数学满分攻略

GRE数学满分攻略长沙新东方学校

1.GRE数学考试形式：

2sections(不考虑加试)35minutesforeachsection20questionsforeachsection

分数区间:130—170

题型

数值比较大小

单选

多选

计算填空

题量

8642选项设置

4选15选14或更多选1或更多无选项2.GRE数学题型及分布QuantitativeComparisonQuestions

比较大小题ColumnAColumnBX>Z,Y>ZX+YZQuantityAisgreater.QuantityBisgreater.Thetwoquantitiesareequal.Therelationshipcannotbedeterminedfromtheinformationgiven.

Multiple-choiceQuestions—单选题

Thefractionscanbewrittenasdecimalsasshownabove,whereNandPrepresentdifferentdigits.WhichofthefollowingisequaltoifSequalsNtimesPandSisadigit?0.0000S0.000S0.00S0.0S0.SABCDEMultiple-choiceQuestions多项选择题（3~12个选项）Whichtwoofthefollowingnumbershaveaproductthatisgreaterthan60?-9-768ABCDNumericEntryQuestions-填空题Amerchantmadeaprofitof＄5onthesaleofacoatthatcostthemerchant＄15.Whatistheprofitexpressedasapercentofthemerchant’scost?Giveyouranswertothenearestwholepercent.

％

2.RectangleRhaslength30andwidth10,andsquareShaslength5.TheperimeterofSiswhatfractionoftheperimeterofR?

英文理解能力差

专业词汇-数学表达Vertex(pl.vertices)Quadrilateral/Pentagon/Hexagon/Heptagon/Octagon/Nonagon/DecagonTheratioofAtoBAistwiceasmuchasB/ThereistwiceasmuchAasB3.常见错误Onacertainnumberline,if-7isadistance4fromnand7isadistanceof18fromn,thenn=?

思维不严谨

-TheprobabilityoftheoccurrenceofmatterAis0.6whilethatofmatterBis0.7,what‘stheprobabilityofthecoincidenceofAandB?-小于100的整数中有多少可被6整除?

计算错误课程结构ArithmeticDataanalysisAlgebraGeometryArithmeticIntegers,wholenumberPositive/negativeAmultipleofEveninteger=integersthataremultiplesof2OddintegerConsecutiveintegerscompositePrime

常见数学表达intermsofX

:用X表示

theratioofatob：a：bTwiceasmanyAasB:A=2B运算中“is”代表“等于”，“of”代表“乘以”2/3of1/2ofwhatnumberis4?OddandEven(奇偶性)（1）n为整数，则2n为偶数，2n+1为奇数（2）奇数个奇数相加减，结果为奇数（3）偶数个奇数相加减，结果为偶数（4）奇数和偶数相加减，结果为奇数（5）任意多个偶数相加减，结果为偶数ArithmeticIfnisanoddinteger,thenn2-1mustbe(A)aprimenumber(B)anoddinteger(C)divisibleby8(D)amultipleof2n(E)apositiveinteger设n=2k+1则n2-1=4k*（k+1）k&k+1是一对连续数，一定是2的倍数GCD,最大取最小LCM,最小取最大求最小公倍数和最大公约数：分解质因数IfMistheleastcommonmultipleof90,196,and300,whichofthefollowingisNOTafactorofM?

