📚 Year 10 Cambridge Maths: Vocabulary & Terminology Quick Memorisation Guide | 十年级剑桥数学：词汇术语速记指南
Mastering mathematical language is the first step to excelling in your Cambridge IGCSE Year 10 Maths. This guide breaks down the essential terms topic by topic, pairing each English term with its Chinese equivalent and clear definitions. Use this as your quick-reference cornerstone for homework, revision, and exam confidence.
掌握数学语言是在剑桥IGCSE十年级数学中取得优异成绩的第一步。本指南按主题梳理核心术语，将每条英文术语与对应的中文释义和清晰定义配对。你可以把它当作快速查阅的基石，用于作业、复习和增强考试信心。
1. Algebra Essentials | 代数基础术语
Algebra uses symbols to represent numbers and relationships. Getting these building blocks right makes all future topics easier to grasp.
代数用符号表示数字和关系。掌握这些基础构件会让你今后学习任何主题都更轻松。
Variable: A letter (like x, y or n) that stands for a number we do not yet know. In 4x + 7, x is the variable.
变量：用一个字母（如 x、y 或 n）代表尚未知道的数。在 4x + 7 中，x 就是变量。
Constant: A fixed value that does not change. In 5y − 3, the number −3 is a constant.
常数：一个固定不变的数值。在 5y − 3 中，数 −3 就是常数。
Coefficient: The number that multiplies a variable. In 2a, the coefficient of a is 2; in −k it is −1.
系数：乘以变量的那个数。在 2a 中，a 的系数是 2；在 −k 中，系数是 −1。
Term: A single number, variable or combination of both multiplied together. E.g., 7, 3ab and −4x² are terms.
项：一个单独的数、变量或者两者相乘的组合。例如 7、3ab 和 −4x² 都是项。
Expression: A collection of terms connected by + or − signs, without an equals sign. E.g., 3x² + 2x − 5.
表达式：由加号或减号连接的一组项，没有等号。如 3x² + 2x − 5。
Equation: A statement that two expressions are equal, containing an '=' sign. E.g., 4x − 1 = 11.
方程：说明两个表达式相等的陈述，包含等号“=”。如 4x − 1 = 11。
Identity: An equation that is true for all values of the variable, often written with ≡. E.g., (x+1)² ≡ x²+2x+1.
恒等式：对变量的所有取值都成立的等式，常写作 ≡。如 (x+1)² ≡ x²+2x+1。
2. Equations and Inequalities | 方程与不等式
This section focuses on statements that compare values. Knowing the precise wording helps you interpret and solve problems correctly.
本节聚焦于比较数值的陈述。精确掌握这些措辞能帮助你正确理解并解题。
Solution / Root: alue(s) of the variable that make the equation true. For x + 3 = 7, the solution is x = 4.
解 / 根：使方程成立的变量的值。对于 x + 3 = 7，解为 x = 4。
Linear equation: : An equation where the variable has an exponent of 1, forming a straight line when graphed. E.g., 2x + 3 = 9.
线性方程：变量的指数为 1 的方程，其图像是一条直线。如 2x + 3 = 9。
Quadratic equation: An equation containing x² as the highest power. General form: ax² + bx + c = 0.
二次方程：含有 x² 作为最高次幂的方程。一般形式：ax² + bx + c = 0。
Quadratic formula: For ax² + bx + c = 0, the solutions are x = (−b ± √b² − 4ac) / 2a.
二次公式：对于 ax² + bx + c = 0，解为 x = (−b ± √b² − 4ac) / 2a。
Inequality: showing that one quantity is less than or greater than another, using symbols <, >, ≤, ≥.
不等式：表明一个量小于或大于另一个量的陈述，使用符号 <、>、≤、≥。
Simultaneous equations: A set of two or more equations with the same variables, solved together to find common solutions.
联立方程组：一组含有相同变量的两个或多个方程，需一并求解找出共同的解。
Discriminant: In a quadratic, b² − 4ac. It tells about the nature of the roots: positive for two real roots, zero for one repeated root, and negative for no real roots.
判别式：二次方程中的 b² − 4ac。它揭示根的性质：正数有两个实根，零有一个重根，负数无实根。
3. Number Types and Operations | 数的类型与运算
Understanding number classifications is fundamental. These terms appear in almost every topic, from fractions to directed numbers.
理解数的分类是基础中的基础。从分数到有向数，这些术语几乎出现在每个课题中。
Natural number: Counting numbers starting from 1: {1, 2, 3, ...}.
自然数：从 1 开始的计数数：{1, 2, 3, ...}。
Integer: Any whole number that is positive, negative or zero. E.g., −3, 0, 14.
整数：任何正整数、负整数或零。如 −3、0、14。
Rational number: A number that can be written as a fraction a/b where a and b are integers and b ≠ 0. E.g., ½, 0.75, −4.
