GRE_Math_Review_1_Arithmetic_18_point_Figures[1]
GRE考试的部分数学概念
GRE考试的部分数学概念GRE考试的部分数学概念1、mode（众数）一堆数中出现频率最高的一个或几个数，例如：mode of 1,1,1,2,3,0,0,0,5 is 1 and 0.2、range（值域）一堆数中最大和最小数之差，例如：range of 1,1,2,3,5 is 5-1=43、mean（平均数）arithmatic mean（算术平均数），geometric mean （几何平均数：n个数之积的n次方根）4、median（中数）将一堆数排序之后，正中间的一个数（奇数个数字），或者中间两个数的平均数（偶数个数字），例如：median of 1,7,4,9,2,2,2,2,2,5,8 is 2，median of 1,7,4,9,2,5 is (5+7)/2=6。
5、standard error（标准偏差）一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的`个数(n)。
例如：standard error of 0,2,5,7,6 is:(|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.46、standard variation一堆数中，每个数与平均数之差的平方之和，再除以n，例如：standard variation of 0,2,5,7,6 is6.87、standard deviation就是standard variation的平方根，标准方差的公式：d^2=[(a1-a)^2+(a2-a)^2+....+(an-a)^2 ]/n，d 为标准方差。
8. 三角形余玄定理C^2=A^2+B^2-2ABCOSt，其中t为AB两条线间的夹角。
9. Y=k1X+B1,Y=k2X+B2，两线垂直的条件为K1K2=-110. 三的倍数的特点：所有位数之和可被3整除。
GRE数学词汇_外语学习-GRE
GRE数学考试词汇Aabscissa 横坐标absolute value 绝对值account for （数量）占acute angle 锐角acute triangle 锐角三角形add 加add to addition 加，加法adjacent 相邻adjacent angles 邻角algebra 代数学algebraic expression 代数式algebraic fraction 分式algebraic term 代数项aliquot 除得尽数aliquant 除不尽数alternate angles 内错角altitude 高度amount 合计angle 角angle bisector 角平分线apex 顶，顶点apiece 每人，每个approximately 近似的，大约的approximation 近似，近似值arc 弧，圆周的任意一段area 面积arithmetic 算术arithmetic(al) average 算术平均数arithmetic(al) mean 算术平均数或等差中项arithmetic(al) progression 或series 算术级数，等差级数assume that 假定义……at random 随机地at right angles with 与……成直角at this rate 以这样的比率，价格或速度average 平均，平均数平均的axis 轴Bbalance 余额bar graph(chart) 条带图base 堤边，底面，幂或乘方的底数base area 底面积be across from 在……对面be closet to 最接近……be composed of 由构成be equal to 与……相等be equivalent to antherequation与另一方程痛解be fewer than 小于be greater than 大于be greater than or equal to 不小于be inscribed in 内接于be less than 小于be less than or equal to 不大于be parallel to 平行于be perpendicular to 垂直于be substituted for 代替billion 109binomial 二项式bisect 把……二等分block 立体blot out 涂掉，删掉bound 辩解，范围；邻接*brand*bulk 大量Ccalculate to threedecimal places计算结果保留三位小数cancellation 约掉，消掉*car poolcatch up withcentcenter 圆心central angle 圆心角*charge 费用，价钱chart 图表chord 弦circle 圆circle graph(chart) 圆形图circular 圆形的，环形的circular cylinder 圆柱circumference 圆的周长clear an equation offractions分式方程整式化clockwise 顺时针coefficient 系数*coincolumn 列，圆柱common denominator 公分母common difference 等差数列的公差common divisor(factor) 共因子；公约数common ratio 等比数列的公比common multiple 公倍数complement 余角complementary angle 余角complete circle 全圆complete quadratic(equation)全二次方程complex fraction 繁分数composite number 和数，指大于一而不是质数的整数compound 混合物；复利compound interest 复利compound annual interest 年复利concentration 浓度concentric circle 同心圆congruent （多边形）全等的consecutive 连续的consecutive integer 连续整数consecutive even(odd)integer连续偶（奇）数consist of 由……构成constant 不变的，永恒的；常数constitute 构成，组成*contractor 承包商convert intocoordinate 坐标coordinate axis system 坐标系coordinate geometry 解析几何coordinate plane 坐标平面corresponding angles 同位角，对应角corresponding side 对应边*cost 成本*cost price 成本价counterclockwise 逆时针cross multiplication 交叉相乘cube 立方体，立方；三次幂cubic 立方体的，立方的cubic block 立方体cubic denominations 立方单位cubic solid 立方体cubic units 立方单位cumulative graph(chart) 累积图curve 曲线curved line 曲线cylinder 圆柱体cylinderic(al) 圆柱体的D*dealer 商人decagon 十角形，十边形decimal 小数；小数的decimal fraction 纯小数decimal place 小数位decimal point 小数点*deck 一幅纸牌decrease 减少，减少量deduct 扣除，减去degree 度；度数（温度和角度）denominator 分母denote 表示，意味着depth 深度diagonal 对角线；对角线的diameter 直径*dietdiffer 不同，相异difference 差，差额digit 数字，位（数）*dime 一角，十分dimension 尺寸，尺度；维（数），度(数)，元(be) direct(inverse)proportional to成正（反）比*discount 折扣discount rate 折扣率distance 距离distinct 与其它不同的，独特的divide 除dividend 被除数divisor 除数，约数divisible 可整除的division 除法*dollar 美元done(drawn) to scale 按比例绘制double*dry mixture*down 付现款地（和分期付款相对）*dozen*dueEeccentric 偏心圆，；不同圆心的edge 立体的变或棱*encloseendpoint 端点equality 相等，等式equation 等式，方程equiangular 等角的equidistance 等距离的equilateral 等边形；等边的equivalent 等面积的，等体积的；等价的，相等的，等量的equivalent fraction 等值分数，如1/2和2/4even integer 偶数evenly even integer 能再平分的偶数（能背4整除）evenly spaced 等间隔的exponent 指数expression 表达式exterior angle 外角Fface 立体的面factor 因子；将……分解因子factorable 可进行因式分解的factorial 阶乘；因子的，阶乘的figure 图形*finish line 终点线*flatfold 对折footcandle （物理）英尺烛光（照度单位）formula 公式，配方fraction 分数from subtract 从……减去……from throughfrom to,inclusiveGgaingeometric mean 几何平均数geometric progression 几何级数，等比级数geometry 几何学graph 图表；用图表来表示greatest common divisor 最大公约数grid 格栅gross 总的，毛的Hhalfway 半途的halve 把……平分为二；将……减半height 高heptagon 七边形hexagon 六边形horizontally 水平地how much more thanhundreds 百位hundredth 第一百个；百分之一hypotenuse （直角三角形）斜边Iidentical 相等的；恒等的*illumination 照明度improper fraction 假分数included angle(side) 夹角（边）incomplete quadraticequationindefinitely 无限定地independent 无关地，独立地independent variables 自变量inequality 不等式；不相等in excess of 超过……infinite decimal 无穷小数，同non-terminatingdecimalinfinite sequence 无穷数列inscribed angle 圆周角，同弧所对圆心角central angle的尺寸是圆周角的二倍inside dimension 内部尺寸installment 分期付款中每一期所付的款项integer 整数integer part 代分数的整数部分，代分数的分数部分是fractional part*intensity 强度intercept 截距；截取egintercepted arc 截弧interest 利息interior angle 内角in terms of 用……来表示intersect 直线相交，point ofinetrsection交点interval 间隔，区间in turn 依次，轮流invert a fraction 求一个分数的倒数irrational number 无理数Jjoint 接合，接合处Lleast(lowest) commonmultiple最小公倍数leg 梯形的两条不平性的边；直角三角形的直角边length 长度lengthwise(lengthways) 纵长的lesslevellike(similar) terms 同类项line 直线，线段linesegment/half line半直线，射线line graph 线型图literal coefficient 字母系数Mmathematical operation 数学运算mean 平均数mean proportional 比例中项measuremeasurementmedian 中数；中线midpoint 中点midway 中途million 106minor arc AB 劣弧ABminuend 被减数minus 减mixed decimal 混合小数，如3.14 mode 众数monomial 单项式*mowermultiple 多倍的，多重的；倍数a multiple of multiplicand 被乘数multiplication 乘法multiplier 乘数multiply 乘Nnatural number 自然数negative number 负数negligible 可忽略不计的n-gon n-边形nickel 五分nonadjacent 不相邻的nonagon 九边形nonzero 非零；非零的not necessarily distinct 不必然不同的number 数，数字number line 数轴，规定了原点，正方向和单位长度的直线，数轴上的点和实数一一对应numerator 分数的分子numerical coefficient 数字系数Oobtuse angle 钝角，大于90度而小于180度的角obtuse triangle 钝角三角形octagon 八边形odd integer 奇数odds 事物发生的可能性，机会of one dimension 线性的on the average 平均operation 运算oppositeorder 顺序，订单ordinate 纵坐标origin 原点,origin ofcoordinates 坐标原点original equation 原方程overhangoverlap 部分重叠，部分搭交Pparallel lines 平行线parallelogram 平行四边形partpartitionpayrollpenny 分pentagon 五边形percent 百分号percent of interest 利率，同rate ofinterestpercent increase 增加的百分率percent decrease 减少的百分率perfect square(cube) 完全平方（立方），e.g.25是5的完全平方perimeter 周长perpendicular lines 垂直线pictograph 统计图表pie gragh(chart) 圆形图，饼型图palce （位）数plane 平面plus 加point 小数点pointer 指针point of tangency 切点polynomial 多项式pool 联营potion 一部分positive 正的power 幂，乘方preceding 在前的，先前的prime number 质数，素数*principal 本金，资本probability 概率product （乘）积progression(series) 级数，同series projected 被预测，被估计proportion 比，比率；比例e.g.in proportion to与……成比例;Qquadrant 象限quadratic equation 二次方程quadrilateral 四边形quantity 数，数量quotient 商Rradical 根号，根式；radius 半径randomly 