Alevel数学词汇
alevel进阶数学中英文
alevel进阶数学中英文English:"Advanced level mathematics, commonly referred to as A-level Further Mathematics, encompasses an array of advanced mathematical topics beyond the scope of standard A-level mathematics. It delves deeper into concepts like calculus, complex numbers, differential equations, and further pure mathematics. A-level Further Mathematics often involves rigorous proof-based approaches and requires a strong foundation in algebra and mathematical reasoning. Students typically explore topics such as matrices, vectors, differential equations, and complex numbers in greater detail, enabling them to tackle more sophisticated problems and applications in mathematics and related fields. The course is designed to develop students' analytical skills, problem-solving abilities, and mathematical intuition to a high level. It is highly valued by universities and employers alike for its emphasis on critical thinking and quantitative reasoning. A-level Further Mathematics is an excellent choice for students aspiring to pursue degrees in mathematics, engineering, physics, computer science, and other quantitative disciplines."中文翻译:"进阶数学，通常称为A-level进阶数学，涵盖了标准A-level数学范围之外的一系列高级数学主题。
A-level数学词汇(P1-P4)
Pure mathematics 1 1 Algebraic expression 代数表达式Index laws 指数定律Indices (index的复数形式) 指数Notation 注释Simplify 化简Power 指数Base 底Exponent 指数Expression 表达式Term 项Numerator 分子Expand 展开Possible 可能Fraction 分数Bracket 括号Product 乘积Multiply 乘Collecting like terms 合并同类项Linear 一次的Diagram 图形Rectangle 长方形Square 正方形Length 长度Width 宽Side length 边长Area 面积Shade 阴影Cuboid 长方体Dimension 维Show that 证明V olume 体积Given that 已知Constant 常数Value 值Factorize 因式分解Factor 因子Opposite 相反的Completely 完全地Common factor 公因式Quadratic 二次的Form 形式Real number 实数Positive 正的Negative 负的Include 包含Surd 无理数Add 加Sum 和Take out 提取Difference 差Difference of two squares 平方差Cancel 取消，相互抵消Similarly 同样的Rational 有理的Rational number 有理数Integer 整数Square root 平方根Evaluate 求…的值Substitute 代替Calculator 计算器Square number 平方数Irrational number 无理数Decimal 小数的Expansion 展开式Never-ending 无限的Never repeat 不循环的Exact 准确的Answer 答案Manipulate 操作Denominator 分母Rationalizing denominator 分母有理化Rearrange 调整Prime 质数Work out 计算Hence 然后Fully 完全地State 陈述Solve 解决Equation 方程2 Quadratics 二次方程式Quadratic equation 二次方程Solution 解Real solution 实根Set 设置Root 根Distinct 不同的Repeated root 重根Case 情况Straightforward 简单直接的Symbol 符号Plus 加，正Minus 减，负Factorization 因式分解Shape 形状Section 部分Formula 公式Reading off 读取Coefficient 系数Necessary 必要的Significant figures 有效数字Choose 选择Suitable 适当的Method 方法Trapezium 梯形Height 高Discard 丢弃Completing the square 完全平方（配方）Frequently 经常的Useful 有用的Process 过程Original 最初的Determine 决定Otherwise 另外Function 函数Mathematical 数学上的Relationship 关系Map 映射Set 集合Input 输入Output 输出Single 单一的Notation 符号Represent 代表Domain 定义域Range 值域，范围Member 成员Define 定义Minimum 最小的Occur 发生Explain 解释Consider 考虑Graph 图像Curve 曲线Parabola 抛物线Sketch 画图Identify 确定Key 关键的Feature 特征Overall 整体的Cross 交叉，横过Axis 轴Coordinate 坐标Turning point 转折点（顶点）Maximum 最大的Since 因为Symmetrical 对称的Symmetry 对称性Line of symmetry 对称轴Half-way 位于中途的Explore 探测Technology 技术Plot 绘制Scale 刻度However 但是，不管怎样Smooth 平滑的Relevant 相关的Intercept 截距Label 标记Axes (axis的复数)坐标轴Discriminant 判别式Sign 符号Check 核实Inequality 不等式Calculate 计算Match 匹配Prove 证明Algebra 代数学Diver 跳水运动员Launch 发射Springboard 跳板Meter 米Pool 水池Second 秒Model 模型High 高的Hit 撞击Reach 达到Non-zero 非零3 Equations and inequalities 方程和不等式Simultaneous 联立的Linear simultaneous equations 一次方程组Elimination 消元法Substitution 置换Quadratic simultaneous equations 二次方程组Up to 直到，多达Make sure 确保Correctly 正确地Simplest 最简的Graphically 以图表形式As 因为Satisfy 满足Intersection 相交Simultaneously 同时地Intersect 相交Once 一次Twice 两次Result 结果，导致Produce 产生Graph paper 坐标纸Accurately 准确地Verify 验证Linear inequalities 一次不等式Set notation 集合符号Number line 数轴Overlap 重叠Separately 单独地Illustrate 图解，阐明Quadratic inequalities 二次不等式Corresponding 相应的Critical 临界的Require 要求Describe 描述Interpret 解释Region 区域，范围Coordinate grid 坐标网Dotted line 虚线Solid line 实线Vertex 顶点Vertices (vertex的复数)顶点Within 在内部，之内4 Graphs and transformations 图像和转换Cubic 三次的Cubic function 三次函数Several 几个Depend on 取决于Touch 接触Coordinate axes 坐标轴Indicate 表明，显示Reciprocal 倒数的Reciprocal function 反比例函数Such as 例如Asymptote 渐近线Approach 接近Reach 到达Quadrant 象限Point of intersection 交点Steeper 更陡峭的Eventually 最后，终于Reason 理由，原因Appropriate 恰当的Number 数量Translate 平移Transform 改变Alter 改动Subtract 减Outside 在外面Vertically 竖直地Translation 平移Vector 矢量Horizontally 水平地Direction 方向In terms of 用…来表示Slide 滑动Stretch 伸缩Scale factor 比例系数Double 两倍Halve 减半，对分Inside 在里面Triple 三倍的Reflection 反射(镜面对称) Alternatively 二选一Parallel 平行Lie on 坐落在Pass through 穿过Apply 应用Unfamiliar 陌生的，不熟悉的Specific 特殊的Origin 原点Position 位置Image 像Suggest 提议Mark 标记5 Straight line graphs 直线图像Gradient 斜率Straight line 直线Join 连接Distance 距离Formula 公式Collinear 共线的Intercept 截距Define 定义Either 两者中的任一个Condition 条件Triangle 三角形General equation 一般式Parallel 平行Perpendicular 垂直Whether 是否Quadrilateral 四边形Trapezium 梯形Right angle 直角Congruent 全等的Neither 两者都不Hypotenuse 直角三角形斜边Line segment 线段Scalene 不等边的Respectively 分别地Go through 通过6 Trigonometric ratios 三角比Cosine rule 余弦定理Miss 缺失Version 版本Exchange 交换Standard 标准Prove 证明Opposite 对边Adjacent 邻边Pythagoras’ theorem 勾股定理Letter 字母Round 四舍五入Final 最终的Coastguard 海岸警卫队Station 驻地Bearing 方位Away from 远离Appropriate 适当的Mark 标记Airport 机场Due north 正北Due east 正东Due west 正西Due south 正南Sail 航行Helicopter 直升飞机Tee 球座Flag 旗Particular 特定的Hole 孔，洞Golf course 高尔夫球场Yard 码（1码=3英尺）Tee shot 发球台Land 着陆Largest 最大的Farmer 农场Field 场地Fence 栅栏Cargo 货物Plane 平面Kilometer 千米Sine rule 正弦定理Refer to 涉及Data 数据Remain 剩余Located on 坐落于Zookeeper 动物管理员Enclosure 围场Llama 骆驼Diagonal 对角线Surveyor 检验员Measure 测量Elevation 高程，仰角Apart 相距Assumption 假设Mathematical 数学的Model 模型Obtuse 钝角Acute 锐角Isosceles 等腰的Circle 圆Radius 半径Centre 圆心Least 最小的Instead 代替Crane 吊车Anchored 固定Wreck 破坏Suspend 悬挂Cable 缆绳Rotate 旋转Level 对准Proof 证明Triangular plot 三角图Involve 涉及Trigonometry 三角函数Encounter 遇到Decide 决定Mast 桅杆In order that 为了Interfere 干扰Efficient 有效的Hiker 徒步旅行者Radar 雷达Perimeter 周长Tangent 正切Periodic 周期性的Repeat 重复的Certain 确定的Interval 间距Period 周期Undefined 无意义的Knowledge 知识Periodicity 周期性Verify 证明Variation 变化Rock pool 潮汐潭Midday 中午During 在…期间Non-exact 非精准的Significant figure 有效数字Windmill 风车Sail 帆Tower 塔Deduce 推导Dune 沙丘Realistic 现实的7 Radians 弧度Radian 弧度So far 到目前为止Probably 大概，可能Degree 度Revolution 循环Around 围绕Circle 圆Subtend 朝着Arc 圆弧Circumference 周长Convert 转换Without 没有Multiple 倍数Arc length 弧长Sector 扇形Radius 半径Contain 包含Perimeter 周长Border 边界Pond 池塘Consist 由…组成Edge 边缘Minor arc 劣弧Major arc 优弧Chord 弦Diameter 直径Template 模板Brooch 