常用数学术语（英语）简介：本文收录了GRE考试之数学术语部分，基本能满足大部分的应用需求，能有效丰富英语的专业词汇。

代数部分1.有关数学运算add，plus加减差乘积除 divisible可被整除的被整除被除数，红利因子，除数 quotient商余数阶乘乘方gn,rootsign根号 roundto四舍五入四舍五入2.有关集合union并集 subset真子集 set解集有关代数式、方程和不等式algebraic term代数项 terms,similar terms同类项 coefficient数字系数 coefficient字母系数不等式 triangle inequality三角不等式值域 equation原方程 equation同解方程，等价方程inear equation线性方程(e.g.5有关分数和小数proper fraction真分数 fraction假分数 number带分数 fraction，common fraction普通分数 fraction简分数fraction繁分数分子分母 denominator(最小)公分母四分之一imal fraction纯小数 decimal无穷小数 decimal循环小数十分位5.基本数学概念arithmetic mean算术平均值 average加权平均值 mean几何平均数指数，幂乘幂的底数,底边立方数，立方体 root平方根cuberoot立方根 logarithm常用对数数字nt常数变量 inversefunction反函数 function余函数一次的，线性的 factorization因式分解 value绝对值，e.g.｜-32｜=32 off四舍五入有关数论natural number自然数 number正数 number负数dd integer,odd number 奇数 integer,even number偶数 number整数 whole number正整数 whole number负整数 number连续整数 lnumber,rational number实数,有理数无理数倒数 number合数 e.g.4,6,8,9,10,12,14,15…… number质数e.g.2,3,5,7,11,13,15……注意：所有的质数(2除外)都是奇数，但奇数不一定是质数reciprocal倒数 divisor公约数倍数 multiple(最小)公倍数质)因子 factor公因子十进制非负的十位个位众数中数 ratio公比数列arithmetic progression(sequence)等差数列 progression(sequence)等比数列其它近似逆)顺时针方向基数序数directproportion正比不同的估计，近似括号 proportion比例排列组合表格 function三角函数单位,位几何部分1.所有的角alternate angle内错角 angle同位角 angle对顶角 angle 圆心角 angle内角 angle外角 aryangles补角aryangle余角 angle邻角ute angle锐角 angle钝角 angle直角round angle周角 angle平角 angle夹角所有的三角形equilateral triangle等边三角形 triangle不等边三角形 triangle等腰三角形 triangle直角三角形斜三角形 triangle内接三角形3.有关收敛的平面图形，除三角形外semicircle半圆concentric circles同心圆四边形五边形六边形七边形八边形九边形十边形多边形平行四边形等边形平面正方形，平方长方形 polygon正多边形菱形梯形其它平面图形arc弧 line直线 segment线段 lines平行线 of a circle弧形有关立体图形cube立方体，立方数 solid长方体 solid/regular polyhedron正多面体 cylinder圆柱体圆锥球体d立体的有关图形上的附属物altitude高深度side边长周长弧度 area 表面积体积直角三角形的股 ssection横截面 of acircle圆心chord弦半径 bisector角平分线对角线直径棱face of a solid立体的面斜边 side夹边三角形的直角边medianofatriangle三角形的中线底边，底数(e.g.2的5次方，2就是底数)直角三角形中的对边中点端点复数形式vertices)顶点切线的截线截距有关坐标coordinate system坐标系 coordinate直角坐标系原点issa 横坐标纵坐标数轴象限斜率 plane复平面其它plane geometry平面几何三角学平分外切内切相交垂直 theorem勾股定理全等的multilateral多边的其它单位类cent美分一美分硬币美分硬币一角硬币en打(12个)廿(20个)摄氏华氏夸脱加仑(1gallon=4quart)码 meter米微米英寸英尺分(角度的度量单位，60分=1度) squaremeasure平方单位制立方米品脱(干量或液量的单位)有关文字叙述题，主要是有关商业intercalary year(leapyear)闰年(366天) year平年(365天)折旧payment直接付款打折利润利润利息 interest单利 interest复利红利to减少到 by减少了 to增加到 by增加了表示 price标价涨价 capita每人比率l price 零售价打例题：A retailer sells a watch at $1840 and makes a profit of 15%. If he wants to double the profit, find the new selling price of the watch.题解：一个制造商生产正方形底的纸箱，箱顶是两块扇掩式的箱盖。

底部因要加强强度而造成双层的。

每个箱的体积是12立方米。

(a) 证明C（做一个箱所需的纸板面积）=3^2 + 4xh(b) 表达C作为只有x的函数© 顺着x>0描绘C的图表(d) (i) 什么尺寸的箱会让所需造箱的纸板面积最少化？(ii) 用来造箱的最少纸板面积是什么？After explaining the question, we are going to answer them as shown below:(a) Ignor99de the fact that the top is a flap opening, the two flaps combine to form one complete surface. Taking into account that the bottom is double-layered, that means t he box has in total 7 surfaces.So, we haveC = 3*x^2 (1 top + 2 bottom) + 4*x*h (4 side faces)Therefore, C = 3x^2 + 4xh(b) As given, the volume of the box should be 12 m^3, that means12 = x^2*hh = 12/x^2Put into C, then C = 3x^2 + 4x(12/x^2)Simplify, we get C = 3x^2 + 48/x© Sorry, I do not know how to upload pictures here! (But this should not be difficult!) For your easy following, make the following table and plot the points accordingly:x0 1 2 3 4 5 6C Inf. 51 36 43 60 84.6 116(From the graph, we could already see that the minimum C occurs at around x=2.)(d) I am not sure whether you have learn differentiation or not. Anyway, if you have n ot learnt calculus yet, you could make use of the graph in © so that you should alread y find that C is minimum at x=2 and the corresponding minimum area is 36 m^3.By differentiation,dC/dx = 6x – 48/x^2For turning points, dC/dx = 0That means, 6x – 48/x^2 = 01d046x^3 – 48 = 0x^3 = 8x = 2 (C is maximum or minimum at x =2)Checking d^2C/dx^2 = 6 + 96/x^3 > 0 (for x = 2),so C is minimum at x=2.So, the minimum area C occurs at x=2,and Cmin = 3(2)^2 + 48/(2) = 12 + 24 = 36 m^3.A fishing boat broke down after traveling 2 hours against a 4km/h current. The boat w as carried back to its staring point by the current. the whole trip took 5.5 hours. Find t he speed of the boat in still water before the motor failed.Two cars leave town at the same time traveling in opposite directions. One travels 51 mi/h and the other travels 45 mi/h. In how many hours will they be 432 miles apart?Sally had a third again as many as David,who had a third as many again as Lucy. Alto gether they had 111. How many did David have?David have 36a third as many again as ,a third again as many as 都是一个意思:4/3a thrid 是1/3 的意思.但是a third as many again as ,a third again as many as 都是一个意思:4/3 !多了一个again 意思是不一样的.把David设为X,可以得到等式4/3X + X + 3/4X = 111.X 就等于36。