常用数学术语(英语)

1、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propersubse

2、t真子集solutionset解集 3.有关代数式、方程和不等式 algebraicterm代数项liketerms,similarterms同类项numericalcoefficient数字系数literalcoefficient字母系数inequality不等式triangleinequality三角不等式range值域originalequation原方程equivalentequation同解方程，等价方程linearequation线性方程(e.g.5x+6=22) 4.有关分数和小数 properfraction真分数improperfraction假分数mixednumber带分

3、数vulgarfraction，commonfraction普通分数simplefraction简分数complexfraction繁分数numerator分子denominator分母(least)commondenominator(最小)公分母quarter四分之一decimalfraction纯小数infinitedecimal无穷小数recurringdecimal循环小数tenthsunit十分位 5.基本数学概念 arithmeticmean算术平均值weightedaverage加权平均值geometricmean几何平均数exponent指数，幂base乘幂的底数,底边cube

4、立方数，立方体squareroot平方根cuberoot立方根commonlogarithm常用对数digit数字constant常数variable变量inversefunction反函数complementaryfunction余函数linear一次的，线性的factorization因式分解absolutevalue绝对值，e.g.-32=32roundoff四舍五入 6.有关数论 naturalnumber自然数positivenumber正数negativenumber负数oddinteger,oddnumber奇数eveninteger,evennumber偶数integer,wh

5、olenumber整数positivewholenumber正整数negativewholenumber负整数consecutivenumber连续整数realnumber,rationalnumber实数,有理数irrational(number)无理数inverse倒数compositenumber合数e.g.4,6,8,9,10,12,14,15primenumber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commondivisor公约数multiple倍数(least)commonmultiple(最小)

6、公倍数(prime)factor(质)因子commonfactor公因子ordinaryscale,decimalscale十进制nonnegative非负的tens十位units个位mode众数median中数commonratio公比 7.数列 arithmeticprogression(sequence)等差数列geometricprogression(sequence)等比数列 8.其它approximate近似(anti)clockwise(逆)顺时针方向cardinal基数ordinal序数directproportion正比distinct不同的estimation估计，近似pa

7、rentheses括号proportion比例permutation排列combination组合table表格trigonometricfunction三角函数unit单位,位 几何部分 1.所有的角 alternateangle内错角correspondingangle同位角verticalangle对顶角centralangle圆心角interiorangle内角exteriorangle外角supplementaryangles补角complementaryangle余角adjacentangle邻角acuteangle锐角obtuseangle钝角rightangle直角rounda

8、ngle周角straightangle平角includedangle夹角 2.所有的三角形 equilateraltriangle等边三角形scalenetriangle不等边三角形isoscelestriangle等腰三角形righttriangle直角三角形oblique斜三角形inscribedtriangle内接三角形 3.有关收敛的平面图形，除三角形外 semicircle半圆 concentriccircles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polygo

9、n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regularpolygon正多边形rhombus菱形trapezoid梯形 4.其它平面图形 arc弧line,straightline直线linesegment线段parallellines平行线segmentofacircle弧形 5.有关立体图形 cube立方体，立方数rectangularsolid长方体regularsolid/regularpolyhedron正多面体circularcylinder圆柱体cone圆锥sphere球体solid立体的

10、 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surfacearea表面积volume体积arm直角三角形的股crosssection横截面centerofacircle圆心chord弦radius半径anglebisector角平分线diagonal对角线diameter直径edge棱faceofasolid立体的面hypotenuse斜边includedside夹边leg三角形的直角边medianofatriangle三角形的中线base底边，底数(e.g.2的5次方，2就是底数)opposite直角

11、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 7.有关坐标 coordinatesystem坐标系rectangularcoordinate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complexplane复平面 8.其它 planegeometry平面几何trigonometry三角学bisect平分circumscribe外切inscribe内切intersect相交perpendic

12、ular垂直pythagoreantheorem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 int

13、ercalaryyear(leapyear)闰年(366天)commonyear平年(365天)depreciation折旧downpayment直接付款discount打折margin利润profit利润interest利息simpleinterest单利compoundedinterest复利dividend红利decreaseto减少到decreaseby减少了increaseto增加到increaseby增加了denote表示listprice标价markup涨价percapita每人ratio比率retailprice零售价tie打例题：Aretailersellsawatchat$

14、1840andmakesaprofitof15%.Ifhewantstodoubletheprofit,findthenewsellingpriceofthewatch.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）=32+4xh (b)表达C作为只有x的函数 顺着x0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？ Afterexplainingthequestion,wearegoingtoanswerthemassho

15、wnbelow: (a)Ignor99dethefactthatthetopisaflapopening,thetwoflapscombinetoformonecompletesurface.Takingintoaccountthatthebottomisdouble-layered,thatmeanstheboxhasintotal7surfaces. So,wehave C=3*x2(1top+2bottom)+4*x*h(4sidefaces) Therefore,C=3x2+4xh (b)Asgiven,thevolumeoftheboxshouldbe12m3,thatmeans 1

16、2=x2*h h=12/x2 PutintoC,thenC=3x2+4x(12/x2) Simplify,wegetC=3x2+48/x Sorry,Idonotknowhowtouploadpictureshere!(Butthisshouldnotbedifficult!) Foryoureasyfollowing,makethefollowingtableandplotthepointsaccordingly: x0123456 CInf.5136436084.6116 (Fromthegraph,wecouldalreadyseethattheminimumCoccursataroun

17、dx=2.) (d)Iamnotsurewhetheryouhavelearndifferentiationornot.Anyway,ifyouhavenotlearntcalculusyet,youcouldmakeuseofthegraphinsothatyoushouldalreadyfindthatCisminimumatx=2andthecorrespondingminimumareais36m3. Bydifferentiation, dC/dx=6x48/x2 Forturningpoints,dC/dx=0 Thatmeans,6x48/x2=0 1d046x348=0 x3=

18、8 x=2(Cismaximumorminimumatx=2) Checkingd2C/dx2=6+96/x30(forx=2), soCisminimumatx=2. So,theminimumareaCoccursatx=2, andCmin=3(2)2+48/(2)=12+24=36m3.Afishingboatbrokedownaftertraveling2hoursagainsta4km/hcurrent.Theboatwascarriedbacktoitsstaringpointbythecurrent.thewholetriptook5.5hours.Findthespeedoftheboatinstillwaterbeforethemotorfailed.Twocarsleavetownatthesametimetravelinginoppositedirections.Onetravels51mi/handtheothertravels45mi/h.Inhowmanyhourswilltheybe432milesa