有理数：可以写成分数 a/b 且 a、b 为整数、b ≠ 0 的数。如 ½、0.75、−4。
Irrational number: A number that cannot be expressed as a simple fraction. Its decimal goes on forever without repeating. E.g., π, √2.
无理数：无法表示为简单分数的数，小数部分无限不循环。如 π、√2。
Real number: All rational and irrational numbers together; any number on the number line.
实数：所有有理数和无理数的总称；数轴上的任何数。
Prime number: An integer greater than 1 that has exactly two factors: 1 and itself. E.g., 2, 3, 5, 7, 11.
质数 / 素数：大于 1 且恰好只有 1 和自身两个因数的整数。如 2、3、5、7、11。
Factor: A number that divides another exactly without leaving a remainder. 3 is a factor of 12.
因数 / 因子：能整除另一个数而不留余数的数。3 是 12 的因数。
Multiple: The product of a number and any integer. 20 is a multiple of 5.
倍数：一个数与任意整数的乘积。20 是 5 的倍数。
HCF (Highest Common Factor): The largest factor shared by two or more numbers. The HCF of 8 and 12 is 4.
最大公因数 (HCF)：两个或多个数共有的最大因数。8 和 12 的最大公因数是 4。
LCM (Lowest Common Multiple): The smallest multiple shared by two or more numbers. The LCM of 6 and 8 is 24.
最小公倍数 (LCM)：两个或多个数共有的最小倍数。6 和 8 的最小公倍数是 24。
4. Geometry Basics: Lines, Angles and Polygons | 几何基础：线、角和多边形
Geometry has a language all its own. These definitions are the gateway to angle theorems, congruence and circle properties.
几何有自己的一套语言。这些定义是学习角定理、全等及圆性质的入口。
Point: An exact location in space, usually labelled with a capital letter, e.g., P.
点：空间中的一个精确位置，通常用大写字母标注，如 P。
Line segment: A part of a line with two endpoints, e.g., AB.
线段：直线上两点之间的部分，有两个端点，如 AB。
Ray: A line with one endpoint that extends infinitely in one direction.
射线：有一个端点并向一个方向无限延伸的线。
Parallel lines: Lines in a plane that never meet; they remain the same distance apart. Symbol: ∥.
平行线：平面上永不相交的直线，它们之间的距离始终相等。符号：∥。
Perpendicular lines: Lines that intersect at a right angle (90°). Symbol: ⊥.
垂直线：以直角（90°）相交的直线。符号：⊥。
Acute angle: An angle greater than 0° and less than 90°.
锐角：大于 0° 且小于 90° 的角。
Right angle: An angle exactly equal to 90°.
直角：恰好等于 90° 的角。
Obtuse angle: An angle greater than 90° and less than 180°.
钝角：大于 90° 且小于 180° 的角。
Reflex angle: An angle greater than 180° and less than 360°.
优角 / 反角：大于 180° 且小于 360° 的角。
Complementary angles: Two angles that add up to 90°.
余角：和为 90° 的两个角。
Supplementary angles: Two angles that add up to 180°.
补角：和为 180° 的两个角。
Polygon: A closed flat shape with straight sides. Triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), etc.
多边形：由直线边组成的封闭平面图形。三角形（3边）、四边形（4）、五边形（5）、六边形（6）等。
5. Right‑Angled Triangles: Pythagoras and Trigonometry | 直角三角形：毕达哥拉斯与三角学
Right‑angled triangles introduce two huge tools: Pythagoras’ theorem for sides, and trigonometry for linking angles and sides.
直角三角形引入了两大工具：用于求边的毕达哥拉斯定理，以及将角和边联系起来的三角学。
Hypotenuse: The longest side of a right‑angled triangle, opposite the right angle.
斜边：直角三角形中最长的边，位于直角的对面。
Pythagoras' theorem: In a right‑angled triangle, a² + b² = c², where c is the hypotenuse.
毕达哥拉斯定理 / 勾股定理：在直角三角形中，a² + b² = c²，其中 c 是斜边。
Sine (sin θ): In a right‑angled triangle, sin θ = opposite / hypotenuse.
正弦 (sin θ)：在直角三角形中，sin θ = 对边 / 斜边。
Cosine (cos θ): cos θ = adjacent / hypotenuse.
余弦 (cos θ)：cos θ = 邻边 / 斜边。
Tangent (tan θ): tan θ = opposite / adjacent.
正切 (tan θ)：tan θ = 对边 / 邻边。
Angle of elevation: The angle formed between the horizontal line of sight and an upward direction to an object.
仰角：水平视线与向上看物体的方向之间形成的角。
Angle of depression: The angle between the horizontal and a downward line of sight.
俯角：水平线与向下看物体的视线之间形成的角。
6. Transformations | 变换
Transformations move or change shapes on a coordinate grid. Knowing the exact vocabulary helps you describe and perform these actions accurately.