(A)600(B)700(C)900(D)2,100(E)4,900Arithmetic

LetSbethesetofallpositiveintegersnsuchthatn2isamultipleofboth24and108.WhichofthefollowingintegersaredivisorsofeveryintegerninS?Indicateallsuchintegers.A12B24C36D72Answer:A,C整除特性：能被2整除的数：末位是0，2，4，6，8的能被3整除的数：各位数字和能被3整除能被4整除的数：末尾的两位数能被4整除：232能被5整除的数：末位是0或5能被6整除的数：能被2和3整除的能被8整除的数：末尾的三位数能被8整除:1264能被9整除的数：各位数字和能被9整除能被11整除的数：奇数位的和=偶数位的和Eachofthefollowingnumbershastwodigitsblottedout.Whichofthenumbercouldbethenumbersofhoursinxdays,wherexisaninteger?A.23■,■06B.50■,■26C.56■,■02D.62■,■50E.65■,■2024x能被24整除能被4整除自然数n次幂的尾数特征尾数为2的数的幂的个位数以2，4，6，8循环尾数为3的数的幂的个位数以3，9，7，1循环尾数为4的数的幂的个位数以4，6循环尾数为7的数的幂的个位数以7，9，3，1循环尾数为8的数的幂的个位数以8，4，2，6循环尾数为9的数的幂的个位数以9，1循环Ifyisthesmallestpositiveintegersuchthat3,150multipliedbyyisthesquareofaninteger,thenymustbe

Arithmetic

14Howmanyfactorsdoes360have?(A)24(B)36(C)48(D)120(E)360因子数公式Arithmetic

10000ab+100c+10d+e10000ed+100c+10b+a9999a+990b-990d-9999eWhatistheleastpositiveintegerthatisnotafactorof25!andisnotaprimenumber?A26B28C36D56E58

余数牢记：

，表示y

除以x，商是k，余数是b.Arithmetic

remainderArithmetic

n=7*a+3n为偶数

a是奇数a=2b+1其中b为任意整数n=7*(2b+1)+3=14*b+10C2.The19thofSeptember1987wasaSaturday.If1988wasaleap-year,whatdayoftheweekwasthe21stofSeptember1990?

A.Monday

B.Tuesday

C.Wednesday

D.Thursday

E.Friday1987.9.19Saturday1990.9.21?19-----21：2days365/7余1,366/7余2ordinaryyear:365Leapyear:3666daysshiftArithmetic

1987----1990：87-882days88-891day89-901day3.Ifsandtarepositiveintegerssuchthats/t=64.12,whichofthefollowingcouldbetheremainderwhensisdividedbyt?2482045Arithmetic

余数一定为3的倍数Fraction&Decimalproperfractionimproperfractionmixednumbercommon/vulgarfractionsimplefractioncomplexfractionnumeratordenominator真分数假分数带分数普通分数简分数繁分数分子分母Arithmetic

(least)commondenominatorquarterinfinitedecimalterminatingdecimalrecurringdecimalroundtothenearestdigitalapproximate(最小)公分母四分之一无穷小数有限小数循环小数四舍五入数字近似识别各位数字名称”7654.321”，其中：“7”:thousands“6”:hundreds“5”:tens“4”:units(orones)“.”:decimalpoint“3”:tenths“2”:hundredths“1”:thousandthsArithmetic

在简分数的情况下，当分母只有2,5这样因数的分数为有限小数Arithmetic

=2.5Arithmetic

If1isexpressedasaterminatingdecimal,howmanynonzerodigitswillthedecimalhave?AOneBTwoCFourDSixEEleven比例,比率及百分比Arithmetic

formulanotationproportionaldirectly/inverselyAintermofBandCadditional公式标记法成比例的正/反（比例）A用B和C来表示额外的19881989Mrxx（1-p）%Msyy（1+p）%totalx+yx（1-p）%+y（1+p）%X+Y-X*P%+Y*P%因为X>Y，所以X*p%>Y*P%所以X+Y>X+Y-X*P%+Y*P%AAArithmetic

3:5mentowomenMen_9000Women_15000Arithmetic

Byweight,liquidAmakesup8percentofsolutionRand18percentofsolutionS.If3gramsofsolutionRaremixedwith7gramsofsolutionS,thenliquidAaccountsforwhatpercentoftheweightoftheresultingsolution?A10%B13%C15%D19%E26%DataAnalysis图表分析题0.753.5385/240=1.6Unit：million8-2349-59AgeMaleFemale比例102.01.8>1301.91.9=1501.21.2=1700.70.8<1900.10.1=1DataAnalysis

Descriptivestatistics1.平均数[Averageor(arithmetic)mean]几何平均数、算数平均数geometricmeanDataAnalysis

