IGCSE数学词汇chapter 1

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igcse数学词汇

igcse数学词汇

IGCSE(International General Certificate of Secondary Education)数学词汇包括了一系列与数学相关的专业术语和概念。

以下是一些常见的IGCSE数学词汇:1. Algebra –代数2. Geometry –几何3. Trigonometry –三角学4. Calculus –微积分5. Functions –函数6. Equations –方程7. Inequalities –不等式8. Probability –概率9. Statistics –统计10. Logarithms –对数11. Exponents –指数12. Fractions –分数13. Decimals –小数14. Percents –百分比15. Ratios –比例16. Proportions –比例关系17. Unit Circle –单位圆18. Trigonometric Identities –三角恒等式19. Vectors –向量20. Matrices –矩阵21. Graphs –图形22. Parabolas –抛物线23. Cubics –立方24. Quadratics –二次25. Polynomials –多项式26. Roots –根27. Integers –整数28. Rational numbers –有理数29. Irrational numbers –无理数30. Real numbers –实数31. Complex numbers –复数32. Absolute value –绝对值33. Distance –距离34. Midpoint –中点35. Angle –角36. Measure –度量37. Perimeter –周长38. Area –面积39. Volume –体积40. Density –密度。

igcse九年级数学知识点

igcse九年级数学知识点

igcse九年级数学知识点IGCSE(国际普通中等教育证书)九年级的数学知识点主要包括以下内容:1. 数:包括自然数、整数(正、负、零)、质数、平方数和立方数、公因数和公倍数、有理数和无理数、实数、倒数等。

2. 语言、符号和维恩图:用于描述和表示数学概念和关系。

3. 数的幂和根:包括使用正方形、方根、立方体、立方根等进行计算。

4. 有向数和小数的分数及百分数:有向数是一个概念,用于表示方向和距离;小数的分数和百分数则是数学表达的一种形式。

5. 按数量大小排序,并熟悉符号:这是对数学中排序和符号规则的理解。

6. 指数:理解指数的含义,包括其基础概念和应用。

7. 整数、小数和分数的计算:包括整数、小数和分数的四则运算,以及带分数和假分数的计算。

8. 数字、数量和长度的估计:能够给出有效数字和小数位数的近似值,并理解精确度的界限。

9. 比例和比率:理解比例和比率的概念,并能够解决与比例相关的问题,如按比例分配、比例尺等。

10. 百分比和数量的计算:能够进行百分比的计算,以及解决与百分比相关的问题。

11. 使用计算器:熟练使用计算器进行数学计算。

12. 时间计算:包括小时、分钟和秒的计算。

13. 解决个人和家庭财务问题:这部分涉及一些与日常生活相关的财务计算,如利息、贷款等。

14. 与人口和金融相关的指数增长和衰减:这是对数学在经济学和社会科学中的应用的理解。

15. 代数表达式:掌握代数表达式的基本概念、性质和运算规则,能够将实际问题转化为代数表达式,并能够通过代数表达式解决问题。

16. 分数和小数:掌握分数和小数的概念、性质和运算规则,能够进行分数和小数的四则运算和比较大小,能够进行百分数和折扣的计算。

17. 面积和体积:掌握常见图形的面积和体积的计算方法,如矩形、正方形、三角形、圆柱体等,同时也需要掌握一些常见的面积和体积的公式,如球的表面积和体积等。

18. 代数方程:掌握代数方程的基本概念、性质和运算规则,能够通过代数方程解决实际问题,如行程问题、工程问题等。

igcse数学知识点总结

igcse数学知识点总结

igcse数学知识点总结数学作为一门学科,历史悠久,在帮助人们理解世界的过程中起着至关重要的作用。

国际通用的IGCSE(国际普通初等教育课程)数学课程也是数学学习的基础。

本文将概述IGCSE数学课程的主要内容,并对IGCSE数学知识点进行总结。

IGCSE数学课程会涵盖数学基础知识、数学运算、数学分析以及应用数学等等。

其中,数学基础知识主要包括自然数,整数,有理数,不定根,分数,百分比,因数,最大公约数和最小公倍数,十进制等。

此外,IGCSE数学课程还会涉及到诸如向量,函数,三角函数,系数,根式,多项式,立体几何,概率,数据和统计等概念,以及把数学联系到实际应用场景中去。

IGCSE数学知识点总结如下:一,数学基础1.握基本的数学概念和定义,如自然数、整数、有理数、不定根、分数、百分比、因数、最大公约数和最小公倍数等;2.握算术运算的基本操作,如加、减、乘、除;3.握因子化因式以及除法运算;4.解数学表达式以及算术运算的等式和不等式;5.会将十进制转换成其他进制,如二进制、八进制、十六进制;6.握数学形式表达如分数、小数、百分数等。

二,几何1.解几何图形的基本概念,如线段、角、三角形、矩形、多边形等;2.握几何图形的基本属性,如周长、面积、高、底面积、体积等;3.握各种形状的周长和面积的计算公式;4.握立体几何的基本概念,如直线、面、几何体的概念,以及它们的属性;5. 了解变换,如旋转、缩放和反射等。

三,函数1.解函数的基本概念以及它们之间的关系,如一元函数、多元函数、基本函数、反函数,以及它们之间的联系;2.握常见函数的特征,如线性函数、二次函数、指数函数、对数函数等;3.会解方程,包括一元多项式方程、二次方程以及不定方程;4.握函数的图像,如函数图像的表达和求解;3.会三角函数的基本概念,包括角的换算,余弦值的求解,三角函数的解析和微分,它们之间的换算公式等。

四,概率1.解概率的基本概念,如事件、样本空间、概率;2. 了解定义概率的规则;3.握联合概率,如独立性、互斥性、条件概率的概念;4.握条件概率的计算;5.握概率的应用,如事件的独立和相关,条件概率的计算等。

IGCSE数学词汇

IGCSE数学词汇

General Vocabulary Chapter 1 Sets of Numbersset M nfinite set 有湿集 infinite set 无溟美 subset 于集 single-element set 单元素集合 union S6t 芥輿 intersection set 交集 complement set 补集 empty set 空集 belong to 属于 not belong to 不 属于 contain 包,含 Lie in 包含亍 true table 真偵表 original proposition 原命题 inverse proposition 逆会题 inverse and negative proposition 题 」‘、statement 浴句 sufficient condition 充分条件 necessary condition 必要条件 sufficient and necessary condition 条件 if and only if 当且仅当 operation 运算 correspondence 对应 • one-to-one correspondence 1-1 对应 converse operation 逆运算 add (addition)加multiply (multiplication)乘 subtract (difference)减 divide (division)除'number 数 natural number/ counting number 数 rational number 有理数 irrational number 无理数 real number 实数 complex number 复数 integer 整数逆否命 充要 自然positive integer 正整数 negative integer 员整数 whole number / nonnegative integer 员整数 traction 分数proper fraction 真分数 improper fraction 假分数 mixed fraction 带分数 compound fraction 繁分数 simple fraction 简分数 numerator 分子denominator 分母 reciprocal 倒数 consecutive integer 连续整数 decimal number system 十进制数系 decimal point 小数点 prime number 素数,质数 composite number 合数 random number 随机数 recurring decimal 循环小数 non-repeating decimal/irrecurringdecimal 不循环小数 infinite recurring decimal 无限循环小数 infinite irrecurring decimal 无限不循环 小数 terminating decimal 有限小数 approximation 近似值number line 数轴 real number line 实数轴 unit length 单位长度 highest common factor最大公纟勺数 least common multiple. 最小公倍数 commutative law 交換律 associative law 结合律 distributive law 分配律 binary operation 二元运算 reflexive property 自 反性 symmetric property对称性 transitive property 传递性 c substitutionprop^rty 育代性Chapter 2 Expression---------------- 1base (对数、幕运算的)底数 Linear Function —次函数 expanded form 扩展式 quadratic function 二次函数 condensed form 紧缩式 cubic function 三次函数index 指数vertical asymptote 竖萱渐近线 zero index 琴指数 horizontal asymptote 水平渐近线 negative index 负指数 slant asymptote 倾斜渐近统rational index 有理数指数 exponential increasing 指数型増蛇 fractional index 分数指数 bound 边界 parentheses 小括号() orbit 轨迹brace 大括号{ } dash line 虚线 bracket 中括号[] solid line 实线anti-logarithm 真数parameter equation 参数方程 common logarithm 常用对数 jc-intercept x 截距 natural logarithm 自然对数 y-intercept y 截强 laws of logarithm 对数运算律parallel line 平行线 change of base formula 对数换底公式 perpendicular 垂亶的 surd expression 根式表达式 nth root n 次方根 , scientific form 科学记数法radical 根式three significant figures 三位有效数字 radical exponent 根指数 polynomial function 多项式函数 radicand 被开方数descending order 递减顺序 common factor 公因式 ascending order 递増顺序 cancel 消去,相消 leading coefficient 首项系数 inequality 不等式 synthetic division 综合除法 interval 区间quotient 商continuous 连续的dividend 被除数 discontinuous 不连续的 remainder 余数 y-axis y 轴 divisor 除数 x-axis x 轴consequence 结论 oblique 斜的 corollary 推论 subscript 下标function 函数Chapter 3 Equation and Inequalitystandard deviation 标准差 standard form 标准形式 solution set 解集Imear programming 线性规划 feasible region 可行区域 constraint condition 约束条件domain 定义域 range 值域 nonnegative number 非负数 constant 常数 composite function 复合函数 dependent variable 因变量independent variable 自变量objective function 目标函故argument自变量optimal solution 最优發distinguish 区别maximum 极大值relation 关糸minimum 极小值mapping 茨射inequality with absolute value 含绝对值function 函数的不等式.element 元素one variable quadratic inequality _兀一symmetric 对称次不等式even number 溪数image 像odd number 奇数inverse image 原像reflection 反射one-one mapping, one-to-one mapping dilation 伸缩--- 映射stretching 伟长two-point form 两点式slir inking 压缩slope-intercept form 斜載式cross multiply 交叉相美point-slope form 点斜式cubic centimeter 立方厘米intercept form 截距式shift left 4 units 向左移4个单位system of inequalities 不等式组symbol 记号origin 原点Chapter 4 Functionabsolute value 縫双值scalar quantity 数量absolute value function 绝对值函数vector quantity 向量reciprocal function 倒数函数bounded 有界的opposite number 相反数unbounded 无界的.. piecewise function 分段函数convex polygon 凸多边形step function 阶跃函数concave polygon 凹多边形greatest integer function 取整函数open half-plane开的半平面open interval 开区间closed half-plane封闭的半平面closed interval 闭区间basic function 基本函数half-open interval半开半闭区间squaring function 平方函数unit circle 单位圆cubing function 立方函数objective function 目标函数square root function 平方根函数optimization 最优化.constant function 常值函数multiple-solution 多解.increasing function 增函数mathematical model 数学模型decreasing function 减函数solve graphically 图解法cryptography 密码术linear system线性系统,线性方程组decipher 解密码parity奇偶性even root偶次方根even function 偶函数radicand被开方数odd function 奇函数ordered pairs有序数对solid line 实线. .inverse function 反函数dashed line 虚线comp osite function 复合函数dotted line 点线vector 向量reverse operation 运算Chapter 5 Graph of Functionslope斜率gradient 斜率angle of inclination 傾斜角quadratic equation 二次方程horizontal distance 水平距离vertical distance 垂直距离point-slope form 点斜式slope-intercept form 斜截式hvo-point form 两点式general form —般式endpoint 現点axis of symmetry 对称軸midpoint formula 中点公式transformation 转移,变换translation 平移upper bound 上界lower bound ' 界symmetric with respect to the y-axis 宇y轴对称reflection 反射intersection 相交congruent triangle 全等三角形similar triangle 相似三角形capacity 容积surface area 表面积perimeter 周长accuracy 精度bar chart*条形图flow chart流程图graphical methods 图解法ordered pair number 有序数对rate of change 受化率vertex顶点downward 向下upward 向上real solution 实数解关imaginary solution 虚数解Chapter 6 Trigonometryangle of depression 俯角angle of elevation 仰角solving triangle 解三角形law of sine 正弦定理law of cosine余弦定理obtuse triangle钝角三角形right triangle 直角三角形acute triangle 锐角三角形oblique triangle 斜三角形Pythagorean theorem 勾股定理hypdtenuse 斜边adjacent 邻边opposite 对边counterexample 反例reduce to lowest terms 化成既约形式sine 正弦cosecant 余割~ cosine 余弦seceint 正割tangent 正切cotangent 余切reference triangle 辅助三角形quadrantal angle 象限角terminal side 终边initial side 始边area S3 积circumference 周长the (first, second, third, fourth) quadranttrigonomtJtrkal ratios 三甬比第一,二,三,四象限Ml 尽trigonometric identity 三角恒等式protractor 量用器region区域amplitude 振险Heron,s formula 海伦公式phase shift周期变换included angle 夹角scale factor比例因于included side 夹边counterclockwise 逆时针opposite the angle 对甫clockwise顺时针correlation 相关性frequency 频率major arc 优抓completing square 配平万minor arc 劣弧periodic function 周期函数sector 扇形vertical shift 竖直平移Chapter 7 Geometryplane 平蘆congruent triangle 全等三角形line线 > 行similar triangle 相似三角形segment 线段skew lines异面直线ray射线hypotenuse 斜边point 点legs of right triangle 直角边midpoint 中点base 底边angle 角base angle 底角right angle 直角parallelogram 平行四边形acute angle 锐角rhombus 菱形obtuse angle 钝角trapezoid 梯形adjacent angle 邻角ratio比,比率complementary angle 余角angle of depression 俯角supplementary angle 补角angle of elevation 仰角congruent angle 等角circle 圆hypothesis 假设semicircle 半圆conclusion 结论diameter 直径theorem 定理radius半径corollary 推论chord 弦converse theorem 逆定理arc 弧.contra-positive theorem 逆否定理.minor arc 劣弧parallel line 平行线major arc 优弧corresponding angles 同位角inscribed angle 圆周角alternate interior angles 内错角secant 割线same-side interior angles 同旁内角tangent 切线interior angle 内角arc length 弧长exterior angle 外角circumference of a circle 圆周长polygon多边形sector of circle 扇形concave polygon 凹多边形segment of a circle 弓形regular polygon 正多边形SBafiftedby CamScannertriangle 二魚形central angle 中心角equiangular triangle 等角三角形auxiliary line 辅助线equilateral triangle 等边三角形diagonal line 对角线regular triangle正三角形(=等边三角形)centroid重心isosceles triangle 等腰三角形scalene triangle不规则三角形,不等边二角形一quadrilateral 四边形rectangle 矩形square 正方形pentagon 五泣形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形undecagon '-[—边形dodecagon 十二边形median 中线included angle 夹角included side 夹边adjacent side 邻边opposite side 对边opposite angle 对角interior angle 内角exterior angle 外角Chapter 8 Analytical Geometryparabola抛物线hyperbola双曲线rectangular hyperbola 等轴双曲线ellipse 椭圆transverse axis 实轴imaginary axis 虚轴polarcoordinate 极坐标polar axis 极轴polar angle 极角polar distance 极径polar equation极坐标方程parameter equation 参数方程complex number 复数perpendicular bisector 中垂线,垂直平分线circumcenter 夕卜心circumscribed circle 外接圆angle bisector 角平分线incenter 内心incircle 内接圆altitude 高orthocenter 垂心cone圆锥cylinder 圆柱Vface 面edge 校lateral face 侧面lateral area 侧面积surface area 表面积base area 底面积pyramid 棱锥prism棱柱right circular cylinder 直圆柱right circular cone 直圆锥coordinate system 坐标系origin 原点jt-axis x轴y-axis y轴ordered pair 有序对quadrant 象限vertical line 垂直线horizontal line 水平线conic sections 圆锥曲线directrix 准线eccentricity 离心率focus 焦点vertex 顶点quadratic equation 二次方程Chapter 9 Sequence and Seriesarithme tic means 算术中项arithmetic sequence 等差数列arithmetic series 等差级数binomial coefficient 二项式系数binoniial theorem 二项式定理common difference 公差common ratio 公比converge,收敛diverge 发散explicit formula 显式公式factorial notation 阶乘记号finite sequence 有限数列geometric means 等比中项the formula of general term 通项公式sequence 数列series 级数geometric sequence 等比数列geometric series 等比级数infinite sequence 无穷数列limit of a sequence 数列极限mathematical induction 数学归纳法nth term 第n项通项partial sum 部分和Pascal's triangle伯斯卡三角形power series 幕级数recursive formula 递推公式sum of an infinite series 无穷级数和terms of a sequence 数列的项major axis 长轴minor axis 短轴focal length 焦瑁fractal geometry 分形几何polar form复数极坐标形式rectangular form复数代数形式pole极点argument 幅角。