随机地rate 率，比率；速度，速率；价格，费用ratio 比，比率ray 射线real number 实数*rebate 回扣，折扣reciprocal 倒数rectangle 矩形rectangular 矩形的；成直角的reduceregularremainder 余数remote interior angles 三角形一个外角对应的两个内错角repeating decimal 无限循环小数revolution 旋转 e.g.revolutions permin每分钟转速rhombus 菱形right 直的root 方根；方程的根round 四舍五入row:column 行Ssatisfy 使……成立scale drawing 按比例绘制（的图）scalene 不等边三角形，不等边的secant 割线section 断面，一部分crosssection横截面sector 扇形segment 弓形；部分sequence 数列set 集合shaded region 阴影side 边，立体的面sign(symbol) 符号similar （三角形）相似的simple annual interest 年单利simple fraction 简分数simultaneously 同时地，同时发生地simultaneous equations 联立方程组slope （直线的）斜率solid 立体；立体的；实心的，单色的e.g.solid lines实线/solid color solution 解，答案sphere 球体square 正方形straight angle 平角，指180度的角straight-line distance 直线距离subdivide 再分，细分subtract…from…从…减去…successive 连续的，相继的such that 使得满足…的条件sum 和supplement 补角，指两角之和为180度surface area 表面积Ttable 表格take fromtangent 切线；相切的term 项throughtimes 倍；乘token 辅币toll 通行税total 合计to the nearest 10% 精确到10% transversal 横截线 e.g. ~ofparallel lines trapezoid 梯形triangle 三角形triangular regiontrinomial 三项式triple 三倍的Uuniform 一直不变的unit 单位unlike terms 非同类项unknown 未知量Vvalue 值variable 变量vertex 顶点vertical 垂直的；直立的；顶点的；对顶的Wwall （容器）壁weight 重量；重力XX-axis X轴X-coordinate X坐标XY-coordinate system 平面直角坐标系，同XY-planeYY-axis Y轴Y-coordinate Y坐标Zzero 零。
gre sub科目
gre sub科目GRE数学（GRE Math）GRE数学是GRE考试中的一个重要科目。
在GRE数学中，主要涵盖了代数、几何、概率与统计等数学领域的知识。
下面将从几个方面介绍GRE数学的一些重要内容。
一、代数（Algebra）代数是GRE数学中的一个重要部分。
代数涉及了方程、不等式、函数、多项式等内容。
在代数的学习中，需要掌握解方程、求根、因式分解、多项式运算等基本技巧。
此外，还需要熟悉各类函数的性质，如线性函数、二次函数、指数函数、对数函数等。
二、几何（Geometry）几何也是GRE数学中的一个重要内容。
几何主要包括平面几何和立体几何两个部分。
在平面几何中，需要掌握平行线、垂直线、三角形、四边形、圆等基本图形的性质和计算方法。
在立体几何中，需要了解立体图形的表面积和体积计算方法，如长方体、正方体、圆柱体、圆锥体等。
三、概率与统计（Probability and Statistics）概率与统计是GRE数学中的另一个重要内容。
概率涉及了事件发生的可能性，需要掌握概率的计算方法和性质。
统计则关注数据的收集、整理和分析，需要了解统计学中的基本概念和统计量的计算方法。
四、数论与离散数学（Number Theory and Discrete Mathematics）数论与离散数学是GRE数学中的一些较为高级的内容。
数论涉及了整数的性质和性质的证明，需要理解素数、最大公约数、最小公倍数等概念。
离散数学则关注离散对象的性质和计算方法，如集合论、图论、逻辑等。
五、数据分析（Data Analysis）数据分析是GRE数学中的一个重要考点。
数据分析主要包括数据的收集、整理、分析和解释等内容。
在数据分析中，需要掌握数据的描述统计方法，如平均数、中位数、众数、标准差等，以及数据的图表表示和解读。
GRE数学是GRE考试中不可忽视的一部分。
在备考过程中，需要对代数、几何、概率与统计、数论与离散数学以及数据分析等内容进行系统的学习和掌握。
gre数学专项考试全攻略
gre数学专项考试全攻略GRE数学专项考试测试内容为，考试者在数学领域内所获得的知识和技能以及能力水平的凹凸，从而帮助院校更好地了解申请人在数学领域的能力状况。
以下是我今天要介绍的gre数学专项考试全攻略。
GRE数学专项考试常识1.历史数学sub开始于1952年。
2.考试规模每年全球参加数学sub考试的人数不到2000人左右，清华数学系每年有十几个人参加。
3.考点在中国(包括香港和台湾)每年只有一次考试，一般在11月初，General考试后第二个或第三个礼拜六进行。
全国有12个考点(详见General Test的bulletin)，北京有3个考点，分别在北外，北语及外交学院的国际交流中心。
(提示：新加坡的考点安排了12月和4月的考试)4.考试时间GRE数学专项考试考试时间是170分钟(什么概念?将近三个小时......)，共66道题，都是单项选择题，每道题5个选项。
5.如何计分每答对1道题目加一分，答错了倒扣0.25分，空着不答不算分。
所有题目用这种方法算下来之后得到一个Raw Score，然后再去标准化一下就得到Scaled Score和Percentile。
最终寄到手上的成绩同时包涵了Raw Score和Scaled Score。
数学sub的percentile是与过去3年的考试者相比较得出来的。
6.报名费150美元7.成绩有效期数学sub成绩有效期为5年。
同时成绩也是累积的。
(如果重考sub，可以换一个通讯地址地址，这样成绩单上就不会有前一次的成绩了)8.分数范围数学sub的分数范围是200~990，不过在2001年之前，由于太多中国大陆的人参加考试，以至于即使考990(当时不用准备可以随便考满分)，percentile也只有82%。
ETS一怒之下，从2001年10月开始对数学sub的分数进行rescale，rescaled之后，出现的最高分一般为890。
如何准备GRE数学专项考试按照ETS的说法，sub考试中50%是微积分方面的题目，25%是线性代数的题目，剩下的25%是其他基本数学内容。
GRE考试数学常考点的详细分析
GRE考试数学常考点的详细分析第1篇：GRE考试数学常考点的详细分析1、高中知识各种三角诱导公式，和，差，倍，半公式与和差化积，积化和差公式，平面解析几何。
说明：crackingthegremathtest里面第一章就是复习高中知识，我看内容基本差不多了，大家也就不用另外找书复习了。
2、数学分析极限，连续的概念，单变量微积分(求导法则，积分法则，微商)，多边量微积分及其应用，曲线及曲面积分，场论初步。
参考书：《数学分析新讲》，walterrudin的principlesofmathematicalanalysis说明：crackingthegremathtest用了两章来复习新gre数学分析，基本够了。
只是另外看了一些场论的公式以及fourier分析的一点内容。
不过sub中有一些数学分析方面的gre数学题目很灵活，要你判断一个命题是否正确，对于错误选项如果想不出反例来就有些麻烦了，大家要注意。
3、微分方程基本概念，各种方程的基本解法。
参考书：wolfgangwalter,ordinarydifferentialequations说明：以crackingthegremathtest中的相关章节为主，一般不难。
4、线*代数普通代数，艾森斯坦因法则，行列式，向量空间，多变量方程组解法，特征多项式及特征向量，线形变换及正交变换，度量空间。
参考书：《高等代数未完，继续阅读 >第2篇：小学数学试卷详细分析查考一、试题整体情况：本次期末考试试卷从总体来看试卷抓住了本年级本册书的重点、难点、关键点。
整个试卷注重了基础知识的训练，体现"数学即生活"的理念，让学生用学到的数学知识，去解决生活中的各种数学问题。
本次试卷不仅考查了学生对基本知识的掌握，而且考查了学生的数学学习技能，还对数学思想进行了渗透。
但是由于试卷印刷质量和排版的不当，给了学生误导，使学生出现了不必要的错误。
二、学生测试情况分析：本次试卷共分为两大部分，第一部分是基础知识，主要包括以下几种类型的题：1、口算题，大多数同学都做对了，只有个别同学出错，原因是平时练习较多，也注重强调了口算的方法，因此失分较少，个别同学还是粗心，方法没掌握，应着重对个别同学加以辅导。
gre数学评分标准
gre数学评分标准
GRE数学部分的评分标准主要包括两个方面：得分范围和评分标准。
得分范围：
- 200-800分：数学部分的得分范围是从200分到800分，其中200为最低分，800为最高分。
评分标准：
GRE数学部分的评分标准主要根据考生在数学知识和解题能力上的表现来确定。
评分标准包括以下几个方面：
- 数学知识：考察考生在初等数学和高等数学中的基础知识掌握程度。
- 解题能力：考察考生解决各种数学问题的能力，包括问题的理解、分析和解决方法的选择与运用等。
- 数学推理和推断能力：考察考生在数学推理和推断方面的能力，包括数学问题的分析和推理能力。
评分标准会根据考生的答案准确性、解题思路和解题速度等因素进行综合评估，并将其转化为相应的分数。
总体而言，得分高低主要取决于考生在数学知识的广度和深度上的掌握程度、解题能力的强弱以及对数学问题的理解和分析能力。
新GRE数学全部知识点汇总讲解
GRE数学解题大全目录GRE数学解题大全 (1)代数与几何部分 (2)概率论部分 (5)1.排列(permutation): (5)2．组合(combination): (5)3．概率 (5)统计学部分 (8)1.mode（众数） (8)2.range（值域） (8)3.mean（平均数） (8)4.median（中数） (8)5.standard error（标准偏差） (9)6.standard variation (9)7.standard deviation (9)8.the calculation of quartile(四分位数的计算) (9)9．The calculation of Percentile (10)10.To find median using Stem-and-Leaf (茎叶法计算中位数) (11)11．To find the median of data given by percentage(按比例求中位数) (12)12：比较,当n<1时，n，1，2 和1，2,3的标准方差谁大 (13)13.算数平均值和加权平均值 (13)14.正态分布题. (13)15．正态分布 (13)GRE数学符号与概念 (16)常用数学公式 (19)精讲20题 (20)GRE数学考试词汇分类汇总 (26)代数-数论 (26)代数-基本数学概念 (27)代数-基本运算, 小数,分数 (27)代数-方程,集合,数列等 (28)几何-三角 (29)几何-平面, 立体 (29)几何-图形概念 (30)几何-坐标 (31)商业术语,计量单位 (31)GRE数学考试词汇首字母查询 (32)代数与几何部分1.正整数n有奇数个因子,则n为完全平方数2.因子个数求解公式:将整数n分解为质因子乘积形式,然后将每个质因子的幂分别加一相乘.n=a*a*a*b*b*c则因子个数=(3+1)(2+1)(1+1)eg. 200=2*2*2 * 5*5 因子个数=(3+1)(2+1)=12个3.能被8整除的数后三位的和能被8整除;能被9整除的数各位数的和能被9整除.能被3整除的数,各位的和能被3整除.4.多边形内角和=(n-2)x1805.菱形面积=1/2 x 对角线乘积6.欧拉公式：边数=面数+顶点数-28.三角形余玄定理C2=A2+B2-2ABCOSβ,β为AB两条线间的夹角9.正弦定理:A/SinA=B/SinB=C/SinC=2R(A,B,C是各边及所对应的角,R是三角形外接圆的半径)10.Y=k1X+B1,Y=k2X+B2，两线垂直的条件为K1K2=-111.N的阶乘公式:N!=1*2*3*....(N-2)*(N-1)*N 且规定0!=1 1!=1Eg:8!=1*2*3*4*5*6*7*812. 熟悉一下根号2、3、5的值sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.23613. ...2/3 as many A as B: A=2/3*B...twice as many... A as B: A=2*B14. 华氏温度与摄氏温度的换算换算公式:(F-32)*5/9=CPS.常用计量单位的换算:（自己查查牛津大字典的附录吧）练习题:1：还有数列题：a1=2，a2=6，a n=a n-1/a n-2，求a150.解答: a n=a n-1/a n-2,所以a n-1=a n-2/a n-3,带入前式得a n=1/a n-3,然后再拆一遍得到a n=a n-6,也就是说,这个数列是以6为周期的,则a150=a144=...=a6,利用a1,a2可以计算出a6=1/3.如果实在想不到这个方法,可以写几项看看很快就会发现a150=a144,大胆推测该数列是以6为周期得,然后写出a1-a13(也就是写到你能看出来规律),不难发现a6=a12,a7=a13,然后那,稍微数数,就可以知道a150=a6了,同样计算得1/3.2：问摄氏升高30度华氏升高的度数与62比大小.key:F=30*9/5=54<623：那道费波拉契数列的题:已知,a1=1 a2=1 a n=a n-1+a n-2，问a1,a2,a3,a6四项的平均数和a1,a3,a4,a5四项的平均数大小比较。
卡梅伦液压数据手册（第 20 版）说明书
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CONTENTS OF SECTION 1
☰ Hydraulics
⌂ Cameron Hydraulic Data ☰
Introduction. . . . . . . . . . . . . ................................................................ 1-3 Liquids. . . . . . . . . . . . . . . . . . . ...................................... .......................... 1-3
4
Viscosity etc.
Steam data....................................................................................................................................................................................... 6
1 Liquid Flow.............................................................................. 1-4
