1、GRE Quantitative Reasoning,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）&GRE数学Algebra部分知识点总结+题目练习 2月6日： GRE数学Geometry部分知识点总结+题目练习& GRE数学Data Analysis部分知识点总结+题目练习（一） 2月7日： GRE数学Data Analysis部分知识点总结+题目练习（二） 2月9日： 综合题目练习讲解
2、+易错点总结+后续复习方案,课程安排：,2011年ETS对GRE进行全面改革，GRE难度大大增加，特别是2015年5月后；中国大陆有一半考生在新GRE数学部分没有上162！就是162！改革后的GRE数学部分，增加了四分位数、百分位数、箱线图、正态分布等高难度内容，在概率统计方面难度大增；ETS出版的OG中，有一半的篇幅是在介绍数学知识点；太多信心满满的考生裸考GRE数学，结果嘞。,GRE Quantitative概述,GRE Quantitative概述,GRE 分数对申请的影响,Harvard, Stanford, MIT, Berkeley, Princeton等大神学校录取分数线为330
3、+（TOP20）;UCLA, UVA, Columbia, John Hopkins, 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。,Prime number Prime factor Divisor Divisible Quotient Numerator Denominator Terminate decimal Variable Coefficient Quadratic equation Quartile Standard deviation Permutation,Exponent Domai
4、n Origin Quadrants Intercept Perpendicular Polygons Triangles Quadrilaterals Vertex Isosceles Hypotenuse Trapezoid Circular cylinder,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,GRE Quantitative 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
5、纳易错点,GRE Quantitative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,eight less than three times y,y=ax2+bx+c （a0）,GRE数学的出题总体基本假设,All numbers used are real numbers.所有的数都是实数 All figures lie on a plane unless otherwise indicated.除
6、非题目中有专门指出，假设所有图形都在同一平面内 All angle measures are positive所有的测量角度都是正数 All line shown as straight are straight. On the computer-based test, lines that appear “jagged” can also be assumed to be straight.所有显示为直线的线都可以当作直线来处理 Figures are intended to provide useful information for answering the questions. Ho
7、wever, except where a figure is accomplish by a “Note” stating that the figure is drawn to scale, solve the problem using your knowledge of mathematics, not by visual measurement or estimation.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drawn to scale）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。,GRE Quantit
8、ative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 Quantitative Comparison Questions 单项选择题 Multiple-choice questionsSelect One Answer Choice 不定项选择题 Multiple-choice questionsSelect One or More Answer Choices 数字填空题 Numeric Entry Questions 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：,Quantitative Comparison questions（数量比较题
9、）,一、题目要求Questions of this type ask you to compare two quantitiesQuantity A and Quantity B, and then determine which of the following statements describes the comparison. Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the informa
10、tion given.,【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（Become familiar with the answer choices） 避免不必要的计算（Avoid unnecessary computations） 谨记几何图形不一定都是按照比例给出（Remember that geometric figures are not necessarily drawn to scale.） 用具体数字代替变量（Plug in numbers）【慎用】 简化计算后再比较（Simplify the comparison） 知道什么时候
11、不能选D（Knowing when the choice D could not be chosen）,B-A=y-x=2x2+7x-3-x=2x2+6x-3,Multiple-choice QuestionsSelect One Answer Choice（单项选择题）,These questions are multiple-choice questions that ask you to select only one answer choice from a list of five choices.,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，
12、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,The figure above shows the graph of the function f defined by f(x)=l2xl+4 for all numbers x. For which of the following functions g, defined for all numbers x, does the graph of g intersect the graph of f? A g(x)=x2 B g(x)=x+3 C g(x)=2x2 D g(x)=2x+
13、3 E g(x)=3x2,斜率：slope 截距：intercept,Multiple-choice QuestionsSelect One or More Answers（不定项选择题）,These questions are multiple-choice questions that ask you to select one or more answer choices from a list of choices. A question may or may not specify the number of choices to select. These questions ar
14、e marked with square boxes beside the answer choices, not circles or ovals. Select one or more answer choices according to the specific question directions. If the question does not specify how many answer choices to select, select all that apply. The correct answer may be just one of the choices or
15、 as many as all of the choices, depending on the question. No credit is given unless you select all of the correct choices and no others. If the question specifies how many answer choices to select, select exactly that number of choices.,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
16、题目要求的答案个数,1. Which two of the following numbers have a product that is between 1 and 0 ? Indicate both of the numbers. A. 20 B. 10 C. 24 D. 32 2. Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Depart
17、ment Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company? Indicate all such amounts. A. $26,000 B. $28,000 C. $29,000 D.
