x2y

223ax2bx223

y2

y

33ab>0,a>0,b>0a>b，c>0，则ac>b若a>b，c<0，则ac<bc (注意c的符号的影响)若|x—a|>b,则x—a>b或x—a<—bn=kpn<pn>kana1(n1)dsn(a1an)n/n(ana1)/d11003的倍数？P201444题Howmanyintegersbetween324,700and458,600havetensdigit1andunitsdigit3?1naaqn11n1qnsna11当q1时， 11

11 P169237Ifthex20x19221220221

x1,x2,x3,xnissuch

x1

xn12xn

n1,P179299The

a1,a2,,an,issuch

an2an1xforallpositive

n

forcertainnumberx39的难题：AorB

a599

a327,whatisthevalueofxABAABI=A+B—AB+AI=A+B+C—AB—BC—CA+ABC+A+B+10025mPnm!/(mm

mnCmnm!/n!(mCmCmmnCmnCmm

m个人中挑出nm+n种方法来完成。mxn种方法来完成。P(A)=A所包含的基本事件数/P(A)C1/C1,P(A)C2/C 5只乒乓球，其中三只白色，两只红色。现从袋中取球两次，每次一只，三个人独立地去破译一个，他们能译出的概率分别为1/5,1/3,1/4,求将此破译出插入练习 蓝皮书P208第487Xavier,Yvonne,andZeldaeachtryindependentlytosolveaproblem.Iftheirindividualprobabilitiesforsuccessare1/4,1/2,and5/8,respectively,whatistheprobabilitythatXavierandYvonne,butnotZelda,willsolvetheproblem?80，1，2·9a只白球，bK(1Kab)C1CaPPC9C4C CCC160

2P164203InTownshipK,1/5ofthehousingunitsareequippedwithcableevision.If1/10ofthehousingunits,including1/3ofthosethatareequippedwithcableevision,areequippedwithvidieocassetterecorders,whatfractionofthehousingunitshaveneithercableevisionnorcassetterecorders?3P182217Acertainjuniorclasshas1,000studentsandacertainseniorclasshas800students.Amongthesestudents,thereare60siblingpairs,eachconsistingof1juniorand1senior.Ifstudentistobeselectedatrandomfromeachclass,whatistheprobabilitythatthe2studentsselectedwillbeasiblingpair?P5P4P4P P3P3 5p5/5上有5个不同的唱歌和3个不同的舞蹈，问：分别按以下要求各可排出几第一，3个舞蹈排在一起；p6p 第二，3个舞蹈彼此分开；P3P5 第三，3个舞蹈先后顺序一定。P8/P3P5挡板模型：0102030405

422C2C4P28题目：1，8，9，11，12，18，19，22，26---30286410个人中有6人是，问组成4人组，三男一女的组合数。答案：C3C1648432P3329．51排，1辆黄色，1辆蓝色，33辆红车不可分辨，问有多少种排PP25PP2P答案： 3或 P3125431C答案：1－ C918091085C答案 C9C答案： C1k

k答案：(2)

(2)

1答案：2)