Viscosity. . . . . . . . . . . . . . . . . ...................................... .......................... 1-5 Pumping. . . . . . . . . . . . . . . . . ...................................... .......................... 1-6 Volume-System Head Calculations-Suction Head. ........................... 1-6, 1-7 Suction Lift-Total Discharge Head-Velocity Head............................. 1-7, 1-8 Total Sys. Head-Pump Head-Pressure-Spec. Gravity. ...................... 1-9, 1-10 Net Positive Suction Head. .......................................................... 1-11 NPSH-Suction Head-Life; Examples:....................... ............... 1-11 to 1-16 NPSH-Hydrocarbon Corrections.................................................... 1-16 NPSH-Reciprocating Pumps. ....................................................... 1-17 Acceleration Head-Reciprocating Pumps. ........................................ 1-18 Entrance Losses-Specific Speed. .................................................. 1-19 Specific Speed-Impeller. .................................... ........................ 1-19 Specific Speed-Suction...................................... ................. 1-20, 1-21 Submergence.. . . . . . . . . ....................................... ................. 1-21, 1-22 Intake Design-Vertical Wet Pit Pumps....................................... 1-22, 1-27 Work Performed in Pumping. ............................... ........................ 1-27 Temperature Rise. . . . . . . ...................................... ........................ 1-28 Characteristic Curves. . ...................................... ........................ 1-29 Affinity Laws-Stepping Curves. ..................................................... 1-30 System Curves.. . . . . . . . ....................................... ........................ 1-31 Parallel and Series Operation. .............................. ................. 1-32, 1-33 Water Hammer. . . . . . . . . . ...................................... ........................ 1-34 Reciprocating Pumps-Performance. ............................................... 1-35 Recip. Pumps-Pulsation Analysis & System Piping...................... 1-36 to 1-45 Pump Drivers-Speed Torque Curves. ....................................... 1-45, 1-46 Engine Drivers-Impeller Profiles. ................................................... 1-47 Hydraulic Institute Charts.................................... ............... 1-48 to 1-52 Bibliography.. . . . . . . . . . . . ...................................... ........................ 1-53
GRE考试数学基本概念
GRE考试数学基本概念1 mode（众数）一堆数中出现频率最高的一个或几个数e.g. mode of 1,1,1,2,3,0,0,0,5 is 1 and 0 2 range （值域）一堆数中最大和最小数之差e.g. range of 1,1,2,3,5 is 5-1=43 mean（平均数）arithmatic mean（算术平均数）（不用解释了吧？）geometric mean （几何平均数） n个数之积的n次方根4 median（中数）将一堆数排序之后，正中间的一个数（奇数个数字），或者中间两个数的平均数（偶数个数字）e.g. median of1,7,4,9,2,2,2,2,2,5,8 is 2median of 1,7,4,9,2,5 is (5+7)/2=65 standard error（标准偏差）一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(n)e.g. standard errorof 0,2,5,7,6 is |0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.46 standard variation一堆数中，每个数与平均数之差的平方之和，再除以ne.g. standard variation of0,2,5,7,6 is:_ 2 2 2 2 2_|_(0-4) +(2-4)+(5-4)+(7-4)+(6-4)_|/5=6.87 standard deviation就是standard variation的平方根标准方差的公式：d^2=[(a1-a)^2+(a2-a)^2+....+(an-a)^2 ]/nd 为标准方差8 三角形余玄定理C^2=A^2+B^2-2ABCOSt t为AB两条线间的夹角9 Y=k1X+B1,Y=k2X+B2，两线垂直的条件为K1K2=-110 三的倍数的特点：所有位数之和可被3整除11 N的阶乘公式:N!=1*2*3*....(N-2)*(N-1)*N且规定0!=1例如8!=1*2*3*4*5*6*7*812 熟悉一下根号2、3、5的值sqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.23613 2/3 as many A as B: A=2/3*B....twice as many... A as B: A=2*B14 a if only b: b->a15 数学常用术语倒数（reciprocal） x的倒数为1/xTHE THIRD POWER是三次方的意思2^5=the fifth power of 2abscissa横坐标ordinate纵坐标quadrant象限coordinate坐标slope斜率intercede截距(有正负之分)solution（方程的）解arithmetic progression等差数列（等差级数）common divisor公约数common factor公因子least common multiple最小公倍数composite number合数prime factor质因子prime number质数factor因数consecutive integer连续的整数set集合sequence数列tenths' digit十分位tenth十分位units' digit个位whole number整数3-digit number三位数denominator分母numerator分子dividend被除数divided evenly被整除divisible可整除的divisor除数quotient商remainder余数round四舍五入fraction分数geometric progression等比数列improper fraction假分数proper fraction真分数increase by增加了increase to增加到integer整数in terms of ..用。
GRE-MathReview_真题无答案(973)
GRE-Math Review(总分75, 做题时间90分钟)Numbers and OperationsThese exercises are designed to help you apply the mathematics concepts just covered. They are not in GRE format, but should help you to identify your areas of strength and weakness.Basic OperationsThese questions will test your knowledge of operations using integers, real numbers, fractions, and decimals.Insert the correct operator in the blanks below.SSS_TEXT_QUSTI1.108 ______ 9=12SSS_TEXT_QUSTI2.7 ______ 2=3.5SSS_TEXT_QUSTI3.SSS_TEXT_QUSTI4.When 5 consecutive odd integers, each greater than 34 are added, what is the smallest possible sum?SSS_TEXT_QUSTI5.What is the Lowest Common Denominator ofSSS_TEXT_QUSTI6.SSS_TEXT_QUSTI7.3(27+2-3)= ______SSS_TEXT_QUSTI8.SSS_TEXT_QUSTI9.**= ______SSS_TEXT_QUSTI10.Squares and Square RootsThese questions will test your knowledge of operations using square roots.Solve the following problems.SSS_TEXT_QUSTI11.7= ______2SSS_TEXT_QUSTI12.SSS_TEXT_QUSTI13.Express 3×3 as a square: ______SSS_TEXT_QUSTI14.72-32=SSS_TEXT_QUSTI15.ExponentsThese questions will test your knowledge of operations using exponents.Fill in the blanks below with the correct number.SSS_TEXT_QUSTI16.2 raised to the power of ______ =8SSS_TEXT_QUSTI17.33=______SSS_TEXT_QUSTI18.22×23=______SSS_TEXT_QUSTI19.125=59______SSS_TEXT_QUSTI20.(24)2=______Scientific NotationThese questions will test your knowledge of operations using scientific notation.Fill in the blanks below with the correct number.SSS_TEXT_QUSTI21.423,700,000=4.237×10 to the power of ______SSS_TEXT_QUSTI22.**×105=______SSS_TEXT_QUSTI23.(2.50×104)÷(1.25×103)= ______SSS_TEXT_QUSTI24.**×10-5=______SSS_TEXT_QUSTI25.**×104=______Mean, Median, and ModeThese questions will test your knowledge of operations involving mean, median, and mode.Fill in the blanks below with the correct number.SSS_TEXT_QUSTI26.Ann scored 88, 93, 84, and 99 on 4 tests. What is her mean test score?SSS_TEXT_QUSTI27.What is the mode of the data given below?7,3,6,7,5,8,9,7SSS_TEXT_QUSTI28.What is the median of the data given below?8, 13, 9, 8, 15, 14, 10SSS_TEXT_QUSTI29.Jordan had 3 hits in his first 4 baseball games and 4 hits in his next 4 games. What is the average number of hits Jordan had in all of his games?SSS_TEXT_QUSTI30.What is the median of the data given below?80, 19, 82, 15, 72, 3Ratio, Proportion, and PercentThese questions will test your knowledge of operations involving ratio, proportion, and percent.Answer the following questions.SSS_TEXT_QUSTI31.