18、$30,000 E. $31,000 F. $32,000,there be *times as much X as Y =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28333,25000 28333,A溶液（25%）,B溶液（35%）,3. Which of the following could be the units digit of 57n, where n is a positive integer? Indicate all such digits. A. 0 B. 1 C. 2 D. 3 E. 4 F. 5 G. 6
19、H. 7 I. 8 J. 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+2 is divided by 5, the remainder? n is positive integer,(8n+3)4=2n3 38n+3就等于33的个位数 7+2=9, 95=1.4,Numeric Entry questions（数字填空题）,Enter your answer as an integer or a decima
20、l if there is a single answer box OR as a fraction if there are two separate boxesone for the numerator and one for the denominator. To enter an integer or a decimal, either type the number in the answer box using the keyboard or use the Transfer Display button on the calculator. First, click on the
21、 answer boxa cursor will appear in the boxand then type the number. To erase a number, use the Backspace key. For a negative sign, type a hyphen. For a decimal point, type a period. To remove a negative sign, type the hyphen again and it will disappear; the number remains. The Transfer Display butto
22、n on the calculator will transfer the answer to the answer box. Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Enter the exact answer unless the question asks you to round your answer. To enter a fraction, type the numerator and the denominator in the respective boxes
23、 using the keyboard. For a negative sign, type a hyphen; to remove it, type the hyphen again. A decimal point cannot be used in a fraction. The Transfer Display button on the calculator cannot be used for a fraction. Fractions do not need to be reduced to lowest terms, though you may need to reduce
24、your fraction to fit in the boxes.,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,A merchant made a profit of $5 on the sale of a sweater that cost the merchant $15. What is the profit expressed as a percent of the merchants cost? Give your answer to the nearest wh
25、ole percent.,%,33,RESULTS OF A USED-CAR AUCTION,small cars large cars Number of cars offered 32 23 Number of cars sold 16 20 Projected sales total for cars offered (in thousands) $70 $150 Actual sales total (in thousands) $41 $120,For the large cars sold at an auction that is summarized in the table
26、 above, what was the average sale price per car?,$,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Transfer Display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There is twice as much A as BEight less than 3 times yDecrease to/ Decrease by 二、考点遗忘
27、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. Six more than 1/2 of the number r equals 14. Three fewer than the square root of the number w equals 1. Quantity A Quantity Br w A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot
28、 be determined from the information given. 2. n is a positive integer. Quantity A Quantity B The remainder when 34n is divided by 10 1 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given.,3. (4,6) is
29、the center of the circle above. Quantity A Quantity B The radius of the circle 6 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal D. The relationship cannot be determined from the information given.,4. Gregs weekly salary is $187，which is 15 percent less than Karla
30、s weekly salary. If Karlas weekly salary increases by 10 percent, by what percent must Gregs weekly salary increase in order to equal Karlas new weekly salary? Give your answer to the nearest tenths of a percent.5. In the ceiling of room, an opening was cut in the shape of a square with sides that a
31、re 1 foot in length. A circular fixture will be placed over the opening. If the circular fixture covers the square opening completely, which of the following could be the diameter of the circular fixture, in inches?(Note:1 foot=12 inches.) Indicate all such diameters A. 12 B. 13 C. 14 D. 15 E. 16 F.
32、 17 G. 18,%,6. A newspaper ad stated: “Deduct an additional 50 percent of the already-reduced price of shoes and youll save 60 percent of the original price” By what percent had the original price of shoes already been reduced? A. 10% B. 20% C. 30% D. 40% E. 50%7. If the sum of two positive integers is 24 and the difference of their squares is 48, what is the product of the two integer? A. 108 B. 119 C. 128 D. 135 E. 143,第一次课结束1月23日见！,链接: http:/ 密码: zx6m,