胸针Ferris wheel 摩天轮Pod 蚕茧，豆荚Estimate 估计Speed 速率Patio 露台Lawn 草坪Design 设计Earring 耳环Nearest 最近点（精确到）Segment 弓形Radii (radius的复数形式) A plot of …的一块Erect 建造Along 沿着Subtract 减Tangent 切线Ratio 比例Bound 关，围入Decimal place 小数Midpoint 中点Semicircular 半圆Drawer 抽屉Handle 把手Difference 差Badge 徽章Equilateral 等边的Railway 铁路Track 轨迹Prism 三棱镜Attempt 尝试Mistake 错误8 Differentiation 微分Gradient 斜率Constantly 不断地Although 然而Comment on 对…评论Copy 抄写，复制Complete 完成Table 表格Hypothesis 假设Derivative 导数Principle 原理Detail 细节Account 解释Originate 起源Formalize 确定，形成Approach 方式，方法Limit 极限Tend to 趋向Gradient function 斜率函数Evaluate 求…的值Fixed value 定值Limiting value 定值Definition 定义One-at-a-time 一次一个Turning point 转折点（顶点）Slope 斜率Disappear 消失Polynomial 多项式Normal 切线First order derivative 一阶导数Second order derivative 二阶导数Rate of change 变化率Respect to 关于Displacement 位移Acceleration 加速度Local 局部的9 Integration 积分Reverse 相反的Differ 不同Integrate 求积分Integral 积分Indefinite 不确定的Indefinite integral 不定积分Elongated 拉长的，伸长的Arrow 箭Fire 射击Castle 城堡Drop off 下降Cliff 悬崖Cyclist 骑行者Pure mathematics 2 1Algebraic methods 代数方法Division 除法Dividing polynomial 多项式除法Finite 有限的Whole number 整数Long division 长除法Quotient 商Remainder 余数Factor theorem 因式定理Remainder theorem 余数定理Logical 逻辑的Structured 有组织的Argument 论据Statement 命题Conjecture 猜想Previously 预先Establish 建立Deduction 推导Desired 想要的Conclusion 结论Odd number 奇数Demonstration 示范，演示Even number 偶数Identical 完全相等的Identity 恒等式Parallelogram 平行四边形Rhombus 菱形Congruent 全等的Exhaustion 穷举法Consecutive 连续的Square number 平方数Break into 拆分Is suited to 适合于Disprove 反驳Counter-example 反例Sufficient 充分的Prime number 质数Divisible 可整除的Either … or…二者择一的Cube number 立方数Hold 有效Claim 宣称Opposite edge 对边Hexagon 六边形Regular hexagon 正六边形Side length 边长Reason 原因2Coordinate geometry in the (x,y) plane 解析几何Bisector 二等分线Perpendicular bisector 中垂线Averaging 求平均值Endpoint 端点Circumcentre 外心Equidistant 等距的Fixed point 定点Vector 向量Property 性质Unique 独一无二的Circumcircle 外接圆3Exponentials and logarithms 指数和对数Exponential 指数的Decrease 减小Increase 增加Smooth 光滑的，平滑的Increasing function 增函数Decreasing function 减函数Justify 证明Logarithms 对数Specific 特定的Button 按钮Typically 典型的Natural logarithms 自然对数Instance 实例Multiplication law 乘法定律Division law 除法定律Power law 指数定律Recognize 识别Attention 注意Condition 条件Complicated 复杂的Whenever 无论何时Convenient 方便的Suppose 假设Notice 注意Particular 特别的4The binomial expansion 二项式展开Binomial 二项式Pascal’s triangle 杨辉三角（帕斯卡三角形）Immediately 直接地Pattern 图案Adjacent 相邻的Investment 投资Interest rate 利率Annum 年，岁Approximation 近似值Ignore 忽略Factorial notation 阶乘Combination 组合Superscript 上标Subscript 下标Probability 可能性Toss 投Likelihood 可能性Ascending powers 升幂Individual 个别的Estimation 估值Engineering 工程学Science 科学Percentage error 百分误差Microchip 微型集成电路片Faulty 有缺点的Chip 芯片Restrict 限制Achieve 达到School fair 学校园游会Prize 奖赏Digit 数字Display 显示5Sequences and series 数列和级数Arithmetic sequence 等差数列Arithmetic progression 等差数列Common difference 公差Arithmetic series 等差级数（等差数列前n 项求和）Exceed 超过Inclusive 包含的Stick 棒子Pentagon 五角形Geometric sequences 等比数列Geometric progression 等比数列Common ratio 公比Converge 收敛Alternating sequence 交错数列Million 百万Geometric series 等比级数（等比数列前n项求和）Sum to infinity 无限项求和Divergent 发散的Convergent 收敛的Recurring 循环的Sigma notation 求和符号Capital 首都，大写字母Signify 表示Recurrence relations 递推关系Previous term 前一项First term 初项Generate 生成，产生Periodic sequence 周期数列Period 周期Salary 薪水Profit 利润Predict 预言Annual 年度的Business 商业Financial 金融的Advisor 顾问Fold 折叠Thickness 厚度Unrealistic 不切实际的Investor 投资人Account 账户Thereafter 以后Deposit 存款，定金Wage 工资Rise 上升Gear 齿轮Successive 连续的Intermediate 中间的Valuable 有价值的Commission 佣金Insurance 保险Policy 政策Prospector 勘探者Drill 钻孔Subsequent 随后的Available 可获得的Payment 报酬Virus 病毒Infect 传染Diagnose 诊断Overfish 过度捕捞Chess 象棋Chessboard 棋盘Sponsored 赞助的Polygon 多边形Appointment 约会，任命6Trigonometric identities and equations 三角恒等式和方程Unit circle 单位圆Anticlockwise 逆时针Quadrant 象限Equivalent 相等的Equilateral triangle 等边三角形Isosceles right-angled triangle 等腰直角三角形Identity 恒等式Reflex 优角(大于180度，在第三、四象限)Principal value 主值Inverse trigonometric function 反三角函数Justification 理由7Differentiation 微分Strictly 严格地Interval 区间Stationary point 驻点Local maximum 局部最大Greatest value 最大值Local minimum 局部最小Least value 最小值Point of inflection 拐点，反曲点Immediate 最接近的Vicinity 邻近，附近Second derivative 二次求导Rate of change 改变的快慢Convex 凸Concave 凹Establish 建立，证实Liter 升Instant 瞬间Tank 水槽Cuboid 长方体的Sheet 薄片Metal 金属Sphere 球体Displacement 位移Cylinder 圆柱体Perimeter 周长Semicircular 半圆的Semicircle 半圆Frame 框架Split 分离，分开Motion 运动Damped 阻尼Spring 弹簧Bent 弯的Biscuit 饼干Tin 罐头Close-fitting 紧贴的Lid 盖子Thin 薄的，瘦的Wastage 损耗Obtain 获得Percentage 百分比Store 储存Capacity 容量Container 容器Calculus 微积分学8Integration 积分Definite integral 定积分Indefinite integral 不定积分Whereas 反之，然而Upper limit 上限Lower limit 下限Square bracket 中括号Magnitude 大小Negligible 可忽略的Straddle 跨坐Unless 除非Complicated 复杂的Trapezium 梯形Trapezium rule 梯形法则Beneath 在…下面Strip 条，带Boundary 边界Adjacent 相邻的Improve 改善Accuracy 精确度Approximation 近似值Underestimate 低估Overestimate 高估Compare 比较Pure mathematics 3 Common multiple 公倍数Improper fraction 假分数Partial fractions 部分分数Degree 次数Modulus function 模函数Absolute value 绝对值Argument 辐角Set notation 集合符号Piecewise-defined function 分段函数Composite function 复合函数Inverse function 反函数Secant 正割Cosecant 余割Cotangent 余切Interval 区间Symmetry 对称性Symmetrical 对称的Chord 弦Inverse trigonometric function 反三角函数Addition formulae 加法公式Compound-angle formulae 复合角公式Double-angle formulae 二倍角公式Round 四舍五入Exponential function 指数函数Natural logarithms 自然对数Trend 趋势Outlier 极值Chain rule 链式法则Product rule 乘法法则Quotient rule 除法法则Continuous 连续的Fixed point iteration 定点迭代Successive 连续的Converge 收敛Staircase diagram 梯形图Cobweb diagram 网状图Diverge 发散Pure mathematics 4 Contradiction 反驳Assert 主张Falsehood 虚假Negation 反论Prime number 质数Split 分解Separate 独立的Parametric equation 参数方程Variable 变量Parameter 参数Revolution 循环Plot 绘图Valid 有效的As long as 只要Condition 条件Accurate 精确的Ascending 上升的Approximation 近似值Implicit differentiation 隐函数微分Explicitly 明确的Implicit 隐含的Rate of change 变化率Hemisphere 半球Cylindrical 圆柱形的Conical 圆锥形的Concave 凹Convex 凸Integrand 被积函数Integration by substitution 换元积分法Integration by part 分部积分法Polynomial 多项式Separating the variables 分离变量General solution 通解Boundary condition 边界条件Directed line segment 有向线段Parallelogram 平行四边形Unit vector 单位向量Column vector 列向量Position vector 位置矢量Scalene 不等边的21Clockwise 顺时针Anticlockwise 逆时针Coplanar 共面的Parallelepiped 平行六面体Trisect 三等分Hexagon 六边形Regular hexagon 正六边形Direction vector 方向向量Anchor 固定Dot product 点乘22。
英国Alevel数学教材内容汇总大全