______ is 30% of 20.SSS_TEXT_QUSTI32.What is the value of x?SSS_TEXT_QUSTI33.As an analyst for the Department of Natural Resources, you analyze samples of river water. A 2-liter sample of water contained about 24 of a particular organism and a 4-liter sample of water contained about 48 such organisms. At this rate, how many of the organisms would you expect to find in a 10-liter sample of water from the same river?SSS_TEXT_QUSTI34.If 20% of x equals 16, then x=______SSS_TEXT_QUSTI35.Jim scored 95 points in 5 basketball games for his school. At this rate, how many points will he have scored by the end of the 12-game season?Absolute ValueThese questions will test your knowledge of operations involving absolute value.Solve the following equations.SSS_TEXT_QUSTI36.If x=-8, what is the value of |x-6|?SSS_TEXT_QUSTI37.Solve |4x-6|=10 for x.SSS_TEXT_QUSTI38.|-15|×|6|=______SSS_TEXT_QUSTI39.Solve |6x+8|=|3x-7| for x.SSS_TEXT_QUSTI40.Simple Probability and OutcomesThese questions will test your knowledge of operations involving simple probability and outcomes.Answer the following questions.SSS_TEXT_QUSTI41.If you roll a single 6-sided die, what is the probability that you will roll an odd number?SSS_TEXT_QUSTI42.A company knows that 2.5% of the CD players it makes are defective. If **pany produces 300,000 CD players, how many will be defective?SSS_TEXT_QUSTI43.When flipping a coin, what is the probability that it will land on tails four times in a row?SSS_TEXT_QUSTI44.If the probability that Dave will go to class is 0.7, what is the probability that he will not go to class?SSS_TEXT_QUSTI45.A bowl contains 20 marbles (8 blue, 6 red, 3 green, 2 yellow, and 1 orange). If you reach in and choose one marble at random, what is the probability that it will be red?Factors and MultiplesThese questions will test your knowledge of operations involving factors and multiples.Answer the following questions.SSS_TEXT_QUSTI46.A certain integer n is a multiple of both 5 and 9. Must n be a multiple of 15?SSS_TEXT_QUSTI47.What are **mon factors of 7 and 42?SSS_TEXT_QUSTI48.What is the Greatest Common Factor of 48 and 72?SSS_TEXT_QUSTI49.What is the Least Common Multiple of 30 and 40?SSS_TEXT_QUSTI50.What is the greatest positive integer x such that 2x is a factor of 1210?Algebra and FunctionsThese exercises are designed to help you apply the mathematics concepts just covered. They are not in GRE format, but should help you to identify your areas of strength and weakness.Linear Equations with One VariableThese questions will test your knowledge of linear equations involving one variable.Solve the following equations.SSS_TEXT_QUSTI1.3x-17=46. Solve for x.SSS_TEXT_QUSTI2.Solve for x.SSS_TEXT_QUSTI3.If x=15, then 4x- ______ =42SSS_TEXT_QUSTI4.Two trains running on parallel tracks are 600 miles apart. One train is moving east at a speed of 90 mph, while the other is moving west at 75 mph. How long will it take for the two trains to pass each other?SSS_TEXT_QUSTI5.3(x-4)=5x-20. Solve for x.Polynomial Operations and Factoring SimpleQuadratic EquationsThese questions will test your knowledge of operations involving polynomial operations and factoring simple quadratic equations.Solve the following equations.SSS_TEXT_QUSTI6.For x=4, 3x2-5x+9=______SSS_TEXT_QUSTI7.(5x3+3x-12)-(2x3-6x+17)=______SSS_TEXT_QUSTI8.(4x2+2x)(x-6)=______SSS_TEXT_QUSTI9.What are the solution sets for x2+2x-48?SSS_TEXT_QUSTI10.(x-4) and (2x+3) are the solution sets for what equation?Systems of EquationsThese questions will test your knowledge of operations involvingsystems of equations.Solve the following systems of equations.SSS_TEXT_QUSTI11.x-2y=14x-4y=-8SSS_TEXT_QUSTI12.4x-2y=6-6x+5y=7SSS_TEXT_QUSTI13.3x-y= 184x=24-6ySSS_TEXT_QUSTI14.8(y+x)=124x-3y=-22SSS_TEXT_QUSTI15.4x-y=633y+x=6Linear Inequalities with One VariableThese questions will test your knowledge of operations involving linear inequalities with one variable.Answer the following questions.SSS_TEXT_QUSTI16.For-5-≤x＜15, x=______SSS_TEXT_QUSTI17.For which values of x is 6x-3＞4x+5?SSS_TEXT_QUSTI18.If x=7, then is 3x+7 greater than or less than 5x-6?SSS_TEXT_QUSTI19.For which values of x is 2x-5＜-3x+20?SSS_TEXT_QUSTI20.Solve for x: -4≤x+3＜18FunctionsThese questions will test your knowledge of operations involving functions.Answer the following questions.SSS_TEXT_QUSTI21.For the function f(x)=x2-4x+8, what is the value of f(6)?SSS_TEXT_QUSTI22.If f(x)=x2, find f(x+1).SSS_TEXT_QUSTI23.If the function f(x)=x+2, and the function g(x)=3x, what is the function g{f(x)}?SSS_TEXT_QUSTI24.For the function what is the value of f(2)?SSS_TEXT_QUSTI25.For the function f(x)=x2+x, what is the value of f(-5)?1。
GRE数学易错考点解读
GRE数学易错考点解读统计学7个高频热门知识点介绍为什么要重点关注GRE数学中的统计学考点?GRE数学考试中涉及到的数学知识点和考点很多，但也并非所有考点都会按照相同的概率出题，有些冷门考点可能几年也没有几道题，有些考点则几乎每场考试都会有相关题目出现，这其中统计学考点就是出现频率相当高的热门考点之一。
而对于中国考生来说，在初高中所学的数学知识点当中，统计学的内容往往是教的比较浅显的，因此很多同学也常会遗忘这个考点相关的各类知识。
特别是众数平均数中位数之类的概念往往是考生的扣分重灾区。
因此特别强调一下GRE数学中统计学考点的重要性也是很必要的。
GRE数学统计学概念实例讲解：mode(众数)一堆数中出现频率最高的一个或几个数举例：mode of 1,1,1,2,3,0,0,0,5 is 1 and 0GRE数学统计学概念实例讲解：range(值域)一堆数中最大和最小数之差 ,所以统计学上又称之为极差.(两极的差)举例：range of 1,1,2,3,5 is 5-1=4GRE数学统计学概念实例讲解：mean(平均数)arithmatic mean(算术平均数): n个数之和再除以ngeometric mean (几何平均数): n个数之积的n次方根GRE数学统计学概念实例讲解：median(中位数)将一堆数排序之后，正中间的一个数(奇数个数字)，或者中间两个数的平均数(偶数个数字)举例：median of 1,7,4,9,2,2,2,2,2,5,8 is 2举例：median of 1,7,4,9,2,5 is (5+7)/2=6GRE数学统计学概念实例讲解：standard error(标准偏差)一堆数中，每个数与平均数的差的绝对值之和，除以这堆数的个数(n)举例：standard error of 0,2,5,7,6 is:(|0-4|+|2-4|+|5-4|+|7-4|+|6-4|)/5=2.4GRE数学统计学概念实例讲解：standard variation一堆数中，每个数与平均数之差的平方之和，再除以n标准方差的公式：d2=[(a1-a)2+(a2-a)2+....+(an-a)2 ]/n举例：standard variation of 0,2,5,7,6 is: average=4((0-4)2 +(2-4)2+(5-4)2+(7-4)2+(6-4)2)/5=6.8GRE数学统计学概念实例讲解：standard deviation就是standard variation的平方根 dGRE数学出题原则有哪些在GRE数学考试中，一般都假定以下信息为真：1，All numbers used are real numbers;2，All figures lie on a plane unless otherwise indicated;3，All angle measures are positive;4，All lines shown as straight are straight. On the computer-based test，lines that appear“jagged" can also be assumed to be straight (lines can look somewhat jagged on the computer screen)：5，Figures are intended to provide useful information for answering the questions. However，except where a figure is accompanied 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.细心的读者会发现，上述假设实际上就是出题原则，即：1，所有的数都是实数;2，除非题目中专门指出假设所有图形都在同一个平面内;3，所有的角的测量值都是正数;4，所有显示为直线的线均可当作直线来处理(在机试中，因为电脑显示器的原因，直线可能会看起来呈“锯齿状”);5，伴随问题的图形将为解题提供有用的信息。
GRE数学考哪些知识点-GRE数学题型有哪些
GRE数学考哪些知识点-GRE数学题型有哪些GRE数学考查的知识点主要可以分为这4大类：计算能力、代数、几何、数据分析;其中计算能力主要涉及百分比计算、各类整数计算、整除问题、因数分解、质数问题、余数奇数偶数等。
以下是关于GRE数学考哪些知识点的具体介绍。
1. 计算能力(Arithmetic)计算能力主要涉及百分比计算、各类整数计算、整除问题、因数分解、质数问题、余数奇数偶数、指数方根以及一些数学概念原理，比如估算、分数、比例、比率、绝对值、数轴、十进制和数列等。