变换能移动或改变坐标格上的图形。准确掌握这些词汇能让你精准描述和执行这些操作。
Translation: Sliding a shape without turning or flipping; described by a column vector (x over y). Every point moves the same distance in the same direction.
平移：不旋转、不翻转地滑动图形；用列向量 (x, y) 描述。每个点沿相同方向移动相同距离。
Reflection: Flipping a shape over a mirror line (line of reflection). The shape is reversed but keeps the same size and area.
反射 / 翻转：将图形沿镜线（反射线）翻转。图形反转但大小和面积不变。
Rotation: Turning a shape around a fixed point (centre of rotation) by a given angle and direction (clockwise or anti‑clockwise).
旋转：将图形绕一个定点（旋转中心）按给定的角度和方向（顺时针或逆时针）转动。
Enlargement: Resizing a shape by a scale factor from a centre of enlargement. A scale factor > 1 enlarges; between 0 and 1 reduces.
放缩 / 放大：通过一个放缩中心，按比例因子改变图形大小。比例因子 > 1 为放大，介于 0 和 1 之间为缩小。
Scale factor: The multiplier that tells how many times larger or smaller the image is compared to the original.
比例因子 / 缩放因子：表示像相较于原图放大或缩小倍数的乘数。
Invariant point: A point that does not move under a transformation. The centre of rotation and points on the mirror line can be invariant.
不变点：在变换下保持不动的点。旋转中心和镜线上的点可能是不变点。
7. Mensuration: Perimeter, Area and Volume | 测量：周长、面积与体积
These terms quantify the size of shapes and solids. Memorising them with their units will save you many marks.
这些术语用来量化平面图形和立体的大小。记住它们及其单位会让你少丢分。
Perimeter: The total distance around the outside of a 2D shape. Measured in cm, m, etc.
周长：围绕一个二维图形外部的总距离。单位用 cm、m 等。
Area: The amount of surface a shape covers. Measured in square units, e.g., cm², m².
面积：图形所覆盖的表面大小。单位用平方单位，如 cm²、m²。
Volume: The space occupied by a 3D solid. Measured in cubic units, e.g., cm³, m³.
体积 / 容积：三维立体所占的空间大小。单位用立方单位，如 cm³、m³。
Surface area: The total area of all faces of a 3D shape. A cube of side s has surface area 6s².
表面积：三维图形所有面的总面积。边长为 s 的立方体表面积为 6s²。
Prism: A 3D solid with a constant cross‑section. Volume = area of cross‑section × length.
棱柱：具有恒定横截面的立体。体积 = 横截面积 × 长。
Compound shape: A 2D shape made by combining two or more basic shapes. Area is found by splitting it into known parts.
复合图形：由两个或更多基本图形组合而成的二维图形。通过拆分成已知部分来求面积。
8. Statistics | 统计
Statistics is the science of collecting, organising and interpreting data. These core terms appear in every data‑handling exercise.
统计学是收集、整理和解读数据的科学。这些核心术语会出现在每一次数据处理练习中。
Mean: The sum of all data values divided by the number of values; often called the average.
平均数 / 均值：所有数据值的总和除以值的个数；常被称为平均值。
Median: The middle value when data is arranged in order. For an even number of values it is the mean of the two middle numbers.
中位数：将数据按顺序排列后位于中间的数值。偶数个数据时则为中间两个数的平均。
Mode: The value that occurs most frequently. A data set can have one mode, more than one mode (bimodal), or no mode.
众数：出现频率最高的数值。一组数据可以有一个众数、多个众数（双众数）或者没有众数。
Range: The difference between the largest and smallest values. Range = max − min.
极差 / 范围：最大值与最小值之间的差。极差 = 最大值 − 最小值。
Frequency: The number of times a particular value or event occurs.
频数 / 频率：某个特定值或事件发生的次数。
Histogram: A diagram that uses bars to display the frequency distribution of continuous data, where bar area represents frequency.
直方图：用条块展示连续数据频数分布的图，条块的面积表示频数。
Bar chart: A diagram with separate bars of equal width to represent categorical or discrete data. Bar height shows frequency.
条形图：用等宽且分开的条形表示分类或离散数据的图。条形高度表示频数。
Pie chart: A circular chart divided into sectors, where each sector's angle is proportional to the frequency it represents.
饼图 / 扇形图：分成扇形的圆形图，每个扇形的圆心角与其所代表的频数成正比。
9. Probability | 概率
Probability measures the chance of an event occurring. The precise language helps you avoid confusion between independent and dependent trials.
概率衡量事件发生的可能性。准确的语言能帮你避免混淆独立试验和相依试验。
Experiment / Trial: An action that produces a result, such as rolling a die or picking a card.
实验 / 试验：产生结果的行为，例如掷骰子或抽牌。
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