1C2(2) C2一个人掷飞标，其靶心的概率为0.7，他连续掷4次飞标，有2次靶心的概率2C4答案：(0.7) 2C45答案：(0.6)5(0.6)4529．A0.6，B0.5A,B都不发生的最大概率？250.560.7=五、数论（自然数的理论1和它本身之外没有别的因子的自然数。2是最小的质数，也是唯一的偶质数。12，3，5，7，11，13。1和它本身之外由别的因子的自然数。4是最小的合数。16，8，9偶数＝＝nn2。A. B. C. D. E.综合例题：若a2b2c2a，b，ca+b+cA.- B.- C. D. E.151121Ifxisaneveninteger,whichofthefollowingisanoddxx14157Ifnisanintegergreaterthan6,whichofthefollowingmustbedivisibleby38n能被abn一定能够被[ab]（其中[ab]表示ab的最小公倍数，另外{ab}ab的最大公约数特别地,a,b互质(即无公因子),则na×b(这里用到了公式[a,b]＝a×b/{a,n812整除，n24整除；n811整除，n88172258258．Theproductofthefirsttwelvepositiveintegersisdivisiblebyallofthefollowing214521521．Ifnandkareintegerswhoseproductsis400.whichofthefollowingstatementsmustbetrue?n+EithernorkisamultipleofIfniseven,thenkisIfnisodd,thenkis7314p=7n＋3p为偶数，37n为奇数，np=7(2q+1)+3=14q+1010。 设两数分别为abba，则(ab)+(ba)=(10a+b)+(10b+a)=11(a+b)11的倍数A。14除余几，则必然结果唯一，任意代入一个数即C=A+B且AmCmBm的倍数互为充分必要条件5整除，只要看它的最后一位。33整除。 66。练习：求265的个位数是多少？265=1616×求365a1×100×B为(1)不充分，(2)如果(1)(2)都充分，则答案一定是D如果一个充分一个不充分，答案就是AB(只要(1)AD)第二阶段：C是好的，E若都不充分，则看(1)和(2)C；否则选E例：买一打（12个）罐装汤，问降低后的价格比起格便宜多少？ （2）降低后的价格一三个。例：W-w>0? W=a+ w=a- CABx2

例 （2）x2= 234114Thereare20peoplebehindPamand20peopleinfrontof Thereare5peoplebetweenPamand 不性例 （1）x2>（2）x3<17例：若n=kp且 n<p2n>k21（（1）k2－4k+4=

2（（1）k－1=k

k=2(1+3（ （2）x-y=-4（ x2y+xy2=：233106106.Isthepositiveintegernequaltothesquareofan Foreveryprimenumberp,ifpisadivisorofn,thensoisp2 nisan 234111111．Ifxandyarepositiveintegersandxisamultipleofy,isy x+2isamultipleofmm的约数。2。234113题113.Ifxandyareintegersbetween10and99,inclusive, xandyhavethesametwodigits,butinreverse

an thetens’digitofxis2morethantheunitsdigit,andthetensdigitofyis2lessthantheunitsdigit. 235122If⊙denotesamathematicaloperation,doesx⊙y=y⊙xforallxandy?Forallxandy,x⊙y=2(x2+y2)Forally,0⊙y=2n124.Ifnisaninteger,

aninteger?

isan isan 236134134.Atotalof774doctoratesinmathematicsweregrantedtoUnitedStatescitizensbyAmericanuniversitiesinthe1972-1973schoolyear,andWofthesedoctoratesweregrantedtowomen.Thetotalofsuchdoctoratesinthe1986-1987schoolyearwas362,andwoftheseweregrantedtowomen.IfthenumberofdoctoratesinmathematicsgrantedtofemalecitizensoftheUnitedStatesbyAmericanuniversitiesdecreasedfromthe1972-1973schoolyeartothe1986-1987schoolyear,wasthedecreaselessthan10percent?(C)

1<W< (2)Aparkinggaragerentsparkingspacesfor$10perweekor$30permonth.Howmuchdoesasaveinayearbyrentingbythemonthratherthanbytheweek?In1979approximay1/3ofthe37.3millionairlinepassengerstravelingtoorfromtheUnitedStatesusedKennedyAirport.IfthenumberofsuchpassengersthatusedMiamiAirportwas1/2thenumberthatusedKennedyAirportand4timesthenumberthatusedLoganAirport,approximayhowmanymillionsofthesepassengersusedLoganAirportthatyear?BenandAnnareamong7contestantsfromwhich4semifinalistsaretobeselected.Ofthedifferentpossibleselections,howmanycontainneitherBennorAnn?567Howmanypositiveintegerskaretheresuchthat100kisafactorofEachoftheintegersform0to9,inclusive,iswrittenonaseparateslipofblandpaperandthetenslipsaredroppedintoahat.Iftheslipsarethendrawnoneatatimewithoutreplacement,howmanymustbedrawntoensurethatthenumbersontwooftheslipsdrawnwillhaveasumof10?Inacertainformula,pisdirectlyproportionaltosandinverselyproportionaltor.Ifp=1whenr=0.5ands=2,whatisthevalueofpintermsofr,ands?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,thenC Note:figurenotdrawntoThetableaboveshowsthecost,indollars,oftravelingtoandfromcitiesA,B,C,D,E,andE.AsalesrepresentativewantstoleavefromA,traveltoC,E,andF,andreturntoA.IfthefirstcitythatthesalesrepresentativetravelstomustbeE,whatistheminimumpossiblecostfortheentiretrip?CityBCDEFCity33273City33455City33124City2455City7556City35456Ifitis6:27intheeveningonacertainday,whattimeinthemorningwasitexactly2,880,717minutesearlier?(Assumestandardtimeinonelocation.)Ifnisaninteger,whichofthefollowingCANNOTbeafactorof45678a,b,c面积=1/2absinγ（γa,b两边之夹角12