2. 代数(Algebra)代数类考点包括指数运算、因式分解和简化、方程式不等式概念、一次和二次方程式不等式计算、方程式实际运用解题以及解析几何(包括函数图形,等式不等式图形，截距和斜度等)。
3. 几何(Geometry)几何类考点包括平行和垂直线、圆形、三角形(包涵等腰三角形、等边三角形、306090度特别角三角形)、四边形、其它多边形、全等近似图形、立体几何图形、面积、周长、体积、勾股定理和角度计算。
4. 数据分析(Data analysis)本考点涉及基础描述性统计数字(包括平均数、中位数、众数、值域、标准偏差、四分位距、分位数和百分位数)、图表数据提取(比如线形图、条状图、饼图、箱线图、散布图和频率分布图)、基本概率(比如复合事件和单独事件概率、条件概率、随机变量)、概率分配(包括一般分配)和计数方法(比如排列组合、维恩图)。
2GRE数学题型有哪些1、数量比较题数量比较题4选1，题还是比较特别的，数量比较题是让我们去比较两个数量A和数量B，这些题型可能会涉及依据题目信息和要求进行一些计算，最后来比较这两个数量谁更大谁更小，或者相等，或者无法比较。
数量比较题在每个setcion 20题的题量大概是7到8题左右。
每一个数量比较题选项设置都是相同的，选项A表示数量A更大，AB，选项B表示数量B更大，BA，选项C表示两个数量相等，A=B，选项D表示无法从已知信息中推断两者关系。
清华的同学写的GRE math sub攻略
清华的同学写的GRE math sub攻略-1GRE math sub考试上次我说的不是很清楚，现在就转载一篇关于GRE math sub的文章，供诸位有志于出国的数学系的师弟师妹们使用：1. 什么是GRE数学专项考试？GRE数学专项考试，即GRE Mathematics Test (Rescaled)，简称数学sub，是8个GRE专项考试（GRE Subject Test）中的一门，其测试内容为考试者在数学领域内所获得的知识和技能以及能力水平的高低，从而帮助院校更好地了解申请人在数学领域领域的能力情况。
2. 为什么要考GRE数学专项考试对于申请基础数学和应用数学方向的同学来说，GRE数学专项考试的成绩基本是必需的。
对于申请统计方向的同学来说，一般来讲只有Top10的学校（比如Stanford）才会要求sub。
不过考了一个好的sub成绩（关于好的标准下面会讨论），有可能提高你的竞争力，特别是对于GPA不是很高的同学。
另外，对于想转专业的同学，美国大学的经济、金融、计算机方向，以及部分的生物、物理、化学方向（主要是做计的一些方向，比如Computational Physics），都接受数学sub的成绩。
考一个数学sub成绩比考一个自己是特别熟悉的领域的sub容易得多，更何况金融和经济没有相应的sub考试（当然，如果想转专业，光有sub成绩是不够的）。
此外，一些学校还明确说明，他们只看sub成绩，不看General Test的成绩（CMU数学系就是如此）。
Verbal和AW成绩不算理想的同学也不用郁闷了。
3. 关于GRE数学专项考试的一些常识考试规模每年全球参加数学sub考试的人数在3000人左右，中国大陆有几百人参加，清华数学系每年有十几个人参加。
考点与考试日期在中国（包括香港和台湾）每年只有一次考试，一般在11月初，General考试后第二个或第三个礼拜六进行。
全国有12个考点（详见General Test的bulletin），北京有3个考点，分别在北外，北语及外交学院的国际交流中心。
GRE数学考试词汇汇总
GRE数学考试词汇分类汇总代数-数论natural number 自然数positive number 正数negative number 负数odd integer/number 奇数even integer/number 偶数Integer/whole number 整数positive whole number 正整数negative whole number 负整数consecutive number 连续整数real/rational number 实数,有理数Irrational number 无理数inverse /reciprocal 倒数mode 众数composite number 合数prime number 质数common divisor 公约数multiple 倍数common multiple 公倍数(prime) factor(质)因子common factor 公因子common ratio 公比nonnegative 非负的mean 平均数median 中值代数-基本数学概念algebra 代数arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数exponent 指数，幂base 乘幂的底数 ,底边cube 立方数，立方体square root 平方根cube root 立方根common logarithm 常用对数divisor 因子,除数,公约数cardinal 基数ordinal 序数constant 常数variable 变量inverse function 反函数complementary function 余函数linear 一次的，线性的factorization 因式分解absolute value 绝对值round to/off ,to the nearest 四舍五入difference 差product 积quotient 商remainder 余数代数-基本运算,小数,分数Add/plus 加subtract 减Multiply / times 乘divide 除divisible 可被整除的divided evenly 被整除dividend 被除数，红利factorial 阶乘power 乘方radical /root sign 根号decimal fraction 纯小数infinite decimal 无穷小数recurring decimal 循环小数proper fraction 真分数improper fraction 假分数mixed number 带分数vulgar /common fraction 普通分数simple fraction 简分数complex fraction 繁分数numerator 分子denominator 分母common denominator 公分母quarter 四分之一ordinary /decimal scale 十进制tens 十位 , 个位tenths unit n分it位s代数-方程,集合,数列等algebraic term 代数项like terms, similar terms 同类项numerical coefficient 数字系数literal 字母系数no e qf u fi acli i y n t不等式triangle inequality 三角不等式range 值域original equation 原方程equivalent equation 同解/等价方程linear equation 线性方程union 并集proper subset 真子集solution set 解集arithmetic progression(sequence)等差数列geometric progression(sequence)等比数列approximate 近似(anti)clockwise (逆) 顺时针方向direct proportion 正比parentheses 括号proportion 比例permutation 排列combination 组合trigonometric function 三角函数几何-三角plane geometry 平面几何plane 平面alternate angle 内错角corresponding angle 同位角vertical angle 对顶角supplementary angles 补角complementary angle 余角adjacent angle 邻角right angle 直角round angle 周角straight angle 平角included angle 夹角central angle 圆心角interior angle 内角exterior angle 外角acute angle 锐角obtuse angle 钝角trigonometry 三角学equilateral 等边三角形c ri a a lne gnl e triangle 不等边三角形isosceles triangle 等腰三角形right 直角三角形o tr bi inqgul e斜三角形inscribed triangle 内接三角形几何-平面,立体quadrilateral 四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形polygon 多边形parallelogram 平行四边形square 正方形，平方rectangle 长方形rhombus 菱形trapezoid 梯形equilateral 等边形regular polygon 正多边形concentric circles 同心圆line, 直线li n n e segment 线段parallel 平行线ec in ngular solid 长方体regular solid/polyhedron 正多面体circular cylinder 圆柱体cone 圆锥sphere 球体solid 立体的几何-图形概念bisect 平分circumscribe 外切inscribe 内切intersect 相交perpendicular 垂直congruent 全等的multilateral 多边的side 边长circumference, perimeter 周长diameter 直径radius 半径chord 弦arc 弧semicircle 半圆radian 弧度center 圆心g rc m le ent of a circle 弧形angle bisector 角平分线diagonal 对角线cube 立方体，立方数face 立体的面tli it u d de高depth 深度volume 体积surface area 表面积edge 棱几何-坐标arm 直角三角形的股hypotenuse 斜边included side 夹边Pythagorean theorem 勾股定理leg 三角形的直角边median (三角形的) 中线base 底边，底数opposite 直角三角形中的对边cross section 横截面vertex (复数形式 vertices)顶点tangent 切线的complex plane 复平面midpoint 中点endpoint 端点coordinate system 坐标系rectangular coordinate 直角坐标系origin 原点abscissa 横坐标ordinate 纵坐标number line 数轴quadrant 象限slope 斜率transversal 截线intercept 截距商业术语,计量单位Intercalary/leap year 闰年(366 天) common year 平年(365 天) depreciation 折旧down payment 直接付款discount 打折 / denote 表示margin /profit 利润interest 利息/ dividend 红利simple interest 单利compounded interest 复利Increase / decrease to 增加/减少到increase /decrease by 增加/减少了list erti iel 标价 /markup 涨价零售价 /per capita 每人nt ic e 美分/penny 一美分硬币nickel 5 美分硬币 /dime 一角硬币dozen 打(12 个) 廿 (20 个) Centigrade 摄氏s Fo renheit 华氏quart 夸脱/ gallon 加仑(1 gallon = 4 quart)yard 码 / inch 英寸/ 英尺meter 米/ micron 微米foot square measure 平方单位制cubic meter 立方米pint 品脱(干量或液量的单位 )GRE数学考试词汇首字母查询Aabscissa 横坐标absolute value 绝对值account for (数量) 占acute angle 锐角acute triangle 锐角三角形add 加 add toaddition 加，加法adjacent 相邻adjacent angles 邻角algebra 代数学algebraic expression 代数式algebraic fraction 分式algebraic term 代数项aliquot 除得尽数aliquant 除不尽数alternate angles 内错角altitude 高度amount 合计angle 角angle bisector 角平分线apex 顶，顶点apiece 每人，每个approximately 近似的，大约的approximation 近似，近似值arc 弧，圆周的任意一段area 面积arithmetic 算术arithmetic(al) average 算术平均数arithmetic(al) mean 算术平均数或等差中项arithmetic(al) progression 或 series 算术级数，等差级数assume that 假定义……at random 随机地at right angles with 与……成直角at 以这样的比率，价格或速度v at e rage 平均，平均数平均的axis 轴Bbalance 余额bar graph(chart) 条带图base 堤边，底面，幂或乘方的底数base area 底面积be across from 在……对面be closet to 最接近……be composed of 由构成be equal to 与……相等be equivalent to anther equation 与另一方程痛解 be fewer than 小于be greater than 大于be greater than or equal to 不小于be inscribed in 内接于be less than 小于be less than or equal to 不大于be 平行于oe perpendicular to 垂直于be substituted for 代替billion 109binomial 二项式bisect 把……二等分block 立体blot out 涂掉，删掉bound 辩解，范围；邻接*brand*bulk 大量Ccalculate to three decimal places 计算结果保留三位小数cancellation 约掉，消掉*car pool catch up withcentcenter 圆心central angle 圆心角*charge 费用，价钱chart 图表chord 弦circle 圆circle graph(chart) 圆形图circular 圆形的，环形的circular cylinder 圆柱circumference 圆的周长clear an equation of fractions 分式方程整式化clockwise 顺时针coefficient 系数*coincolumn 列，圆柱common denominator 公分母common difference 等差数列的公差common divisor(factor) 共因子；公约数common ratio 等比数列的公比common multiple 公倍数complement 余角complementary angle 余角complete circle 全圆complete