IGSCE数学词汇

IGSCE数学词汇

I G C S E?数学中英对照词汇?代数部分?1.基础?add,plus?加?subtract?减?difference?差?multiply?times?乘?product?积?divide?除?divisible?可被整除的?divided?evenly?被整除?dividend?被除数?divisor?因子,除数?quotient?商?remainder?余数?factorial?阶乘?power?乘方?radical?sign,?root?sign?根号?round?to?四舍五入?to?the?nearest?四舍五入?2.有关集合?union?并集?proper?subset?真子集?solution?set?解集?subset子集nonemptysubset空集intersection交集complement补集universalset全集3.有关代数式、方程和不等式? algebraic?term?代数项?like?terms,?similar?terms?同类项?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?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? digit?数字?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?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?奇整数,?odd?number?奇数?even?integer,?even?number?偶数?integer,?whole?number?整数rationalnumber有理数realnumber实数complexnumber复数irrationalnumber无理数?4.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?tenths?unit十分位?irrational(number)无理数?inverse倒数?composite?number合数?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?prime?number质数?ordinary?scale,?decimal?scale十进制nonnegative非负的?tens十位?units个位?mode众数?median中数?common?ratio公比?positive?whole?number?正整数? negative?whole?number?负整数? consecutive?number?连续整数?real?number,?rational?number?实数,有理数? arentheses?括号=32?proportion?比例?permutation?排列?combination?组合?table?表格?trigonometric?function?三角函数?unit?单位,位?numerical?coefficient?数字系数? inequality?不等式?triangle?inequality?三角不等式?range?值域?original?equation?原方程?equivalent?equation?同解方程等价方程? linear?equation?线性方程??7.数列?arithmetic?progression(sequence)等差数列? geometric?progression(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?direct?proportion?正比? distinct?不同的?estimation?估计,近似?几何部分?1.所有的角?alternate?angle?内错角? corresponding?angle?同位角? vertical?angle?对顶角? central?angle?圆心角? interior?angle?内角?exterior?angle?外角supplementary?angles?补角? complementary?angle?余角? adjacent?angle?邻角?acute?angle?锐角?obtuse?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?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?tangent?切线的?transversal?截线?intercept?截距solid?立体的?cone?圆锥?sphere?球体??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?cross?section?横截面?center?of?acircle?圆心?chord?弦?radius?半径?angle?bisector?角平分线?diagonal?对角线?diameter?直径?edge?棱?ace?of?a?solid?立体的面? hypotenuse?斜边?3.有关收敛的平面图形,除三角形外? semicircle?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?segment?线段?parallel?lines?平行线?segment?of?a?circle?弧形?其它相关词汇?cent?美分?penny?一美分硬币?included?side?夹边?leg?三角形的直角边?median?of?a?triangle?三角形的中线?base?底边,底数(e.g.2?的5?次方,2?就是底数)? opposite?直角三角形中的对边?midpoint?中点?endpoint?端点?vertex(复数形式vertices)顶点?quart?夸脱?gallon?加仑(1gallon=4quart)?yard?码?meter?米?micron?微米?inch?英寸?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?Number?line?数轴?quadrant?象限?slope?斜率?complex?plane?复平面?8.其它?plane?geometry?平面几何?trigonometry?三角学?bisect?平分?circumscribe?外切?inscribe?内切?intersect?相交?nickel?5?美分硬币?dime?一角硬币?dozen?打(12?个)?score?廿(20?个)?Centigrade?摄氏?Fahrenheit?华氏?foot?英尺?minute?分(角度的度量单位,60?分=1?度)? square?measure?平方单位制?cubic?meter?立方米?pint?品脱(干量或液量的单位)? perpendicular?垂直?Pythagorean?theorem?勾股定理? congruent?全等的?multilateral?多边的?。

(完整版)数学英文词汇大全

(完整版)数学英文词汇大全

(完整版)数学英文词汇大全微积分第一章函数与极限Chapter1 Function and Limit集合set元素element子集subset空集empty set并集union交集intersection差集difference of set基本集basic set补集complement set直积direct product笛卡儿积Cartesian product开区间open interval闭区间closed interval半开区间half open interval有限区间finite interval区间的长度length of an interval无限区间infinite interval领域neighborhood领域的中心centre of a neighborhood领域的半径radius of a neighborhood左领域left neighborhood右领域right neighborhood映射mappingX到Y的映射mapping of X ontoY满射surjection单射injection一一映射one-to-one mapping双射bijection算子operator变化transformation函数function逆映射inverse mapping复合映射composite mapping自变量independent variable因变量dependent variable定义域domain函数值value of function函数关系function relation值域range自然定义域natural domain单值函数single valued function多值函数multiple valued function单值分支one-valued branch函数图形graph of a function绝对值函数absolute value符号函数sigh function整数部分integral part阶梯曲线step curve当且仅当if and only if(iff)分段函数piecewise function上界upper bound下界lower bound有界boundedness无界unbounded函数的单调性monotonicity of a function 单调增加的increasing单调减少的decreasing单调函数monotone function函数的奇偶性parity(odevity) of a function 对称symmetry偶函数even function奇函数odd function函数的周期性periodicity of a function周期period反函数inverse function直接函数direct function复合函数composite function中间变量intermediate variable函数的运算operation of function基本初等函数basic elementary function 初等函数elementary function幂函数power function指数函数exponential function对数函数logarithmic function三角函数trigonometric function反三角函数inverse trigonometric function 常数函数constant function双曲函数hyperbolic function双曲正弦hyperbolic sine双曲余弦hyperbolic cosine双曲正切hyperbolic tangent反双曲正弦inverse hyperbolic sine反双曲余弦inverse hyperbolic cosine反双曲正切inverse hyperbolic tangent极限limit数列sequence of number收敛convergence收敛于a converge to a发散divergent极限的唯一性uniqueness of limits收敛数列的有界性boundedness of a convergent sequence子列subsequence函数的极限limits of functions函数当x趋于x0时的极限limit of functions as x approaches x0 左极限left limit右极限right limit单侧极限one-sided limits水平渐近线horizontal asymptote无穷小infinitesimal无穷大infinity铅直渐近线vertical asymptote夹逼准则squeeze rule单调数列monotonic sequence高阶无穷小infinitesimal of higher order低阶无穷小infinitesimal of lower order同阶无穷小infinitesimal of the same order--------------------------------------------------------------------------------2 高等数学-翻译等阶无穷小equivalent infinitesimal函数的连续性continuity of a function增量increment函数在x0连续the function is continuous at x0左连续left continuous右连续right continuous区间上的连续函数continuous function函数在该区间上连续function is continuous on an interval不连续点discontinuity point第一类间断点discontinuity point of the first kind第二类间断点discontinuity point of the second kind初等函数的连续性continuity of the elementary functions定义区间defined interval最大值global maximum value (absolute maximum)最小值global minimum value (absolute minimum)零点定理the zero point theorem介值定理intermediate value theorem第二章导数与微分Chapter2 Derivative and Differential速度velocity匀速运动uniform motion平均速度average velocity瞬时速度instantaneous velocity圆的切线tangent line of a circle切线tangent line切线的斜率slope of the tangent line位置函数position function导数derivative可导derivable函数的变化率问题problem of the change rate of a function 导函数derived function左导数left-hand derivative右导数right-hand derivative单侧导数one-sided derivatives在闭区间【a,b】上可导is derivable on the closed interval [a,b] 切线方程tangent equation角速度angular velocity成本函数cost function边际成本marginal cost链式法则chain rule隐函数implicit function显函数explicit function二阶函数second derivative三阶导数third derivative高阶导数nth derivative莱布尼茨公式Leibniz formula对数求导法log- derivative参数方程parametric equation相关变化率correlative change rata微分differential可微的differentiable函数的微分differential of function自变量的微分differential of independent variable微商differential quotient间接测量误差indirect measurement error绝对误差absolute error相对误差relative error第三章微分中值定理与导数的应用Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives 罗马定理Rolle’s theorem费马引理Fermat’s lemma拉格朗日中值定理Lagrange’s mean value theorem驻点stationary point稳定点stable point临界点critical point辅助函数auxiliary function拉格朗日中值公式Lagrange’s mean value formula柯西中值定理Cauchy’s mean value theorem洛必达法则L’Hospital’s Rule0/0型不定式indeterminate form of type 0/0不定式indeterminate form泰勒中值定理Taylor’s mean value th eorem泰勒公式Taylor formula余项remainder term拉格朗日余项Lagrange remainder term麦克劳林公式Maclaurin’s formula佩亚诺公式Peano remainder term凹凸性concavity凹向上的concave upward, cancave up凹向下的,向上凸的concave downward’concave down 拐点inflection point函数的极值extremum of function极大值local(relative) maximum最大值global(absolute) mximum极小值local(relative) minimum最小值global(absolute) minimum目标函数objective function曲率curvature弧微分arc differential平均曲率average curvature曲率园circle of curvature曲率中心center of curvature曲率半径radius of curvature渐屈线evolute渐伸线involute根的隔离isolation of root隔离区间isolation interval切线法tangent line method第四章不定积分Chapter4 Indefinite Integrals原函数primitive function(antiderivative)积分号sign of integration被积函数integrand积分变量integral variable积分曲线integral curve积分表table of integrals换元积分法integration by substitution分部积分法integration by parts分部积分公式formula of integration by parts有理函数rational function真分式proper fraction假分式improper fraction第五章定积分Chapter5 Definite Integrals曲边梯形trapezoid with曲边curve edge窄矩形narrow rectangle曲边梯形的面积area of trapezoid with curved edge积分下限lower limit of integral积分上限upper limit of integral积分区间integral interval分割partition积分和integral sum可积integrable矩形法rectangle method积分中值定理mean value theorem of integrals函数在区间上的平均值average value of a function on anintegvals 牛顿-莱布尼茨公式Newton-Leibniz formula 微积分基本公式fundamental formula of calculus换元公式formula for integration by substitution递推公式recurrence formula反常积分improper integral反常积分发散the improper integral is divergent反常积分收敛the improper integral is convergent无穷限的反常积分improper integral on an infinite interval无界函数的反常积分improper integral of unbounded functions绝对收敛absolutely convergent第六章定积分的应用Chapter6 Applications of the Definite Integrals元素法the element method面积元素element of area平面图形的面积area of a luane figure直角坐标又称“笛卡儿坐标(Cartesian coordinates)”极坐标polar coordinates抛物线parabola椭圆ellipse旋转体的面积volume of a solid of rotation旋转椭球体ellipsoid of revolution, ellipsoid of rotation曲线的弧长arc length of acurve可求长的rectifiable光滑smooth功work水压力water pressure引力gravitation变力variable force第七章空间解析几何与向量代数Chapter7 Space Analytic Geometry and Vector Algebra向量vector自由向量free vector单位向量unit vector零向量zero vector相等equal平行parallel向量的线性运算linear poeration of vector三角法则triangle rule平行四边形法则parallelogram rule交换律commutative law结合律associative law负向量negative vector差difference分配律distributive law空间直角坐标系space rectangular coordinates坐标面coordinate plane卦限octant向量的模modulus of vector向量a与b的夹角angle between vector a and b方向余弦direction cosine方向角direction angle向量在轴上的投影projection of a vector onto an axis数量积,外积,叉积scalar product,dot product,inner product 曲面方程equation for a surface球面sphere旋转曲面surface of revolution母线generating line轴axis圆锥面cone顶点vertex旋转单叶双曲面revolution hyperboloids of one sheet旋转双叶双曲面revolution hyperboloids of two sheets柱面cylindrical surface ,cylinder圆柱面cylindrical surface准线directrix抛物柱面parabolic cylinder二次曲面quadric surface椭圆锥面dlliptic cone椭球面ellipsoid单叶双曲面hyperboloid of one sheet双叶双曲面hyperboloid of two sheets旋转椭球面ellipsoid of revolution椭圆抛物面elliptic paraboloid旋转抛物面paraboloid of revolution双曲抛物面hyperbolic paraboloid马鞍面saddle surface椭圆柱面elliptic cylinder双曲柱面hyperbolic cylinder抛物柱面parabolic cylinder空间曲线space curve空间曲线的一般方程general form equations of a space curve 空间曲线的参数方程parametric equations of a space curve 螺转线spiral螺矩pitch投影柱面projecting cylinder投影projection平面的点法式方程pointnorm form eqyation of a plane法向量normal vector平面的一般方程general form equation of a plane两平面的夹角angle between two planes点到平面的距离distance from a point to a plane空间直线的一般方程general equation of a line in space方向向量direction vector直线的点向式方程pointdirection form equations of a line方向数direction number直线的参数方程parametric equations of a line两直线的夹角angle between two lines垂直perpendicular直线与平面的夹角angle between a line and a planes平面束pencil of planes平面束的方程equation of a pencil of planes行列式determinant系数行列式coefficient determinant第八章多元函数微分法及其应用Chapter8 Differentiation of Functions of Several Variables and Its Application 一元函数function of one variable多元函数function of several variables内点interior point外点exterior point边界点frontier point,boundary point聚点point of accumulation开集openset闭集closed set连通集connected set开区域open region闭区域closed region有界集bounded set无界集unbounded setn维空间n-dimentional space二重极限double limit多元函数的连续性continuity of function of seveal连续函数continuous function不连续点discontinuity point一致连续uniformly continuous偏导数partial derivative对自变量x的偏导数partial derivative with respect to independent variable x高阶偏导数partial derivative of higher order二阶偏导数second order partial derivative混合偏导数hybrid partial derivative全微分total differential偏增量oartial increment偏微分partial differential全增量total increment可微分differentiable必要条件necessary condition充分条件sufficient condition叠加原理superpostition principle全导数total derivative中间变量intermediate variable隐函数存在定理theorem of the existence of implicit function 曲线的切向量tangent vector of a curve法平面normal plane向量方程vector equation向量值函数vector-valued function切平面tangent plane法线normal line方向导数directional derivative梯度gradient数量场scalar field梯度场gradient field向量场vector field势场potential field引力场gravitational field引力势gravitational potential曲面在一点的切平面tangent plane to a surface at a point曲线在一点的法线normal line to a surface at a point无条件极值unconditional extreme values条件极值conditional extreme values拉格朗日乘数法Lagrange multiplier method拉格朗日乘子Lagrange multiplier经验公式empirical formula最小二乘法method of least squares均方误差mean square error第九章重积分Chapter9 Multiple Integrals二重积分double integral可加性additivity累次积分iterated integral体积元素volume element三重积分triple integral直角坐标系中的体积元素volume element in rectangular coordinate system 柱面坐标cylindrical coordinates柱面坐标系中的体积元素volume element in cylindrical coordinate system 球面坐标spherical coordinates球面坐标系中的体积元素volume element in spherical coordinate system 反常二重积分improper double integral 曲面的面积area of a surface质心centre of mass静矩static moment密度density形心centroid转动惯量moment of inertia参变量parametric variable第十章曲线积分与曲面积分Chapter10 Line(Curve)Integrals and Surface Integrals对弧长的曲线积分line integrals with respect to arc hength第一类曲线积分line integrals of the first type对坐标的曲线积分line integrals with respect to x,y,and z第二类曲线积分line integrals of the second type有向曲线弧directed arc单连通区域simple connected region复连通区域complex connected region格林公式Green formula第一类曲面积分surface integrals of the first type对面的曲面积分surface integrals with respect to area有向曲面directed surface对坐标的曲面积分surface integrals with respect to coordinate elements第二类曲面积分surface integrals of the second type有向曲面元element of directed surface高斯公式gauss formula拉普拉斯算子Laplace operator格林第一公式Green’s first formula通量flux散度divergence斯托克斯公式Stokes formula环流量circulation旋度rotation,curl第十一章无穷级数Chapter11 Infinite Series一般项general term部分和partial sum余项remainder term等比级数geometric series几何级数geometric series公比common ratio调和级数harmonic series柯西收敛准则Cauchy convergence criteria, Cauchy criteria for convergence 正项级数series of positive terms达朗贝尔判别法D’Alembert test柯西判别法Cauchy test交错级数alternating series绝对收敛absolutely convergent条件收敛conditionally convergent柯西乘积Cauchy product函数项级数series of functions发散点point of divergence收敛点point of convergence收敛域convergence domain和函数sum function幂级数power series幂级数的系数coeffcients of power series阿贝尔定理Abel Theorem收敛半径radius of convergence收敛区间interval of convergence泰勒级数Taylor series麦克劳林级数Maclaurin series二项展开式binomial expansion近似计算approximate calculation舍入误差round-off error,rounding error欧拉公式Euler’s formula魏尔斯特拉丝判别法Weierstrass test三角级数trigonometric series振幅amplitude角频率angular frequency初相initial phase矩形波square wave谐波分析harmonic analysis直流分量direct component基波fundamental wave二次谐波second harmonic三角函数系trigonometric function system傅立叶系数Fourier coefficient傅立叶级数Forrier series周期延拓periodic prolongation正弦级数sine series余弦级数cosine series奇延拓odd prolongation偶延拓even prolongation傅立叶级数的复数形式complex form of Fourier series第十二章微分方程Chapter12 Differential Equation解微分方程solve a dirrerential equation常微分方程ordinary differential equation偏微分方程partial differential equation,PDE微分方程的阶order of a differential equation微分方程的解solution of a differential equation微分方程的通解general solution of a differential equation初始条件initial condition微分方程的特解particular solution of a differential equation 初值问题initial value problem微分方程的积分曲线integral curve of a differential equation 可分离变量的微分方程variable separable differential equation 隐式解implicit solution隐式通解inplicit general solution衰变系数decay coefficient衰变decay齐次方程homogeneous equation一阶线性方程linear differential equation of first order非齐次non-homogeneous齐次线性方程homogeneous linear equation非齐次线性方程non-homogeneous linear equation常数变易法method of variation of constant暂态电流transient stata current稳态电流steady state current伯努利方程Bernoulli equation全微分方程total differential equation积分因子integrating factor高阶微分方程differential equation of higher order悬链线catenary高阶线性微分方程linera differential equation of higher order 自由振动的微分方程differential equation of free vibration强迫振动的微分方程differential equation of forced oscillation 串联电路的振荡方程oscillation equation of series circuit二阶线性微分方程second order linera differential equation线性相关linearly dependence线性无关linearly independce二阶常系数齐次线性微分方程second order homogeneourlinear differential equation with constant coefficient二阶变系数齐次线性微分方程second order homogeneous linear differential equation with variable coefficient特征方程characteristic equation无阻尼自由振动的微分方程differential equation of free vibration with zero damping固有频率natural frequency简谐振动simple harmonic oscillation,simple harmonic vibration微分算子differential operator待定系数法method of undetermined coefficient共振现象resonance phenomenon欧拉方程Euler equation幂级数解法power series solution数值解法numerial solution勒让德方程Legendre equation微分方程组system of differential equations常系数线性微分方程组system of linera differential equations with constant coefficient线性代数Aadjont(adjugate) of matrix A A 的伴随矩阵augmented matrix A 的增广矩阵Bblock diagonal matrix 块对角矩阵block matrix 块矩阵basic solution set 基础解系CCauchy-Schwarz inequality 柯西-许瓦兹不等式characteristic equation 特征方程characteristic polynomial 特征多项式coffcient matrix 系数矩阵cofactor 代数余子式cofactor expansion 代数余子式展开column vector 列向量commuting matrices 交换矩阵consistent linear system 相容线性方程组Cramer’s rule 克莱姆法则Cross- product term 交叉项DDeterminant 行列式Diagonal entries 对角元素Diagonal matrix 对角矩阵Dimension of a vector space V 向量空间V的维数Eechelon matrix 梯形矩阵eigenspace 特征空间eigenvalue 特征值eigenvector 特征向量eigenvector basis 特征向量的基elementary matrix 初等矩阵elementary row operations 行初等变换Ffull rank 满秩fundermental set of solution 基础解系G[center]grneral solution 通解Gram-Schmidt process 施密特正交化过程Hhomogeneous linear equations 齐次线性方程组Iidentity matrix 单位矩阵inconsistent linear system 不相容线性方程组indefinite matrix 不定矩阵indefinit quatratic form 不定二次型infinite-dimensional space 无限维空间inner product 内积inverse of matrix A 逆矩阵Llinear combination 线性组合linearly dependent 线性相关linearly independent 线性无关linear transformation 线性变换lower triangular matrix 下三角形矩阵Mmain diagonal of matrix A 矩阵的主对角matrix 矩阵[center]negative definite quaratic form 负定二次型negative semidefinite quadratic form 半负定二次型nonhomogeneous equations 非齐次线性方程组nonsigular matrix 非奇异矩阵nontrivial solution 非平凡解norm of vector V 向量V的范数normalizing vector V 规范化向量Oorthogonal basis 正交基orthogonal complement 正交补orthogonal decomposition 正交分解orthogonally diagonalizable matrix 矩阵的正交对角化orthogonal matrix 正交矩阵orthogonal set 正交向量组orthonormal basis 规范正交基orthonomal set 规范正交向量组[b]Ppartitioned matrix 分块矩阵positive definite matrix 正定矩阵positive definite quatratic form 正定二次型positive semidefinite matrix 半正定矩阵positive semidefinite quadratic form 半正定二次型Qquatratic form 二次型[center]R[/center]rank of matrix A 矩阵A的秩r(A) reduced echelon matrix 最简梯形阵row vector 行向量Sset spanned by { } 由向量{ }所生成similar matrices 相似矩阵similarity transformation 相似变换singular matrix 奇异矩阵solution set 解集合standard basis 标准基standard matrix 标准矩阵Isubmatrix 子矩阵subspace 子空间symmetric matrix 对称矩阵Ttrace of matrix A 矩阵A 的迹tr(A)transpose of A 矩阵A的转秩triangle inequlity 三角不等式trivial solution 平凡解Uunit vector 单位向量upper triangular matrix 上三角形矩阵Vvandermonde matrix 范得蒙矩阵vector 向量vector space 向量空间Zzero subspace 零子空间zero vector 零空间(本文已被浏览133 次)概率统计概率论与数理统计词汇英汉对照表Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成,分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的,立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差。