ab

ab343周长②梯形（abh）③平行四边形（边长为a，bh）周长④矩形（a，b）周长⑤正方形（a）周长⑥圆（R）周长（n-长方体（a，b，c）表面积正方体（立方体（a）表面积圆柱（Rh）表面积②坐标(a,b)y=-x的对称点为(-b,-a) （斜截式，kslope，b②x/ay/b （截距式，ax轴上截距，by轴上截距③(y-y2x-x2y1-y2)/(x1-x2)（两点式，已知④(y-y1)/(x-x1 （点斜式，已知(x1,y1)，斜率例xy2030x,y≥0meann1n a,b>0a=b 1a2a2b22

aba2a2b2221

a2

Whatistheaverage(arithmeticmean)ofthenumbers15,16,17,17,18,and19?Astudent'saverage(arithmeticmean)testscoreon4testsis78.Whatmustbestudent'sscoreona5thtsetforthestudent'saveragescoreonthe5teststo80?期望偏差方差n1n

ED标准差（standarddeviation）D中间数Forthepositivenumbersn,n+1,n+2,n+4andn+8,themeanishowmuchgreaterthemedian?众数2。P31—7人数人数

Amarketingfirmdeterminedthat,of200householdssurveyed,80usedneitherAnorBrandBsoap,60usedonlyBrandAsoap.andforeveryhouseholdthatusedbothbrandsofsoap,3usedonlyBrandBsoap.Howmanyofthe200usedbothbrandsofsoap?范围Raffleticketsnumberedconsecutivelyfrom101through350areplacedinabox.Whatistheprobabilitythataticketselectedatrandomwillhaveanumberwithahundredsdigitof2?

527Ifxandyareprimenumbers,whichofthefollowingCANNOTbethesumofxandy59Ifeachoffollowingfractionswerewrittenasarepeatingdecimal,whichwouldhavethelongestsequenceofdifferentdigits?whatisthelowestpositiveintegerthatisdivisiblebyeachoftheintegers1through7,Ifapositiveintegernisdivisiblebyboth5and7,thennmustalsobedivisiblebywhichofthe(1) (2) (3)(1)(2)(1)and(2)andInacertainpopulation,thereare3timesasmanypeopleaged21orunderastherearepeople21.Theratioofthose21orundertothetotalpopulation1to1to1to2to3toFermatprimesareprimenumbersthatcanbewrittenintheformpowerof2,whichofthefollowingisNOTaFermatprime?35

2k1,wherekisanintegerAcomputerchipmanufacturerexpectstheratioofthenumberofdefectivechiptothetotalnumberofchipsinallfutureshipmentstoequalthecorrespondingratioforshipmentsS1,S2,S3,andS4of60,000chips?NumberofchipsintheTotalnumberchipsinthe2564 Twointegerswillberandomlyselectedfromthesetsabove,oneintegersetAandoneintegerfromsetB.Whatistheprobabilitythatthesunofthetwointegerswillequal9?黄皮书指南P160—65Inthelistabove,ifnisanintegerbetween1and10,inclusive,thenthemedianmusteither4oreither5oreither6ornAgymclasscabbedividedinto8teamswithanequalnumberofplayersoneachteamorinto12teamswithanequalnumberofplayersoneachteam.Whatisthelowestpossiblenumberofstudentsintheclass?Inaincreasingsequenceof10consecutiveintegers,thesumofthefirst5integersis560.Whatisthesumofthelast5integersinthesequence?黄皮书指南P164--93Ifthemedianofthenumbersinlist1aboveisequaltothemedianofthenumbersinthelist2above,whatisthevalueofx?6789Acertaincompanyretirementplanhasa“ruleof70”provisionthatallowsanemployeetoretirewhentheemployee’sageplusyearsofemploymentwiththecompanytotalatleast70.Inwhatyearcouldafemaleemployeehiredin1986onher32ndbirthdayfirstbeeligibletoretireunderthisOnascalethatmeasurestheintensityofacertainphenomenon,areadingofn+1correspondstoanintensitythatis10timestheintensitycorrespondingtoareadingofn.Onthatscale,theintensitycorrespondingtoareadingof8ishowmanytimesasgreatastheintensitycorrespondingtoareadingof3?5