2.中数mediansequence（序列）中间进行考虑中数是个体概念，平均数是整体概念个数是奇数、偶数时的不同DataAnalysis

3.众数(mode)众数是指一组数中出现频率最高的数。例如：Themodeof7,9,6,7,2,1is7例如：Thelistof4,4,4,6,7,8,8,11,11,11,18twomodes:4,11DataAnalysis

4.值域rangeRange是表明数的分布的量，其定义为最大值减最小值的差。

注意：Range在一组数中仅依赖于最大值和最小值两个量。根据下列数值，分别计算mean，median，mode，range-2-40-1-3-1-200000-4-1-1-50-1-5-2数值次数0-1-2-3-4-5753122total20ThemediansalaryofA,B,C,D,Eis$20000,therangeofthesefivepeople'ssalaryislessthan$50000.WehavealreadyknownthatthesalariesofA,B,Care$20000,$40000,$50000,respectively.Whatistheprobableaveragesalaryofthesefivepeople?(A)$20000

(B)$32000

(C)$18000(D)$23000

(E)$3100054222max54200min分别为59999,60000,60001180000/3=60000四分位数算法：

1）将n个数从小到大排列2）中位数将所有数据平均分成左右两组相等的数据（不含中位数本身），就是左边数列的中位数，就是右边数列的中位数

如：2,4,5,8,9

2,3,5,6,8,9Boxplots箱线图LQ1MQ3HOG297-5正态分布钟形曲线，曲线下方面积为1对称轴为均值方差决定曲线平缓程度：

方差越大曲线越平缓；越小越陡准则μ-σ<X≤μ+σ：涵盖68%数据（概率68%）μ-2σ<X≤μ+2σ：涵盖95%数据（概率95%）μ-3σ<X≤μ+3σ：涵盖99%数据（概率99%）Thefigureshowsanormaldistributionwithmeanmandstandarddeviationd,includingapproximatepercentsofthedistributioncorrespondingtothesixregionsshown.

Supposetheheightsofapopulationof3,000adultpenguinsareapproximatelynormallydistributedwithameanof65centimetersandastandarddeviationof5centimeters.(a)Approximatelyhowmanyoftheadultpenguinsarebetween65centimetersand75centimeterstall?(b)Ifanadultpenguinischosenatrandomfromthepopulation,approximatelywhatistheprobabilitythatthepenguin’sheightwillbelessthan60centimeters?Giveyouranswertothenearest0.053000*(34%+14%)集合（维恩图）If75percentofaclassansweredthefirstquestiononacertaintestcorrectly,55percentansweredthesecondquestiononthetestcorrectly,and20percentansweredneitherofthequestionscorrectly,whatpercentansweredbothcorrectly?A.10%B.20%C.30%D.50%E.65.%75%55%20%xOfthe200studentsatcollegeTmajoringinoneormoreofthescience,130aremajoringinchemistryand150aremajoringinbiology.Ifatleast30ofthestudentsarenotmajoringineitherchemistryorbiology,thenthenumberofstudentsmajoringinbothchemistryandbiologycouldbeanynumberfromA.20-50B.40-70C.50-130D.110-130E.110-150130150Total:200None:>30xmin当两个圆重叠的时候，X最大，x=130Ofthe300subjectswhoparticipatedinanexperimentusingvirtual-realitytherapytoreducetheirfearofheight,40percentexperiencedsweatypalms,30percentexperiencedvomiting,and75percentexperienceddizziness.Ifallofthesubjectsexperiencedatleastoneoftheseeffectsand35percentofthesubjectsexperiencedexactlytwooftheseeffects,howmanyofthesubjectsexperiencedonlyoneoftheseeffects?A.105B.125C.130D.180E.195S120V90D225Total:300