IGCSE数学词汇chapter 1

IGCSE数学词汇chapter 1

IGCSE-MathematicsChapter 1: Reviewing number concepts一:Glossary&Expressions1.1Different types of numbers1.natural number [ 数] 自然数(5 星)2.whole number 整数(5 星)3.even number [ 数] 偶数(5 星)4.odd number [ 数] 奇数(5 星)5.integer ['intid ʒə] n. [ 数] 整数;整体;完整的事物(5 星)6.prime number [ 数] 素数(5 星)7.prime [praim] adj. 主要的;最好的;基本的(4 星)8.square [skwεə] n. 平方;正方形adj. 平方的;正方形的;直角的;正直的vt. 使成方形; vi. 成方形 adv. 成直角地(5 星)9.square number [ 数] 平方数(5 星)10.fraction ['frækʃən] n. 分数;部分;小部分;(5星)11.negative['neɡət iv]n.负数;adj.[数]负的;(5星)12.negative integers 负整数(5 星)13.consecutive [k ən'sekjutiv] adj. 连贯的;连续不断的(5 星)mon fraction [ 数] 普通分数; [数] 简分数(5 星)15.decimal ['desim əl] n. 小数adj. 小数的;十进位的(5 星)16.is equal to 等于(5 星)17.equal ['i:kw əl] n.相等的事物adj. 平等的;相等的;vt. 等于;比得上(5 星)18.is not equal to 不等于(5 星)19.is approximately e qual to 约等于(4 星)20.approximately [ ə'prɔksimitli] adv. 大约,近似地;近于(4 星)21.is less than 小于(5 星)22.is less than or e qual to 小于等于(5 星)23.is greater than 大于(5 星)24.is greater than or equal to 大于等于( 5 星)25.therefore ['ðεəfɔ:] adv. 因此;所以(4 星)26.square root of 的算术平方根(5 星)27.add [æd] n. 加法,加法运算vi. 加;增加;加起来;做加法vt. 增加,添加;计算…总和(5 星)28.addition [ ə'diʃən] n. 添加;[数] 加法;增加物(5 星)29.mi nus ['main əs] prep. 减,减去 n. 负号,减号;不足;负数 adj. 减的;负的(5星)30.subtract [s əb'trækt] vt. 减去;(5 星)31.subtraction [s əb'trækʃən] n. [ 数] 减法;减少;差集(5 星)32.t im e s[t aim z]n.时代(time的复数);[数]次数p re p.乘以v.使…相乘(5星)33.multiply ['m ʌltiplai] adj. 多层的;多样的 vt. 乘;使增加;使相乘 vi. 乘;增加(5 星)34.divide[di'vaid]vt.除;(5星)35.divided by 除以(5 星)36.sum [s ʌm] n. 总数 vt. 总结;合计 vi. 概括(5 星)37.difference ['dif ərən s] n. 差异;不同;(5 星)38.product ['pr ɔdək t, - ʌkt] n. 产品;结果; [数] 乘积;(5星)39.quotient ['kw əuʃənt] n. [ 数] 商;系数;(5 星)40.remai n d e r [ri'meind ə] n. [ 数] 余数,残余;剩余物; adj. 剩余的;吃剩的 vt. 廉价出售;削价出售vi. 廉价出售;削价出售(5 星)41.divisible [di'viz əbl] adj. 可分的;可分割的(5 星)42.reciprocal[ri'sipr əkəl] n. [ 数] 倒数; adj. 倒数的(5 星)43.finding 找,求1.2Multiples and factors1.multiples ['m ʌltiplz] n. [ 数] 倍数;(5星)2.factors n. 因素(factor 的复数)v.分解…的因子;(5 星)mon multiple 公倍;[数] 公倍数(5 星)4.the lowest common mulitiples(LCM) 最小公倍数(5 星)mon factors [ 数] 公因数(5 星)6.the highest common factor (HCF )最大公约数( 5 星)1.3Prime numbers1.prime numbers 质数;素数(5 星)posite ['k ɔmp əz it] n. 复合材料;合成物;adj. 复合的;合成的;vt. 使合成;使混合(5 星)posite numbers 【数学】合数, (区别于 prime number) (5 星)4.prime factors 质因子(5 星)5.division [di'vi ʒən] n. [ 数] 除法;(5 星)6.divisibility [di,vizi'bil əti] n. 可分性;[数] 可除性(5 星)7.digits ['did ʒits] n. [ 计] 数字;(5 星)1.4P owers and r oots1.powers n.幂(p o we r的复数形式);(5星)2.roots n. [ 数][植] 根;(4 星)3.square root [ 数] 平方根;二次根(5 星)4.symbol ['simb əl] n. 象征;符号;标志(4 星)5.cube [kju:b] n. 立方;立方体;骰子 vt. 使成立方形;使自乘二次;量…的体积(5星)6.cube numbers 立方数(5 星)7.cube roots [ 数] 立方根(5 星)1.5Working with directed n umbers1.directed numbes 有向数(4 星)2.directed[di'rektid, dai-] v. 指导;管理(d irect 的过去式和过去分词)adj. 定向的;(4 星)3.order [' ɔ:də] n. 命令;顺序;规则;(4 星)4.number line 实数直线;数值轴(5 星)5.ascending [ ə'sendiŋ] adj. 上升的 v. 上升;(5 星)6.descending [di'sendiŋ] n. 递减;下行v. 下降 adj. 下降的;下行的(5 星)1.6Order of operations1.operations n.运营;运作;(5星)2.division [di'vi ʒən] n. [ 数] 除法;(5 星)3.multiplication [,m ʌltipli'kei ʃən] n. [ 数] 乘法;增加(5 星)4.addition [ ə'diʃən] n. 添加;[数] 加法;增加物(5 星)5.subtraction [s əb'trækʃən] n. [ 数] 减法;减少;差集(5 星)6.brac k e t s[b rækət s]n.方括号;(5星)7.power [pau ə] n. [ 数] 幂(3 星)8.working with 使用(3 星)9.working with brackets 使用括号( 3 星)10.BODMAS (bracket, of, divide, multiply, add, subtract )(5 星)1.7Rounding numbers1.rounding n. [ 数]凑整;v. 把…弄成整数[数]凑整的;环绕的(4 星)2.rounding numbers 四舍五入(4 星)3.accuracy ['ækjur əs i] n. [ 数] 精确度,准确性(4 星)4.correct to 取值至;准确至;精确到(5 星)5.decimal place [ 数] 小数位(5 星)6.significant [sig'nifik ənt] adj. 重大的;有效的;有意义的;(4 星)7.significant figures [ 计] 有效数字(5 星)8.round down 下舍入(4 星)9.round up 上舍入(4 星)10.standard form 标准形式科学记数法(5星)11.calculator['kælkjulei tə]n.计算器;(5星)12.calculator use 用计算器(3 星)。

igcse数学知识点总结

igcse数学知识点总结

igcse数学知识点总结igcse学是世界上最常考的数学考试之一,也是很多学生在准备考试过程中最重要的一部分。

准备igcse数学的过程中,学生们必须掌握其中的大量知识点,深入理解和操练,以保证能达到优异的考试成绩。

本文将集中讨论igcse数学知识点,为学生们提供参考。

igcse数学首先涉及到几何方面。

几何包含很多概念,例如:几何图形的周长和面积;三角形的内角和外角的和;四边形的属性,如角平分线、对角线、角的长度等;几何图形的轴对称性和镜像对称性;直角三角形的勾股定理;坐标系等等,学生需要熟练掌握这些知识点。

igcse数学还包括基本的代数,主要包括方程和不等式等,学生需要清楚地理解这些知识点,要会在复杂的实际情况中运用其中的概念来求解方程,并能正确推导出结果。

此外,igcse数学还包括数据分析和概率统计的知识,例如:使用表格、图形和统计指标来组织和分析数据;概率定义;概率计算;伯努利概率;独立性、互斥性;伯努利实验;均值、方差;概率分布和随机变量等,学生要深入理解这些概念和计算方法,以便在考试中熟练运用。

最后,igcse数学还涉及到微积分等方面的知识,学生们需要掌握常用的微积分概念,包括:微分、积分、微分方程等,并要深入理解与之相关的一些经典定理及其证明,同时要熟练掌握与之相关的计算方法,以备考试之用。

