香港大学多元卓越计划数学备考-数学专有名词中英文对照

第第页香港大学多元卓越计划数学备考——数学专有名词中英文对照一、常用数学指令与逻辑表达中文英文例句已知givenGiven,findthevalueof.证明proveProvethatisirrational.证明showthatShowthatforallrealnumbers.求findFindthederivativeof.计算calculateCalculate.确定DetermineDeterminethedomainofthefunction.因此HenceTheequationgives;hencethesolutionis.推断DeduceFromand,wededuce.保留…位小数correctto…decimalplacesThevalueofcorrectto5decimalplacesis.二、基础运算与算术中文英文例句加法additionTheadditionofandgivesthesum.减法SubtractionSubtractionshowsthat.乘法multiplicationMultiplicationisrepeatedaddition:.除法DivisionDivisionsplitsanumber:.和sumThesumofandiswrittenas.差DifferenceThedifferencebetweenandis.积ProductTheproductofandis.商QuotientIn,thequotientis.余数RemainderWhenisdividedby,theremainderis.三、数的分类与基本性质中文英文例句自然数naturalnumberNaturalnumbersare(sometimesincluding).整数IntegerIntegersinclude有理数rationalnumberArationalnumbercanbeexpressedaswhere.无理数irrationalnumberisanirrationalnumberbecauseitcannotbewrittenasafraction.实数realnumberRealnumbersincludebothrationalandirrationalnumbers.复数complexnumberAcomplexnumberisoftheform,where.绝对值absolutevalueTheabsolutevalue.相反数oppositenumberTheoppositeofis.倒数reciprocalThereciprocalofis.四、分数、小数、比与比例中文英文例句分数fractionThefractionmeanspartsoutof.分子NumeratorIn,thenumeratoris.分母denominatorIn,thedenominatoris.真分数properfractionAproperfractionhasnumeratorlessthandenominator,e.g..假分数improperfractionAnimproperfractionlikecanbewrittenasamixednumber.带分数mixednumberThemixednumberequals.小数DecimalThedecimalisequivalentto.循环小数repeatingdecimalisarepeatingdecimal.比ratioTheratioofboystogirlsis.比例proportionAproportionstatesthattworatiosareequal,e.g..百分比percentmeansperhundred,or.五、代数中文英文例句变量VariableIntheexpression,isavariable.常数ConstantIn,thenumberisaconstant.系数CoefficientIn,thecoefficientofis.方程EquationSolvetheequation.不等式InequalityTheinequalitymeansisgreaterthan.函数FunctionThefunctionmapseachinputtoitssquare.根RootTherootsofareand.指数ExponentIn,theexponentis,meaning.对数LogarithmThelogarithmbecause.六、函数相关中文英文例句定义域DomainThedomainofisallnon‑negativerealnumbers:.值域RangeFor,therangeis.自变量independentvariableIn,istheindependentvariable.因变量dependentvariableIn,isthedependentvariable.单调递增strictlyincreasingAfunctionisstrictlyincreasingifimplies.单调递减strictlydecreasingIfimplies,thefunctionisstrictlydecreasing.奇函数oddfunctionAnoddfunctionsatisfies;forexample,.偶函数evenfunctionAnevenfunctionsatisfies;forexample,.复合函数compositefunctionThecompositefunctionmeans.区间IntervalThesetofallnumbersbetweenandisaninterval.开区间openintervaldenotestheopenintervalfromto,excludingendpoints.闭区间closedintervalistheclosedintervalincludingbothand.半开区间half‑openintervalTheintervalincludesbutnot;includesbutnot.无穷区间infiniteintervalisaninfiniteintervalextendingtonegativeinfinity.区间表示法intervalnotationInintervalnotation,iswrittenas.最大值MaximumThefunctionattainsitsmaximumvalueat.最小值MinimumTheminimumvalueofis,achievedat.七、方程相关中文英文例句解方程solveanequationTosolve,wefind.解(名词)solutionThesolutionofisor.解集solutionsetThesolutionsetofis.根rootTherootsofareand.恒等式Identityisanidentity,trueforall.一次方程linearequationAlinearequationinonevariablehastheform.二次方程quadraticequationisaquadraticequation.参数方程parametricequationTheparametricequations,describeacircle.八、不等式相关中文英文例句严格大于strictlygreaterthanmeans5isstrictlygreaterthan3.小于等于lessthanorequaltomeansislessthanorequalto10.解不等式solveaninequalitySolvinggives.三角不等式triangleinequalityThetriangleinequalitystates.绝对值不等式absolutevalueinequalityTheinequalityisequivalentto.不等式组systemofinequalitiesAsystemlikeandhassolution.九、几何中文英文例句点PointApointhasnosize,onlyposition,e.g.point.线LineAstraightlineextendsinfinitelyinbothdirections.线段linesegmentThedistancebetweenpointsandisthelengthofsegment.