GRE数学全程班课件.ppt

GREQuantitativeReasoning,赵立仪2017.1.21,笔记本,草稿纸,最简单计算器,1月21日：GRE数学概述+题型介绍+做题技巧1月23日：GRE数学Arithmetic部分知识点总结+题目练习（一）1月25日：GRE数学Arithmetic部分知识点总结+题目练习（二）UCLA,UVA,Columbia,JohnHopkins,Pennsylvania等录取平均分为325+（TOP20-50）;TOP100的录取分数线为320+;数据为大致估计，会有些许误差。,PrimenumberPrimefactorDivisorDivisibleQuotientNumeratorDenominatorTerminatedecimalVariableCoefficientQuadraticequationQuartileStandarddeviationPermutation,ExponentDomainOriginQuadrantsInterceptPerpendicularPolygonsTrianglesQuadrilateralsVertexIsoscelesHypotenuseTrapezoidCircularcylinder,质数质因子因子/除数可被整除的商分子分母有限小数变量系数二次方程四份位数标准差排列,指数定义域原点象限截距垂直多边形三角形四边形顶点等腰斜边梯形排列,GREQuantitative复习的四大注意方面,全面复习考点熟悉数学词汇以及英语中数学语言的表达习惯熟悉做题的技巧总结归纳易错点,GREQuantitative考试目的,1.精通算术运算2.精通代数方程的求解3.具有将文字信息转换为数学术语的能力4.具有构想几个图像以及数之间关系的能力5.具有用直觉和非常规的方法去解决一般数学问题的能力6.具有在真实生活场景中运用数学的能力,eightlessthanthreetimesy,y=ax2+bx+c（a0）,GRE数学的出题总体基本假设,Allnumbersusedarerealnumbers.所有的数都是实数Allfigureslieonaplaneunlessotherwiseindicated.除非题目中有专门指出，假设所有图形都在同一平面内Allanglemeasuresarepositive所有的测量角度都是正数Alllineshownasstraightarestraight.Onthecomputer-basedtest,linesthatappear“jagged”canalsobeassumedtobestraight.所有显示为直线的线都可以当作直线来处理Figuresareintendedtoprovideusefulinformationforansweringthequestions.However,exceptwhereafigureisaccomplishbya“Note”statingthatthefigureisdrawntoscale,solvetheproblemusingyourknowledgeofmathematics,notbyvisualmeasurementorestimation.伴随问题的图形将为解题提供有用的信息。但是，只有在问题中指出相应图形是按比例画出drawntoscale）时，才可以用目测或者估计而得到的信息去解题。否则只能运用你的数学知识去回答问题。,GREQuantitative题型及答题策略,在新GRE的数学考试里面，会遇到四种题型。分别是：数量比较题QuantitativeComparisonQuestions单项选择题Multiple-choicequestionsSelectOneAnswerChoice不定项选择题Multiple-choicequestionsSelectOneorMoreAnswerChoices数字填空题NumericEntryQuestions下面我们将简要的把各个题型的要求与解题技巧给大家呈现出来：,QuantitativeComparisonquestions（数量比较题）,一、题目要求QuestionsofthistypeaskyoutocomparetwoquantitiesQuantityAandQuantityB,andthendeterminewhichofthefollowingstatementsdescribesthecomparison.QuantityAisgreater.QuantityBisgreater.Thetwoquantitiesareequal.Therelationshipcannotbedeterminedfromtheinformationgiven.,【ps】如果出现了A大于等于B的情况，应该选什么？,二、解题的技巧熟悉四个选项所表示的意思（Becomefamiliarwiththeanswerchoices）避免不必要的计算（Avoidunnecessarycomputations）谨记几何图形不一定都是按照比例给出（Rememberthatgeometricfiguresarenotnecessarilydrawntoscale.）用具体数字代替变量（Pluginnumbers）【慎用】简化计算后再比较（Simplifythecomparison）知道什么时候不能选D（KnowingwhenthechoiceDcouldnotbechosen）,B-A=y-x=2x2+7x-3-x=2x2+6x-3,Multiple-choiceQuestionsSelectOneAnswerChoice（单项选择题）,Thesequestionsaremultiple-choicequestionsthataskyoutoselectonlyoneanswerchoicefromalistoffivechoices.,解题技巧从选项中寻找解题线索，快速排除明显错误的选项没有思路时，可以尝试代入法，答案一定在5个选项当中基于题目给的条件去做，不要脑补其他任何条件利用枚举法的时候要非常注意列举顺序,Thefigureaboveshowsthegraphofthefunctionfdefinedbyf(x)=l2xl+4forallnumbersx.Forwhichofthefollowingfunctionsg,definedforallnumbersx,doesthegraphofgintersectthegraphoff?Ag(x)=x2Bg(x)=x+3Cg(x)=2x2Dg(x)=2x+3Eg(x)=3x2,斜率：slope截距：intercept,Multiple-choiceQuestionsSelectOneorMoreAnswers（不定项选择题）,Thesequestionsaremultiple-choicequestionsthataskyoutoselectoneormoreanswerchoicesfromalistofchoices.Aquestionmayormaynotspecifythenumberofchoicestoselect.Thesequestionsaremarkedwithsquareboxesbesidetheanswerchoices,notcirclesorovals.Selectoneormoreanswerchoicesaccordingtothespecificquestiondirections.Ifthequestiondoesnotspecifyhowmanyanswerchoicestoselect,selectallthatapply.Thecorrectanswermaybejustoneofthechoicesorasmanyasallofthechoices,dependingonthequestion.Nocreditisgivenunlessyouselectallofthecorrectchoicesandnoothers.Ifthequestionspecifieshowmanyanswerchoicestoselect,selectexactlythatnumberofchoices.,解题技巧（单选的五个技巧全部保留）如果可能，将答案范围写在草稿纸上答案选项从3个到12个不等，不要为了多选而多选注意题目要求的答案个数,1.Whichtwoofthefollowingnumbershaveaproductthatisbetween1and0?Indicatebothofthenumbers.A.20B.10C.24D.322.EachemployeeofacertaincompanyisineitherDepartmentXorDepartmentY,andtherearemorethantwiceasmanyemployeesinDepartmentXasinDepartmentY.Theaverage(arithmeticmean)salaryis$25,000fortheemployeesinDepartmentXand$35,000fortheemployeesinDepartmentY.Whichofthefollowingamountscouldbetheaveragesalaryforalloftheemployeesofthecompany?Indicateallsuchamounts.A.