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 subtract减 difference差 multiply,times乘 product积comeasyouare divide除 divisible可被整除的 dividedevenly被整除 dividend被除数，红利 divisor因子，除数 quotient商 remainder余数 factorial阶乘 power乘方 radicalsign,rootsign根号 roundto四舍五入 tothenearest四舍五入
2.有关集合
union并集 proper subt真子集 solution t解集
3. 有关代数式、方程和不等式
algebraic term代数项 like terms,similar terms同类项 numerical coefficient数字系数 literal coefficient字母系数 inequality不等式 triangle inequality三角不等式 range值域 origin
al equation原方程 equivalent equation同解方程，等价方程 linear equation线性方程(e.g.5 x +6=22)
qu4. 有关分数和小数
proper fraction真分数 improper fraction假分数 mixed number带分数 vulgar fraction，common fraction普通分数 simple fraction简分数 complex fraction繁分数 numerator分子 denominator分母 (least)common denominator(最小)公分母 quarter四分之一 decimal fraction纯小数 infinite decimal无穷小数 recurring decimal循环小数 tenthsunit十分位
5.基本数学概念
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 ba乘幂的底数,底边 cube立方数，立方体 square root平方根 cuberoot立方根 common logarithm常用对数 digit数字 constant常数 variable变量 inverfunction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，e.g.｜-32｜=32 round off四舍五入
6. 有关数论
natural number自然数 positive number正数 negative number负数 odd integer,odd number 奇数 even integer,even number偶数 integer,whole number整数 positive whole number正整数 negative whole number负整数 concutive number连续整数 rea lnumber,rational number实数,有理数 irrational(number)无理数 inver倒数 composite number合数&4,6,8,9,10,12,14,15…… prime 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 common divisor公约数 multiple倍数 (least)common multiple(最小)公倍数 (prime)factor(质)因子 common factor公因子 ordinaryscale,decimalscale十进制 nonnegative非负的 tens十位 units个位 mode众数 median中数 common ratio公比
7. 数列
arithmetic progression(quence)等差数列 geometric progression(quence)等比数列
8. 其它 approximate近似 (anti)clockwi(逆)顺时针方向 cardinal基数 ordinal序数directproportion正比 distinct不同的 estimation估计，近似 parenthes括号 proportion比例 permutation排列 combination组合 table表格 trigonometric function三角函数 unit单位,位
几何部分
1.所有的角
alternate angle内错角 corresponding angle同位角非诚勿扰男生出场音乐 vertical angle对顶角 central angle 圆心角 interior angle内角 exterior angle外角 supplement aryangles补角 complement aryangle余角 adjacent angle邻角 acute angle锐角 obtu angle钝角 right angle直角 round angle周角 straight angle平角 included angle夹角
2. 所有的三角形
equilateral triangle等边三角形 scalene triangle不等边三角形 isosceles triangle等腰三角形 right triangle直角三角形 oblique斜三角形 inscribed triangle内接三角形
3. 有关收敛的平面图形，除三角形外
micircle半圆
concentric circles同心圆 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 equilateral等边形 plane平面 square正方形，平方 rectangle长方形 regular polygon正多边形 rhombus菱形 trapezoid梯形
4. 其它平面图形
arc弧 line,straight line直线 line gment节哀顺变英文线段 parallel lines平行线 gment of a circle弧形
描述一个人5. 有关立体图形
cube立方体，立方数 rectangular solid长方体 regular solid/regular polyhedron正多面体 circular cylinder圆柱体 cone圆锥 sphere球体 solid立体的
6. 有关图形上的附属物
altitude高 depth深度 side边长 circumference,perimeter周长 radian弧度 surface area 表面积 volume体积 arm直角三角形的股 cros sction横截面 center of acircle圆心 chord弦 radius半径 angle bictor角平分线 diagonal对角线 diameter直径 edge棱 face of a solid立体的面 hypotenu斜边 included side夹边 leg三角形的直角边 medianofatriangle三角形的中线 ba底边，底数(e.g.2的5次方，2就是底数) opposite直角三角形中的对边 midpoint中点 endpoint端点 vertex(复数形式vertices)顶点 tangent切线的 transversal截线 intercept截距hillary
7. 有关坐标
coordinate system坐标系 rectangular coordinate直角坐标系 origin原点 abscissa横坐标 ordinate纵坐标 numberline数轴 quadrant象限 slope斜率 complex plane复平面
英语四级成绩查询时间2020年9月
8. 其它
plane geometry平面几何 trigonometry三角学 bict平分 circumscribe外切 inscribe内切 interct相交 perpendicular垂直 pythagorean theorem勾股定理 congruent全等的 multilateral多边的
其它
1. 单位类
cent美分 penny一美分硬币 nickel5美分硬币 dime一角硬币 dozen打(12个) score廿(20个) Centigrade摄氏 Fahrenheit华氏 quart夸脱 gallon加仑(1gallon=4quart) yard码 meter米 micron微米 inch英寸 foot英尺 minute分(角度的度量单位，60分=1度) squaremeasure平方单位制 cubicmeter立方米 pint品脱(干量或液量的单位)
2. 有关文字叙述题，主要是有关商业
intercalary year(leapyear)闰年(366天) common year平年(365天) depreciation折旧 down payment直接付款 discount打折 margin利润 profit利润 interest利息 simple interest单利 compounded interest复利 dividend红利 decrea to减少到 decrea by减少了 increa to增加到 increa by增加了 denotebenifit表示 list price标价 markup涨价 per capita每人 ratio比率 retail price零售价 tie打
例题：A retailer lls a watch at $1840 and makes a profit of 15%. If he wants to double the profit, find the new lling 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
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(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 the box has in total 7 surfaces.
So, we have
C = 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 means
12 = x^2*h
h = 12/x^2
Put 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:
x 0 1 2 3 4 5 6
C Inf. 51 36 43 60 84.6 116
(From the graph, we could already e 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 not learnt calculus yet, you could make u of the graph in © so that you should already find that C is minimum at x=2 and the corresponding minimum area is 36 m^3.
武汉达内By differentiation,
dC/dx = 6x – 48/x^2
For turning points, dC/dx = 0
That means, 6x – 48/x^2 = 0
1d046x^3 – 48 = 0
x^3 = 8
x = 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 was carried back to its staring point by the current. the whole trip took 5.5 hours. Find the 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. Altogether they had 111. How many did David have?
David have 36
a third as many again as ,a third again as many as 都是一个意思:4/3
a 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
