📚 Year 11 CIE Mathematics: Quick Memorisation Guide for Vocabulary Terms | CIE 数学：词汇术语速记指南
Mastering the language of mathematics is half the battle in any exam. This guide breaks down the most essential Year 11 CIE IGCSE Mathematics terms, pairing them with memorable definitions and examples to help you recall them faster. Each section targets a key topic area, ensuring you build a strong foundation of vocabulary that will make problem-solving smoother and boost your confidence on exam day.
掌握数学语言是赢得任何考试的关键。本指南分解了Year 11 CIE IGCSE数学中最核心的术语，配以易记的定义和示例，助你更快回忆。每一节针对一个关键主题领域，确保你打下坚实的词汇基础，使解题更顺畅，并在考试当天提升信心。
1. Essential Number Terms | 基础数字术语
Integer: A whole number that can be positive, negative, or zero, but never a fraction or decimal. Examples: -3, 0, 7, 2024.
整数：可以为正、负或零的完整数字，绝不是分数或小数。示例：-3、0、7、2024。
Rational Number: Any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero. This includes terminating and recurring decimals.
有理数：任何可表示为分数a/b的数，其中a和b为整数且b不为零。这包括有限小数和循环小数。
Irrational Number: A number that cannot be written as a simple fraction; its decimal expansion goes on forever without repeating. Examples: π, √2, e.
无理数：无法写成简单分数的数；其小数展开无限不循环。示例：π、√2、e。
Prime Number: A whole number greater than 1 that has exactly two distinct factors: 1 and itself. 2 is the only even prime number.
质数（素数）：大于1的整数，且恰好只有两个不同的因数：1和它本身。2是唯一的偶质数。
Factor: A number that divides into another number exactly, leaving no remainder. 12 has factors 1, 2, 3, 4, 6, 12.
因数：能整除另一个数且无余数的数。12的因数有1、2、3、4、6、12。
Multiple: The result of multiplying a number by an integer. The multiples of 5 are 5, 10, 15, 20, . . .
倍数：一个数与整数相乘的结果。5的倍数有5、10、15、20…
Square Number: The product of an integer multiplied by itself, e.g., 3² = 9, so 9 is a square number.
平方数：一个整数自乘的积，例如3² = 9，故9是平方数。
Cube Number tained when an integer is multiplied by itself twice, e.g., 2³ = 8, so 8 is a cube number.
立方数：一个整数自乘两次所得的积，例如2³ = 8，故8是立方数。
Surd: An expression containing an irrational root, such as √3 or 5 + 2√7. Surds are left in root form for exactness.
根式（无理根式）：包含无理根的表达式，如√3或5 + 2√7。根式保留根号形式以保证精确。
2. Algebra Basics | 代数基础
Variable sents a number whose value may change or is unknown. In y = 2x + 1, x and y are variables.
变量：通常用字母表示的符号，代表可能变化或未知的数值。在y = 2x + 1中，x和y是变量。
Coefficient: The numerical factor multiplying a variable in a term. In 7x³, 7 is the coefficient of x³.
系数：在项中乘以变量的数值因子。在7x³中，7是x³的系数。
Term: A single number, variable, or numbers and variables multiplied together, separated by + or - signs in an expression. 4x², -2y, and 5 are terms.
项：单个数字、变量或数字与变量的乘积，在表达式中由+或-号分隔。4x²、-2y和5都是项。
Expression: A combination of terms using mathematical operations, without an equals sign. Example: 3a² - 2a + 7.
表达式：使用数学运算组合项而成，没有等号。示例：3a² - 2a + 7。
Equation s two expressions are equal, always containing an equals sign. 2x + 3 = 11 is an equation.
方程：表明两个表达式相等的数学陈述，总是包含等号。2x + 3 = 11是一个方程。
Identity: An equation that is true for all values of the variable(s), often denoted by the symbol ≡. Example: (x + 1)² ≡ x² + 2x + 1.
恒等式：对所有变量取值都成立的等式，常用符号≡表示。示例：(x + 1)² ≡ x² + 2x + 1。
Simplify: To reduce an expression to its most compact form by collecting like terms and applying arithmetic rules.
化简：通过合并同类项和应用算术规则，把表达式化为最紧凑的形式。
Expand: To remove brackets by multiplying each term inside by the factor outside. For instance, expanding 3(x + 4) gives 3x + 12.