$26,000B.$28,000C.$29,000D.$30,000E.$31,000F.$32,000,therebe*timesasmuchXasY=X=*Y,x2y,最小值为25000最大值档x趋近于2y时，将x=2y带入，可得最大值无限趋近于28333,2500028333,A溶液（25%）,B溶液（35%）,3.Whichofthefollowingcouldbetheunitsdigitof57n,wherenisapositiveinteger?Indicateallsuchdigits.A.0B.1C.2D.3E.4F.5G.6H.7I.8J.9,7n的个位数循环规律为4个一循环分别是7、9、3、1、7、9、3、1,3n的个位数循环规律为4个一循环分别是3、9、7、1、3、9、7、1,2n的个位数循环规律为4个一循环分别是2、4、8、6、2、4、8、6,38n+3+2isdividedby5,theremainder?nispositiveinteger,(8n+3)4=2n.338n+3就等于33的个位数7+2=9,95=1.4,NumericEntryquestions（数字填空题）,EnteryouranswerasanintegeroradecimalifthereisasingleanswerboxORasafractioniftherearetwoseparateboxesoneforthenumeratorandoneforthedenominator.Toenteranintegeroradecimal,eithertypethenumberintheanswerboxusingthekeyboardorusetheTransferDisplaybuttononthecalculator.First,clickontheanswerboxacursorwillappearintheboxandthentypethenumber.Toeraseanumber,usetheBackspacekey.Foranegativesign,typeahyphen.Foradecimalpoint,typeaperiod.Toremoveanegativesign,typethehyphenagainanditwilldisappear;thenumberremains.TheTransferDisplaybuttononthecalculatorwilltransfertheanswertotheanswerbox.Equivalentformsofthecorrectanswer,suchas2.5and2.50,areallcorrect.Entertheexactanswerunlessthequestionasksyoutoroundyouranswer.Toenterafraction,typethenumeratorandthedenominatorintherespectiveboxesusingthekeyboard.Foranegativesign,typeahyphen;toremoveit,typethehyphenagain.Adecimalpointcannotbeusedinafraction.TheTransferDisplaybuttononthecalculatorcannotbeusedforafraction.Fractionsdonotneedtobereducedtolowestterms,thoughyoumayneedtoreduceyourfractiontofitintheboxes.,解题技巧：确保你的答案与题目的要求是否一致（四舍五入）合理使用计算器等同的正确答案也可以给分，不要一味的追求约分（4/9）通过常识来验证你的答案是否正确,Amerchantmadeaprofitof$5onthesaleofasweaterthatcostthemerchant$15.Whatistheprofitexpressedasapercentofthemerchantscost?Giveyouranswertothenearestwholepercent.,%,33,RESULTSOFAUSED-CARAUCTION,smallcarslargecarsNumberofcarsoffered3223Numberofcarssold1620Projectedsalestotalforcarsoffered(inthousands)$70$150Actualsalestotal(inthousands)$41$120,Forthelargecarssoldatanauctionthatissummarizedinthetableabove,whatwastheaveragesalepricepercar?,$,6000,大多数的计算不需要计算器，不要因为TA在那儿就非要使用一些简单的计算，尽量不要使用计算器注意运算顺序有些计算很巧妙的回避计算过程，不要过分依赖计算器（极限问题）使用TransferDisplay时，注意近似的位数4.4456在做分数题的时候，计算结果有小数的时候,GRE数学考试中常见的错误,一、英文理解能力不够好ThereistwiceasmuchAasBEightlessthan3timesyDecreaseto/Decreaseby二、考点遗忘多三、读题信息遗漏四、审题有问题（脑补其它条件，空前的求知欲）五、手抖算错选错六、不会检查,课后练习习题：1.Sixmorethan1/2ofthenumberrequals14.Threefewerthanthesquarerootofthenumberwequals1.QuantityAQuantityBrwA.QuantityAisgreater.B.QuantityBisgreater.C.ThetwoquantitiesareequalD.Therelationshipcannotbedeterminedfromtheinformationgiven.2.nisapositiveinteger.QuantityAQuantityBTheremainderwhen34nisdividedby101A.QuantityAisgreater.B.QuantityBisgreater.C.ThetwoquantitiesareequalD.Therelationshipcannotbedeterminedfromtheinformationgiven.,3.(4,6)isthecenterofthecircleabove.QuantityAQuantityBTheradiusofthecircle6A.QuantityAisgreater.B.QuantityBisgreater.C.ThetwoquantitiesareequalD.Therelationshipcannotbedeterminedfromtheinformationgiven.,4.Gregsweeklysalaryis$187，whichis15percentlessthanKarlasweeklysalary.IfKarlasweeklysalaryincreasesby10percent,bywhat