英国Alevel 数学教材内容汇总大全部门：xxx时间：xxx整理范文，仅供参考，可下载自行编辑英国A-LEVEL 教材汇总Core Mathematics1<AS/A2 )——核心数学11.Algebra and functions ——代数和函数2.Quadratic functions ——二次函数3.Equations and inequalities ——等式和不等式4.Sketching curves ——画图<草图)5.Coordinate geometry in the <x ，y)plane ——平面坐标系中的坐标几何6.Sequences and series ——数列7.Differentiation ——微分8.Integration ——积分Core Mathematics2<AS/A2 )——核心数学21.Algebra and functions ——代数和函数2.The sine and cosine rule ——正弦和余弦定理3.Exponentials and logarithm ——指数和对数4.Coordinate geometry in the <x ，y)plane ——平面坐标系中的坐标几何5.The binomial expansion ——二项展开式6.Radian measure and its application 弧度制及其应用7.Geometric sequences and series等比数列8.Graphs of trigonometric functions ——三角函数的图形9.Differentiation ——微分10.Trigonometr icidentities and simple equations ——三角恒等式和简单的三角等式b5E2RGbCAP11.Integration ——积分Core Mathematics3<AS/A2 )——核心数学31.Algebra fractions ——分式代数2.Functions ——函数3.The exponential and log functions ——指数函数和对数函数4.Numerical method ——数值法5.Transforming graph of functions ——函数的图形变换6.Trigonometry ——三角7.Further trigonometric and their applications ——高级三角恒等式及其应用p1EanqFDPw8.Differentiation ——微分Core Mathematics4<AS/A2 )——核心数学41.Partial fractions ——部分分式2.Coordinate geometry in the <x ，y)plane ——平面坐标系中的坐标几何3.The binomial expansion ——二项展开式4. Differentiation 微分6. Integration ——积分A-Level ：核心数学Core Maths ，力学数学，统计数学，决策数学Core Mathematics1<AS/A2 )——核心数学11.Algebra and functions ——代数和函数2.Quadratic functions ——二次函数3.Equations and inequalities ——等式和不等式4.Sketching curves ——画图<草图)5.Coordinate geometry in the <x ，y)plane ——平面坐标系中的坐标几何6.Sequences and series ——数列7.Differentiation ——微分8. Integration 每章内容：积分5. Vectors 向量SimPHfying an expression by COIIeCting Iike terms The IaWS Of indicesEXPanding an expression FaCtOrlSlng an expression FaCtOnSing a quadratic expression The IaWS Of indices for all rational exponentsThe USe and InaniPUIatiOn Of SUrdSRatiOnaliSMg the denominator Of a fractionWhenPIOtting the graphs Of qua SOIVingquadratic equa √ιs b y 怡ClOrisati COmPIeting the squ<y丁SOIVing quadratic eq就•扮SOlVing quadra∏c zv nations by U SketChing grap UadratiC fottιulaSOlVing Sinx∕anc<>^ιs Ihldar eqι∣.∣tions by elimination SOlVing SimUltaneOlKJiUSing SUbStitUtiOn SOjVing IinCar in阿UaSOIVing quadraticaphs Of CUbiC functions aphs Of CUbiC functionsSketChintrttfe reciprocal function tπ⅝∕intersection POintS Of graphs Offunctions to SOlVe equations (ect Of the transformations f(x + “)and f(x - a) effect Of the transformations f(αx) and αf(x) Onning transformations On the SketCheS Of CUA r eSAlgebra and functions1 2 3 4 5 6 7 81 1 1 1 1 1 1 1 SUmnlary Of key POintS2 3 4 5 7 9 10 13 QUadratiC functions 2.1 2.2 2.3 2.4 2.5 2.614141517 18 20 21 24 SUInmary Of kιy EqUatiOnS ar; 325 25 26 27 28 32 37 tions by SUbStitUtiOne equation IS IInCar and the OthCr is quadratic San^mary Of key POintS38 384345 48 51 56 60 64Sketclfi6^ SqUare 3.4 3.5SUmmary Of key 4 4 SketChing q1 2 3 4 5Core Mathematics2<AS/A2 )——核心数学21. Algebra and functions ——代数和函数2. The sine and cosine rule 正弦和余弦定理3. Exponentials and logarithm ——指数和对数4. Coordinate geometry in the <x ，y)plane ——平面坐标系中的坐标几何5. The binomial expansion 二项展开式6. Radian measure and its application ——弧度制及其应用7. Geometric sequences and series ——等比数列8.Graphs of trigonometric functions ——三角函数的图形9.Differentiation ——微分10.Trigonometricidentities and simple equations ——三角恒等式和简单的三角等式DXDiTa9E3d11. Integration积分每章内容：5. The binomial expansion 二项展开式AIgeDra ana functions1.1 1.2 1.3 1.4SimPlifying algebraic fractions by division DiViding aPOIynOmial by (X ± P) FaetOriSing a POlynOmial USing the FaCtOr TheOrem USing the Remainder TheOrem SUmmary Of key POintSThe Sine and COSine rule2.1 2.2 2.3 2.4 2.5 2.6 2.7 SUmmary Of key Poirt C Z ^ £ EXPOnentialS anc l ^og≥ι<hms3.1 3.23.33.43.5 3.6 SUmmary Of keyUSing the Sine rule to find missing sidesUSing the Sine rule to find UnkXQWn angles The ruleand finding two SO l 札USing the COSine rule to find USing the COSine rule tc Qd a SSing an USing the Sine rule, tl ••严 ^rUIe Z ^n CaIeUIating the area dr⅛ US The func∣l F Writing Uf CaleUIating I LaWS Of IOgarithmS SOIVing CqUatiOnS Changingthe baj F Or a m TheOrem1317 37 37 39 40 ovφ C∞rdinate ge2∏1Kt>M n the (X f y) PIane 4.1 The mi Iine 4.2 The dis*. een two POintS On a Iine 4.3 The CqUat f a CirCle SUmmary Of 、封 POintSInomTal expansion's triangleCOmbinatiOnS and factorial notation 43 USing (；) In the binomial expansion、5.4 EXPanding (a + bxγι USing the binomial expansionSUmmary Of key POintS18 18 21 23 24 2730 32 36 43 45 48 49 49 57 60 68 70 70 72 73 75 79Core Mathematics3<AS/A2 )——核心数学31. Algebra fractions ——分式代数2. Functions 函数3. The exponential and log functions指数函数和对数函数 4. Numerical method ——数值法5. Transforming graph of functions函数的图形变换6. Trigonometry ——三角7. Further trigonometric and their applications——高级三角恒等式及其应用RTCrpUDGiT8. Differentiation ——微分每章内容：平面坐标系中Core Mathematics4<AS/A2 )——核心数学 41. Partial fractions ——Coordinate geometry in the <x ， y ) plane的坐标几何The binomial expansion ——二项展开式 2. 3. 4. Differentiation —— 分—微分 5. Vectors ——向量 6. Inte每章内容：申明：所有资料为本人收集整理，仅限个人学习使用，勿做商业用途。
alevel数学常见词汇
alevel数学常见词汇常见的Alevel数学词汇包括：微积分、向量、三角函数、概率、统计、函数、方程、不等式、导数、积分、极限、数列、级数等等。
接下来，我将以这些词汇为主题，为大家简要介绍一些与之相关的概念和应用。
微积分是数学中的一个重要分支，涉及到函数的导数和积分。
导数描述了函数在某一点处的变化率，可以用来研究函数的增减性、最值点等问题；而积分则是导数的逆运算，用于计算曲线下的面积、求解定积分等问题。
微积分在物理、经济学等领域有广泛的应用，例如用导数来描述物体的运动状态，用积分来计算物体的位移与速度之间的关系。
向量是具有大小和方向的量，可以用箭头来表示。
在数学中，向量可以用来表示力、速度、位移等物理量。
向量的运算包括加法、减法、数量乘法等，这些运算可以用来求解平面几何问题、力的合成与分解等。
三角函数是以角为自变量的函数，其中最常见的三个三角函数是正弦函数、余弦函数和正切函数。
三角函数在几何、物理、工程等领域有广泛的应用，例如用正弦函数来描述波的形状，用余弦函数来计算物体的周期性运动等。
概率是研究随机事件发生的可能性的数学分支。
概率可以用来描述事件发生的可能性大小，常用的概率分布包括均匀分布、正态分布等。
概率论在统计学、金融学、生物学等领域有广泛的应用，例如用概率来预测股票价格的波动、计算生物实验中的随机误差等。
统计是研究收集、整理、分析和解释数据的科学。
统计学包括描述统计和推断统计两个方面。
描述统计用来总结和展示数据的特征，常用的统计量有平均数、方差、标准差等；推断统计则是根据样本数据推断总体特征的方法，其中常用的方法有假设检验、置信区间等。
函数是数学中的一个基本概念，描述了输入和输出之间的关系。
函数有不同的类型，例如线性函数、指数函数、对数函数等。
函数在数学中有广泛的应用，例如用函数来描述物体的运动规律、模拟经济模型中的供需关系等。
方程是含有未知数的等式，求解方程就是找到满足等式的未知数的值。
alevel数学p2知识点
alevel数学p2知识点（最新版）目录1.Alevel 数学 P2 的定义与意义2.Alevel 数学 P2 的主要知识点3.Alevel 数学 P2 的难点与解决方法4.Alevel 数学 P2 的学习建议正文【1】Alevel 数学 P2 的定义与意义Alevel 数学 P2 是英国普通中等教育证书考试（A-Level）中的一门课程，主要面向 16-18 岁的学生。
它是 Alevel 数学的第一个部分，通常与 P1 一起教授。
P2 主要涉及纯数学的知识，包括代数、几何、三角函数等。
学习 Alevel 数学 P2 不仅有助于提高学生的数学技能，还能为进入大学学习更高阶的数学课程奠定基础。
【2】Alevel 数学 P2 的主要知识点Alevel 数学 P2 的主要知识点如下：1）代数：二次方程、二次不等式、指数与对数、函数与导数。
2）几何：平面几何、空间几何、几何变换。
3）三角函数：正弦、余弦、正切、反三角函数、三角恒等式。
4）概率与统计：事件与概率、条件概率、离散型随机变量、连续型随机变量、统计量、参数估计、假设检验。
【3】Alevel 数学 P2 的难点与解决方法Alevel 数学 P2 的难点主要体现在以下几个方面：1）复杂的代数运算：学生需要熟练掌握代数运算法则，解决复杂的方程和不等式。
2）几何证明：空间几何中的证明问题需要学生具备严密的逻辑思维和空间想象能力。
3）三角函数的运算与应用：学生需要熟练掌握各种三角函数的性质，解决实际问题。
解决这些难点的方法有：多做练习题，总结规律，加强对数学概念的理解；及时向老师请教，解决自己不能解决的问题；培养良好的学习习惯，提高学习效率。
