📚 Year 11 Eduqas Maths Vocabulary Quick-Memorisation Guide | 数学词汇术语速记指南
Mastering mathematical vocabulary is a key step to success in the Year 11 Eduqas GCSE exam. When you understand the exact meaning of terms, you can interpret questions correctly, follow methods logically and communicate your reasoning clearly. This guide pairs essential terms with concise definitions, memory aids and Chinese translations, so you can build a bilingual maths glossary that sticks.
在 Year 11 Eduqas GCSE 数学考试中，精准掌握词汇术语是成功的关键。当你准确理解每个词汇的含义，就能正确解读题目、有条理地执行解题步骤并清晰表达推理过程。本指南将核心术语配上简明定义、记忆窍门和中文翻译，帮助你建立牢固的双语数学词汇表。
1. Number and Arithmetic | 数与算术
Integer: A whole number that can be positive, negative or zero, with no fractional or decimal part. Think ‘integer’ sounds like ‘intact’ – a number that stays whole.
整数：可以是正数、负数或零的完整数字，没有小数或分数部分。可以联想‘整’就是完整无缺的意思，不破碎。
Rational number: Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. The word ‘rational’ contains ‘ratio’ – it is all about ratios of integers.
有理数：能写成 a/b（a 和 b 为整数，b ≠ 0）形式的数。‘有理’可以谐音‘有比’，强调它总可以表示为两个整数之比。
Irrational number: A number that cannot be expressed as a simple fraction; its decimal expansion is non‑terminating and non‑repeating, like π or √2. ‘Ir‑’ means ‘not’, so it is ‘not rational’.
无理数：不能表达为简单分数的数，小数部分无限不循环，例如 π 和 √2。‘无’表示否定，即‘不是有理数’。
Prime number: A whole number greater than 1 that has exactly two distinct factors: 1 and itself. Remember that 2 is the only even prime.
质数（素数）：大于 1 且只有两个不同因数的整数，即 1 和它本身。特别记住 2 是唯一的偶质数。
Factor: A whole number that divides exactly into another number without leaving a remainder. A quick check: if you multiply the factor by another integer you get the original number.
因数（因子）：能整除另一个数的整数，没有余数。检验方法：将这个因数乘以某个整数，能否得到原数。
Square root (√): A value that, when multiplied by itself, gives the original number. The symbol √ is a radical sign; √9 = 3 because 3² = 9.
平方根（√）：一个数与自己相乘后得到原数。符号 √ 是根号；√9 = 3，因为 3² = 9。
2. Algebraic Expressions | 代数表达式
Variable: A symbol, usually a letter such as x or y, that represents an unknown or changeable number. Think of it as a ‘varying’ value.
变量：通常用字母如 x、y 表示未知或可改变的数。可以联想‘变化’的量。
Coefficient: The numerical factor that multiplies a variable in a term. In 5x, 5 is the coefficient; it tells you how many times the variable is taken.
系数：项中乘以变量的数因数。在 5x 中，5 是系数，表示变量的数量倍数。
Expression: A combination of numbers, variables and operation signs (+, −, ×, ÷) without an equals sign. For example, 3a + 2b − 7.
表达式：由数字、变量和运算符号组合而成，没有等号。如 3a + 2b − 7。
Expand: To multiply out brackets and simplify. Often you use the distributive law: a(b + c) = ab + ac. Think ‘expand’ = ‘spread out’ the product.
展开：将括号乘开并化简。常用分配律 a(b + c) = ab + ac。可以联想‘展开’就是把乘积像扇子一样打开。
Factorise: The reverse of expanding: writing an expression as a product of its factors. Pull out the highest common factor first whenever possible.
因式分解：展开的逆过程，将表达式写成因数乘积。优先提取最大公因数，就像把公共部分提出来。
3. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement that two expressions are equal, shown by an equals sign (=). Solving it means finding the value(s) that make it true.
方程：含有等号、表示两式相等的陈述。解方程就是找出使等式成立的值。
Inequality: A statement that compares two expressions using symbols <, >, ≤, ≥ or ≠. Solutions often form a range rather than a single number.