展开：通过将括号外的因子乘以括号内的每一项来去掉括号。例如，展开3(x + 4)得3x + 12。
Factorise panding; writing an expression as a product of its factors, e.g., x² - 9 = (x + 3)(x - 3).
因式分解：展开的逆运算；将表达式写为因子的乘积，例如x² - 9 = (x + 3)(x - 3)。
3. Equations and Inequalities | 方程与不等式
Linear Equation st : An equation where the highest power of the variable is 1, forming a straight line when graphed. Example: 5x - 2 = 18.
线性方程（一次方程）：变量最高次幂为1的方程，图形为一条直线。示例：5x - 2 = 18。
Quadratic Equation ere the highest power is 2, usually in the form ax² + bx + c = 0. Its graph is a parabola.
二次方程：最高次幂为2的方程，通常形式为ax² + bx + c = 0。其图像为抛物线。
Root (Solution) equation true when substituted for the variable. The roots of x² - 5x + 6 = 0 are 2 and 3.
根（解）：代入变量后使方程成立的值。x² - 5x + 6 = 0的根是2和3。
Discriminant 4ac. It determines the nature of the roots: if positive, two distinct real roots; if zero, one repeated real root; if negative, no real roots.
判别式：对于二次式ax² + bx + c = 0，即b² - 4ac。它决定根的性质：正数则有两个不等实根；零则有一个重实根；负数则无实根。
Inequality: A statement comparing two expressions using signs <, >, ≤, or ≥. Example: 3x + 2 > 8.
不等式：使用<、>、≤或≥比较两个表达式的陈述。示例：3x + 2 > 8。
Region satisfies one or more inequalities. A solid line shows ≤ or ≥, a dashed line shows < or >.
区域：图形上满足一个或多个不等式的区域。实线表示≤或≥，虚线表示<或>。
Simultaneous Equations: A set of two or more equations with the same variables, solved together to find the common solution. Often solved by substitution or elimination.
联立方程（方程组）：一组具有相同变量的两个或多个方程，一同求解公共解。常用代入法或消元法求解。
4. Sequences and Series | 数列与级数
Sequence: An ordered list of numbers following a rule. Each number is a term. Example: 2, 5, 8, 11, . . . (arithmetic).
数列：按规则排列的有序数字列表。每个数字是一个项。示例：2, 5, 8, 11, . . . （等差数列）。
Arithmetic Progression (AP): A sequence where the difference between consecutive terms is constant, called the common difference d. The nth term is a + (n - 1)d.
等差数列：相邻两项之差为常数的数列，该常数称为公差d。第n项为a + (n - 1)d。
Geometric Progression (GP): A sequence where each term is obtained by multiplying the previous term by a constant r, the common ratio. The nth term is a rⁿ⁻¹.
等比数列：每一项都是前一项乘以常数r（公比）所得。第n项为a rⁿ⁻¹。
nth Term: A formula that allows you to find any term in a sequence without listing all previous terms. For 4, 7, 10, . . . the nth term is 3n + 1.
第n项（通项公式）：能让你无需列出所有前面项便求出数列中任意一项的公式。数列4, 7, 10, . . . 的第n项是3n + 1。
Series: The sum of the terms of a sequence. The sum of the first n terms of an AP is n/2 [2a + (n - 1)d].
级数：数列各项之和。等差数列前n项和为 n/2 [2a + (n - 1)d]。
Recurrence Relation A rule that defines each term using the previous one(s), e.g., uₙ₊₁ = 2uₙ + 1 with u₁ = 3.
递推关系：利用前一项或前几项定义每一项的规则，如uₙ₊₁ = 2uₙ + 1且u₁ = 3。
5. Geometry Terms | 几何术语
Parallel Lines: Lines in the same plane that never meet, no matter how far they are extended. They are marked with identical arrows.
平行线：在同一平面内无论延伸多远都永不相交的直线。用相同的箭头标记。
Perpendicular Lines: Two lines that intersect at a right angle (90°). The product of their slopes is -1 if they are not vertical/horizontal.
垂直线：相交成直角（90°）的两条直线。若非垂直/水平线，它们的斜率之积为-1。
Congruent: Shapes that are identical in size and shape; one can be exactly superimposed on the other. SSS, SAS, ASA, RHS are congruence conditions for triangles.
全等：形状与大小完全相同的图形；一个可与另一个完全重合。SSS、SAS、ASA、RHS是三角形的全等判定条件。
Similar: Shapes that have the same shape but different sizes; corresponding angles are equal and sides are in proportion. Enlargement preserves similarity.
