📚 Year 11 Cambridge Mathematics: Key Terminology Quick Guide | 词汇术语速记指南
Mastering mathematical vocabulary is essential for success in Year 11 Cambridge Mathematics. This quick guide provides clear English and Chinese explanations of key terms across all major topics, helping you remember them faster and apply them confidently in exams.
掌握数学词汇是 Year 11 剑桥数学成功的关键。本速记指南覆盖所有主要话题，提供核心术语的清晰中英文释义，助你快速记忆并在考试中自信运用。
1. Number | 数字
Integer: A whole number that can be positive, negative, or zero.
整数：可以是正数、负数或零的完整数字。
Prime number: A number greater than 1 that has exactly two distinct factors: 1 and itself.
质数：大于 1 且只有两个不同因数（1 和它本身）的数。
Square root: The value that, when multiplied by itself, gives the original number; denoted by the symbol √.
平方根：一个数自乘后等于原数的值，用符号 √ 表示。
Rational number: Any number that can be expressed as a fraction a/b, where a and b are integers and b ≠ 0.
有理数：可以表示为分数 a/b 的数，其中 a、b 为整数且 b ≠ 0。
Significant figures: The digits in a number that carry meaning contributing to its precision, counting from the first non-zero digit.
有效数字：从一个数第一个非零数字开始计算的、反映其精确度的有意义数字。
Standard form: A way of writing very large or very small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
标准形式：将极大或极小的数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10 且 n 为整数。
2. Algebra | 代数
Variable: A symbol, usually a letter, that represents an unknown or changeable value.
变量：一个符号（通常是字母），表示未知或可变的值。
Coefficient: The numerical factor multiplying a variable in a term; for example, in 3x, 3 is the coefficient.
系数：项中与变量相乘的数字因子；例如在 3x 中，3 是系数。
Expression: A combination of numbers, variables, and operation symbols without an equals sign.
表达式：由数字、变量和运算符号组成的式子，不含等号。
Like terms: Terms that have exactly the same variable part raised to the same power; only coefficients differ.
同类项：变量及其指数完全相同的项，只有系数不同。
Expand: To multiply out brackets in an algebraic expression, e.g., a(b + c) = ab + ac.
展开：将代数表达式中的括号乘开，如 a(b + c) = ab + ac。
Factorise: The reverse process of expanding; to write an expression as a product of its factors.
因式分解：展开的逆过程，将一个表达式写成其因子的乘积。
3. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement that asserts the equality of two expressions, connected by an equals sign ‘=’.
方程：用等号 ‘=’ 连接、表示两个表达式相等的数学陈述。
Inequality: A relation that compares two expressions using symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
不等式：使用符号 <（小于）、>（大于）、≤（小于或等于）、≥（大于或等于）比较两个表达式的关系。
Solve: To find the value(s) of the variable that make an equation or inequality true.
求解：找出使方程或不等式成立的变量的值。
Linear equation: An equation where the variable appears only to the power of 1, producing a straight-line graph, e.g., y = mx + c.
线性方程：变量指数为 1 的方程，图像是一条直线，如 y = mx + c。
Quadratic equation: An equation of the form ax² + bx + c = 0, where a ≠ 0, and the highest power of the variable is 2.
二次方程：形如 ax² + bx + c = 0 的方程，其中 a ≠ 0，变量的最高次幂为 2。
Simultaneous equations: A set of two or more equations with the same variables that are solved together.
联立方程组：含有相同变量的两个或多个方程，需一起求解。
4. Graphs and Functions | 图像与函数
Function: A special relationship where each input (x) has exactly one output (y), often written as f(x).
函数：一种特殊关系，每个输入 (x) 恰好对应一个输出 (y)，常写作 f(x)。
Gradient: A measure of the steepness of a line, calculated as (change in y)/(change in x).
斜率：衡量直线倾斜程度的量，计算公式为 (y 的变化量)/(x 的变化量)。
Intercept: The point where a line or curve crosses one of the axes. The y-intercept is where it crosses the y-axis.
截距：直线或曲线与坐标轴的交点。y 轴截距是与 y 轴的交点。
Parabola: The symmetrical U-shaped graph of a quadratic function y = ax² + bx + c.
抛物线：二次函数 y = ax² + bx + c 的对称 U 形图像。
Asymptote: A line that a curve approaches arbitrarily closely but never actually touches.
渐近线：曲线无限接近但永不真正触及的直线。
Coordinate: A pair of numbers (x, y) that uniquely locate a point on a plane.