总之,igcse数学考试涉及到很多方面的知识点,如几何、代数、数据分析和概率、微积分等等,要想取得理想的成绩,学生们必须掌握这些知识点,努力学习,不断复习,多练习,努力达到理想的考试成绩。

igcse数学考试的准备对学生来说是一项重要的任务。

上述就是igcse数学知识点的总结,希望能给学生们提供帮助。

虽然数学考试是一门困难的学科,但只要认真学习,勤加练习,克服困难,一定能取得理想的成绩。

高等数学名词(中英文对照)

高等数学名词(中英文对照)

高等数学名词(中英文)第一章函数与极限Chapter1 Function and Limit 集合set 元素element子集subset空集empty set并集union交集intersection 差集difference of set基本集basic set 补集complement set直积direct product笛卡儿积Cartesian product开区间open interval 闭区间closed interval 半开区间half open interval 有限区间finite interval区间的长度length of an interval无限区间infinite interval邻域neighborhood邻域的中心centre of a neighborhood 邻域的半径radius of a neighborhood 左邻域left neighborhood右邻域right neighborhood映射mappingX 到Y 的映射mapping of X onto Y 满射surjection单射injection一一映射one-to-one mapping双射bijection算子operator变化transformation函数function逆映射inverse mapping复合映射composite mapping自变量independent variable 因变量dependent variable定义域domain函数值value of function函数关系function relation值域range自然定义域natural domain单值函数single valued function多值函数multiple valued function单值分支one-valued branch函数图形graph of a function绝对值函数absolute value符号函数sigh function整数部分integral part阶梯曲线step curve当且仅当if and only if(iff)分段函数piecewise function上界upper bound下界lower bound有界boundedness无界unbounded函数的单调性monotonicity of a function 单调增加的increasing单调减少的decreasing单调函数monotone function函数的奇偶性parity(odevity) of a function 对称symmetry偶函数even function奇函数odd function函数的周期性periodicity of a function周期period反函数inverse function直接函数direct function复合函数composite function中间变量intermediate variable函数的运算operation of function基本初等函数basic elementary function初等函数elementary function幂函数power function指数函数exponential function对数函数logarithmic function三角函数trigonometric function反三角函数inverse trigonometric function 常数函数constant function双曲函数hyperbolic function双曲正弦hyperbolic sine双曲余弦hyperbolic cosine双曲正切hyperbolic tangent反双曲正弦inverse hyperbolic sine反双曲余弦inverse hyperbolic cosine反双曲正切inverse hyperbolic tangent极限limit数列sequence of number收敛convergence收敛于converge to发散divergent极限的唯一性uniqueness of limits收敛数列的有界性boundedness of a convergent sequence子列subsequence函数的极限limits of functions函数当x 趋于x0 时的极限limit of functions as x approaches x0左极限left limit右极限right limit单侧极限one-sided limits水平渐近线horizontal asymptote无穷小infinitesimal无穷大infinity铅直渐近线vertical asymptote夹逼准则squeeze rule单调数列monotonic sequence高阶无穷小infinitesimal of higher order 低阶无穷小infinitesimal of lower order 同阶无穷小infinitesimal of the same order 等阶无穷小equivalent infinitesimal 函数的连续性continuity of a function增量increment函数在x0 连续the function is continuous at x0左连续left continuous右连续right continuous区间上的连续函数continuous function函数在该区间上连续function is continuous on an interval不连续点discontinuity point第一类间断点discontinuity point of the first kind第二类间断点discontinuity point of the second kind初等函数的连续性continuity of the elementary functions定义区间defined interval最大值global maximum value (absolute maximum)最小值global minimum value (absolute minimum)零点定理the zero-point theorem介值定理intermediate value theorem第二章导数与微分Chapter2 Derivative and Differential速度velocity匀速运动uniform motion平均速度average velocity瞬时速度instantaneous velocity圆的切线tangent line of a circle切线tangent line切线的斜率slope of the tangent line位置函数position function导数derivative可导derivable函数的变化率问题problem of the change rate of a function导函数derived function左导数left-hand derivative右导数right-hand derivative单侧导数one-sided derivatives在闭区间[a, b] 上可导is derivable on the closed interval [a,b]切线方程tangent equation角速度angular velocity成本函数cost function边际成本marginal cost链式法则chain rule隐函数implicit function显函数explicit function二阶函数second derivative三阶导数third derivative高阶导数nth derivative莱布尼茨公式Leibniz formula对数求导法log- derivative参数方程parametric equation相关变化率correlative change rata微分differential可微的differentiable函数的微分differential of function自变量的微分differential of independent variable微商differential quotient间接测量误差indirect measurement error 绝对误差absolute error相对误差relative error第三章微分中值定理与导数的应用Chapter3 Mean Value Theorem ofDifferentials and the Application ofDerivatives罗马定理Rolle’s theorem费马引理Fermat’s lemma拉格朗日中值定理Lagrange’s mean value theorem驻点stationary point稳定点stable point 临界点critical point辅助函数auxiliary function拉格朗日中值公式Lagrange’s mean value formula柯西中值定理Cauchy’s mean value theorem 洛必达法则L’Hospital’s Rule0/0 型不定式indeterminate form of type 0/0 不定式indeterminate form泰勒中值定理Taylor’s mean value theorem 泰勒公式Taylor formula余项remainder term拉格朗日余项Lagrange remainder term麦克劳林公式Maclaurin’s formula佩亚诺公式Peano remainder term凹凸性concavity凹向上的concave upward, concave up凹向下的,向上凸的concave downward’ concave down拐点inflection point函数的极值extremum of function极大值local(relative) maximum最大值global(absolute) maximum极小值local(relative) minimum最小值global(absolute) minimum目标函数objective function曲率curvature弧微分arc differential平均曲率average curvature曲率园circle of curvature曲率中心center of curvature曲率半径radius of curvature渐屈线evolute渐伸线involute根的隔离isolation of root隔离区间isolation interval切线法tangent line method第四章不定积分Chapter4 Indefinite Integrals原函数primitive function(anti-derivative)积分号sign of integration被积函数integrand积分变量integral variable积分曲线integral curve积分表table of integrals换元积分法integration by substitution分部积分法integration by parts分部积分公式formula of integration by parts 有理函数rational function真分式proper fraction假分式improper fraction第五章定积分Chapter5 Definite Integrals曲边梯形trapezoid with曲边curve edge窄矩形narrow rectangle曲边梯形的面积area of trapezoid with curved edge积分下限lower limit of integral积分上限upper limit of integral积分区间integral interval分割partition积分和integral sum可积integrable矩形法rectangle method积分中值定理mean value theorem of integrals函数在区间上的平均值average value of a function on an intervals牛顿-莱布尼茨公式Newton-Leibniz formula微积分基本公式fundamental formula of calculus换元公式formula for integration by substitution递推公式recurrence formula反常积分improper integral 反常积分发散the improper integral is divergent反常积分收敛the improper integral is convergent无穷限的反常积分improper integral on an infinite interval无界函数的反常积分improper integral of unbounded functions绝对收敛absolutely convergent第六章定积分的应用Chapter6 Applications of the Definite Integrals元素法the element method面积元素element of area平面图形的面积area of a plane figure直角坐标又称“笛卡儿坐标(Cartesian coordinates)”极坐标polar coordinates抛物线parabola椭圆ellipse旋转体的面积volume of a solid of rotation 旋转椭球体ellipsoid of revolution, ellipsoid of rotation曲线的弧长arc length of a curve可求长的rectifiable光滑smooth功work水压力water pressure引力gravitation变力variable force第七章空间解析几何与向量代数Chapter7 Space Analytic Geometry and Vector Algebra向量vector自由向量free vector单位向量unit vector零向量zero vector相等equal平行parallel向量的线性运算linear poeration of vector三角法则triangle rule 平行四边形法则parallelogram rule 交换律commutative law结合律associative law负向量negative vector差difference分配律distributive law空间直角坐标系space rectangular coordinates坐标面coordinate plane卦限octant向量的模modulus of vector向量a 与b 的夹角angle between vector a and b方向余弦direction cosine方向角direction angle向量在轴上的投影projection of a vector onto an axis数量积,外积,叉积scalar product,dot product,inner product曲面方程equation for a surface球面sphere旋转曲面surface of revolution母线generating line轴axis 圆锥面cone 顶点vertex旋转单叶双曲面revolution hyperboloids of one sheet旋转双叶双曲面revolution hyperboloids of two sheets柱面cylindrical surface ,cylinder圆柱面cylindrical surface准线directrix抛物柱面parabolic cylinder二次曲面quadric surface 椭圆锥面dlliptic cone椭球面ellipsoid单叶双曲面hyperboloid of one sheet 双叶双曲面hyperboloid of two sheets 旋转椭球面ellipsoid of revolution 椭圆抛物面elliptic paraboloid 旋转抛物面paraboloid of revolution 双曲抛物面hyperbolic paraboloid 马鞍面saddle surface椭圆柱面elliptic cylinder 双曲柱面hyperbolic cylinder 抛物柱面parabolic cylinder 空间曲线spacecurve空间曲线的一般方程general form equations of a space curve空间曲线的参数方程parametric equations of a space curve螺转线spiral 螺矩pitch投影柱面projecting cylinder投影projection平面的点法式方程pointnorm form eqyation of a plane法向量normal vector平面的一般方程general form equation of a plane两平面的夹角angle between two planes点到平面的距离distance from a point to a plane空间直线的一般方程general equation of a line in space方向向量direction vector直线的点向式方程pointdirection form equations of a line方向数direction number直线的参数方程parametric equations of a line两直线的夹角angle between two lines垂直perpendicular直线与平面的夹角angle between a line and a planes平面束pencil of planes平面束的方程equation of a pencil of planes 行列式determinant系数行列式coefficient determinant第八章多元函数微分法及其应用Chapter8 Differentiation of Functions of Several Variables and Its Application一元函数function of one variable多元函数function of several variables内点interior point外点exterior point边界点frontier point,boundary point聚点point of accumulation开集openset闭集closed set 连通集connected set 开区域open region 闭区域closed region 有界集bounded set 无界集unbounded setn 维空间n-dimentional space二重极限double limit多元函数的连续性continuity of function of seveal连续函数continuous function不连续点discontinuity point 一致连续uniformly continuous 偏导数partial derivative对自变量x 的偏导数partial derivative with respect to independent variable x高阶偏导数partial derivative of higher order 二阶偏导数second order partial derivative 混合偏导数hybrid partial derivative 全微分total differential偏增量oartial increment偏微分partial differential 全增量total increment 可微分differentiable 必要条件necessary condition 充分条件sufficient condition叠加原理superpostition principle全导数total derivative中间变量intermediate variable 隐函数存在定理theorem of the existence of implicit function曲线的切向量tangent vector of a curve法平面normal plane向量方程vector equation 向量值函数vector-valued function 切平面tangent plane法线normal line方向导数directional derivative梯度gradient 数量场scalar field 梯度场gradient field 向量场vector field 势场potential field引力场gravitational field引力势gravitational potential曲面在一点的切平面tangent plane to a surface at a point曲线在一点的法线normal line to a surface at a point无条件极值unconditional extreme values 条件极值conditional extreme values 拉格朗日乘数法Lagrange multiplier method 拉格朗日乘子Lagrange multiplier 经验公式empirical formula最小二乘法method of least squares均方误差mean square error第九章重积分Chapter9 Multiple Integrals二重积分double integral可加性additivity累次积分iterated integral体积元素volume element三重积分triple integral直角坐标系中的体积元素volume element in rectangular coordinate system柱面坐标cylindrical coordinates柱面坐标系中的体积元素volume element in cylindrical coordinate system球面坐标spherical coordinates球面坐标系中的体积元素volume element in spherical coordinate system反常二重积分improper double integral曲面的面积area of a surface质心centre of mass静矩static moment密度density形心centroid转动惯量moment of inertia参变量parametric variable第十章曲线积分与曲面积分Chapter10 Line (Curve) Integrals andSurface Integrals对弧长的曲线积分line integrals with respect to arc hength第一类曲线积分line integrals of the first type对坐标的曲线积分line integrals with respect to x,y,and z第二类曲线积分line integrals of the second type有向曲线弧directed arc单连通区域simple connected region 复连通区域complex connected region 格林公式Green formula第一类曲面积分surface integrals of the first type对面的曲面积分surface integrals with respect to area 有向曲面directed surface对坐标的曲面积分surface integrals with respect to coordinate elements第二类曲面积分surface integrals of the second type有向曲面元element of directed surface高斯公式gauss formula 拉普拉斯算子Laplace operator 格林第一公式Green’s first formula 通量flux散度divergence 斯托克斯公式Stokes formula 环流量circulation旋度rotation,curl第十一章无穷级数Chapter11 Infinite Series一般项general term 部分和partial sum 余项remainder term等比级数geometric series几何级数geometric series公比common ratio 调和级数harmonic series柯西收敛准则Cauchy convergence criteria, Cauchy criteria for convergence 正项级数series of positive terms 达朗贝尔判别法D’Alembert test柯西判别法Cauchy test 交错级数alternating series 绝对收敛absolutely convergent条件收敛conditionally convergent柯西乘积Cauchy product 函数项级数series of functions 发散点point of divergence 收敛点pointof convergence 收敛域convergence domain 和函数sumfunction幂级数power series幂级数的系数coeffcients of power series阿贝尔定理Abel Theorem 收敛半径radius of convergence 收敛区间interval of convergence 泰勒级数Taylor series 麦克劳林级数Maclaurin series 二项展开式binomial expansion 近似计算approximate calculation舍入误差round-off error,rounding error 欧拉公式Euler’s formula 魏尔斯特拉丝判别法Weierstrass test 三角级数trigonometric series振幅amplitude角频率angular frequency初相initial phase矩形波square wave 谐波分析harmonic analysis 直流分量direct component 基波fundamental wave 二次谐波second harmonic三角函数系trigonometric function system 傅立叶系数Fourier coefficient 傅立叶级数Forrier series周期延拓periodic prolongation正弦级数sine series 余弦级数cosine series 奇延拓oddprolongation 偶延拓evenprolongation傅立叶级数的复数形式complex form of Fourier series第十二章微分方程Chapter12 Differential Equation 解微分方程solve a differential equation 常微分方程ordinary differential equation 偏微分方程partial differential equation,PDE 微分方程的阶order of a differential equation 微分方程的解solution of a differential equation 微分方程的通解general solution of a differential equation初始条件initial condition微分方程的特解particular solution of a differential equation初值问题initial value problem微分方程的积分曲线integral curve of a differential equation可分离变量的微分方程variable separable differential equation隐式解implicit solution 隐式通解inplicit general solution 衰变系数decay coefficient衰变decay齐次方程homogeneous equation 一阶线性方程linear differential equation of first order 非齐次non-homogeneous齐次线性方程homogeneous linear equation 非齐次线性方程non-homogeneous linear equation常数变易法method of variation of constant 暂态电流transient state current 稳态电流steady state current 伯努利方程Bernoulli equation 全微分方程total differential equation 积分因子integrating factor高阶微分方程differential equation of higher order悬链线catenary高阶线性微分方程linear differential equation of higher order 自由振动的微分方程differential equation of free vibration强迫振动的微分方程differential equation of forced oscillation串联电路的振荡方程oscillation equation of series circuit二阶线性微分方程second order lineardifferential equation线性相关linearly dependence线性无关linearly independence 二阶常系数齐次线性微分方程second order homogeneous linear differential equation with constant coefficient二阶变系数齐次线性微分方程second order homogeneous linear differential equation with variable coefficient特征方程characteristic equation无阻尼自由振动的微分方程differential equation of free vibration with zero damping 固有频率natural frequency 简谐振动simple harmonic oscillation,simple harmonic vibration微分算子differential operator待定系数法method of undetermined coefficient共振现象resonance phenomenon欧拉方程Euler equation 幂级数解法power series solution 数值解法numerial solution 勒让德方程Legendre equation微分方程组system of differential equations 常系数线性微分方程组system of linear differential equations with constant coefficie。