【4】Alevel 数学 P2 的学习建议学习 Alevel 数学 P2，建议如下：1）打牢基础知识：重视基础知识的学习，加强对数学概念的理解。
2）多做练习：通过大量的练习题来提高自己的解题能力，总结解题规律。
3）及时复习：学习新知识的同时，不要忘记复习旧知识，确保自己的学习效果。
alevel数学知识点讲解三角函数trigonometry弧度radians
alevel数学知识点讲解三角函数trigonometry弧度radians
A-level数学知识点讲解三角函数trigonometry弧度radians是一种围绕原点的旋转形式，它可以用来表示一个角度的大小。
在数学中，通常使用弧度来测量角度，而不是使用角度。
弧度是一个角度值与总弧长之间的比值，其中总弧长是2π（即360°）。
例如，如果角度值是45°，则弧度值是π/4（或0.78539816339 radians），它表示1/4圆的总弧长。
弧度的重要性在于，它是数学中三角函数的基础。
三角函数是一组以角度值作为输入参数的函数，它们用来计算特定角度的特定值（例如正弦、余弦和正切）。
这些函数只能在弧度中使用，因此必须将角度转换为弧度才能计算三角函数。
alevel m1 单词
alevel m1 单词
A Level M1是指英国高中水平的数学课程中的一部分，主要包括一些数学专业课程的内容。
在这门课程中，学生需要掌握一些数学相关的专业术语和单词。
以下是一些与A Level M1课程相关的常见单词：
1. Vector（向量），在数学和物理学中，向量是有大小和方向的量，通常用箭头表示。
2. Matrix（矩阵），矩阵是一个由数字排列成的矩形阵列。
3. Differentiation（微分），微分是求函数导数的过程，用来研究函数的变化率。
4. Integration（积分），积分是微分的逆运算，用来求函数的面积或体积。
5. Trigonometry（三角学），三角学是研究三角形和三角函数的数学分支。
6. Kinematics（运动学），运动学是研究物体运动的数学和物理学分支。
7. Mechanics（力学），力学是研究物体运动和力的科学。
以上是一些与A Level M1课程相关的常见单词，这些单词在课程学习和理解数学概念时都会经常出现。
希望这些信息能够帮助你更好地理解A Level M1课程的内容。
alevel p2 词汇
alevel p2 词汇**Science and Mathematics**- Atom 原子- Biology 生物学- Chemical reaction 化学反应- Circuit 电路- Data 数据- Decimal 小数- DNA 脱氧核糖核酸- Electric current 电流- Force 力- Geometry 几何学- Gravity 重力- Heart 心脏- Hypothesis 假设- Kinetic energy 动能- Laboratory 实验室- Mass 质量- Matter 物质- Maths 数学- Newton's laws of motion 牛顿运动定律- Observational study 观察性研究- Oscillation 振荡- Parallax 视差- Physics 物理学- Population 人口- Pressure 压力- Quantum 量子- Radioactivity 放射性- Resistance 电阻- Solar system 太阳系- Speed 速度- Temperature 温度- Universe 宇宙**Social Sciences and Humanities** - Anthropology 人类学- Art 艺术- Civilization 文明- Culture 文化- Democracy 民主- Economy 经济- Education 教育- Empire 帝国- Ethics 伦理学- Fiction 小说- Gender 性别- Government 政府- History 历史- Human rights 人权- Language 语言- Literature 文学- Myth 神话- Novel 小说- Philosophy 哲学- Politics 政治- Psychology 心理学- Society 社会- Slavery 奴隶制- Species 物种- Stereotype 刻板印象- Subculture 亚文化- Technology 技术**General Vocabulary**- Abundant 丰富的- Accommodation 住处；适应- Accurate 精确的- Achieve 实现- Acquire 获取- Advantage 优势- Analyse 分析- Argument 论点- Association 协会- Authentic 真正的- Calculate 计算- Categories 类别- Chronic 慢性的- Circumstance 情况- Clarify 澄清- Community 社区- Compass 指南针- Compassion 同情- Concept 概念- Concrete 具体的- Conservation 保护- Construct 建造- Context 背景- Contract 合同- Contribution 贡献- Control 控制- Convince 说服- Core 核心- Criterion 标准- Culture 文化- Cynic 愤世嫉俗者- Define 定义- Delegate 委派- Demographic 人口统计的- Determine 确定- Develop 发展- Device 设备- Distribute 分配- Diversity 多样性- Domestic 国内的- Duration 持续时间- Economy 经济- Emotion 情感- Environment 环境- Epidemic 流行病- Evident 明显的- Evaporation 蒸发- Example 例子- Explicit 明确的- Extinct 灭绝的- Factor 因素-Fade 逐渐消失- Fashion 时尚- Feature 特征- Finance 金融- Focus 焦点- Force 力量- Frequency 频率- Function 功能- Generate 产生- Global 全球的- Graph 图表- Gravity 重力- Habit 习惯-哈耶克（F.A. Hayek）-哈耶克（F.A. Hayek）-Identical 相同的- Institution 机构- Interrupt 打断- Invalidate 使无效- Inventory 清单- Issue 问题- Iterate 迭代- Judge 判断- Jury 陪审团- Kinetic 运动的- Landslide 山体滑坡- Legacy 遗产- Magnet 磁铁- Margin 边缘- Marathon 马拉松- Mass 质量- Maximise 最大化- Merge 合并- Method 方法- Misconception 误解- Modify 修改- Movement 运动- Multiply 乘以- Neutral 中性的- Novel 新颖的- Obtain 获取- Opposition 反对- Participate 参与- Pattern 模式- Phenomenon 现象- Philosophy 哲学- Pollution 污染- Population 人口- Portable 便携的- Potentially 潜在地- Poverty 贫困- Precise 精确的- Predict 预测- Preference 偏好- Prepare 准备- Presence 存在- Principle 原则- Priority 优先事项- Probability 概率- Produce 生产- Product 产品- Profile 轮廓- Propaganda 宣传- Prosperity 繁荣- Psychology 心理学- Qualify 取得资格- Quantity 数量- Questionnaire 问卷- Random 随机的- React 反应- Reflect 反映- Region 地区- Religion 宗教- Replace 替换- Representative 代表- Reservoir 水库- Restrict 限制- Revenue 收入- Sample 样本- Scarcity 稀缺性- Sector 部门- Significant 显著的- Simulate 模拟- Society 社会- Specific 具体的- Spectrum 光谱- Succeed 成功- Sufficient 足够的- Survey 调查- Symbol 符号- Target 目标- Theory 理论- Thread 线程- Transport 运输- Understand 理解- Uniform 均匀的- Utilise 利用- Validate 验证- Variable 变量- Vector 向量-Violation 违反- Vision 视力；愿景- Volunteer 志愿者这些词汇只是一部分，你可以根据具体的学科或主题进一步扩展词汇列表。
ALEVEL数学词汇
一、基本平面图形：三角形：triangle矩形：rectangle正方形：square平行四边形：parallelogram梯形：trapezoid菱形：rhombus圆：circle四边形：quadrilateral二、基本立体图形：正方体：cube长方体：rectangular prism圆柱体：right circular cylinder 圆锥体：right circular cone球体： sphere三、基本计算量：长度：length面积：area体积（容积）：volume周长：perimeter表面积：surface area底面积：base area四、有关集合：union并集proper subset真子集solution set解集五、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nonnegative非负的tens十位units个位mode众数median中数common ratio公比六、数列：arithmetic progression(sequence)等差数列geometric progression(sequence)等比数列七、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,位八、几何常用名词：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supplement aryangles 补角complement aryangle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多边的九、基本数学词汇：加：plus/and/positive减：minus/negative/subtract 差：difference乘：multiplied by/times乘方：power积：product除：divided bydivisible可被整除的divided evenly被整除dividend被除数divisor因子，除数商：quotientremainder余数阶乘：factorial等于：equal不等于：not equal to大于：greater than小于：less than大于等于：equal or greater than 小于等于：equal or less than约等于：approximately equal Round to/to the nearest 四舍五入因为：because所以：therefore开平方：square root of开立方：cube root ofRadical sign, root sign根号绝对值：the absolute value函数：function图形：figure角：angle直角：right angle锐角：acute angle对折：fold分数：fractionX-轴：X-axesY-轴：Y-axes其他sequence 次序geometric 几何的Integer 整数ratio 比例positive 正的tangent 切线（也是正切tan）radius/radii 半径inequality 不等式vertex 顶点range值域like terms, similar terms同类项original equation原方程(least)common denominator(最小)公约数arithmetic mean算术平均值weighted average加权平均值exponent指数，幂variable变量inverse function反函数factorization因式分解dozen打(12个)score廿(20个)quart夸脱gallon加仑(1gallon=4quart)学通国际课程培训中心自2008年起一直致力于ALEVEL、IGCSE、IB、AP、SAT2等主流国际课程中30多门科目的提分与培优，经11年深耕教学，目前已拥有教师团队80余人，其中20%为博士，80%为名校海归硕士，平均国际课程教龄8年以上，每年为学生提供50000小时以上的高品质课程。
A-Level数学词汇大全，三天就能背完！