坐标：唯一确定平面上一点的一对数字 (x, y)。
5. Geometry | 几何
Right angle: An angle that measures exactly 90°.
直角：恰好等于 90° 的角。
Parallel lines: Lines in a plane that are always the same distance apart and never meet, often marked with arrows.
平行线：平面上始终等距、永不相交的直线，常用箭头标记。
Perpendicular lines: Lines that intersect at a right angle (90°).
垂直线：相交时形成直角 (90°) 的直线。
Congruent: Two shapes are congruent if they are identical in size and shape, even if one is rotated or reflected.
全等：两个图形在大小和形状上完全相同，即使其中一个经过旋转或反射。
Similar: Shapes that have the same shape but different sizes; corresponding angles are equal and corresponding sides are in proportion.
相似：形状相同但大小不同的图形；对应角相等，对应边成比例。
Pythagoras’ theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².
勾股定理：在直角三角形中，斜边的平方等于两直角边的平方和：a² + b² = c²。
6. Mensuration | 测量
Perimeter: The total distance around the boundary of a two-dimensional shape.
周长：围绕二维图形边界线的总长度。
Area: The amount of surface enclosed within a 2D shape, measured in square units.
面积：二维图形内部表面的大小，以平方单位计量。
Volume: The amount of three-dimensional space occupied by a solid, measured in cubic units.
体积：三维立体所占空间的大小，以立方单位计量。
Surface area: The total area of all the outer faces of a 3D solid.
表面积：三维立体所有外表面的总面积。
Prism: A 3D shape with a constant cross-section along its length, such as a triangular prism or cylinder.
棱柱：沿其长度方向横截面不变的三维形状，如三棱柱或圆柱。
Compound shape: A shape made up of two or more simpler shapes; its area or perimeter is found by summing or subtracting parts.
复合图形：由两个或多个简单图形组成的形状；其面积或周长通过部分相加或相减求得。
7. Trigonometry | 三角学
Sine (sin): In a right-angled triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse.
正弦 (sin)：直角三角形中，一个角的对边长度与斜边长度之比。
Cosine (cos): The ratio of the adjacent side to the hypotenuse.
余弦 (cos)：邻边与斜边之比。
Tangent (tan): The ratio of the opposite side to the adjacent side; also equals sin/cos.
正切 (tan)：对边与邻边之比，也等于 sin/cos。
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。
Angle of elevation: The angle formed between the horizontal line and the upward line of sight to an object.
仰角：水平线与向上观察物体的视线之间形成的角。
Angle of depression: The angle between the horizontal line and the downward line of sight to an object.
俯角：水平线与向下观察物体的视线之间形成的角。
8. Statistics | 统计
Mean: The arithmetic average of a data set, calculated by summing all values and dividing by the number of values.
平均数：数据集的算术平均值，用所有数据之和除以数据个数计算。
Median: The middle value when data is arranged in ascending order; for an even number of values, it is the mean of the two middle numbers.
中位数：将数据按升序排列后的中间值；若数据个数为偶数，则为中间两个数的平均值。
Mode: The value that appears most frequently in a data set.
众数：数据集中出现次数最多的值。
Range: A measure of spread, calculated as the difference between the largest and smallest values.
极差：衡量数据分散程度的量，等于最大值与最小值的差。
Interquartile range (IQR): The difference between the upper quartile (Q3) and lower quartile (Q1), representing the spread of the middle 50% of data.
四分位距 (IQR)：上四分位数 (Q3) 与下四分位数 (Q1) 之差，表示中间 50% 数据的离散程度。
Frequency: The number of times a particular value or event occurs in a data set.
频数：特定数值或事件在数据集中出现的次数。
9. Probability | 概率
Experiment: A repeatable process with a well-defined set of possible outcomes, such as tossing a coin.
试验：有明确定义的可能结果集的可重复过程，如抛硬币。
Outcome: A single possible result of a probability experiment.
结果：概率试验的一个可能结果。
Event: A set of one or more outcomes, often described as something we are interested in happening.
事件：一个或多个结果的集合，常描述为我们关心是否发生的情形。
Sample space: The set of all possible outcomes of an experiment, often denoted by S.
样本空间：试验所有可能结果的集合，常用 S 表示。
Independent events: Two events are independent if the occurrence of one does not affect the probability of the other occurring.
独立事件：如果一件事的发生不影响另一件事发生的概率，则这两个事件独立。
Mutually exclusive events: Events that cannot happen at the same time; if one occurs, the other cannot.
互斥事件：不可能同时发生的事件；一个发生，另一个就不会发生。
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