ALevel,IGCSE学科词汇表

ALevel,IGCSE学科词汇表

Majestic International CollegeIGCSE & A-Level 专业词汇数学代数部分1、有关基本运算add,plus加subtract减difference差multiply, times乘product积divide除divisible可被整除的divided evenly被整除dividend被除数divisor因子,除数quotient商remainder余数factorial阶乘power乘方radical sign, root sign根号round to四舍五入to the nearest四舍五入2.有关集合union并集proper subset真子集solution set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original 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)4.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tenths unit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digit数字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,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consecutive number连续整数real number, rational number实数,有理数irrational(number)无理数inverse倒数composite number合数prime number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ordinary scale, decimal scale十进制Non-negative非负的tens十位units个位mode众数median中数common ratio公比7.数列arithmetic progression(sequence)等差数列geometric progression(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direct proportion正比distinct不同的estimation估计,近似parentheses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vertical angle对顶角central angle圆心角interior angle内角exterior angle外角supplementary angles补角complementary angle余角adjacent angle邻角acute angle锐角obtuse 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semicircle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 segment线段parallel lines平行线segment of a circle弧形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cross section横截面center of a circle圆心chord弦radius半径angle bisector角平分线diagonal对角线diameter直径edge棱face of a solid立体的面hypotenuse斜边included side夹边leg三角形的直角边median of a triangle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complex plane复平面8. 其它plane geometry平面几何trigonometry三角学bisect平分circumscribe外切inscribe内切intersect相交perpendicular垂直Pythagorean theorem勾股定理congruent全等的multilateral多边的单位部分cent 美分penny 一美分硬币nickel 5美分硬币dime 一角硬币dozen 打(12个)score (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) Square measure 平方单位制Cubic meter 立方米pint 品脱(干量或液量的单位)函数部分function 函数argument 自变量domain 定义域range 值域interval 区间closed interval 闭区间open interval 开区间graph of function 函数的图象mapping 映射image 象inverse image 原象monotone 单调increasing function 增函数decreasing function 减函数monotone interval 单调区间inverse function 反函数exponent 指数radical 根式radical exponent 根指数radicand 被开方数exponential function 指数函数logarithm 对数common logarithm 常用对数natural logarithm 自然对数logarithmic function 对数函数圆锥曲线curve 曲线method of coordinate 坐标法analytic geometry 解析几何Descartes 笛卡儿standard equation 标准方程general equation 一般方程parameter equation 参数方程parameter 参数point conic 圆锥曲线ellipse 椭圆focus, focal points 焦点focal length 焦距major axis 长轴minor axis 短轴eccentricity 离心率hyperbola 双曲线real axis 实轴imaginary axis 虚轴asymptote 渐近线parabola 抛物线directrix 准线物理kinetic energy 动能potential energy 势能mechanical energy 机械能thermal energy 热能electrical energy 电能electromagnetic energy 电磁能nuclear energy 核能heat energy 热能law of conservation energy 能量守恒energy transformation 能量转化temperature 温度heat flow 热流量thermodynamics 热力学heat/energy loss 热量损失efficiency 效率/功率entropy 熵absorb 吸收release 释放electric current 电流charge 电荷coulomb 库仑electrode 电极voltage 电压voltage source 电源battery 电池polar 两极的electrical conductivity 导电率resistor 电阻器resistance 电阻circuit 电路capacitor 电容器voltmeter 伏特计;电压表ammeter 安培计;电流表ohmmeter 欧姆计;电阻表conductor 导体semiconductor 半导体superconductor 超导体insulator 绝缘体potential difference 电势差magnet 磁铁magnetic force 磁力magnetic field 磁场electromagnetic induction 电磁感应electromagnet 电磁铁wave 波electromagnetic wave 电磁波mechanical wave 机械波medium 媒介vacuum 真空amplitude 振幅crest 波峰trough 波谷wavelength 波长frequency 频率hertz 赫兹transverse wave 横波longitudinal wave 纵波compression 压缩rarefaction 稀疏sound wave 声波vibrate 震动intensity 强度decibel 分贝light wave 光波visible light 可见光infrared light 红外线ultraviolet 紫外线photon 光子spectroscopy 光谱学spectrum 光谱radiation 辐射refection 反射refraction 折射diffraction 衍射interference 干涉motion 移动reference point 参考点distance 距离displacement 位移(方向)speed 速度velocity 速度(方向)acceleration加速度deceleration 减速度slope 斜率force 力net force 净力/合力inertia 惯性gravitation 万有引力gravity 重力specific gravity 比重action and reaction force 作用力与反作用力momentum动量work 功joule 焦耳inclined plane 倾斜面lever 杠杆pulley 滑轮fluid dynamics 流体动力学buoyancy 浮力air pressure 气压aerodynamic 空气动力学partial pressure 气体分压friction 摩擦力stationary 静止的lubricate 润滑stress 压力resistance 阻力drag force 阻力stain 拉力aqueous tension 水的张力atmospheric pressure 大气压强impact碰撞deform变形elasticity 弹性oscillate 振荡;摆动resonance 共振density 密度viscosity 粘度nuclear fission核裂变nuclear fusion 核聚变critical/threshold 临界的blast 爆炸explosion 爆炸contact area 接触面积conductivity 传导率cross section area 横截面积piston 活塞isothermal 等温的absolute zero 绝对零度coating 涂层convection 对流optical 光学的bulb灯泡lens 透镜rod 棍;杆spring 弹簧scale 秤weight 砝码meter stick 米尺clamp 夹子tabletop桌面chain 链条hinge 铰链wire 金属线rope 绳索concave lens 凹透镜convex lens 凸透镜prism 棱镜detector 探测器pendulum 物理摆block 块sensor 传感器twist 扭曲seal 密封airtight 密封的launch 发射slide 滑动rotate 旋转torsion 扭转torque 扭转力calibrate 校正deviation 偏差化学1.The Ideal-Gas Equation理想气体状态方程2.Partial Pressures分压3.Real Gases: Deviation from Ideal Behavior真实气体:对理想气体行为的偏离4.The van der Waals Equation范德华方程5.System and Surroundings系统与环境6.State and State Functions状态与状态函数7.Process过程8.Phase相9.The First Law of Thermodynamics热力学第一定律10.Heat and Work热与功11.Endothermic and Exothermic Processes吸热与发热过程12.Enthalpies of Reactions反应热13.Hess’s Law盖斯定律14.Enthalpies of Formation生成焓15.Reaction Rates反应速率16.Reaction Order反应级数17.Rate Constants速率常数18.Activation Energy活化能19.The Arrhenius Equation阿累尼乌斯方程20.Reaction Mechanisms反应机理21.Homogeneous Catalysis均相催化剂22.Heterogeneous Catalysis非均相催化剂23.Enzymes酶24.The Equilibrium Constant平衡常数25.the Direction of Reaction反应方向26.Le Chatelier’s Principle列·沙特列原理27.Effects of Volume, Pressure, Temperature Changes and Catalysts 体积,压力,温度变化以及催化剂的影响28.Spontaneous Processes自发过程29.Entropy (Standard Entropy)熵(标准熵)30.The Second Law of Thermodynamics热力学第二定律31.Entropy Changes熵变32.Standard Free-Energy Changes标准自由能变33.Acid-Bases酸碱34.The Dissociation of Water水离解35.The Proton in Water水合质子36.The pH Scales pH值37.Bronsted-Lowry Acids and Bases Bronsted-Lowry酸和碱38. Proton-Transfer Reactions质子转移反应39. Conjugate Acid-Base Pairs共轭酸碱对40. Relative Strength of Acids and Bases酸碱的相对强度41. Lewis Acids and Bases路易斯酸碱42. Hydrolysis of Metal Ions金属离子的水解43. Buffer Solutions缓冲溶液44. The Common-Ion Effects同离子效应45. Buffer Capacity缓冲容量46. Formation of Complex Ions配离子的形成47. Solubility溶解度48. The Solubility-Product Constant K sp溶度积常数49. Precipitation and separation of Ions离子的沉淀与分离50. Selective Precipitation of Ions离子的选择沉淀51. Oxidation-Reduction Reactions氧化还原反应52. Oxidation Number氧化数53. Balancing Oxidation-Reduction Equations氧化还原反应方程的配平54. Half-Reaction半反应55. Galvani Cell原电池56. Voltaic Cell伏特电池57. Cell EMF电池电动势58. Standard Electrode Potentials标准电极电势59. Oxidizing and Reducing Agents氧化剂和还原剂60. The Nernst Equation能斯特方程61. Electrolysis电解62. The Wave Behavior of Electrons电子的波动性63. Bohr’s Model of The Hydrogen Atom氢原子的波尔模型64. Line Spectra线光谱65. Quantum Numbers量子数66. Electron Spin电子自旋67. Atomic Orbital原子轨道68. The s (p, d, f) Orbital s(p,d,f)轨道69. Many-Electron Atoms多电子原子70. Energies of Orbital轨道能量71. The Pauli Exclusion Principle泡林不相容原理72. Electron Configurations电子构型73. The Periodic Table周期表74. Row行75. Group族76. Isotopes, Atomic Numbers, and Mass Numbers同位素,原子数,质量数77. Periodic Properties of the Elements元素的周期律78. Radius of Atoms原子半径79. Ionization Energy电离能80. Electronegativity电负性81. Effective Nuclear Charge有效核电荷82. Electron Affinities亲电性83. Metals金属84. Nonmetals非金属85. Valence Bond Theory价键理论86. Covalent Bond共价键87. Orbital Overlap轨道重叠88. Multiple Bonds重键89. Hybrid Orbital杂化轨道90. The VSEPR Model价层电子对互斥理论91. Molecular Geometries分子空间构型92. Molecular Orbital分子轨道93. Diatomic Molecules双原子分子94. Bond Length键长95. Bond Order键级96. Bond Angles键角97. Bond Enthalpies键能98. Bond Polarity键矩99. Dipole Moments偶极矩100. Polarity Molecules极性分子101. Polyatomic Molecules多原子分子102. Crystal Structure晶体结构103. Non-Crystal非晶体104. Close Packing of Spheres球密堆积105. Metallic Solids金属晶体106. Metallic Bond金属键107. Alloys合金108. Ionic Solids离子晶体109. Ion-Dipole Forces离子偶极力110. Molecular Forces分子间力111. Intermolecular Forces分子间作用力112. Hydrogen Bonding氢键113. Covalent-Network Solids原子晶体114. Compounds化合物115. The Nomenclature, Composition andStructure of Complexes配合物的命名,组成和结构116. Charges, Coordination Numbers, and Geometries电荷数、配位数、及几何构型117. Chelates螯合物118. Isomerism异构现象119. Structural Isomerism结构异构120. Stereoisomerism立体异构121. Magnetism磁性122. Electron Configurations in Octahedral Complexes八面体构型配合物的电子分布123. Tetrahedral and Square-planar Complexes四面体和平面四边形配合物124. General Characteristics共性125. s-Block Elements s区元素126. Alkali Metals碱金属127. Alkaline Earth Metals碱土金属128. Hydrides氢化物129. Oxides氧化物130. Peroxides and Superoxides过氧化物和超氧化物131. Hydroxides氢氧化物132. Salts盐133. p-Block Elements p区元素134. Boron Group (Boron, Aluminium, Gallium, Indium, Thallium)硼族(硼,铝,镓,铟,铊)135. Borane硼烷136. Carbon Group (Carbon, Silicon, Germanium, Tin, Lead)碳族(碳,硅,锗,锡,铅)137. Graphite, Carbon Monoxide, Carbon Dioxide石墨,一氧化碳,二氧化碳138. Carbonic Acid, Carbonates and Carbides碳酸,碳酸盐,碳化物139. Occurrence and Preparation of Silicon硅的存在和制备140. Silicic Acid,Silicates硅酸,硅酸盐141. Nitrogen Group (Phosphorus, Arsenic, Antimony, and Bismuth)氮族(磷,砷,锑,铋)142. Ammonia, Nitric Acid, Phosphoric Acid氨,硝酸,磷酸143. Phosphorates, phosphorus Halides磷酸盐,卤化磷144. Oxygen Group (Oxygen, Sulfur, Selenium, and Tellurium)氧族元素(氧,硫,硒,碲)145. Ozone, Hydrogen Peroxide臭氧,过氧化氢146. Sulfides硫化物147. Halogens (Fluorine, Chlorine, Bromine, Iodine)卤素(氟,氯,溴,碘)148. Halides, Chloride卤化物,氯化物149. The Noble Gases稀有气体150. Noble-Gas Compounds稀有气体化合物151. d-Block elements d区元素152. Transition Metals过渡金属153. Potassium Dichromate重铬酸钾154. Potassium Permanganate高锰酸钾155. Iron Copper Zinc Mercury铁,铜,锌,汞156. f-Block Elements f区元素157. Lanthanides镧系元素158. Radioactivity放射性159. Nuclear Chemistry核化学160. Nuclear Fission核裂变161. Nuclear Fusion核聚变162. analytical chemistry分析化学163. qualitative analysis定性分析164. quantitative analysis定量分析165. chemical analysis化学分析166. instrumental analysis仪器分析167. titrimetry滴定分析168. gravimetric analysis重量分析法169. regent试剂170. chromatographic analysis色谱分析171. product产物172. electrochemical analysis电化学分析173. on-line analysis在线分析174. macro analysis常量分析175. characteristic表征176. micro analysis微量分析177. deformation analysis形态分析178. semimicro analysis半微量分析179. systematical error系统误差180. routine analysis常规分析181. random error偶然误差182. arbitration analysis仲裁分析183. gross error过失误差184. normal distribution正态分布185. accuracy 准确度186. deviation偏差187. precision 精密度188. relative standard deviation 相对标准偏差(RSD)189. coefficient variation 变异系数(CV)190. confidence level 置信水平191. confidence interval 置信区间192. significant test 显著性检验193. significant figure 有效数字194. standard solution 标准溶液195. titration滴定196. stoichiometric point 化学计量点197. end point 滴定终点198. titration error 滴定误差199. primary standard 基准物质200. amount of substance物质的量生物ecology生态学ecosystem生态系统egg卵细胞embryo胚胎emphysema肺气肿endocrine gland内分泌腺endonuclease核酸内切酶endosperm胚乳endothermy温血状态,体温的生理调节energy能量environmental resistance环境的阻力enzyme酶epidermis表皮epididymis附睾eutrophication富营养作用excretion排泄,分泌factor-8因子8(血友病的凝血因子)fair testing客观的实验fermentation发酵fermenter发酵器fern蕨类植物fertilisation受精fertiliser肥料fever发热fibre纤维fibrin纤维蛋白fibrinogen纤维蛋白质filament细丝fish farming养鱼业flaccidity软弱,枯萎foetus胚胎food chian食物链food preservation食物保存fossil fuel矿物燃料fruit果实fungus真菌,菌类gall bladder胆囊gamete配子gene probe基因探针gene transfer转基因gene vector基因载体gene基因genus类,属geotropism向地性global warming全球变暖glucagon胰高血糖素glucose葡萄糖glycogen糖原gonorrhoea淋病Graafian follicle格拉夫卵泡,囊状卵泡graphs线图greenhouse effect温室效应grey and white matter灰质和白质guanine鸟嘌吟gut消化道,内脏absorption吸收accommodation调节acetobacter醋菌属acid rain酸雨acne粉刺active site活性部位active transport主动转运adaptation适应additives添加剂adenine腺嘌呤amylase淀粉酶anaemia贫血症angina心绞痛angiosperm被子植物anopheles疟蚊anorexia厌食antagonistic pair相互拮抗的anther花粉囊antibiotic抗生素antibody抗体monoclonal单克隆antigen抗原antiseptic防腐剂aorta主动脉aphid蚜虫artery,coronary冠状动脉artery,hepatic肝动脉artery,pulmonary肺动脉artery,renal肾动脉artery,umbilical脐动脉arthritis关节炎arthropod节肢动物artificial selection人工选择athlete`s foot脚气atmosphere大气ATP(adenosine triphosphate)ATP(三磷酸腺苷)atrium心房autotroph自养生物axes轴axon轴突bacteriocide杀菌剂bacteriostatic抑菌剂bacterium细菌baking烘焙barbiturate巴比妥酸盐base pair碱基对bee蜜蜂bicarbonate indicator碳酸氢盐指示剂biceps二头肌bile胆汁biogas沼气biological control生物防治bioreactor生物反应器bladder膀胱blind spot盲点red blood cell红细胞white blood cell白细胞blood血液BOD(biological oxygen demand)生物耗氧body temperature体温brain脑bread面包bronchitis支气管炎budding出芽A-Level生物词汇caffeine咖啡因calcium钙cambium形成层(植)bladder cancer膀胱癌colon cancer结结肠癌lung cancer肺癌skin cancer皮肤癌cap(diaphragm)子宫帽capillary毛细血管carbohydrate糖类carbon cycle碳循环carbon dioxide二氧化碳carnivore食肉动物carrier proteins转运蛋白carrier转运者,载体carrying capacity转运能力cartilage软骨catalyst催化剂cell division细胞分裂cell membrane细胞膜cellulose cell wall植物纤维细胞壁cellulose植物纤维centromere着丝粒cerebellum小脑cerebral cortex大脑皮层cervix子宫颈CFC(chlorofluorocarbon)含氯氟烃chlorophyll叶绿素chloroplast叶绿体cholera霍乱cholesterol胆固醇choroid脉络膜chromatid染色单体chromosome染色体ciliary muscle睫状肌cirrhosis肝硬化clinistix尿糖试纸clone克隆cobalt chloride paper氯化钴试纸coil避孕环color blindness色盲combustion燃烧community群落cone cell视锥细胞constipation便秘consumer消费者cornea角膜cotyledon子叶cuticle表皮cystic fibrosis囊性纤维化cytoplasm细胞质cytosine胞嘧啶DDT滴滴涕(杀虫剂的一种)deamination去氨基decomposition分解腐烂denaturation变性denitrification脱氮作用depression抑郁diabetes糖尿病dialysis透析diaphragm横膈膜diarrhoea腹泻adequate diet足量饮食balanced diet平衡饮食diffusion扩散digestion消化diploid二倍体disease疾病DNA脱氧核糖核酸dominant显性double helix双螺旋Down`s syndrome唐氏综合症drugs药物habitat栖息地haemoglobin血红蛋白haemophilia血友病haploid单倍体的hayfever花粉热,干草热heat热度,热量hepatitis肝炎herbicide除草剂herbivore食草类动物heroin海洛因heterotroph异养生物heterozygous咋合的homeostasis平衡状态,稳态homologous pair同源染色体对homozygous纯合子的,同型结合的hormone荷尔蒙horticulture园艺human growth hormone人类生长激素humerus肱骨humidity潮湿的,温度Huntington’s disease杭廷顿氏舞蹈病hybridoma杂交瘤hydrochloric acid盐酸hyperglycaemia多糖症,高血糖症hypoglycaemia低血糖hypothalamus丘脑下部hypothermia体温过低hypothesis假设active/passive/natural/artificial immunity主动/被动/天然/人工免疫independent assortment自由组合,独立分配influenza流行性感冒insect昆虫insecticide杀虫剂insulin胰岛素iron铁irradiation放射,照射IUD(intra-uterine device)子宫内器件joint关节karyotype染色体组型key关键kidney肾脏kingdom界kwashiorkor夸休可尔症,恶性营养不良lacteal乳汁lactic acid乳酸large intestine大肠lead铅leaf树叶lens晶体ligament韧带ligase连接酶light光照limewater石灰水limiting factor限制因素Linnaeus林奈lipase脂肪酶lipid脂类liver肝脏loop of Henle亨利氏襻louse虱子LSD麦角酸二乙基酰胺(致幻药)lung肺lymphocyte淋巴细胞lysozyme溶菌酶A-Level生物词汇magnesium镁malnutrition营养不良mammal哺乳动物mammary gland乳腺marasmus消瘦,衰弱medulla脊髓meiosis减数分裂Mendel`s law孟德尔遗传定律meninges脑膜meningitis脑膜炎menstrual cycle月经周期menstruation月经meristem分裂组织,生长点mesophyll叶肉metabolism新陈代谢methane沼气,甲烷microorganism微生物micropyle珠孔mineral ions矿物离子mitochondria线粒体mitosis有丝分裂moss苔藓mould霉菌mouth口腔movement运动muscle肌肉mutagen诱变剂mutation突变myelin sheath髓鞘natural selection自然选择negative feedback负反馈nephron肾单位nervous system神经系统neurone神经元neurotransmitter神经递质night blindness夜盲nitrate硝酸盐nitrification硝化作用nitrogen fixation固氮作用nitrogen cycle氮循环nitrogen氮气node of Ranvier郎飞氏结nucleotide核苷nucleus细胞核obesity肥胖症oesophagus食道oestrogen雌激素oil油optic nerve视神经osmosis渗透osteoporosis骨质疏松ovary卵巢,子房oviduct输卵管ovulation ovule胚珠oxygen debt氧债oxygen氧ozone臭氧painkiller止痛药pancreas胰腺parasite寄生虫pasteurisation巴氏灭菌法pathogen病原体penicillin青霉素penis阴茎pepsin胃蛋白酶peristalsis蠕动pest害虫pesticide杀虫剂petal花瓣PH氢离子浓度phagocyte吞噬细胞phenotype显型pheromone信息素phloem韧皮部phosphate磷酸盐photosynthesis光合作用phototropism趋光性Pill药丸pituitary hormones脑垂体placenta胎盘经济financial crisis 金融危机real estate 房地产share 股票macroeconomic 宏观经济saving account 储蓄帐户go under 破产take a nosedive (股市)大跌tumble 下跌pension fund 养老基金budget 预算deficit 赤字money-loser 亏损企业inventory 存货traded company, trading enterprise 上市公司transparency 透明度market fundamentalist 市场经济基本规则entrepreneur 企业家volatility 波动diversification 多元化merger 并购bad debt 坏帐fiscal stimulus 财政刺激a store of value 保值Treasury bond 财政部公债pickup in rice 物价上涨inflation 通货膨胀deflation 通货紧缩tighter credit 紧缩信贷monetary policy 货币政策foreign exchange 外汇spread 差幅contract 合同at par 平价global corporation 跨国公司bailout 救助take over 收购falter 摇摇欲坠alleviate the Asian financial crisis 缓解亚洲金融危机apply economic sanctions against that country 对那个国家进行经济制裁。