A-Level数学词汇⼤全，三天就能背完！线性代数篇①algebraic cofactor代数余⼦式array数组canonical form标准型characteristic polynomial特征多项式characteristic root特征根coefficient matrix系数矩阵column列column rank列秩component分量determinant⾏列式diagonal element对⾓元素diagonal matrix对⾓矩阵dimension维数diagonalisable matrix可对⾓化矩阵eigenvalue特征值eigenvector特征向量fundamental solution基本解geometric multiplicity⼏何重数homogeneous equation齐次⽅程identity matrix单位矩阵infinite dimensional⽆穷维的inverse matrix逆矩阵least squares problem最⼩⼆乘问题linear combination线性组合②linear dependence线性相关linear equation线性⽅程linear independence线性⽆关linear transformation线性变换main diagonal主对⾓线matrix矩阵multidimensional多维nonsingular matrix⾮奇异矩阵normal equation法⽅程normal form标准型normal matrix正规矩阵orthogonal matrix正交矩阵principal minor主⼦式rank秩rectangular matrix长⽅阵row⾏row rank⾏秩row (column) vector⾏（列）向量③scalar标量singular matrix奇异矩阵singular matrix奇异矩阵square matrix⽅阵symmetric matrix对称矩阵trace迹transposed matrix转置矩阵unit vector单位向量vector向量zero element零元素zero vector零向量基础数学篇①axiom公理theorem定理calculation计算operation运算prove证明hypothesis, hypotheses(pl.)假设proposition命题arithmetic算术plus(prep.), add(v.), addition(n.)加augend, summand被加数addend加数sum和minus(prep.), subtract(v.), subtraction(n.) 减minuend被减数subtrahend减数②remainder差times(prep.), multiply(v.), multiplication(n.)乘multiplicand, faciend被乘数multiplicator乘数product积divided by(prep.), divide(v.), division(n.)除dividend被除数divisor除数quotient商equals, is equal to, is equivalent to等于is greater than⼤于is lesser than⼩于is equal or greater than⼤于等于is equal or lesser than⼩于等于③operator运算符digit数字number数natural number⾃然数integer整数decimal⼩数decimal point⼩数点fraction分数numerator分⼦denominator分母ratio⽐positive正negative负null, zero, nought, nil零④decimal system⼗进制binary system⼆进制hexadecimal system⼗六进制weight, significance权carry进位truncation截尾round四舍五⼊round down下舍⼊round up上舍⼊significant digit有效数字insignificant digit⽆效数字⑤algebra代数formula, formulae(pl.)公式monomial单项式polynomial, multinomial多项式coefficient系数unknown, x-factor, y-factor, z-factor未知数equation等式，⽅程式simple equation⼀次⽅程quadratic equation⼆次⽅程cubic equation三次⽅程quartic equation四次⽅程inequation不等式⑥factorial阶乘logarithm对数exponent指数，幂power乘⽅square⼆次⽅，平⽅square⼆次⽅，平⽅cube三次⽅，⽴⽅the power of four, the fourth power四次⽅the power of n, the nth powern次⽅evolution, extraction开⽅square root⼆次⽅根，平⽅根cube root三次⽅根，⽴⽅根the root of four, the fourth root四次⽅根the root of n, the nth rootn次⽅根⑦aggregate集合element元素void空集subset⼦集intersection交集union并集complement补集mapping映射function函数domain, field of definition定义域range值域constant常量variable变量⑧monotonicity单调性parity奇偶性periodicity周期性image图象series数列，级数calculus微积分differential微分derivative导数limit极限infinite(a.) infinity(n.)⽆穷⼤infinitesimal⽆穷⼩integral积分definite integral定积分indefinite integral不定积分rational number有理数irrational number理数real number实数imaginary number虚数complex number复数matrix矩阵determinant⾏列式geometry⼏何⑨point点line线plane⾯solid体segment线段radial射线parallel平⾏intersect相交angle⾓degree⾓度radian弧度acute angle锐⾓right angle直⾓obtuse angle钝⾓straight angle平⾓perigon周⾓base底side边height⾼triangle三⾓形acute triangle锐⾓三⾓形right triangle直⾓三⾓形leg直⾓边hypotenuse斜边Pythagorean theorem勾股定理obtuse triangle钝⾓三⾓形scalene triangle不等边三⾓形isosceles triangle等腰三⾓形equilateral triangle等边三⾓形quadrilateral四边形⑩parallelogram平⾏四边形rectangle矩形length长width宽rhomb, rhombus, rhombi(pl.), diamond菱形square正⽅形trapezoid梯形trapezoid梯形right trapezoid直⾓梯形isosceles trapezoid等腰梯形pentagon五边形hexagon六边形heptagon七边形octagon⼋边形enneagon九边形decagon⼗边形hendecagon⼗⼀边形dodecagon⼗⼆边形polygon多边形equilateral polygon正多边形circle圆centre(BrE), center(AmE)圆⼼radius半径diameter直径pi圆周率arc弧semicircle半圆sector扇形ring环ellipse椭圆circumference圆周perimeter周长area⾯积locus, loca(pl.)轨迹similar相似similar相似congruent全等tetrahedron四⾯体pentahedron五⾯体hexahedron六⾯体parallelepiped平⾏六⾯体cube⽴⽅体heptahedron七⾯体octahedron⼋⾯体enneahedron九⾯体decahedron⼗⾯体hendecahedron⼗⼀⾯体dodecahedron⼗⼆⾯体icosahedron⼆⼗⾯体polyhedron多⾯体pyramid棱锥prism棱柱frustum of a prism棱台rotation旋转axis轴cone圆锥cylinder圆柱frustum of a cone圆台sphere球hemisphere半球undersurface底⾯surface area表⾯积volume体积space空间coordinates坐标系x-axis, y-axis, z-axis坐标轴x-coordinate横坐标y-coordinate纵坐标origin原点hyperbola双曲线parabola抛物线trigonometry三⾓sine正弦cosine余弦tangent正切cotangent余切secant正割cosecant余割arc sine反正弦arc cosine反余弦arc tangent反正切arc cotangent反余切arc secant反正割arc cosecant反余割phase相位period周期amplitude振幅incentre(BrE), incenter(AmE)内⼼excentre(BrE), excenter(AmE)外⼼escentre(BrE), escenter(AmE)旁⼼orthocentre(BrE), orthocenter(AmE)垂⼼barycentre(BrE), barycenter(AmE)重⼼inscribed circle内切圆circumcircle外切圆statistics统计average平均数weighted average加权平均数variance⽅差root-mean-square deviation, standard deviation标准差propotion⽐例percent百分⽐percentage百分点percentile百分位数permutation排列combination组合probability概率，或然率distribution分布normal distribution正态分布abnormal distribution⾮正态分布graph图表bar graph条形统计图histogram柱形统计图broken line graph折线统计图curve diagram曲线统计图pie diagram扇形统计图微积分微积分①analytic expression解析表达式analytic geometry解析⼏何antiderivative原函数asymptote渐进average value平均值boundary边界boundary integral边界积分bounded有界的calculus微积分chain rule链式法则change of variable变量替换closed set闭集complement补集complete完全的conditionally convergent条件收敛continuity连续性continuous everywhere处处连续②continuously differentiable连续可微convergence收敛convolution卷积covering覆盖critical point临界点cross product向量积cross section截⾯decay衰变definite integral定积分derivative导数differentiable everywhere处处可微differentiation微分divergence发散dot product点积double integral⼆重积分③elementary function初等函数empty set空集even function偶函数first derivative⼀阶导数Fourier series傅⾥叶级数Fourier transform傅⾥叶变换function series函数级数fundamental theorem基本定理generalised integral⼴义积分gradient梯度higher order derivative⾼阶导数identity function恒等函数implicit differentiation隐式求导implicit function隐函数④improper integral反常积分increment增量indefinite integral不定积分infinitesimal⽆穷⼩infinity⽆穷⼤inflection point拐点integrable可积的integral, integration积分integral sign积分号integrand被积函数integration by parts分部积分法integration by substitution换元积分法integration constant积分常数intermediate value theorem介值定理intersection交集⑤inverse mapping逆映射isolated point孤⽴点least value最⼩值limit极限L’Hospital’s rule洛必达法则Maclaurin series麦克劳林级数maximal value极⼤值mean value theorem中值定理minimum极⼩monotone function单调函数multiple integral多重积分multivariable function多元函数multivariate多变量natural exponential function⾃然指数函数natural logarithm⾃然对数neighbourhood邻域numerable可数的open set开集open set开集⑥ordinal number序数parameter参数parametric equation参数⽅程partial derivatives偏导数partial differential偏微分partial fraction部分分式power series幂级数product rule乘积法则proper subset真⼦集properly include真包含quantity量quotient rule商法则rate of change变化率remainder term余项second derivative⼆阶导数sequence序列set theory集合论⑦singular point奇异点smooth function光滑函数solid of revolution旋转体space curve空间曲线sub下标subset⼦集super上标surface integral⾯积分surface of revolution旋转曲⾯Taylor’s expansion泰勒展开式Taylor’s series泰勒级数total differential全微分triple integral三重积分unbounded function⽆界函数unbounded set⽆界集uncountable set不可数集uniformly bounded⼀致有界uniformly continuous⼀致连续uniformly convergent⼀致收敛union并集upper (lower) limit上（下）极限variation变差。
alevel数学考试内容
alevel数学考试内容A-level学是一个非常重要的考试，对于想要获得一个扎实的数学基础来准备未来大学学习，或者想要从事数学相关工作的人来说，考取A-level学是非常重要的。
A-level学考试内容丰富多样，它分为数学课程和内容两个部分，考试的主要内容包括以下几点：一、函数（Functions）：学生需要学会如何使用函数，以及对函数进行求导、定义域、单调性和极值等的考察。
二、极限（Limits）：学生需要学会函数的零点、收敛性和极限的计算，以及其他涉及极限的知识。
三、微积分（Calculus）：学生需要学会基本的微积分知识，如求导、定积分、曲线积分和微分方程等。
