GRE数学全程班课件

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） 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 Divisi

2、ble Quotient Numerator Denominator Terminate decimal Variable Coefficient Quadratic equation Quartile Standard deviation Permutation Exponent Domain 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

3、 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 t

4、han three times y y=ax2+bx+c （a0） a b 2a bac 4 4 2 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 tes

5、t, 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. However, except where a figure is accomplish by a “Note” stating that the figure is drawn to scale, solve the problem using your knowl

6、edge 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 Quantitative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

7、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） 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 foll

8、owing statements describes the comparison. Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information 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 unnecessar

9、y 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 Cho

10、ice（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，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

11、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+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-ch

12、oice 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 are marked with square boxes beside the answer choices, not circles or ovals. Select one or more answer choices according to the

13、 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 as many as all of the choices, depending on the question. No credit is given unless you select all of the correct choices and

14、 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

15、. 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 Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Dep

16、artment 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. $30,000 E. $31,000 F. $32,000 there be *times as much X as Y =X=*Y yx yx 3500025000 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

17、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 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

18、2、4、8、6、2、4、8、6 38n+3+2 is divided by 5, the remainder? n is positive integer (8n+3)4=2n.3 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 decimal if there is a single answer box OR as a fraction if there are two separate boxesone for the numerator an

19、d 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 answer boxa cursor will appear in the boxand then type the number. To erase a number, use the Backspace k

20、ey. 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 button on the calculator will transfer the answer to the answer box. Equivalent forms of the correct answer, su

21、ch 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 using the keyboard. For a negative sign, type a hyphen; to remove it, type the hyphen again. A decimal po

22、int 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 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

23、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 whole percent. % 33 RESULTS OF A USED-CAR AUCTION small cars large cars Number of cars offered 32 23 Number

24、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 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

25、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 B Eight less than 3 times y Decrease to/ Decrease by 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. Six more than 1/2 of the number r

26、equals 14. Three fewer than the square root of the number w equals 1. Quantity A Quantity B r w 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. 2. n is a positive integer. Quantity A Quantity B T

27、he 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 the center of the circle above. Quantity A Quantity B The radius of the circle 6 A. Quantity A

28、 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 Karlas weekly salary. If Karlas weekly salary increases by 10 percent, by what percent must Gregs weekly salary increase in order t