IGCSE-词汇表-(一)

IGCSE-词汇表-(一)

培民学校三宝垄校区2012 - 2013中四IGCSE 华文考试词汇表(一)IGCSE Mandarin Chinese Vocabulary Adjectival and attributive phrases别的,bie de另外一个,ling wai yi ge 一般,yi ban 唯一,wei yi 业余,ye yu 有的, you deAdverbs不一定,bu yi ding 也,ye都,dou很,hen真,zhen太,tai非常,fei chang 相当,xiang dang 很少,hen shao 还,hai还是,hai shi不,bu不常,bu chang 常,chang常常,chang chang 经常,jing chang 从来,cong lai总是,zong shi 又,you只,zhi只好,zhi hao 别,bie才,cai就,jiu刚,gang刚才,gang cai已经,yi jing忽然,hu ran马上,ma shang 正在,zheng zai 先,xian再,zai更,geng最,zui本来,ben lai当然,dang ran 另,ling差不多,cha bu duo 大概,da gai没,mei也许,ye xu一定,yi ding一共,yi gong一块儿,yi kuai er 一起,yi qi特别,te bieAuxiliary verbs得(dĕi),会,hui能,neng 想,xiang 要,yao敢,gan希望,xi wang 喜欢,xi huan 需要,xu yao 应该,ying gai 愿意,yuan yi 必须,bi xu不用,bu yong 不准,bu zhun 将要,jiang yao 可能,ke neng 可以, ke yiColours颜色,yan se 白,bai 黄,huang 黑,hei 红,hong 灰,hui 蓝,lan 绿,lv紫,zi橘黄(色),ju huang se 银(色),yin se金(色),jin se棕(色),zong se咖啡色, ka fei seContainer measure words杯,bei 盘,pan 壶,hu 瓶,ping 碗,wan 包, baoMeasure words把,ba 本,ben 顶,ding 段,duan 封,feng 个,ge 家,jia 件,jian 节,jie 口,kou 辆,liang 双,shuang 所,suo 条,tiao位,wei 张,zhang 只,zhi 支,zhi 座,zuo 匹,pi 遍,bian 次,ci 些,xie 种, zhongNumbers一,yi 幺,yao 二,er 两,liang 三,san 四,si 五,wu 六,liu 七,qi 八,ba 九,jiu 十,shi 百,bai 千,qian 万,wan 半,ban 零,ling 第,di左右,zuo yoParticles====Word行业资料分享--可编辑版本--双击可删==== 吧,ba的,de得,de地,de过,guo了,le吗,ma呢,ne着, zhe源-于-网-络-收-集。

igcse0580数学大纲

igcse0580数学大纲

igcse0580数学大纲IGCSE 0580 Mathematics Syllabus1. IntroductionThe IGCSE 0580 Mathematics Syllabus is designed to help students develop their mathematical knowledge and skills. This syllabus is suitable for students who intend to pursue further studies in mathematics or related fields.2. Syllabus ContentThe IGCSE 0580 Mathematics Syllabus covers a wide range of mathematical topics. It includes the study of numbers, algebra, geometry, trigonometry, statistics, and probability. The content is divided into different sections to enable students to grasp each topic thoroughly.3. NumberThe number section of the syllabus focuses on understanding and manipulating numbers. It includes topics such as prime numbers, factors and multiples, fractions, decimals, percentages, and ratios. Students will learn how to perform calculations and solve problems using these number concepts.4. AlgebraAlgebra plays a significant role in the IGCSE 0580 Mathematics Syllabus. Students will explore various algebraic concepts such as equations, inequalities, functions, graphs, and sequences. They will develop problem-solving skills by applying algebraic techniques to real-life situations.5. GeometryThe geometry section of the syllabus introduces students to the study of shapes, angles, and spatial reasoning. Topicscovered include properties of triangles, quadrilaterals, circles, and three-dimensional shapes. Students will learn geometric principles and apply them to solve problems related to areas, volumes, and constructions.6. TrigonometryTrigonometry is an essential branch of mathematics that deals with the relationships between angles and sides of triangles. In the IGCSE 0580 Mathematics Syllabus, studentswill learn trigonometric ratios, trigonometric identities,and how to solve trigonometric equations. They will develop skills to apply trigonometry in both practical andtheoretical contexts.7. Statistics and ProbabilityIn the statistics and probability section, students will explore data analysis, representation, and interpretation. They will learn how to collect data, organize it into various forms, and analyze it using statistical measures.Additionally, students will understand the concept of probability and learn how to calculate probabilities in different scenarios.8. ConclusionThe IGCSE 0580 Mathematics Syllabus provides a comprehensive foundation for students to develop their mathematical abilities. It covers essential topics in numbers, algebra, geometry, trigonometry, statistics, and probability. By studying this syllabus, students will acquire thenecessary mathematical skills and knowledge to excel academically and in real-world applications.。

cie ig数学词汇表

cie ig数学词汇表

cie ig数学词汇表根据我了解的信息,CIE(剑桥国际考试)IGCSE(国际通用中等教育证书)数学课程通常包含一些特定的数学词汇。

下面是一些可能出现在CIE IGCSE数学考试中的常见数学词汇:1.Addition(加法):•Sum(和)•Plus(加)2.Subtraction(减法):•Difference(差)•Minus(减)3.Multiplication(乘法):•Product(积)•Times(乘)4.Division(除法):•Quotient(商)•Divide by(除以)5.Fractions(分数):•Numerator(分子)•Denominator(分母)6.Decimals(小数):•Decimal point(小数点)•Decimal places(小数位数)7.Percentages(百分比):•Percentage(百分比)•Percent(百分之)8.Ratio and Proportion(比例和比率):•Ratio(比率)•Proportion(比例)9.Algebra(代数):•Variable(变量)•Equation(方程)•Expression(表达式)10.G eometry(几何):•Point(点)•Line(直线)•Angle(角)•Triangle(三角形)•Circle(圆)11.S tatistics and Probability(统计学和概率):•Mean(平均数)•Median(中位数)•Mode(众数)•Range(范围)•Probability(概率)12.C oordinate Geometry(坐标几何):•Coordinates(坐标)•Gradient(斜率)•Intercept(截距)这只是一个简要的词汇表,实际考试可能涉及更多的数学概念和词汇。

建议参考CIE IGCSE数学课程的官方教材和考试说明,以获取详细的数学词汇表和相关概念。

IGCSE Maths 英语数学词汇知识点总结(配图)

IGCSE Maths 英语数学词汇知识点总结(配图)