四、线性代数（Linear Algebra）：学生需要学会矩阵计算、向量空间、行列式、线性变换、线性方程组解法等知识。
五、概率（Probability）：学生需要学会概率理论和概率统计的基本概念，以及条件概率、联合概率和随机变量的基本概念。
六、统计（Statistics）：学生需要学会概率分布、抽样方法、统计非参数检验和统计参数检验等基础知识。
A-level学考试不仅涉及数学理论，还涉及一些实践性的知识，比如，学生需要学会应用矩阵运算、解出参数方程，甚至包括编程的一些知识，如熟悉C、Java、C++等编程语言，来解决一些计算机界面的问题。
总的来说，A-level学考试的内容包括了所有的基础数学知识，以及一些实践性的知识，要想考取优异的成绩，学生不仅要做功课，更要有充足的考前准备，以便能够准确、熟练地回答考官提出的各种问题。
因此，对于参加A-level学考试的学生来说，要想在这次考试中取得优异成绩，必须强烈的坚持学习，好好把握考试的时间，准备考试的内容，努力复习，这样才能够在最后的考试中取得优异的成绩。
alevel数学p2知识点
1. Complex Numbers and EquationsComplex numbers can be represented as (z = a + bi), where (a) and (b) are real numbers and (i) is the imaginary unit. Key concepts related to complex numbers and equations include:•Addition and subtraction of complex numbers: To add or subtract complex numbers, add or subtract the real and imaginary parts separately.•Multiplication of complex numbers: To multiply complex numbers, use the distributive property and simplify using the fact that (i^2 = -1).•Division of complex numbers: To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator and simplify.•Complex conjugate: The complex conjugate of (z = a + bi) is ({z} = a - bi). The product of a complex number and its conjugate is always a real number.•Modulus of a complex number: The modulus of (z = a + bi) is denoted as (|z|) and is calculated as (). The modulus gives the distance of the complex number from the origin in the complex plane.•Argand diagram: An Argand diagram is used to represent complex numbers geometrically as points in a Cartesian plane. The real part represents the x-coordinate, and the imaginary part represents the y-coordinate.2. Functions and GraphsFunctions play a significant role in A-Level Mathematics and are represented by (y = f(x)). Key concepts related to functions and graphs include:•Domain and range: The domain of a function represents all possible input values that the function can accept, while the range represents allpossible output values.•Graphs of functions: The graph of a function represents the relationship between the input and output values. It can be plotted on aCartesian plane using coordinate points.•Transformations of functions: Transformations involve shifting, stretching, or reflecting the graph of a function. These transformations can be applied to the x-axis or y-axis, and they affect the domain, range, and shape of the graph.•Composite functions: Composite functions are formed by taking one function and substituting it into another function.•Inverses of functions: The inverse of a function (f) is denoted as (f^{-1}) and can be found by interchanging the x and y variables. The graph of afunction and its inverse are symmetric about the line (y = x).3. CalculusCalculus involves the study of differentiation and integration. Key concepts related to calculus include:•Differentiation: Differentiation allows us to find the rate of change of a function at a specific point. The derivative of a function (f(x)) with respect to (x) is denoted as () or (f’(x)).•Rules of differentiation: Differentiation rules include the power rule, product rule, quotient rule, and chain rule. These rules help us differentiatefunctions of various forms.•Maxima and minima: The derivative helps us identify the points of maximum and minimum on a graph. A point where the derivative equals zero or does not exist can indicate a local maximum or minimum.•Integration: Integration helps us find the area under the curve of a function. The integral of a function (f(x)) with respect to (x) is denoted as (f(x) dx).•Definite and indefinite integrals: A definite integral has limits of integration, while an indefinite integral represents a family of functions.•Fundamental theorem of calculus: The fundamental theorem of calculus relates integration and differentiation. It states that if (F(x)) is theantiderivative of (f(x)), then (_a^b f(x) dx = F(b) - F(a)).4. VectorsVectors have both magnitude and direction and are denoted as (). Key concepts related to vectors include:•Vector notation and representation: Vectors can be represented geometrically as directed line segments or algebraically using component form or column form.•Addition and subtraction of vectors: Vector addition and subtraction involve adding or subtracting the corresponding components of vectors.•Scalar multiplication: Scalar multiplication involves multiplying a vector by a scalar (real number).•Unit vectors: Unit vectors have a magnitude of 1 and are used to define the direction of a vector.•Dot product: The dot product of two vectors (a) and (b) is calculated as (a b = |a| |b| ), where () is the angle between the vectors.•Cross product: The cross product of two vectors (a) and (b) is denoted as (a b) and is a vector perpendicular to both (a) and (b). Its magnitude iscalculated as (|a b| = |a| |b| ).These are just some of the key knowledge points related to A-Level Mathematics Paper 2. Understanding and applying these concepts will greatly help in solving a variety of mathematical problems.。
alevel 数学教材介绍
以下是一些常见的A级数学教材介绍：
1. "Further Mathematics for A Level" by Bostock and Chandler - 这本教材适合学生在高中阶段深入学习数学，并准备参加高级别的数学考试。
它涵盖了广泛的主题，包括微积分、线性代数、微分方程等。
2. "Mathematical Methods in the Physical Sciences" by Mary L. Boas - 这本教材主要面向那些对数学与物理科学领域有兴趣的学生。
它涵盖了微积分、微分方程、矩阵代数等内容，并提供了大量的实际应用例子。
3. "Pure Mathematics for Advanced Level" by Hugh Neill and Douglas Quadling - 这本教材适合学生准备参加纯数学A级考试。
它涵盖了代数、几何、三角学、向量和微积分等主题，并提供了丰富的练习题和解答。
4. "Mechanics for A Level" by Douglas Quadling - 这本教材专注于力学领域，适合学生准备参加A级力学考试。
它介绍了基本的运动学和动力学概念，并提供了大量的例题和习题。
这些仅是一些常见的A级数学教材，选择适合自己的教材可以根据个人学习需求和课程要求来决定。
A-level数学词汇分类整理——微积分篇(二)