quadratic (equation) 全二次方程complex fraction 繁分数composite number 和数，指大于一而不是质数的整数compound 混合物；复利compound interest 复利compound annual interest 年复利concentration 浓度concentric circle 同心圆congruent (多边形) 全等的consecutive 连续的consecutive integer 连续整数consecutive even(odd) integer 连续偶 (奇) 数consist of 由……构成constant 不变的，永恒的；常数constitute 构成，组成*contractor 承包商convert intocoordinate 坐标coordinate axis system 坐标系coordinate geometry 解析几何coordinate plane 坐标平面corresponding angles 同位角，对应角corresponding side 对应边*cost 成本*cost price 成本价counterclockwise 逆时针cross multiplication 交叉相乘cube 立方体，立方；三次幂cubic 立方体的，立方的cubic block 立方体cubic denominations 立方单位cubic solid 立方体cubic units 立方单位cumulative graph(chart) 累积图curve 曲线curved line 曲线cylinder 圆柱体cylinderic(al) 圆柱体的D*dealer 商人decagon 十角形，十边形decimal 小数；小数的decimal fraction 纯小数decimal place 小数位decimal point 小数点*deck 一幅纸牌decrease 减少，减少量deduct 扣除，减去degree 度；度数 (温度和角度) denominator 分母denote 表示，意味着depth 深度diagonal 对角线；对角线的diameter 直径*dietdiffer 不同，相异difference 差，差额digit 数字，位 (数) *dime 一角，十分dimension 尺寸，尺度；维 (数)，度(数)，元(be) direct(inverse) proportional to 成正 (反) 比*discount 折扣discount rate 折扣率distance 距离distinct 与其它不同的，独特的divide 除dividend 被除数divisor 除数，约数divisible 可整除的division 除法*dollar 美元done(drawn) to scale 按比例绘制double*dry mixture*down 付现款地 (和分期付款相对)*dozen*dueEeccentric 偏心圆，；不同圆心的edge 立体的变或棱*encloseendpoint 端点equality 相等，等式equation 等式，方程equiangular 等角的equidistance 等距离的equilateral 等边形；等边的equivalent 等面积的，等体积的；等价的，相等的，等量的equivalent fraction 等值分数，如 1/2 和 2/4even integer 偶数evenly even integer 能再平分的偶数 (能背 4 整除) evenly spaced 等间隔的exponent 指数expression 表达式exterior angle 外角Fface 立体的面factor 因子；将……分解因子factorable 可进行因式分解的factorial 阶乘；因子的，阶乘的figure 图形*finish line 终点线*flatfold 对折footcandle (物理) 英尺烛光 (照度单位) formula 公式，配方fraction 分数from subtract 从……减去……from throughfrom to,inclusiveGgaingeometric mean 几何平均数geometric progression 几何级数，等比级数geometry 几何学graph 图表；用图表来表示greatest common divisor 最大公约数grid 格栅gross 总的，毛的Hhalfway 半途的halve 把……平分为二；将……减半height 高heptagon 七边形hexagon 六边形horizontally 水平地how much more thanhundreds 百位hundredth 第一百个；百分之一hypotenuse (直角三角形) 斜边Iidentical 相等的；恒等的*illumination 照明度improper fraction 假分数included angle(side) 夹角 (边) incomplete quadratic equation indefinitely 无限定地independent 无关地，独立地independent variables 自变量inequality 不等式；不相等in excess of 超过……infinite decimal 无穷小数，同 non-terminating decimalinfinite sequence 无穷数列inscribed angle 圆周角，同弧所对圆心角 central angle 的尺寸是圆周角的二倍inside dimension 内部尺寸installment 分期付款中每一期所付的款项integer 整数integer part 代分数的整数部分，代分数的分数部分是fractionalpart*intensity 强度intercept 截距；截取eg intercepted arc 截弧interest 利息interior angle 内角in terms of 用……来表示intersect 直线相交，point of inetrsection 交点interval 间隔，区间in turn 依次，轮流invert a fraction 求一个分数的倒数irrational number 无理数Jjoint 接合，接合处Lleast(lowest) common multiple 最小公倍数leg 梯形的两条不平性的边；直角三角形的直角边length 长度lengthwise(lengthways) 纵长的lesslevellike(similar) terms 同类项line 直线，线段line segment/half line 半直线，射线line graph 线型图literal 字母系数coefficientMmathematical operation 数学运算mean 平均数mean proportional 比例中项measuremeasurementmedian 中数；中线midpoint 中点midway 中途million 106minor arc AB 劣弧ABminuend 被减数minus 减mixed decimal 混合小数，如3. 14 mode 众数monomial 单项式*mowermultiple 多倍的，多重的；倍数a multiple ofmultiplicand 被乘数multiplication 乘法multiplier 乘数multiply 乘Nnatural number 自然数negative number 负数negligible 可忽略不计的n-gon n-边形nickel 五分nonadjacent 不相邻的nonagon 九边形nonzero 非零；非零的not necessarily distinct 不必然不同的number 数，数字number line 数轴，规定了原点，正方向和单位长度的直线，数轴上的点和实数一一对应numerator 分数的分子numerical coefficient 数字系数Oobtuse angle 钝角，大于90 度而小于180 度的角obtuse triangle 钝角三角形octagon 八边形odd integer 奇数odds 事物发生的可能性，机会ofone dimension 线性的on the average 平均operation 运算oppositeorder 顺序，订单ordinate 纵坐标origin 原点,origin of coordinates 坐标原点original equation 原方程overhangoverlap 部分重叠，部分搭交Pparallel 平行线p li reasl lelogram 平行四边形partpartitionpayrollpenny 分pentagon 五边形percent 百分号percent of interest 利率，同ratepercent increase 增加的百分率interestpercent decrease 减少的百分率perfect square(cube) 完全平方 (立方)， e.g.25 是5 的完全平方perimeter 周长perpendicular lines 垂直线pictograph 统计图表pie gragh(chart) 圆形图，饼型图palce (位) 数plane 平面plus 加point 小数点pointer 指针point of tangency 切点polynomial 多项式pool 联营potion 一部分positive 正的power 幂，乘方preceding 在前的，先前的prime number 质数，素数*principal 本金，资本probability 概率product (乘) 积progression(series) 级数，同series projected 被预测，被估计proportion 比，比率；比例e.g. 与… …成比例; proportionQquadrant 象限quadratic equation 二次方程quadrilateral 四边形quantity 数，数量quotient 商Rradical 根号，根式；radius 半径randomly 随机地rate 率，比率；速度，速率；价格，费用ratio 比，比率ray 射线real number 实数*rebate 回扣，折扣reciprocal 倒数rectangle 矩形rectangular 矩形的；成直角的reduceregularremainder 余数remote interior angles 三角形一个外角对应的两个内错角repeating decimal 无限循环小数revolution 旋转e.g. revolutions per min 每分钟转速rhombus 菱形right 直的root 方根；方程的根round 四舍五入row:column 行Ssatisfy 使……成立scale drawing 按比例绘制 (的图)scalene 不等边三角形，不等边的secant 割线section 断面，一部分cross section 横截面sector 扇形segment 弓形；部分sequence 数列set 集合shaded region 阴影side 边，立体的面sign(symbol) 符号similar (三角形) 相似的simple annual interest 年单利simple fraction 简分数simultaneously 同时地，同时发生地simultaneous equations 联立方程组slope (直线的) 斜率solid 立体；立体的；实心的，单色的e.g. solid 实线/solid colorol in ut es ion 解，答案sphere 球体square 正方形straight angle 平角，指180 度的角straight-line distance 直线距离subdivide 再分，细分subtract…from… 从…减去…successive 连续的，相继的such that 使得满足…的条件sum 和supplement 补角，指两角之和为180 度surface area 表面积Ttable 表格take fromtangent 切线；相切的term 项throughtimes 倍；乘token 辅币toll 通行税total 合计to the nearest 10% transversal 横截线trapezoid 梯形triangle 三角形triangular region trinomial 三项式triple 三倍的精确到10% e.g.linesWwall (容器) 壁weight 重量；重力XX-axis X 轴X-coordinate X 坐标XY-coordinate system 平面直角坐标系，同XY-planeYY-axis Y 轴Y-coordinate Y 坐标Zzero 零Uuniform 一直不变的unit 单位unlike terms 非同类项unknown 未知量Vvalue 值variable 变量vertex 顶点vertical 垂直的；直立的；顶点的；对顶的。
gre sub math教材
Gre sub math 教材1. Gre 数学考试介绍1.1 Gre 考试简介Gre（Graduate Record Examination）是美国研究生入学考试，包括数学、语文、写作三个部分。
数学考试（Gre math）部分主要考察考生的数学基本功和解决问题的能力，包括代数、几何、数据分析和数学推理等内容。
1.2 Gre 数学考试难度Gre 数学考试的题目难度适中，要求考生熟练掌握基本的数学知识，具备一定的数学思维和解题能力。
1.3 Gre 数学考试教材在备考 Gre 数学考试时，选择适合的教材对于提高考试成绩至关重要。
下面我们就来介绍一些常用的 Gre 数学教材。
2. 常用的 Gre 数学教材推荐2.1 《Gre 数学精要》《Gre 数学精要》是一本辅助考生备考 Gre 数学考试的权威教材，内容涵盖了 Gre 数学考试的各种题型和题目类型，对数学考试的各个知识点进行了系统的梳理和总结，适合对数学成绩有要求的考生选用。
2.2 《Gre 数学真题精解》《Gre 数学真题精解》是一本专门针对 Gre 数学考试题目进行解析和讲解的教材，该教材收录了大量的 Gre 数学考试真题，并对每道题目进行了详细的解析和讲解，有助于考生深入理解和掌握 Gre 数学考试的解题技巧和方法。
2.3 《Gre 数学分册版》《Gre 数学分册版》是一本包含了 Gre 数学考试各种数学知识点和考点的专题教材，该教材内容详尽，覆盖了 Gre 数学考试的各个知识点和难点，适合对数学基础要求较高的考生选用。
2.4 《Gre 大学数学教程》《Gre 大学数学教程》是一本由 Gre 考试官方推荐的 Gre 数学备考教材，该教材内容丰富，结构明确，适合对 Gre 数学考试要求全面掌握的考生选用。
3. 如何选择适合自己的 Gre 数学教材3.1 根据个人的数学基础水平选择在选择适合自己的 Gre 数学教材时，考生应该根据自己的数学基础水平和备考的时间安排进行选择。
GRE 数学 Quantitative Reasoning Concepts and Tips