角AngleArightanglemeasures.三角形TriangleAnequilateraltrianglehasthreeequalsides.正方形SquareTheareaofasquareis,whereisthesidelength.矩形rectangleTheareaofarectangleis.圆CircleAllpointsonacircleareequidistantfromitscenter.半径RadiusTheradiusishalfthediameter:.直径diameterThediameter.周长PerimeterTheperimeterofasquareis.面积areaTheareaofarectangleis.体积VolumeThevolumeofacubeis.平行ParallelParallellinesnevermeet:.垂直perpendicularTwolinesareperpendiculariftheyintersectatarightangle:.全等CongruenceTwotrianglesarecongruentiftheircorrespondingsidesandanglesareequal.相似similarityTrianglesaresimilariftheircorrespondinganglesareequalandsidesareproportional.勾股定理PythagoreantheoremInarighttriangle,,whereisthehypotenuse.等腰三角形isoscelestriangleAnisoscelestrianglehastwoequalsides.等边三角形equilateraltriangleAllsidesofanequilateraltriangleareequal.直角三角形righttriangleArighttrianglecontainsoneangle.平行四边形parallelogramAparallelogramhasoppositesidesparallelandequal.梯形trapezoidAtrapezoidhasatleastonepairofparallelsides.菱形rhombusArhombusisaparallelogramwithallsidesequal.圆周长CircumferenceThecircumferenceofacircleis.圆周率piTheconstant.弧arcAnarcisapartofthecircumferenceofacircle.扇形SectorTheareaofasectorwithcentralangle(inradians)is.切线TangentAtangentlinetouchesacircleatexactlyonepoint.弦ChordAchordisalinesegmentwhoseendpointslieonthecircle.十、指数、根式与科学记数法中文英文例句幂Powerisreadas“2tothefifthpower”.底数baseIn,thebaseis.平方根squarerootThesquarerootofis,writtenas.立方根cuberootbecause.根式RadicalTheexpressionisaradical.科学记数法scientificnotationThespeedoflightisaboutm/s.十一、多项式与代数式中文英文例句单项式Monomialisamonomial.多项式PolynomialApolynomiallikehasmultipleterms.二项式binomialisabinomial.三项式trinomialisatrinomial.次数DegreeThedegreeofis.同类项liketermsandareliketerms;theycanbecombined.因式分解factorizationThefactorizationofis.展开ExpansionExpandinggives.十二、数列与级数中文英文例句数列SequenceThesequenceisanarithmeticsequence.项TermThefirsttermofthesequenceis.通项公式generaltermformulaForthesequence,thefirsttermis.等差数列arithmeticsequenceInanarithmeticsequence,thedifferencebetweenconsecutivetermsisconstant:.公差commondifferenceFor,thecommondifferenceis.等比数列geometricsequenceInageometricsequence,eachtermismultipliedbyacommonratio:.公比commonratioThecommonratioofis.级数seriesThesumofasequenceisaseries,e.g..十三、集合论基础中文英文例句集合setAsetisacollectionofdistinctobjects,e.g..元素Elementisanelementoftheset,writtenas.子集SubsetIfeveryelementofisalsoin,thenisasubsetof:.并集UnionTheunioncontainsallelementsinor.交集IntersectionTheintersectioncontainselementsinbothand.补集ComplementThecomplementof(within)is.空集emptysetTheemptysetcontainsnoelements.全集universalsetTheuniversalsetcontainsallobjectsunderconsideration.十四、概率与统计中文英文例句概率ProbabilityTheprobabilityofrollingaonafairdieis.平均数Average/MeanThemeanofis.中位数MedianThemedianofis.众数ModeIntheset,themodeis.方差VarianceVariancemeasuresspread:.标准差standarddeviationStandarddeviationisthesquarerootofvariance.正态分布normaldistributionThenormaldistributionhasthepdf.十五、排列、组合与概率初步中文英文例句阶乘Factorial.排列PermutationThenumberofpermutationsofobjectstakenatatimeis.组合CombinationThenumberofcombinationsis.事件EventTheeventofrollinganevennumberonadiehasprobability.样本空间samplespaceThesamplespacefortossingacoinis.互斥事件mutuallyexclusiveeventsEventsandaremutuallyexclusiveif.独立事件independenteventsTwoeventsareindependentif.十六、解析几何（坐标几何）中文英文例句坐标系coordinatesystemTheCartesiancoordinatesystemusesandaxes.横坐标x‑coordinate(abscissa)Thepointhas‑coordinate.纵坐标y‑coordinate(ordinate)Its‑coordinateis.斜率SlopeTheslopeofalinethroughandis.截距interceptThe‑interceptofis.距离公式distanceformulaThedistancebetweenandis.中点公式midpointformulaThemidpointis.圆方程equationofacircleThecirclewithcenterandradiusis.抛物线parabolaThegraphofisapa