相似：形状相同但大小不同的图形；对应角相等且边长成比例。放缩变换保持相似性。
Polygon: A closed 2D shape with straight sides. Regular polygons have all sides and angles equal. Examples: pentagon (5), hexagon (6), octagon (8).
多边形：由直线段围成的封闭二维图形。正多边形所有边和角均相等。示例：五边形（5边）、六边形（6边）、八边形（8边）。
Circle Theorem: Rules relating angles within a circle. For instance, the angle in a semicircle is always 90°; angles in the same segment are equal.
圆定理：圆内角度关系规则。例如：半圆上的圆周角始终为90°；同弧上的圆周角相等。
Tangent: A straight line that touches a circle at exactly one point. The radius to the point of tangency is perpendicular to the tangent.
切线：与圆恰好相交于一点的直线。过切点的半径垂直于切线。
6. Trigonometry Terms | 三角学术语
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle. It is always the side opposite the 90° angle.
斜边：直角三角形中最长的边，位于直角对面。它永远是对着90°角的边。
Opposite and Adjacent: In a right-angled triangle, for a given acute angle, the opposite side is the side across from it; the adjacent side is the side next to the angle that is not the hypotenuse.
对边与邻边：在直角三角形中，对于给定的锐角，对边是正对该角的边；邻边是紧挨该角且不是斜边的边。
Sine (sin) triangle, the ratio of the opposite side to the hypotenuse. sin θ = opposite / hypotenuse.
正弦（sin）：直角三角形中对边与斜边的比。sin θ = 对边 / 斜边。
Cosine (cos): The ratio of the adjacent side to the hypotenuse. cos θ = adjacent / hypotenuse.
余弦（cos）：邻边与斜边的比。cos θ = 邻边 / 斜边。
Tangent (tan) osite side to the adjacent side. tan θ = opposite / adjacent. Also equal to sin θ / cos θ.
正切（tan）：对边与邻边的比。tan θ = 对边 / 邻边。也等于 sin θ / cos θ。
Angle of Elevation: The angle measured upwards from the horizontal line to the line of sight when looking at an object above.
仰角：从水平线向上测量到视线的夹角，当观察上方物体时。
Angle of Depression: The angle measured downwards from the horizontal to the line of sight when looking at an object below.
俯角：从水平线向下测量到视线的夹角，当观察下方物体时。
Sine Rule n-right-angled triangles, especially when given two angles and a side or two sides and a non-included angle.
正弦定理：a / sin A = b / sin B = c / sin C。用于非直角三角形，特别是已知两角一边或两边及一对角时。
Cosine Rule hree sides and one angle; used when given two sides and the included angle or three sides.
余弦定理：a² = b² + c² - 2bc cos A。联系三边与一角；用于已知两边及夹角或三边时。
7. Mensuration Terms | 计量术语
Perimeter: The total distance around the outside of a 2D shape. For a rectangle, P = 2(l + w).
周长：二维图形外边界总长度。对于长方形，P = 2(长 + 宽)。
Area sured in square units. Rectangle area = length x width; triangle area = ½ x base x height.
面积：二维图形内部的表面积，以平方单位计量。长方形面积 = 长 x 宽；三角形面积 = ½ x 底 x 高。
Volume : The space occupied by a 3D object, measured in cubic units. Cuboid volume = length x width x height.
体积：三维物体所占空间，以立方单位计量。长方体体积 = 长 x 宽 x 高。
Surface Area: The total area of all the faces of a 3D solid. For a cylinder, it is 2πr² + 2πrh.
表面积：三维立体所有面的总面积。对于圆柱体，表面积为2πr² + 2πrh。
Arc Length mference of a circle. Arc length = (θ/360) x 2πr, where θ is the central angle in degrees.
弧长：沿圆周长某一段的距离。弧长 = (θ/360) x 2πr，其中θ是圆心角的度数。
Sector Area: The area of a 'pizza slice' of a circle. Sector area = (θ/360) x πr².
扇形面积：圆形中“比萨切片”的面积。扇形面积 = (θ/360) x πr²。
Prism: A 3D solid with a uniform cross-section. Its volume = area of cross-section x length.
棱柱：具有均匀横截面的三维立体。其体积 = 横截面积 x 长度。
Pyramid lygonal base and triangular faces that meet at an apex. Volume = 1/3 x base area x height.
棱锥：具有多边形底和交汇于顶点的三角形侧面的三维图形。体积 = 1/3 x 底面积 x 高。
8. Statistics Terms | 统计术语
Mean: The average of a set of numbers, calculated by summing all values and dividing by the count. It is sensitive to outliers.