A-level数学词汇分类整理——微积分篇（二）接上期，今天索引留学小编整理的是A-level数学微积分词汇整理~【微积分篇】analytic expression解析表达式analytic geometry解析几何antiderivative原函数asymptote渐进average value平均值boundary边界boundary integral边界积分bounded有界的calculus微积分chain rule链式法则change of variable变量替换closed set闭集complement补集complete完全的conditionally convergent条件收敛continuity连续性continuous everywhere处处连续continuously differentiable连续可微convergence收敛convolution卷积covering覆盖critical point临界点cross product向量积cross section截面decay衰变definite integral定积分derivative导数differentiable everywhere处处可微differentiation微分divergence发散dot product点积double integral二重积分elementary function初等函数empty set空集even function偶函数first derivative一阶导数Fourier series傅里叶级数Fourier transform傅里叶变换function series函数级数fundamental theorem基本定理generalised integral广义积分gradient梯度higher order derivative高阶导数identity function恒等函数implicit differentiation隐式求导implicit function隐函数improper integral反常积分increment增量indefinite integral不定积分infinitesimal无穷小infinity无穷大inflection point拐点integrable可积的integral, integration积分integral sign积分号integrand被积函数integration by parts分部积分法integration by substitution换元积分法integration constant积分常数intermediate value theorem介值定理intersection交集inverse mapping逆映射isolated point孤立点least value最小值limit极限L’Hospital’s rule洛必达法则Maclaurin series麦克劳林级数maximal value极大值mean value theorem中值定理minimum极小monotone function单调函数multiple integral多重积分multivariable function多元函数multivariate多变量natural exponential function自然指数函数natural logarithm自然对数neighbourhood邻域numerable可数的open set开集ordinal number序数parameter参数parametric equation参数方程partial derivatives偏导数partial differential偏微分partial fraction部分分式power series幂级数product rule乘积法则proper subset真子集properly include真包含quantity量quotient rule商法则rate of change变化率remainder term余项second derivative二阶导数sequence序列set theory集合论singular point奇异点smooth function光滑函数solid of revolution旋转体space curve空间曲线subscript下标subset子集superscript上标surface integral面积分surface of revolution旋转曲面Taylor’s expansion泰勒展开式Taylor’s series泰勒级数total differential全微分triple integral三重积分unbounded function无界函数unbounded set无界集uncountable set不可数集uniformly bounded一致有界uniformly continuous一致连续uniformly convergent一致收敛union并集upper (lower) limit上（下）极限variation变差精彩待续~~。
Alevel数学-caie-as-maths-9709-mechanics知识点笔记
TABLE OF CONTENTS 2 CHAPTER 1Velocity & Acceleration3 CHAPTER 2Force & Motion3 CHAPTER 3Vertical Motion3 CHAPTER 4Resolving Forces4 CHAPTER 5Friction4 CHAPTER 6Connected Particles7 CHAPTER 7Work, Energy & Power7 CHAPTER 8Momentum8 CHAPTER 9General Motion in a Straight LineGradient = speed1.3 Velocity-Time GraphGradient = accelerationArea under graph = change in displacement{S12-P42} Question 7:The small block has mass 0.15kg. The surface is horizontal. The frictional force acting on it is 0.12N. Block set in motion from X with speed 3ms . It hits vertical surface at Y2s later. Block rebounds from wall−0.8=t=1.25sDraw velocity-time graph with data calculated:Part (ii)Calculate displacement from X to Ys=(3×2)+(−0.8)(2) s=4.4m Calculate displacement from Y to Zs=(1×1.25)+12(−0.8)(1.25)s=0.625m in tℎe opposite direction Draw displacement-time graph with data calculated:1.4 Average VelocityFor an object moving with constant acceleration over a period of time, these quantities are equal:o The average velocityLet s be the distance travelled by A and s for BNewton’s 1 Law of Motion:Object remains at rest or moves with constant velocity unless an external force is applied Newton’s 2nd Law of Motion:F=ma3.V ERTICAL M OTIONWeight: directly downwardsNormal contact force: perpendicular to place of contact 3.1 Common Results of Vertical Motion Finding time taken to reach maximum height by a projectile travelling in vertical motion:v=u+atLet v=0 and find tThe time taken to go up and come back to original position would be double of this tFinding maximum height above a launch point use:v =u −2as Therefore, time above tower =5−1=4 seconds Part (ii)Displacement of P is S , and of P is S & relationship:S =25+SCreate equations for S and SS =30t+12(−10)t S =10t+12(−10)t Substitute back into initial equation30t+12(−10)t =25+10t+12(−10)t Simple cancellingt=1.25sFind velocitiesv=u+atV =30−10(1.25)=17.5msV =10−10(1.25)=−2.5msPart (iii)We know when P and P at same height t=1.25s. Find time taken to reach max height for Pv=u+atLami’s Theorem:For any set of three forces P,Q and R in equilibriumQ sinβ=R sinγ5.F RICTIONFriction = Coefficient of Friction × Normal Contact ForceF=μrFriction always acts in the opposite direction of motion Limiting equilibrium: on the point of moving, friction at max (limiting friction)Smooth contact: friction negligibleContact force:o Refers to both F and No Horizontal component of Contact force = Fo Vertical component of Contact force = No Magnitude of Contact force given by the formula:C= F +N{W11-P43} Question 6: The ring has a mass of 2kg. Thehorizontal rod is rough and thecoefficient of friction betweenring and rod is 0.24. Find the twovalues of T for which the ring is inSolution: The ring is in limiting equilibrium in two differentin both:Scenario 1: ring is about to move upwards−Weigℎt of Ring Since the system is in equilibrium, resultant = 0:cos30Max Value Min ValueThe particle is about tomove upThus, friction force actsdown the slopeP=F+mg sinθThe particle is about slipdownThus, frictional forceacts up the slopeF+P=mg sinθ{W12-P43} Question 6:Coefficient of friction is 0.36 and the particle is in equilibrium. Find the possible values of PSolution: The magnitude of friction on particle in both scenarios is the same but acting in opposite directions Calculate the magnitude of friction first:Contact Force=6cos25P AGE 4 OF 9A train pulls two carriages:The forward force of the engine is F=2500N. Find the acceleration and tension in each coupling. TheF−T −200=1000a2500−T −200=1000×1.08T =1220NTo find T , look at AT −90=400aT −90=400×1.08T =522N6.1 PulleysEquation 1:No backward force ∴T=2aEquation 2:3g−T=3a {W05-P04} Question 3:The strings are in equilibrium. The pegs are smooth. All the weights are vertical. Find W and W Resolving forces at A vertically:W cos40+W cos60=5 Resolving forces at A horizontally:W sin40=W sin60Substitute second equation into first:W sin60sin40cos40+W cos60=5Solve to find W :W =3.26NPut this value back into first equation to find WW =4.40N{S12-P41} Question 6:has a mass of 0.6kg and Q has a mass of 0.4kg pulley and surface of both sides are smooth. The base of triangle is horizontal. It is given that sinθ=0.8 Initially particles are held at rest on slopes with string taut. Particles are released and move along the slope Find tension in string. Find acceleration ofparticles while both are moving.Speed of P when it reaches the ground isAGE OFAGE OF Part (ii) Use kinematics equations to find the time which it takes P to reach the ground:a = and t = . t =1.25s When P reaches the ground, only force acting on Q is its own weight in the direction of slope =3.2NF =ma −3.2=0.4aa =−8ms Now calculate the time taken for Q to reach max height This occurs when its final velocity is 0. −8=0−2t t =0.25s Now do simple addition to find total time: Total Time =1.25+0.25=1.5s 6.2 Force Exerted by String on PulleyPulley Case 1 Force on pulley =Acts: downwardsPulley Case 2 Force on pulley = T √2 Acts: along dotted line Pulley Case 3 Force on pulley = 2T cos θ Acts: inwards along dotted line which bisects θ6.3 Two Particles {S10-P43} Question 7:A andB are