新gre数学重要考点汇总.pdf

文档介绍：该【新gre数学重要考点汇总 】是由【秋江孤影】上传分享，文档一共【7】页，该文档可以免费在线阅读，需要了解更多关于【新gre数学重要考点汇总 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。新gre数学重要考点汇总
所以,从今日起,针对新版gre数学复****每天给考生整理一个重要考点,
这些概念在考试中肯定会考到的。盼望考生能再接再厉,取得一个好成绩,
突破新版gre数学难的逆境。
新版gre数学复****重要考点:SumofArithmeticProgression
Thesumofn-numbersofanarithmeticprogressionisgivenby
S=nx*dn(n-1)/2
wherexisthefirstnumberanddistheconstantincrement.
example:
sumoffirst10positiveoddnumbers:10*1+2*10*9/2=10+90=100
sumoffirst10multiplesof7startingat7:
10*7+7*10*9/2=70+315=385
remember:
ForadescendingAPtheconstantdifferenceisnegative.
由于美国数学根底训练的难度增加导致数学考试越来越难,但新gre
数学复****考点都是高中时候学到的学问点,考生不要过于紧急,把根本概
念弄明白,再记住一些新版gre数学必备的词汇,那么信任新版gre数学
应当没有问题。
AP
Averageofnnumbersofarithmeticprogression(AP)isthe

ofmnumbercanalsobewrittenasx+d(m-1)/2.
Example:
Theaverageofallintegersfrom1to5is(1+5)/2=3
Theaverageofalloddnumbersfrom3to3135is(3+3135)/2=1569
Theaverageofallmultiplesof7from14to126is(14+126)/2=70
remember:
Makesurenonumberismissinginthemiddle.
Withmorenumbers,averageofanascendingAPincreases.
Withmorenumbers,averageofadescendingAPdecreases.
AP:numbersfromsum
giventhesumsofmnumbersofanAPwithconstantincrement
d,thenumbersinthesetcanbecalculatedasfollows:
thefirstnumberx=s/m-d(m-1)/2,andthen-thnumberiss/m
+d(2n-m-1)/2.
Example:
ifthesumof7consecutiveevennumbersis70,thenthefirst
numberx=70/7-2(7-1)/2=10-6=4.
thelastnumber(n=m=7)is70/7+2(2*7-7-1)/2=10+6=
theevennumbersfrom4to16.
Remember:
giventhefirstnumberx,itiseasytocalculateothernumbers
usingtheformulaforn-thnumber:x+(n-1)
AP:numbersfromaverage

firstnumberx=c-d(m-1)/2,andthen-thnumberisc+d(2n-m-1)/2,
wherecistheaverageofmnumbers.
Example:
iftheaverageof15consecutiveintegersis20,thenthefirst
numberx=20-1*(15-1)/2=20-7=13andthelastnumber(n=m=15)is
20+1*(2*15-15-1)/2=20+7=27.
iftheaverageof33consecutiveoddnumbersis67,thenthe
firstnumberx=67-2*(33-1)/2=67-32=35andthelastnumber(n=m=33)
is67+2*(2*33-33-1)/2=67+32=99.
Remember:
sumofthemnumbersisc*m,wherecistheaverage.
SequenceofNumbers

fixedpatterncanbeexpressedbyanequationorbyaproperty.
Example:
Asetofconsecutiveintegers:1,2,3,4,5(Fixedgap)
Asetofconsecutiveevennumbers:4,6,8,10,12(Fixedgap)
Asetofconsecutiveprime:2,3,5,7,11(Fixedgap)
Asetofconsecutivepowerof2:4,8,16,32,64(Fixedgap)
Remember:
Asequencecanbeinascendingordescedingorder.
Mode
Themodeofasetofnumbersisthenumberthatrepeatsthemost
intheset.
Example:
Modeoftheset{1,2,3,2,4,5}is2.
Thesetofnumbers{1,2,4,1,2,3,6,8}hastwomodes:1and2.
Remember:
Therecanbemorethanonenumberwiththehighestrepeatcount.
Inthatcaseallofthemwiththehighestrepeatcountaremodes.


membersintheset.
Example:
Thesetofevennumbersbetween2and10isofsize
5:{2,4,6,8,10}.
Thesetofprimesbetween2and10isofsize4:{2,3,5,7}.
Remember:
EachmemberofsetAbelongstoAorisinthesetA.
Asetcannothaverepeatingmember:{1,3,1,2}isnotaset.
Rearrangingtheorderofthemembersdoesnotchangethe
set:{1,2,3}issameas{3,2,1}.
IntersectionofSets
Intersectionoftwosetsisanothersetwithonlythemembers
,
theintersectionistheemptysetwithnomember.
Example:
Intersectionof{1,2,3}and{2,3,5}istheset{2,3}.
Intersectionofthesetwithallprimesandthesetwithall
evennumbersistheset{2}sinceonly2isbothevenandprime.
Intersectionof{1,2,3}and{4,5,6}istheemptyset{}.
Remember:
Intersectioncontainsonlythecommonmembers.
Twosetsaredisjointiftheyhavenomemberincommon,that
istheyhaveanemptyintersection.
UnionofSets
Unionoftwosetsisanothersetwithallthemembersfromboth
sets.
Example:
Unionof{2,3,5}and{1,3,4}istheset{1,2,3,4,5}.
Unionof{1,2,1}and{1,2}istheset{1,2,1}.
Remember:
Thecommonmembersdonotrepeatintheunion.
TotalMembers
Sometimestherearemembersthatdonotbelongtoeitherset
=SizeA+SizeB-Number
ofcommonmembers+NumberofmembersnotinAorB.
Example:
Inanoffice,35peopledrinkcoffee,27drinktea,12drink
both,
=35+27-12+4=54.
Inaclassof40students,20studyalgebra,15studygeometry,

either=40-(20+15-8)=13.
Remember:
Thisisarelationbetweenfivenumbers,andanyonecanbe
calculatedgiventheotherfour