1.∅: The empty set (proper subset)2.∈: is an element of {set}3.∉: is not an element of {set}4.0.7 recurring as a fraction: 10f = 7.777..., 10f-f=7, 9f=7, f=7/95.0.3181818 recurring as a fraction: 100f =31.818181..., 100f-f=31.5, 99f=31.5, f=315/990=7/226.1/2(a+b)h: Area of a trapezium7.1 centiliter =: 10 ml8.1 cm cubed =: 1 ml9.2-²: 1/4 (The reciprocal of the number without the negative)10.(2x⁵)³ =: 8x to the power of 1511.-3²=-9: (-3)²=912.1000 cm cubed =: 1L13.1000 kg =: 1 tonne14.1000 Litres =: 1 metre cubed15.1000 milliliters =: 1L16.A ∩ B: Intersection of A and B (items in both)17.A ∪ B: Union of A and B (items in A or B or both)18.A ⊂ B: A is a proper subset of B19.A ⊆ B: A is a subset of B20.a/b + c/d: (ad + bc)/bd21.a/b - c/d: (ad - bc)/bd22.a/b x c/d: ac/bd23.Adding and subtracting fractions: For fractions to beadded or subtracted, the denominator MUST be the same. 24.Adding and subtracting indices: Powers and variablesmust be the same25.Adding and subtracting matrices: For matrices to beadded or subtracted they must be of the same order.26.Angles in a circle - centre, circumference:If an angle is extended to the centre of a circle from arc ABand another angle is extended to the circumference from arc AB then the angle at the circumference will be half the angle atthe centre.27.Angles in a circle - cyclic quadrilaterals: Opposite anglesin a cyclic quad add to 180 degrees.28.Angles in a circle - same arc at circumference:All angles extending out to the circumference from arc AB willhave the same angle.29.Angles in a circle - two semi-circles:If a diameter is drawn and an angle in the semi-circle uses it as its base (with its third point touching the circumference) then the angle at the circumference is 90 degrees.30.Angles in a quadrilateral...: add to 360 degrees31.Angles in a triangle...: add to 180 degrees32.A polygon is regular if...: all interior angles are equal andall its sides are the same length. e.g. square, pentagon,hexagon, octagon.33.A power to a power (x²)³: If a power is raised a variable thatis already being squared, you multiply the indices. Theexample will equal x to the power of 6.34.A ratio as a fraction: You can express particular numbers inthe ratio as fractions by finding what the whole ratio adds up to and using that as the denominator. e.g. 3/5 is the first part of the ratio 3:235.Arc: An arc is a section of the circumference of a circleIGCSE Maths英语数学词汇知识点总结(配图)36.Area and volume scale factor: Used in similar shapes. Thisapplies the same principles as the linear scale factor but issquared or cubed. To find the linear scale factor from these, find the square or cube root.37.area of cross-section x length: volume of a prism38.a/sinA=b/sinB=c/sinC: The sine rule (can be inverted sosines are on top)39.Average speed: Distance/time40.ax to the power of -5: a/x to the power of 541.Bar charts:All bars are the same width, the heights represent frequency. A dual chart is sometimes useful to compare two bar charts withsimilar data.42.base x height: Area of a square, rectangle and parallelogram43.Calculating probability: Probability can be found with aprobability fraction. The fraction of P(outcome) is the number of ways the outcome can happen/the total number of possible outcomes. This can then be changed to a decimal orpercentage.44.Calculating the angles of a pie chart: To find what angle asector will be, take the frequency divided by the total number and then times that by 360. These angles do not have tolabelled on the chart45.Choosing the right rule - two angles and a side: Sinerule46.Choosing the right rule - two sides and included angle:Cosine rule followed by sine rule47.Chords:A chord is a line in a circle where both ends touch thecircumference, cutting a section of the bined frequency of two events: You can illustrate thepossibilities of two combined events on a possibility diagram where all the possible outcomes for one variable is on oneaxis and for the other on the other axis. Every possibleoutcome for both variables is then represented on the diagram and the probability can be found.posite function expressions: To make an expressionfor the composite function fg(x), put the expression for g, in the place of x in the expression for f. "Take x, apply g, thenapply f"posite functions: When functions are put together, readthem backwards. e.g. fg(2) means start with 2, apply g thenapply fpound interest: amount x 1. percentage to number ofyearspound interest formula: P(1+r/100)^n where r is thepercentage, n is the time and P is the amount invested.53.Congruent shapes: Shapes with the same size and shape aseach other are congruent, even if they are placed in different positions.54.Construct a perpendicular from a point to a line: Withthe point as the centre, draw an arc that intersects the line on either side. Using these points as the centre, follow the same directions as constructing a perpendicular.55.Constructing a line bisector:Open compass to abut three quarters the length of the line and draw a semi-circle arc from either point on the line. The bisector is the point where the two arcs intersect.56.Constructing an accurate trapezium: To construct atrapezium accurately, use first a protractor and a ruler andthen a set square to find the parallel side.57.Constructing an angle bisector:With the vertex of the angle as the centre, draw an arc through both lines and then, with centres where the arc intersects both lines, draw two more arcs. The angle bisector extends from the vertex to the point where the two arcs intersect.58.Constructing a triangle: Draw the longest side as the base.Draw the next longest side with a compass as an arc and do the same with the shortest side. The draw the straight line to where the two arcs intersect.59.Continuous data: Data that can have any value within a rangeof values, for example mass, height, time.60.CosA= b squared+c squared - a squared/2bc:The cosine rule61.Cosine rule notes: b and c in the rule are the sides makingthe angle being calculated and a is the opposite side. Is not restricted to right-angled triangles62.Cubic sequences: Compare to cube number first. Differencebetween the second difference is the same (3rd difference). 1/6 of the 3rd difference will be the coefficient of n cubed. Take that away from the original sequence and find the rule for the remaining numbers.63.Cumulative frequency diagrams: A frequency table wherethe next the value has been added on to the previous value so that the number is always rising. This can then be plotted with the top value of the class group against the cumulativefrequency. Plots can be joined with a freehand curve.64.Currency conversions: Use value that is not one for bothexchanges (either times by for currency represented by 1 ordivide by for currency represented by point something)65.Decreases in ratios: Decrease 450 in the ratio 5:3. 450=5parts, need to find 3 parts. Decreased amount = (3/5) x 450 66.Describing translations with vectors: As shapes that havebeen translated are congruent, all points have moved thesame amount. The translation is how any one point movedfrom its original place to its new place with its movementacross on top and up and down on the bottom of the fraction without a line.67.Different form of function notation - f:x→3x-5: This isthe same as f(x)=3x-568.Discrete data: This is data which contains separate numberslike goals scored, number of children or shoe size.69.Dividing a quantity in a ratio: To divide a quantity in a ratio,you must first find the total number of parts. Divide thequantity by the total number of parts to find one part and then multiply this to find parts of the ratio.70.Dividing fraction: first term x reciprocal of second term71.Dividing fractions: To divide fractions, times the first fractionby the reciprocal (turned upside down) of the second.72.Dividing with indices: Subtract indices, numbers stay73.ℰ: Universal set74.Enlarging a shape: An enlargment will occur about a pointand the distance away from this point should be taken intoconsideration as well as the size. The lengths of each side can be easily found by multiplying the original length by the scale factor.75.Enlarging a shape - ray method: If you need to find thepoint from which the shape was enlarged, the ray method ishelpful. Draw lines through corresponding points on the shape.The point where these lines meet is the point from which the shape was enlarged.76.Equilateral triangular prism: It has four planes of symmetry.One from each of the points lengthways and one widthways halfway down. It also has two axis of rotational symmetry. 77.Estimating gradients: You can estimate the gradient of acurved line by drawing a tangent to it and finding the gradient of that line.78.Estimating the median from a cumulative frequencydiagram: The median can be found by looking at the mark on the vertical axis which is half of the total. Follow this along to meet the curve and the value on the horizontal axis down from this is an estimate of the median. The median is also the 50th percentile79.Exponential graphs: This graph will have a changing gradient80.Exponential growth: Use same formula as compoundinterest81.Exponential growth and decay: Use compound interestprinciples82.Exterior angles: The sum of the exterior angles of anypolygon is 360 degrees83.Factorising quadratic equations with coefficients(ax²+bx+c): Write out the factors of a and c. Find the pair ofa factors that multiply with the pair of c factors to make twonumbers that add to b.84.Factorising simple quadratic equations (x²+bx+c):Factorise in the morning - AM stands for add, multiply. Findtwo numbers that add to the second number and multiply to the third number.85.Factorising tips: Factor out ALL common factors even ifthese are brackets, numbers and multiple variables.86.F angles on parallel lines:Called corresponding angles. They are equal87.Finding a matrix transformation: To do this, you only needto find the vector for two points. Find where 1 0 (over eachother) and 0 1 (over each other) will end up and put thevectors for these together in a matrix. Put the image vector of the vector that started on the x-axis first.88.Finding the area of a triangle using sine: 1/2 ab sinC (twosides with included angle)89.Finding the interquartile range.: The interquartile range canbe found by taking the upper quartile (75th percentile, 75%)and taking away the lower quartile (25th percentile, 25%) togive the middle 50%. The upper and lower quartile can befound in the same way as the median but by finding 1/4 and3/4 of the data instead of 1/2.90.Finding the inverse of a 2 x 2 matrix: Of matrix abcd,swap the positions of a and d and change the signs of b and c.Then divide all the numbers by the determinant.91.Finding the multiplier: A multiplier is the percentage dividedby 100 to find the decimal. However to decrease a quantity by 7%, the multiplier used will be 0.93. If a quantity has beendecreases by 7%, the amount left will be 93% of the total 92.Finding the points of a quadratic graph: Draw out a tableand in each row put a separate component of the equation and the answer, then add these all together to find the points. 93.Frequency table:A tally chart of the all the options. The first column is theoptions or numbers you are tallying, the second is the tallys and the third is the numerical value of the number of tallys inthe second column.94.Function notation: f(x)=3x-695.Histograms: Histograms are similar to bar charts except,there are no gaps between bars, the horizontal axis has acontinuous scale, the area of each bar represents thefrequency.96.Histograms with bars of unequal width: Frequency isrepresented by area. THe vertical axis should read frequency density. To find the height of a bar where class widths aredifferent, use the formula: frequency density=frequency of class interval/width of class interval.97.Histograms with unequal width - proportionality: Areasare proportional to frequencies98.If the determinant of a matrix is 0...: It is a singular matrixand the inverse does not exist99.Increase or decrease by a percentage: Find the multiplier(24%=0.24)100.Increases in ratios: Increase 450 in the ratio 5:3. 450 = 3 parts, need to find 5 parts. Increased amount = (5/3) x 450 101.Integers: Whole, positive, negative102.Interior angles: The sum of the interior angles of any polygon can be found using 180 x (n-2) where n is the number of sides103.Inter-quartile range: Bases the measure of spread on the middle 50% of the data removing extreme values104.Inverse functions - f-¹(x): To find the inverse of a function, replace f(x) with y and rearrange the equation to make x the subject. In the final answer, change the y to x.105.Kite:Two pairs of equal adjacent sides. Has one long diagonal and one short diagonal that bisect each other at right angles. The opposite angles between the sides of different lengths areequal.106.length x width x height: volume of a cuboid107.Linear scale factor: Used in similar shapes. To find it, find two corresponding sides and put the bigger side as thenumerator of a fraction. Simplify the fraction.108.Linear sequences: Look for: difference between each number in sequence, difference between that and the first term 109.Line of symmetry (mirror line): A line that can be drawn through a shape so that what can be seen on one side is amirror image of what can be seen on the other side.110.Locus (loci): A locus is a shape or a line which is always the same distance from a given point or line. You may be alsoasked to draw a locus that is equidistant from two points. This will usually be a straight line.111.Map scales: 1:900000 (1cm on map = 900000cm on ground).1cm = 9km. Actual distance km = distance on map cm x 9km 112.Mean: The mean is the sum of all the values in a set divided by the total number of values in the set. IT uses all the values although extreme values can affect it and it has to becalculated.113.Median: The middle value when put in order of size. It is not heavily affected by extreme values and is easy to find forungrouped data. But, it doesn't use all the values and can be hard to understand.114.Mensuration: The part of geometry concerning lengths, areas and volumes115.Mode: The value that occurs most often in a set of data. It can be used for qualitative data, is easy to find and is not affected by extreme values. But, it doesn't use all the values and may not exist.116.Multiplying fractional indices: Fractional indices can be added in multiplication in the same way as normal indices.They should be left as improper fractions not mixed numbers. 117.Multiplying fractions: Put the product orf the numerators over the product of the denomiators and then simplify ifneeded.118.Multiplying matrices together: When you multiply two matrices together, each row in the first matrix combines with each column of the second to give a single number. (The first to the left will combine with the uppermost, the second to the left will combine with the second down)119.Multiplying with indices: Add indices, numbers stay120.n(A): Number of elements in set A121.Natural numbers: Whole, positive122.Negative indices: If something is raised to a negative indices, find the reciprocal.123.Obtuse cosine: The cosine of an obtuse angle is equal to the negative of its supplementary angle (cos100 = -cos80)124.Obtuse sine: The sine of an obtuse angle is equal to that of its supplementary angle (sin100 = sin80)125.Order of multiplied matrices: You can only multiply matrices if the number of columns in the first is equal to the number of rows in the second. The other two values willcombine to give the order of he product.126.Order of operations: BEDMAS127.Order of the matrix: The number of rows and columns in a matrix. Written as rows x columns128.Parallel lines on a graph: For a line to be parallel it must have the same gradient, so variable m must be the same inboth equations in y=mx + c 129.Parallelogram:Opposite sides are parallel and equal. Opposite angles areequal.130.Percentage change: change/original x 100131.Perpendicular lines on a graph: If a line is perpendicular to the other line, the gradient will be the negative reciprocal of it.Also, the product of both gradients will be 1132.Pictograms:Pictograms are frequency tables which use pictures to represent frequency. Each picture represents a number of items.It helps people to understand it more quickly but doesn'tallow for fractions of pictures.133.Pie charts:These do not show individual frequencies but instead compare the frequencies. Each is represented as a sector of the circle where the angle of each sector is proportional to the frequency it represents. The sectors should always be labelled. 134.pi x diameter: Circumference of a circle135.pi x radius squared: area of a circle136.Prime factorisation: Writing a number as a product of its prime factors (use a factor tree, until all bottom numbers are prime)137.Proper subset: All subsets except the original set (P)138.Quadratic graphs - parabolas: This will have either a u or upside down u shape and will be a smooth, continuous curve with no straight lines139.Quadratic sequences: Compare to square numbers first.Difference between the difference between each number (2nd difference) is the same. 1/2 of the 2nd difference will be thecoeffecient of n squared. Take that away from originalsequence and find the rule for the remaining numbers.140.Range: The range is the highest value in the set minus the lowest value in the set. It shows the spread of the data, it can help to compare data and consistency.141.Rates: Speed applied more generally to show changes in quantities. e.g. temperature goes down by 5 degrees everyminute142.Ratio: Ratio is a way of comparing the sizes of two or more quantities. and will be set out in the form x:y. It can also begiven in the form x/y. All the units in a ratio must be the same 143.Ratios when only some information is known: Find one part of the ratio. If 30 is 2 parts of the total ratio, divide it by 2 to find one part.144.Real numbers: Integers including decimals - two subsets 145.Real numbers - irrational: Decimals or numbers that cannot be written as a fraction146.Real numbers - rational: Integers or fractions147.Reciprocal graphs - y=a/x: Values should be rounded to two decimal points. x will never equal zero. It will besymmetrical. The graph never touches either axes.148.Reflecting a shape over an axis: The easiest and most effective methods is counting how many squares away each individual point is from the mirror line and then making thepoint that many squares away on the opposite side. Thisshould be done using the most direct route (even diagonally through squares)149.Relative frequency: Also known as experimental probability, it is given by frequency of the outcome of event/total number of trials. This relative frequency is an estimate of theprobability150.Reverse percentages - multiplier method: 110%=x. Find the original amount: x/1.1 (the multiplier) = the original amount.88%=x. Find the original amount: x/0.88 (the multiplier) = the original amount.151.Reverse percentages - unitary method: 110%=x. Find the original amount: 1%=x/110 original price = 1% x 100 (Used for decreases as well)152.Rhombus:All sides are equal, opposite sides are parallel. Diagonals bisect at right angles. Opposite angles are equal 153.Rotating a shape: The easiest and most effective way torotate a shape about a point is to count how many squaresacross and up and down each individual point is away from the axis, then turn your paper the amount required and count the squares using the new axes.154.Rotational symmetry: A 2D shape has rotational symmetry if it can be rotated about a point to look exactly the same in a new position. It can be represented by the order of rotational symmetry or number of times it can be rotated to look exactly the same until it is back to its original position. e.g. anequilateral triangle has a rotational symmetry of three155.Rotational symmetry of 3D shapes: 3D shapes have axes of symmetry. A cubiod has three axes of symmetry. Each axis has its own order of rotational symmetry.156.Scatter diagrams:Compares two variables by plotting corresponding values ona graph. They can have positive, negative or zero correlationbetween the points.157.Sector: Part of a circle bounded by two radii and one of the arcs.158.Similar shapes: Shapes are similar if one is an enlargement or reduction of the other. The corresponding angles of similar shapes are equal. Their sides can be found using ratios orlinear scale factors159.Simplifying algebraic fractions: Always fully factorise and cancel common brackets. Brackets that are the same withopposite sides are equal to -1 on the numerator. Two negatives over each other cancel each other out. Variables should be in brackets before they are cancelled.160.sine/cosine/tangent of known angle = side/side is used to: calculate the length of a side in a right-angledtriangle161.Sine rule notes: When you are calculating a side, use the rule with sides on top. When you are calculating an angle, use the rule with sines on top. Is not restricted to right angledtriangles162.Sketching an inequalities graph - linear programming: Sketch a broken line if the symbol is not equal to. Sketch asolid line if it is. Shade the unwanted region, e.g. if the wanted is y is less than x, shade the region where y is more than x. 163.Solve Direct proportion (a ∝ b): Divide to find the constant of proportionality (a=kb, k=constant)164.Solve Inverse proportion (a ∝ the reciprocal of b): Find total by multiplying values (a=k/b, k=constant)165.Solve x²+6x-7 by completing the square: (x+(6/2))^2 -(6/2)^2 - 7 = (x+3)^2 -3^2 - 7 = (x+3)^2 - 16.x=-2 +or- the square root of 16166.Solving problems of angles of elevation and depression: Use the trigonometric ratios(sine/cosine/tangent)167.Solving quadratic equations by completing the square: Solves quadratic equations by rewriting x squared + px +q in the form (x+a)^2 +b. Found by putting it into the form (x+(p/2))^2 -(p/2)^2 + q and rearranging to solve.168.Symmetry in circles - bisector of chords: The perpendicular bisector of a chord passes through the centre of the circle169.Symmetry in circles - chords: Two chords of equal length are the same distance from the centre of the circle.170.Symmetry in circles - tangents: Two tangents extending from a point to touch the circle at any two points will be the same length171.Symmetry of 3D shapes:3D shapes have planes of symmetry. One is a reflection of the other half. A cuboid has 3 planes of symmetry 172.Tangent: A tangent is a straight line that touches a circle or curve as one point only. It is drawn perpendicular to the radius 173.The determinant of a matrix: The determinant helps find the inverse. It can be represented by two lines around theletter representing the matrix. It is found using the formula ad -bc of matrix abcd 174.The identity matrix: A 2 x 2 matrix with 1 0 as its top numbers and 0 1 as its bottom numbers. This matrix is thesame as multiplying it by 1.175.The inverse sine/cosine/tangent of known side/known side is used to: Find the angles in a right-angled triangle 176.The magnitude of a vector: the square root of x square plus y squared - written with two vertical lines on either side of the vector177.Theoretical probability vs experimental probability: The way of calculating a probability is actually only theoreticaland in practice, this probability is only an estimate of the real results. However, the more times you take data, the closer the experimental probability will get to the theoretical probability 178.The probability of an event occurring =: 1 - the probability of the event not occurring.179.The probability scale: The probability scale goes from 0 being impossible to 1 being certain. Any probability values fall in between 0 and 1.180.the quadratic formula:181.The zero matrix (Z): The zero matrix is a 2 x 2 matrix which is just zeros and acts like a normal zero in equations.182.Three sides: Cosine rule followed by sine rule183.Transformations using matrices: You can transform a shape using matrices, the matrix for a shape is the vector for each point put together e.g. a triangle will form a 2 x 3 matrix.You can then multiply it by a specific 2 x 2 matrix to find the vectors of the transformed shape.184.Trapezium:Two parallel sides. The sum of the interior angles at the ends of each non-parallel side is 180 degrees.185.Tree diagrams: Probabilities of sequences of events can be shown on a tree diagram. Each brach represents an outcome which branches into more outcomes. When doing this type of diagram, whether the outcome is put back into the total should be taken into consideration.186.U angles on parallel lines:Called interior angles. They add up to 180 degrees187.Upper and lower bounds: Minimum and maximum any rounded number could possibly be188.Upper and lower bounds e.g. 27.5≥x>28.5: The upper bound is the maximum possible the rounded number couldhave been before rounding and the lower bound the opposite.Upper bound will be the number with 5 after the last decimal or as a unit depending on how it is rounded. The lower bound is the number 5 after one less than the last unit.ing coordinates - gradient: difference between y-coordinates/difference between x-coordinatesing coordinates - midpoints: Add end values and divide by two for each x and y separatelying coordinates -the distance between two points: Use pythagoras' thereom to find the distance by using thegradients as the sides of a right angled triangleing frequency tables to find the mean: To find the mean, the frequency must be multiplied by the by the class it is in. These final values should then be added up and divided by the total frequency. If the classes are grouped, use themiddle value for the multiplication.ing frequency tables to find the median: To find the median from a frequency table, add all the values to find the total number of cars surveyed then divide this by 2 to find the middle value. Now add the frequencies up cumulatively to find which group contains this middle number.ing rates: Temperature lowers 5 degrees every minute.After 6 minutes, temperature lowers (5x6=30) 30 degrees.Temperature lowers by 1 degree in (1/5=0.2) 0.2 minutes.Temperature lowers by 15 degrees in (15/5=3) 3 minutes 195.Vectors: Vectors have both a magnitude and a direction. They can be represented by the start and end points with an arrow over top or as a lower case letter printed in bold ORunderlined. On graphs they are represented by lines witharrows indicating direction196.Vectors on a coordinate grid: On a coordinate grid, vectors can be represented by two numbers in a bracket as a fraction without the line. The top number is the amount moved across (negative left) and the bottom number is the amountmoved vertically (negative down)197.Venn diagrams - A': Complement of A (all items not in A)198.Vulgar fraction: A fraction represented by a numerator and denominator and not by decimals.199.Vulgar fractions: All fractions excluding mixed fractions 200.Which ratio to use: SOHCAHTOA201.x to the power of -5: The reciprocal of x to the power of 5 (1/x to the 5)202.x to the power of ½: the square root of x203.x to the power of -¼: 1/the fourth root of x204.x to the power of ¾: (the fourth root of x)cubed205.x to the power of -¾: 1/(the fourth root of x)cubed 206.y=mx + c: m is the gradient of the line, c is where the line intercepts the y axis.207.Z angles on parallel lines:Called alternate angles. They are the same. 208.θ/360 x pi x diameter: Arc length209.θ/360 x pi x radius squared: Sector area210.θ (theta): the angle at the centre of a sector。