rectangular boxes of identical sizes and are at rest on rough horizontal plane. A mass =200kg and B mass =250kg . If P ≤3150 boxes remain at rest. If P >3150 boxes move i. Find coefficient of friction between B and floor ii. Coefficient of friction between boxes is 0.2. Given that P >3150 and no sliding occurs between boxes. Show that the acceleration of boxes is not greater than 2ms iii. Find the maximum possible value of P in the above scenarioSolution: Part (i) F =μNF = to max P that does not move the boxes N = to contact force of both boxes acting on floor∴3150=μ×(2000+2500)(Work) is the energy caused by driving force acting on the object(Work) is the energy used up by frictional force or any resistive force{S05-P04} Question 7: Car travelling on horizontal straight road, mass 1200kg. Power of car engine is 20kW and constant. Resistanceto motion of car is 500N and constant. Car passes point A with speed 10ms . Car passes point B with speed 25ms . Car takes 30.5s to move from A to B.i.Find acceleration of the car at Aii.Find distance AB by considering work & energySolution: Part (i)Use formula for power to find the force at AP=Fv20000=10F Driving force=2000NWe must take into account the resistance to motion∴F=Driving Force−Resistance=2000−500p=mvPrinciple of conservation of linear momentum: when bodies in a system interact, total momentum remains constant provided no external force acts on the system.Before Afterm u +m u =m v +m vWhen both particles A and B move towards each other Before Afterm u −m u =m v +m vWhen both particles stick together, their velocity becomes the same after impact.Before Afterm u +m u (m +m )vAGE OF 9P AGE 8 OF 9p =(4×6)+2(0)+3(0)=24 kgms Calculate momentum of system after collision:p =(4×2)+2v Apply conservation of momentum:total momentum before = total momentum after 24=8+2v v ==8.0 ms Part (ii) Calculate momentum of system before collision:p =(8×2)+(3×0)=16 kgms Calculate momentum of system after collision: Note: The masses B and C combine to form Dp =(2+3)vp =5v Apply conservation of momentum:16=5v v =165=3.2 ms 9. G ENERAL M OTION IN A S TRAIGHT L INEdisplacement v velocity acceleration Particle at instantaneous rest, v =0 Maximum displacement from origin, v =0 Maximum velocity, a =0dt =0.006t −0.24t +1.8 Stationary points occur where =0 ∴0.006t −0.24t +1.8=0 Solve for t in simple quadratic fashion: t =30 and 10 Naturally T comes before T ∴T =10s and T =30 Finding distance OP by integrating ∴s = v dt s = (0.002t −0.12t +1.8t +5) dt s =[0.0005t −0.04t +0.9t +5t ] s =285 mPart (ii) Do basic substitution to find v v =0.002t −0.12t +1.8t +5 t =30 v =5 To draw graph, find v of P at T using substitution and plot roughly DIFFERENTIATEINTEGRATEP AGE 9 OF 9 Part (i) and (ii) Part (ii) First find s when t =20, this will produce a constant since 20≤t ≤26 s =12(8)(8)+12(8+2)(12)=92m Finding s when 20≤t ≤26: s =ut +12at Since the distance before 20 seconds has already been taken into consideration:t =t −20 6.5−2。
A-level数学常用词汇汇总
Chapter1 coordinates,points and lines 坐标,点和线
Axis
轴
Bisect
平分；角平分线；等分
Cartesian corrdinates
直角坐标系；笛卡尔坐标
Diagonal
对角线
Diameter
直径
Dimensions
次；元；度（数）；维（数）
Divided by 除
Congruent to 全等于
Equals 等于
Denotes an operation（表示一个操作）
Approximately equals 约等于
Therefore 因此
Not equal to不等于
because 因为 由于
Less than 小于
Ratio sign ;divided by ;is to 除以 是
parentheses括号perpendicularrightanglessquarebrackets方括号anglebraces花括号rightangle直角今天环球教育名师为考生们带来alevel数学常用词汇汇总希望能给alevel考生们带来帮助
A-level数学常用词汇汇总
今天环球教育名师为考生们带来A-level数学常用词汇汇总，希望能给alevel考生们带来帮助。
菱形
Steepness
险峻，陡心
Triangle
三角形；三角形物体
Vertices
顶点
Plus;positive 加
Is a member of the set是一个集的成员
Minus;negative 减
Is a subset of 是…的一个子集
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三次方方，立立方方 cube 四次方方 the power of four, the fourth power n次方方 the power of n, the nth power 开方方 evolution, extraction 二二次方方根，平方方根 square root 三次方方根，立立方方根 cube root 四次方方根 the root of four, the fourth root n次方方根 the root of n, the nth root 集合 aggregate 元素 element 空集 void 子子集 subset 交集 intersection
运算符 operator 数字 digit 数 number 自自然数 natural number 整数 integer 小小数 decimal 小小数点 decimal point 分数 fraction 分子子 numerator 分⺟母 denominator 比比 ratio 正 positive 负 negative 零 null, zero, nought, nil 十十进制 decimal system 二二进制 binary system 十十六进制 hexadecimal system 权 weight, significance 进位 carry 截尾 truncation 四舍五入入 round
几几何 geometry 点 point 线 line 面面 plane 体 solid 线段 segment 射线 radial 平行行行 parallel 相交 intersect ⻆角 angle ⻆角度 degree 弧度 radian 锐⻆角 acute angle 直⻆角 right angle 钝⻆角 obtuse angle 平⻆角 straight angle 周⻆角 perigon 底 base 边 side 高高 height 三⻆角形 trialement 映射 mapping 函数 function 定义域 domain, field of definition 值域 range 常量量 constant 变量量 variable
单调性 monotonicity 奇偶性 parity 周期性 periodicity 图象 image 数列列，级数 series 微积分 calculus 微分 differential 导数 derivative 极限 limit 无无穷大大 infinite(a.) infinity(n.) 无无穷小小 infinitesimal 积分 integral 定积分 definite integral 不不定积分 indefinite integral 有理理数 rational number 理理数 irrational number 实数 real number 虚数 imaginary number 复数 complex number 矩阵 matrix 行行行列列式 determinant
算术 arithmetic 加 plus(prep.), add(v.), addition(n.) 被加数 augend, summand 加数 addend 和 sum 减 minus(prep.), subtract(v.), subtraction(n.) 被减数 minuend 减数 subtrahend 差 remainder 乘 times(prep.), multiply(v.), multiplication(n.) 被乘数 multiplicand, faciend 乘数 multiplicator 积 product 除 divided by(prep.), divide(v.), division(n.) 被除数 dividend 除数 divisor 商 quotient 等于 equals, is equal to, is equivalent to 大大于 is greater than 小小于 is lesser than 大大于等于 is equal or greater than 小小于等于 is equal or lesser than
A-level数学必学词汇汇总
数学 mathematics, maths(BrE), math(AmE) 公理理 axiom 定理理 theorem 计算 calculation 运算 operation 证明 prove 假设 hypothesis, hypotheses(pl.) 命题 proposition
锐⻆角三⻆角形 acute triangle 直⻆角三⻆角形 right triangle 直⻆角边 leg 斜边 hypotenuse 勾股定理理 Pythagorean theorem 钝⻆角三⻆角形 obtuse triangle 不不等边三⻆角形 scalene triangle 等腰三⻆角形 isosceles triangle 等边三⻆角形 equilateral triangle 四边形 quadrilateral 平行行行四边形 parallelogram 矩形 rectangle ⻓长 length 宽 width 菱形 rhomb, rhombus, rhombi(pl.), diamond 正方方形 square 梯形 trapezoid 直⻆角梯形 right trapezoid 等腰梯形 isosceles trapezoid 五边形 pentagon 六边形 hexagon
下舍入入 round down 上舍入入 round up 有效数字 significant digit 无无效数字 insignificant digit 代数 algebra 公式 formula, formulae(pl.) 单项式 monomial 多项式 polynomial, multinomial 系数 coefficient 未知数 unknown, x-factor, y-factor, z-factor 等式，方方程式 equation 一一次方方程 simple equation 二二次方方程 quadratic equation 三次方方程 cubic equation 四次方方程 quartic equation 不不等式 inequation 阶乘 factorial 对数 logarithm 指数，幂 exponent 乘方方 power 二二次方方，平方方 square