810Ifxandyaredifferentprimenumbers,eachgreaterthan2,,whichofthefollowingmustbe doesn’tequalx-yisanevenx/yisnotan(2)(1)and(2)(1)and(3)(2)and(3)(1)(2)andEach*intheagetableaboverepresentsanentryindicatingthedistancebetweenapairofthefivecities.Ifthetablewereextendedtorepresentthedistancesbetweenallpairsof30citiesandeachdistanceweretoberepresentedbyonlyoneentry,howmanyentrieswouldthetablethenhave?CityCityCityCityCityCity****City***City**City*CityThereare8teamsinacertainleagueandeachteamplayseachoftheotherteamsexactlyonce.Ifeachgameisplayedby2teams,whatisthetotalnumberofgamesplayed?Itwouldtakeonemachine4hourstocompletealargeproductionorderandanothermachine3hourstocompletethesameorder.Howmanyhourswouldittakebothmachines,workingsimultaneouslyattheirrespectiveconstantrates,tocompletetheorder?1217327Onarecenttrip,Cindydrovehercar290,roundedtothenearest10mails,andused12gallonsofgasoline,roundedtothenearestgallon.TheactualnumberofpergallonthatCindy’scargotonthistripmusthavebeenbetween290/12.5and295/12and284/12and284/12.5and295/12.5andxyIftheoperationQisdefinedbyxQy=xy

forallpositivenumbersxandy,then(5Q45)Inthefigureabove,Vrepresentsanobservationpointatoneendofapool.FromV,anobjectthatisactuallylocatedonthebottomofthepoolatpointRappearstobeatpointS.IfVR=10feet,whatisthedistanceRS,infeet,betweentheactualpositionandtheperceivedpositionoftheobject?3103222224V Atoystoreregularlysellsallstockatadiscountof20percentto40percent.Ifanadditional25percentweredeductedfromthediscountpriceduringaspecialsale,whatwouldbethelowestpossiblepriceofatoycosting$16beforeanydiscount?Jackisnow14yearsolderthanBill.Ifin10yearsJackwillbetwiceasoldasBill,howoldwillJackbein5years?9Iftheproductoftheintegersw,x,yandzis770,and

1wxyz,whatisthevalueofTheprobabilityis1/2thatacertaincoinwillturnupheadsonanygiventoss.Ifthecoinistobetossedthreetimes,whatistheprobabilitythatonatleastoneofthetossesthecoinwillturnuptails?ThetableaboveshowsthenumberofstudentsinthreeclubsatMcAuliffeschool.Althoughnostudentisinallthreeclubs,,10studentsareinbothChessandDrama,5studentsareinbothChessandMath,and6studentsareinbothDandM.Howmanydifferentstudentsareinthethreeclubs?Inanationwidepoll,Npeoplewereinterviewed,If1/4ofthemanswered“yes”toquestion1,andofthose,1/3answered“yes”toquestion2,whichofthefollowingexpressionsrepresentsthenumberofpeopleinterviewedwhodidnotanswer“yes”tobothquestions?Theratiooftwoyiesis3to4.Ifeachofthetiesisincreasedby5,whatistheratioofthesetwonewties?ItcannotbedeterminedfromtheinformationIfpisanevenintegerandqisanoddinteger,whichofthefollowingmustbeanoddinteger?PatwalkfromintersectionXtointersectionYalongaroutethatisconfinedtothesquaregri