Quantitative Reasoning Concepts and TipsNote: Due to the limitations of current web technology, the appearance of mathematical equations, symbols, graphs and diagrams may be slightly distorted. It may help to view this material in Arial 18 pt. font.The Quantitative Reasoning section of the General Test is designed to measure basic mathematical skills and understanding of elementary mathematical concepts as well as the ability to reason quantitatively and to solve problems in a quantitative setting.In general, the mathematics required does not extend beyond that usually covered in high school. It is expected that examinees are familiar with conventional symbolism, such as x < y (x is less than y),(x is not equal to y), m || n (line m is parallel to line n), m n (line m is perpendicular to line n), and the symbol for a right angle in a figure:Also, standard mathematical conventions are used in the test questions unless otherwise indicated. For example, numbers are in base 10, the positive direction of a number line is to the right and distances are nonnegative. Whenever nonstandard notation or conventions are used in a question, they are explicitly introduced in the question.Many of the questions are posed as word problems in a real-life setting, with quantitative information given in the text of a question or in a table or graph of data. Other questions are posed in a pure-math setting that may include a geometric figure, a graph, or a coordinate system. The following conventions about numbers and figures are used in the quantitative section.Numbers and Units of MeasurementAll numbers used are real numbers.Numbers are to be used as exact numbers, even though in some contexts they are likely to have been rounded. For example, if a question states that "30 percent of the company's profit was from health products," then 30 percent is to be used as an exact percent. It is not to be used as a rounded number obtained from, say, 29 percent or 30.1 percent.An integer that is given as the number of objects in a real-life or pure-math setting is to be taken as the total number of these objects. For example, if a question states that "a bag contains 50 marbles, and 23 of the marbles are red," then 50 is to be taken as the total number of marbles in the bag and 23 is to be taken as the total number of red marbles in the bag. Therefore, the other 27 marbles are not red.Questions may involve units of measurement such as English units or metric units. If an answer to a question requires converting one unit of measurement to another, then the relationship between the units is provided, unless the relationship is a common one such as minutes to hours or centimeters to meters.FiguresGeometric figures that accompany questions provide information useful in answering the questions. However, unless a note states that a geometric figure is drawn to scale, you should solve these problems not by estimating sizes by sight or by measurement, but by reasoning about geometry.Geometric figures consist of points, lines (or line segments), curves (such as circles), angles, regions, etc., and labels that identify these objects or their sizes. (Note that geometric figures may appear somewhat jagged on a computer screen.)Geometric figures are assumed to lie in a plane unless otherwise indicated.Points are indicated by a dot, a label or the intersection of two or more lines or curves.Points on a line or curve are assumed to be in the order shown; points that are on opposite sides of a line or curve are assumed to be oriented as shown.Lines shown as straight are assumed to be straight (though they may look jagged on a computer screen). When curves are shown, they are assumed to be not straight.Angle measures are assumed to be positive and less than or equal to 360°.To illustrate some of these conventions, consider the following geometric figures:From the figures, it can be determined that:∙ABD and DBC are triangles.∙Points A, D and C lie on a straight line, so ABC is also a triangle.∙Point D is a distinct point between points A and C.∙Point E is the only intersection point of line segment BC and the small curve shown.∙Points A and E are on opposite sides of line BD.∙Point F is on line segment BD.∙The length of line segment AD is less than the length of line segment AC.∙The length of line segment AB is 10.∙The measure of angle ABD is less than the measure of angle ABC.∙The measure of angle ACB is 35 degrees.∙Lines m and n intersect the closed curve at three points: R, S and T.From the figures, it cannot be determined whether:∙The length of line segment AD is greater than the length of line segment DC.∙The measures of angles BAD and BDA are equal.∙The measure of angle ABD is greater than the measure of angle DBC.∙Angle ABC is a right angle.When a square, circle, polygon or other closed geometric figure is described in words with no picture, the figure is assumed to enclose a convex region. It is also assumed that such a closed geometric figure is not just a single point. For example, a quadrilateral cannot be any of the following:When graphs of real-life data accompany questions, they are drawn as accurately as possible so you can read or estimate data values from the graphs (whether or not there is a note that the graphs are drawn to scale).Standard conventions apply to graphs of data unless otherwise indicated. For example, a circle graph represents 100 percent of the data indicated in the graph's title and the areas of the individual sectors are proportional to the percents they represent. Scales, gridlines, dots, bars, shadings, solid and dashed lines, legends, etc., are used on graphs to indicate the data. Sometimes, scales that do not begin at zero are used, as well as broken scales.Coordinate systems such as number lines and xy-planes are generally drawn to scale.The questions in the quantitative sections include four broad content areas: arithmetic, algebra, geometry and data analysis.ArithmeticQuestions that test arithmetic include those involving the following topics: arithmetic operations (addition, subtraction, multiplication, division and powers) on real numbers, operations on radical expressions, the number line, estimation, percent, absolute value and properties of integers (for example, divisibility, factoring, prime numbers and odd and even integers).Some facts about arithmetic that may be helpfulFor any two numbers on the number line, the number on the left is less than the number on the right; for example, -4 is to the left of -3, which is to the left of 0.The sum and product of signed numbers will be positive or negative depending on the operation and the signs of the numbers; for example, the product of a negative number and a positive number is negative.Division by zero is undefined; that is, is not a real number for any x.If n is a positive integer, then x n denotes the product of n factors of x; for example, 34 means(3)(3)(3)(3) = 81. If , then x0 = 1.Squaring a number between 0 and 1 (or raising