Inaninsurancecompany,eachpolicyhasapaperrecordandanelectricrecord.Forthosepolicieshavingincorrectpaperrecord,60%alsohavingincorrectelectricrecord;Forthosepolicieshavingincorrectelectricrecord,75%alsohavingincorrectpaperrecord.3%ofallpolicieshavebothincorrectpaperandincorrectelectricrecords.Ifwerandomlypickoutonepolicy,what'stheprobabilitythattheonehavingbothcorrectpaperandcorrectelectricrecords?(A)0.80(B)0.94(C)0.75(D)0.88(E)0.92设文件共1003%=100*3%=3排列组合及概率从n个不同元素中,任取m个元素,按照一定的顺序排成一列,叫做从n个不同元素中取出m个元素的一个排列.2.组合的定义:从n个不同元素中,任取m个元素,并成一组,叫做从n个不同元素中取出m个元素的一个组合.permutation3.排列数公式:4.组合数公式:1.排列的定义:排列与组合的区别与联系:与顺序有关的为排列问题,与顺序无关的为组合问题.例1

学校组织老师学生一起看电影，同一排电影票12张。8个学生，4个老师，要求老师在学生之间，且老师互不相邻，共有多少种不同的坐法？解先排学生共有种排法,然后把老师插入学生之间的空档，共有7个空档可插,选其中的4个空档,共有种选法.根据乘法原理,共有的不同坐法为种.结论1

插空法分析此题涉及到的是不相邻问题,并且是对老师有特殊的要求,因此老师是特殊元素,在解决时就要特殊对待.所涉及问题是排列问题.例2

5个男生3个女生排成一排,3个女生要排在一起,有多少种不同的排法?

解

因为女生要排在一起,所以可以将3个女生看成是一个人,与5个男生作全排列,有种排法,其中女生内部也有种排法,根据乘法原理,共有种不同的排法.结论2

捆绑法:分析此题涉及到的是排队问题,对于女生有特殊的限制,因此,女生是特殊元素,并且要求她们要相邻,因此可以将她们看成是一个元素来解决问题.例3

在高二年级中的8个班,组织一个12个人的年级学生分会,每班要求至少1人,名额分配方案有多少种?解

此题可以转化为:将12个相同的白球分成8份,有多少种不同的分法问题,因此须把这12个白球排成一排,在11个空档中放上7个相同的黑球,每个空档最多放一个,即可将白球分成8份,显然有种不同的放法,所以名额分配方案有种.结论3

转化法（插拔法）:分析此题若直接去考虑的话,就会比较复杂.但如果我们将其转换为等价的其他问题,就会显得比较清楚,方法简单,结果容易理解.例5

期中安排考试科目9门,语文要在数学之前考,有多少种不同的安排顺序?解

不加任何限制条件,整个排法有种,“语文安排在数学之前考”,与“数学安排在语文之前考”的排法是相等的,所以语文安排在数学之前考的排法共有种.结论5

对等法:分析对于任何一个排列问题,就其中的两个元素来讲的话,他们的排列顺序只有两种情况,并且在整个排列中,他们出现的机会是均等的,因此要求其中的某一种情况,能够得到全体,那么问题就可以解决了.并且也避免了问题的复杂性.7.Ifthe5cardsshownaboveareplacedinarowsothat■isneverateitherend,howmanydifferentarrangementsarepossible?Whatisthetotalnumberofdifferent5-digitnumbersthatcontainallofthedigits1,2,3,4,and5and1)inwhichnoneoftheodddigitsoccurnexttoeachother?2)Inwhichnoneoftheevendigitsoccurnexttoeachother?InhowmanydistinguishablewayscanthesevenlettersinthewordMINIMUMbearranged,ifallthelettersareUsedeachtime?A.7B.42C.420D.840E.5040DataAnalysis7.概率题

所有的概率都是一个由分母和分子组成得到的。分子是符合条件的所有可能性；分母是总的可能性。2.Onthediskshownabove,aplayerspinsthearrowtwice.Thefractionisformed,whereaisthenumberofthesectorwherethearrowstopsafterthefirstspinandbisthenumberofthesectorwherethearrowstopsafterthesecondspin.Oneveryspin,eachofthenumberedsectorshasanequalprobabilityofbeingthesectoronwhichthearrowstops.Whatistheprobabilitythatthefractionisgreaterthan1？1000/8=125概率：125/1000=1/8P(x=1)=0.2