平均数（均值）：一组数值的平均值，通过总和除以个数计算。易受极端值影响。
Median: The middle value when data is arranged in ascending order. For an even number of values, it is the average of the two middle numbers.
中位数：将数据按升序排列后位于中间的值。若数值个数为偶数，则为中间两数的平均值。
Mode: The value that appears most frequently in a data set. A set may have no mode, one mode (unimodal), or more than one mode.
众数：数据集中出现频率最高的值。一组数据可能没有众数、一个众数（单峰）或多个众数。
Range fference between the largest and smallest values in a data set. Range = maximum - minimum.
极差（范围）：衡量离散度的量；数据集中最大值与最小值的差。极差 = 最大值 - 最小值。
Quartiles: Values that divide an ordered data set into four equal parts. Q₁ is the lower quartile (25th percentile), Q₂ is median, Q₃ is upper quartile (75th percentile).
四分位数：将有序数据集分为四等份的数值。Q₁为下四分位数（第25百分位），Q₂为中位数，Q₃为上四分位数（第75百分位）。
Interquartile Range (IQR) ween the upper and lower quartiles; IQR = Q₃ - Q₁. It measures the spread of the middle 50% of data.
四分位距 (IQR)：上四分位数与下四分位数的差；IQR = Q₃ - Q₁。衡量中间50%数据的离散度。
Frequency: The number of times a data value occurs. A frequency table lists values alongside their frequencies.
频数：某个数据值出现的次数。频数表将数值与其频数一同列出。
Histogram: A bar chart where the area of each bar represents the frequency, and the width of the bar is proportional to the class interval. For equal widths, height shows frequency.
直方图：一种条形图，其中每条的面积表示频数，条宽与组距成比例。若组距相等，高度表示频数。
Cumulative Frequency: A running total of frequencies up to a certain value. The cumulative frequency curve (ogive) is used to estimate medians and quartiles.
累积频数：截至某一数值的频数累计。累积频数曲线（折线）用于估计中位数和四分位数。
9. Probability Terms | 概率术语
Probability Scale: A number line from 0 to 1, where 0 represents impossible, 1 represents certain, and 0.5 represents an even chance.
概率标度：一条从0到1的数轴，0代表不可能，1代表必然，0.5代表均等机会。
Sample Space: The set of all possible outcomes of an experiment. For tossing two coins, the sample space is {HH, HT, TH, TT}.
样本空间：一次试验所有可能结果的集合。抛两枚硬币，样本空间为{HH, HT, TH, TT}。
Event: A set of one or more outcomes from the sample space. Rolling an even number on a die is an event {2, 4, 6}.
事件：样本空间中一个或多个结果的集合。掷骰子出现偶数是事件{2, 4, 6}。
Mutually Exclusive Events t : Events that cannot happen at the same time. For mutually exclusive A and B, P(A or B) = P(A) + P(B).
互斥事件：不可能同时发生的事件。对于互斥的A和B，P(A或B) = P(A) + P(B)。
Independent Events es : Events where the outcome of one does not affect the outcome of the other. For independent A and B, P(A and B) = P(A) x P(B).
独立事件：一个事件的结果不影响另一个事件的结果。对于独立的A和B，P(A且B) = P(A) × P(B)。
Conditional Probability: The probability that event A occurs given that event B has already occurred, written as P(A|B). It is calculated by P(A and B) / P(B).
条件概率：在事件B已发生的条件下事件A发生的概率，记为P(A|B)。由P(A且B) / P(B)计算。
Tree Diagram: A branching diagram used to show all possible outcomes of multiple events, with probabilities written on branches. Multiply along branches and add across outcomes.
树形图：用于展示多个事件所有可能结果的分支图，分支上标注概率。沿分支相乘，结果间相加。
10. Graphs and Functions | 图形与函数
Function written as f(x) = 2x + 5. The x is the independent variable, y is the dependent variable.
函数：每个输入 (x) 恰好对应一个输出 (y) 的关系。常写作 f(x) = 2x + 5。x是自变量，y是因变量。
Domain he : The set of all possible input values (x-values) for which a function is defined. For f(x) = √x, the domain is x ≥ 0.
定义域：函数有定义的所有可能输入值（x值）的集合。对于f(x) = √x，定义域为x ≥ 0。
Range ssible output values (y-values) a function can produce. For f(x) = x², the range is y ≥ 0.