it to a higher power) results in a smaller number; for example,and (0.5)3 = 0.125.An odd integer power of a negative number is negative, and an even integer power is positive; for example,(-2)3 = -8 and (-2)2 = 4.The radical sign means "the nonnegative square root of"; for example, and. The negative square root of 4 is denoted by . If x < 0, then is not areal number, for example, is not a real number.The absolute value of x, denoted by |x|, is equal to x if and equal to -x if x < 0; for example, |8| = 8 and |-8| = -(-8) = 8.If n is a positive integer, then n! denotes the product of all positive integers less than or equal to n; for example, 4! = (4)(3)(2)(1) = 24.The sum and product of even and odd integers will be even or odd depending on the operation and the kinds of integers; for example, the sum of an odd integer and an even integer is odd.If an integer P is a divisor (also called a factor) of another integer N, then N is the product of P and another integer, and N is said to be a multiple of P; for example, 3 is a divisor (or a factor) of 6, and 6 is a multiple of 3.A prime number is a positive integer that has only two distinct positive divisors: 1 and itself. For example, 2, 3, 5, 7 and 11 are prime numbers, but 9 is not a prime number because it has three positive divisors: 1, 3 and 9.Algebra (including coordinate geometry)Questions that test algebra include those involving the following topics: rules of exponents, factoring and simplifying algebraic expressions, concepts of relations and functions, equations and inequalities and coordinate geometry (including slope, intercepts and graphs of equations andinequalities). The skills required include the ability to solve linear and quadratic equations and inequalities and simultaneous equations; the ability to read a word problem and set up the necessary equations or inequalities to solve it; and the ability to apply basic algebraic skills to solve problems.Some facts about algebra that may be helpfulIf ab = 0, then a = 0 or b = 0; for example, if (x - 1)(x + 2) = 0, it follows that either x - 1 = 0 or x + 2 = 0; therefore, x = 1 or x = -2.Adding a number to or subtracting a number from both sides of an equation preserves the equality. Similarly, multiplying or dividing both sides of an equation by a nonzero number preserves the equality. Similar rules apply to inequalities, except that multiplying or dividing both sides of an inequality by a negative number reverses the inequality. For example, multiplying the inequality 3x - 4 > 5 by 4 yields the inequality 12x - 16 > 20; however, multiplying that same inequality by -4 yields -12x + 16 < -20.The following rules for exponents may be useful. If r, s, x and y are positive numbers, then:The rectangular coordinate plane, or xy-plane, is shown below:The x -axis and y -axis intersect at the origin O , and they partition the plane into four quadrants, as shown. Each point in the plane has coordinates (x, y ) that give its location with respect to the axes; for example, the point P (2, -8) is located 2 units to the right of the y -axis and 8 units below the x -axis. The units on the x -axis are the same length as the units on the y -axis, unless otherwise noted.Equations involving the variables x and y can be graphed in the xy -plane. For example, the graph ofthe linear equation y = x - 2 is a line with a slope of and a y -intercept of -2, as shown below:GeometryQuestions that test geometry include those involving the following topics: properties associated with parallel lines, circles, triangles (including isosceles, equilateral, and 30° - 60° - 90° triangles),rectangles, other polygons, area, perimeter, volume, the Pythagorean Theorem and angle measure in degrees. The ability to construct proofs is not measured.Some facts about geometry that may be helpfulIf two lines intersect, then the opposite angles (called vertical angles) are equal; for example, in the figure below, x = y .If two parallel lines are intersected by a third line, certain angles that are formed are equal. Asshown in the figure below, if , then x = y = z.The sum of the degree measures of the angles of a triangle is 180.The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the two legs (Pythagorean Theorem).The sides of a 45° - 45° - 90° triangle are in the ratio and the sides of a 30° - 60° - 90°triangle are in the ratioDrawing in lines that are not shown in a figure can sometimes be helpful in solving a geometry problem; for example, by drawing the dashed lines in the pentagon below, the total number of degrees in the angles of the pentagon can be found by adding the number of degrees in each of the three triangles: 180 + 180 + 180 = 540.The number of degrees of arc in a circle is 360.If O is the center of the circle in the figure below, then the length of arc ABC is times the circumference of the circle.The volume of a rectangular solid or a right circular cylinder is the product of the area of the base and the height; for example, the volume of a cylinder with a base of radius 2 and a height of 5 isData AnalysisQuestions that test data analysis include those involving the following topics: basic descriptive statistics (such as mean, median, mode, range, standard deviation and percentiles), interpretation of data given in graphs and tables (such as bar and circle graphs and frequency distributions) and elementary probability. The questions assess the ability to synthesize information, to select appropriate data for answering a question and to determine whether or not the data provided are sufficient to answer a given question. The emphasis in these questions is on the understanding of basic principles (for example, basic properties of a normal distribution) and reasoning within the context of given information.Some facts about descriptive statistics and probability that may be helpfulIn a distribution of n measurements, the (arithmetic) mean is the sum of the measurements divided by n. The median is the middle measurement after the measurements are ordered by size if n is odd or it is the mean of the two middle measurements if n is even. The mode is the most frequently occurring measurement (there may be more than one mode). The range is the difference between the greatest measurement and the least measurement. Thus, for the measurements 70, 72, 72, 76,78 and 82, the mean is 450 ÷ 6 = 75, the median is (72 + 76) ÷ 2 = 74, the mode is 72 and the range is 12.The probability that an event will occur is a value between 0 and 1, inclusive. If p is the probabilitythat a particular event will occur, then and the probability that the event will not occur is 1 - p. For example, if the probability is 0.85 that it will rain tomorrow, then the probability that it will not rain tomorrow is 1 - 0.85 = 0.15.。