P(x=2)=0.5

P(x=3)=0.25

P(x=4)=0.05

So,P(xiseither1or2）=P(x=1orx=2)=P(x=1)+P(x=2)=0.2+0.5=0.7Algebra指数运算(RulesofExponents)Algebraexponentbasecubesquarerootcuberootdecimaldigitconstantvariable指数,幂乘幂的底数,底边立方数,立方体平方根立方根十进制；小数数字常数变量Powerandcorrespondingvalue2^112^242^382^4162^5322^6642^71282^82562^95122^1010243^133^293^3273^4813^52435^155^2255^31255^46255^53125=3AlgebraIfk,n,xandyarepositivenumberssatisfyingand,whatisintermsofnandk?algebraictermliketerms,similartermsnumericalcoefficientliteralcoefficientrangeoriginalequationequivalentequationlinearequation代数项同类项数字系数字母系数值域原方程同解方程,等价方程直线方程EquationsQuadraticequations:一元二次方程ax2+bx+c=0x1,2=但一般更常用的是因式分解法(十字相乘法)：x2-2x-3=0---(x-3)(x+1)=0---x1=3,x2=-1AlgebraSimultaneouslinearequations:

多元一次方程组*基本方法：消元法。例1：3x+y=5(1)2x+y=4(2)(1)－(2),消去y,得x=1,y=2*注意：并不是任何二元一次方程组都有唯一解。

例2: 3x+y=5(1) 6x+2y=10(2)

上述方程有无穷多组解。因此，方程的数量须等于未知数的数量，此时多元一次方程有唯一的一组解。

Algebra设贷款额为x，则有25000*0.04+(x-25000)*0.05+0.03*x=6000X=78125Thefabricneededtomake3curtainssellsfor$8.00peryardandcanbepurchasedonlybythefullyard.Ifthelengthoffabricrequiredforeachcurtainis1.6yardsandallofthefabricispurchasedasasinglelength,whatisthetotalcostofthefabricthatneedstobepurchasedforthe3curtains?A$40.00B$38.40C$24.00D$16.00E$12.8010,-10,11,-11,12,-12,13,-13,14,-14,

AAlgebra利息问题(interest)利息的计算方式：(principal)

×(interestrate)利率×(time)

单利simpleinterest复利compoundinterestannualBiannualBiennialAlgebraIf$8000isinvestedat6percentsimpleannualinterest,howmuchinterestisearnedafter3months?If$10,000isinvestedat10percentsimpleannualinterest,compoundsemiannually,whatisthebalanceafter1year?AlgebraIf$8000isinvestedat6percentsimpleannualinterest,howmuchinterestisearnedafter3months?If$10,000isinvestedat10percentsimpleannualinterest,compoundsemiannually,whatisthebalanceafter1year?12*360/48000=0.09Algebra折扣问题(discount)atadiscountof/discountedby/offoriginalprice×(100-n)%Thepriceofanitemisdiscountedby20percentandthenthisreducedpriceisdiscountedbyanadditional30percent.Thesetwodiscountsareequaltoanoveralldiscountofwhatpercent?AlgebraThedailyrateforahotelroomthatsleeps4peopleis$39foronepersonandxdollarsforeachadditionalperson.If3peopletaketheroomforonedayandeachpays$21fortheroom,whatisthevalueofx?(A)6(B)8(C)12(D)13(E)24BCoordinateGeometry解析几何*直线的标准方程：y=kx+b

；即斜截式，其中k为斜率slope，b为y轴截距y-intercept*斜率的计算：K=(Y2-Y1)/(X2-X1)*两点或一点加斜率确定一条直线。*两直线垂直，其斜率的乘积为－1。Geometrycoordinatesystemrectangularcoordinateoriginabscissaordinatenumberlinequadrantslopetransversalintercept坐标系直角坐标系原点横坐标纵坐标数轴象限斜率截线截距bisectintersectperpendicularline,straightlinelinesegmentparallelli