值域：函数可产生的所有可能输出值（y值）的集合。对于f(x) = x²，值域为y ≥ 0。
Gradient (Slope) calculated as rise / run or change in y / change in x. For y = mx + c, m is the gradient.
斜率（坡度）：衡量直线倾斜程度，计算为垂直增量/水平增量，即y的变化量/x的变化量。对于y = mx + c，m是斜率。
y-intercept: The point where a line or curve crosses the y-axis. In y = mx + c, c is the y-intercept.
y轴截距：直线或曲线与y轴相交的点。在y = mx + c中，c是y轴截距。
Turning Point: A point on a graph where the curve changes direction from increasing to decreasing (maximum) or decreasing to increasing (minimum). The vertex of a parabola is its turning point.
转折点：图上曲线从递增变为递减（极大值）或从递减变为递增（极小值）的点。抛物线的顶点即转折点。
Asymptote urve approaches but never touches. The graph of y = 1/x has asymptotes at x = 0 and y = 0.
渐近线：曲线无限接近但永不触及的直线。y = 1/x的图像在x = 0和y = 0处有渐近线。
Exponential Function: A function of the form y = aˣ, where a > 0 and a is not 1. Growth or decay is rapid; e.g., y = 2ˣ shows exponential growth.
指数函数：形式为y = aˣ的函数，其中a > 0且a ≠ 1。增长或衰减极为快速；如y = 2ˣ呈指数增长。
11. Vectors and Transformations | 向量与变换
Vector: A quantity that has both magnitude (size) and direction, often represented by a column matrix or bold letters. The vector from A to B is written as AB⃗.
向量：既有大小（量值）又有方向的量，常用列矩阵或粗体字母表示。从A到B的向量写作AB⃗。
Scalar: A quantity that has only magnitude, no direction, e.g., speed, distance, mass. Scalars are used to multiply vectors, changing their size.
标量：只有大小没有方向的量，如速率、距离、质量。标量用于与向量相乘，以改变其大小。
Resultant Vector: The single vector that results from adding two or more vectors. Use the triangle or parallelogram law to find it.
合向量：两个或多个向量相加所得的单一向量。用三角形法则或平行四边形法则求解。
Translation: A transformation that moves every point of a shape the same distance in the same direction. Described by a vector, e.g., (3, -2).
平移：将图形每一点沿相同方向移动相同距离的变换。用向量描述，如(3, -2)。
Rotation: A turn of a shape about a fixed point (centre of rotation) through a given angle and direction. Clockwise rotation of 90° is common.
旋转：绕固定点（旋转中心）将图形转动给定角度和方向的变换。顺时针旋转90°常见。
Reflection a line (mirror line). The line y = x, y = -x, x-axis, and y-axis are typical mirror lines.
反射（轴对称）：关于一条直线（镜线）的镜像。直线y = x、y = -x、x轴和y轴是常见的镜线。
Enlargement: A transformation that changes the size of a shape by a scale factor from a centre of enlargement. If scale factor k > 1, the shape gets larger; if 0 < k < 1, it shrinks.
放缩：以放缩中心为基点，按比例因子改变图形大小的变换。若k > 1，图形变大；若0 < k < 1，图形缩小。
Magnitude of a Vector: The length or size of a vector, found using Pythagoras' theorem. For vector v = (a, b), |v| = √a² + b².
向量的模（大小）：向量的长度或大小，用毕达哥拉斯定理求得。对于向量v = (a, b)，|v| = √a² + b²。
12. Exam Tips for Memorising Key Terms | 考试术语记忆技巧
Flashcards: Write the term on one side and a concise definition with an example on the reverse. Review them daily in short bursts. Use digital apps like Anki if you prefer.
抽认卡：一面写术语，另一面写简洁定义和示例。每天短时多次复习。喜欢数字化可选用Anki等应用。
Mnemonic Devices: Create acronyms or silly sentences. For trigonometry, 'SOH CAH TOA' elps recall sin = Opposite/Hypotenuse, cos = Adjacent/Hypotenuse, tan = Opposite/Adjacent.
记忆术：创造首字母缩略词或荒诞句子。三角学中“SOH CAH TOA”助记正弦对/斜、余弦邻/斜、正切对/邻。
Active Recall: Instead of just re-reading notes, close the book and try to write out the definitions and draw diagrams from memory. Check accuracy afterwards.
Published by TutorHao | Year 11 Mathematics Revision Series | aleveler.com
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