iseb数学知识点

iseb数学知识点

iseb数学知识点【最新版】目录1.IGCSE 数学与 ISCE 数学的关系2.IGCSE 数学的主要知识点3.IGCSE 数学的考试形式与评分标准4.IGCSE 数学对学生的能力要求5.IGCSE 数学的学习建议正文IGCSE(International General Certificate of Secondary Education)数学是针对全球中学生的一项重要课程,旨在为学生提供一种国际认可的学历证书。

在我国,IGCSE 数学与 ISCE(International Standard Certificate Examinations)数学有密切关系,它们在课程设置、知识点和考试形式上都有很多相似之处。

对于学生而言,学习 IGCSE 数学不仅能够提高自己的数学能力,还能为后续的学术发展奠定坚实基础。

IGCSE 数学的主要知识点包括:数与量、代数、几何、测量与统计等。

在这些知识点中,数与量部分涉及有理数、整数、小数等基本数学概念;代数部分则包括方程与不等式、函数、数列等;几何部分主要研究点、线、面的性质以及空间几何;测量与统计部分则涉及数据的收集、整理、分析和解释等。

这些知识点的学习将帮助学生建立扎实的数学基础,培养逻辑思维、分析问题和解决问题的能力。

IGCSE 数学的考试形式分为笔试和口试两部分。

笔试部分包括选择题、填空题、解答题等,主要考察学生的计算能力、推理能力和应用能力。

口试部分则通过面试的形式,考察学生的数学沟通能力和思维能力。

考试的评分标准分为 A*、A、B、C、D、E 六个等级,其中 A*为最高等级。

对于学生而言,学习 IGCSE 数学需要具备一定的数学能力、逻辑思维能力和英语阅读能力。

为了更好地应对 IGCSE 数学考试,学生可以参考历年真题进行模拟练习,加强知识点的巩固和理解。

同时,学生还应学会运用数学知识解决实际问题,提高自己的综合素质。

在学习 IGCSE 数学的过程中,学生可以采取以下建议:首先,要注重基础知识的学习,打牢基本功;其次,要通过大量的练习题来提高自己的解题能力;最后,要关注历年真题和考试大纲,了解考试的重点和难点。

igcse数学词汇

igcse数学词汇

igcse数学词汇代数部分1.基础在代数中,我们需要掌握一些基本的术语和符号,例如:add,plus 表示加法subtract 表示减法difference 表示差multiply,times 表示乘法product 表示积divide 表示除法divisible 表示可被整除的divided XXX 表示被整除dividend 表示被除数divisor 表示除数XXX 表示商remainder 表示余数factorial 表示阶乘power 表示乘方radical sign,root sign 表示根号round to 表示四舍五入to the nearest 表示四舍五入到最近的数2.有关集合在代数中,我们还需要了解一些集合的概念,例如:n 表示并集XXX 表示真子集XXX 表示解集3.有关代数式、方程和不等式在代数中,我们需要掌握一些代数式、方程和不等式的术语,例如:algebraic term 表示代数项like XXX,similar XXX 表示同类项4.基本数学概念在代数中,我们需要掌握一些基本的数学概念,例如:XXX 表示算术平均值XXX 表示加权平均值geometric mean 表示几何平均数XXX 表示指数,幂base 表示乘幂的底数、底边cube 表示立方数、立方体square root 表示平方根XXX root 表示立方根common XXX 表示常用对数digit 表示数字constant 表示常数variable 表示变量XXX 表示反函数XXX 表示余函数linear 表示一次的、线性的XXX 表示因式分解absolute value 表示绝对值round off 表示四舍五入5.有关数论在代数中,我们需要了解一些数论的概念,例如:natural number 表示自然数positive number 表示正数negative number 表示负数odd integer 表示奇整数odd number 表示奇数even integer,even number 表示偶数integer,whole number 表示整数6.有关分数和小数在代数中,我们需要了解一些分数和小数的概念,例如:XXX 表示真分数XXX 表示假分数mixed number 表示带分数vulgar n,common XXX 表示普通分数XXX 表示简分数XXX 表示繁分数numerator 表示分子XXX 表示分母least) common denominator 表示(最小)公分母XXX 表示四分之一Decimal ns are numbers that have no whole number component。

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IGCSE-Mathematics
Chapter 1: Reviewing number concepts
一:Glossary&Expressions
1.1Different types of numbers
1. natural number [数] 自然数(5星)
2. whole number 整数(5星)
3. even number [数] 偶数(5星)
4. odd number [数] 奇数(5星)
5. integer ['intid??] n. [数] 整数;整体;完整的事物(5星)
6. prime number [数] 素数(5星)
7. prime [praim] adj. 主要的;最好的;基本的(4星)
8. square [skwε?] n. 平方;正方形adj. 平方的;正方形的;直角的;正直的vt. 使成方形;vi. 成方形adv. 成直角地(5星)
9. square number [数] 平方数(5星)
10. fraction ['fr?k??n] n. 分数;部分;小部分;(5星)
11. negative ['neɡ?tiv] n. 负数;adj. [数] 负的;(5星)
12. negative integers 负整数(5星)
13. consecutive [k?n'sekjutiv] adj. 连贯的;连续不断的(5星)
14. common fraction [数] 普通分数;[数] 简分数(5星)
15. decimal ['desim?l] n. 小数adj. 小数的;十进位的(5星)
16. is equal to 等于(5星)
17. equal ['i:kw?l] n.相等的事物adj. 平等的;相等的;vt. 等于;比
得上(5星)
18. is not equal to不等于(5星)
19. is approximately equal to 约等于(4星)
20. approximately [?'pr?ksimitli] adv. 大约,近似地;近于(4星)
21. is less than 小于(5星)
22. is less than or equal to 小于等于(5星)
23. is greater than 大于(5星)
24. is greater than or equal to 大于等于(5星)
25. therefore ['eε?f?:] adv. 因此;所以(4星)
26. square root of 的算术平方根(5星)
27. add [?d] n. 加法,加法运算vi. 加;增加;加起来;做加法vt. 增加,添加;计算…总和(5星)
28. addition [?'di??n] n. 添加;[数] 加法;增加物(5星)
29. minus ['main?s] prep. 减,减去n. 负号,减号;不足;负数adj. 减的;负的(5星)
30. subtract [s?b'tr?kt] vt. 减去;(5星)
31. subtraction [s?b'tr?k??n] n. [数] 减法;减少;差集(5星)
32. times [taimz] n. 时代(time的复数);[数] 次数prep. 乘以v. 使…相乘(5星)
33. multiply ['m?ltiplai] adj. 多层的;多样的vt. 乘;使增加;使相乘vi. 乘;增加(5星)
34. divide [di'vaid] vt. 除;(5星)
35. divided by 除以(5星)
36. sum [s?m] n.总数vt. 总结;合计vi. 概括(5星)
37. difference ['dif?r?ns] n. 差异;不同;(5星)
38. product ['pr?d?kt, -?kt] n. 产品;结果;[数] 乘积;(5星)
39. quotient ['kw?u??nt] n. [数] 商;系数;(5星)
40. remainder [ri'meind?] n. [数] 余数,残余;剩余物;adj. 剩余的;吃剩的vt. 廉价出售;削价出售vi. 廉价出售;削价出售(5星)
41. divisible [di'viz?bl] adj. 可分的;可分割的(5星)
42.reciprocal[ri'sipr?k?l]n. [数] 倒数;adj. 倒数的(5星)
43. finding 找,求
1.2Multiples and factors
1. multiples ['m?ltiplz] n. [数] 倍数;(5星)
2. factors n. 因素(factor的复数)v.分解…的因子;(5星)
3. common multiple 公倍;[数] 公倍数(5星)
4. the lowest common mulitiples(LCM) 最小公倍数(5星)
5. common factors [数] 公因数(5星)
6. the highest common factor (HCF)最大公约数(5星)
1.3 Prime numbers
1. prime numbers 质数;素数(5星)
2. composite ['k?mp?zit] n. 复合材料;合成物;adj. 复合的;合成的;vt. 使合成;使混合(5星)
3. composite numbers 【数学】合数,(区别于prime number) (5星)
4. prime factors 质因子(5星)
5. division [di'vi??n] n. [数] 除法;(5星)
6. divisibility [di,vizi'bil?ti] n. 可分性;[数] 可除性(5星)
7. digits ['did?its] n. [计] 数字;(5星)
1.4 Powers and roots
1. powers n. 幂(power的复数形式);(5星)
2. roots n. [数][植] 根;(4星)
3. square root [数] 平方根;二次根(5星)
4. symbol ['simb?l] n. 象征;符号;标志(4星)
5. cube [kju:b] n. 立方;立方体;骰子vt. 使成立方形;使自乘二次;量…的体积(5星)
6. cube numbers 立方数(5星)
7. cube roots [数] 立方根(5星)
1.5 Working with directed numbers
1. directed numbes 有向数(4星)
2. directed [di'rektid, dai-] v. 指导;管理(direct的过去式和过去分词)adj. 定向的;(4星)
3. order ['?:d?] n. 命令;顺序;规则;(4星)
4. number line 实数直线;数值轴(5星)
5. ascending [?'sendi?] adj. 上升的v. 上升;(5星)
6. descending [di'sendi?] n. 递减;下行v. 下降adj. 下降的;下行的(5星)
1.6 Order of operations
1. operations n. 运营;运作;(5星)
2. division [di'vi??n] n. [数] 除法;(5星)
3. multiplication [,m?ltipli'kei??n] n. [数] 乘法;增加(5星)
4. addition [?'di??n] n. 添加;[数] 加法;增加物(5星)
5. subtraction [s?b'tr?k??n] n. [数] 减法;减少;差集(5星)
6. brackets [br?k?ts] n.方括号;(5星)
7. power [pau?] n. [数] 幂(3星)
8. working with 使用(3星)
9. working with brackets 使用括号(3星)
10. BODMAS (bracket, of, divide, multiply, add, subtract)(5星)
1.7 Rounding numbers
1. rounding n. [数]凑整;v. 把…弄成整数[数]凑整的;环绕的(4星)
2. rounding numbers 四舍五入(4星)
3. accuracy ['?kjur?si] n. [数] 精确度,准确性(4星)
4. correct to 取值至;准确至;精确到(5星)
5. decimal place [数] 小数位(5星)
6. significant [sig'nifik?nt] adj. 重大的;有效的;有意义的;(4星)
7. significant figures [计] 有效数字(5星)
8. round down 下舍入(4星)
9. round up 上舍入(4星)
10. standard form 标准形式科学记数法(5星)
11. calculator ['k?lkjuleit?] n. 计算器;(5星)12.calculator use 用计算器(3星)。

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