不等式：使用 <、>、≤、≥ 或 ≠ 比较两个表达式的陈述。解通常是范围，而不是单一数值。
Solve: To find the unknown value(s) that satisfy an equation or inequality. Remember to perform the same operation on both sides to keep balance.
求解：找出使方程或不等式成立的未知数值。始终记住等式两边做相同运算，保持平衡。
Solution: The value (or set of values) that makes an equation or inequality true. Always check your solution by substituting it back.
解：使方程或不等式成立的值（或值的集合）。务必代入原式检验你的解。
Identity: An equation that is true for all values of the variable, often written with a triple bar (≡). For instance, x + x ≡ 2x for any x.
恒等式：对所有变量取值都成立的等式，常用三横线 ≡ 表示。例如 x + x ≡ 2x 对任意 x 都成立。
4. Sequences | 数列
Sequence: An ordered list of numbers or terms that follow a rule. Each number in the list is called a term.
数列：按照一定规则排列的一列数。列中的每一个数叫做项。
nth term: A formula that allows you to find any term in a sequence by substituting the position number n. For the sequence 3, 5, 7, 9, …, the nth term is 2n + 1.
第 n 项（通项公式）：通过代入位置编号 n 就能求出数列中任意一项的公式。如数列 3, 5, 7, 9, … 的通项是 2n + 1。
Arithmetic sequence: A sequence where the difference between consecutive terms is constant (common difference). Example: 4, 7, 10, 13, … with common difference 3.
等差数列：相邻两项的差为常数的数列。例：4, 7, 10, 13, …，公差是 3。
Geometric sequence: A sequence where each term is found by multiplying the previous term by a constant (common ratio). Example: 2, 6, 18, 54, … with common ratio 3.
等比数列：每一项都是前一项乘以常数（公比）得到的数列。例：2, 6, 18, 54, …，公比是 3。
Fibonacci sequence: A special sequence where each term is the sum of the two before it: 1, 1, 2, 3, 5, 8, … Think of ‘Fibonacci’ as two numbers adding up to the next.
斐波那契数列：每一项是前两项之和的特殊数列：1, 1, 2, 3, 5, 8, … 可以联想斐波那契就是‘累加’成下一个数。
5. Graphs and Functions | 图像与函数
Function: A special relationship where each input has exactly one output, often written as f(x). Think of it as a machine: you put in x, and out comes f(x).
函数：每个输入值恰好对应一个输出值的关系，常记作 f(x)。可以想象成一个机器：输入 x，就输出 f(x)。
Linear graph: A straight‑line graph whose equation can be written as y = mx + c. ‘Linear’ means ‘line‑like’ – it never curves.
一次函数图像：方程为 y = mx + c 的直线图像。‘线性’就是直线特性，绝不弯曲。
Gradient: A measure of the steepness of a line, calculated as rise/run or (change in y)/(change in x). On y = mx + c, m is the gradient.
斜率（坡度）：衡量直线陡峭程度的量，计算为 纵向变化/横向变化。在 y = mx + c 中，m 就是斜率。
y-intercept: The point where a graph crosses the y‑axis, when x = 0. In y = mx + c, c is the y‑intercept.
y 轴截距：图像与 y 轴相交的点，此时 x = 0。在 y = mx + c 中，c 就是 y 轴截距。
Parabola: The U‑shaped curve of a quadratic function (y = ax² + bx + c). Its name sounds like ‘para–bowl’ – think of a bowl shape that can open up or down.
抛物线：二次函数 y = ax² + bx + c 产生的 U 形曲线。名称‘抛物’可以联想抛出的物体轨迹，形状像碗，开口可朝上或朝下。
6. Geometry: Angles and Lines | 几何：角与线
Acute angle: An angle that measures between 0° and 90°. A cute little angle – sharp and small.
锐角：度数在 0° 到 90° 之间的角。可以联想‘锐’就是尖尖的小角。
Obtuse angle: An angle that measures between 90° and 180°. ‘Obtuse’ sounds like ‘ob‑too‑se’ – it is wider and ‘obtuse’ means blunt.
钝角：度数在 90° 到 180° 之间。‘钝’有笨重不尖锐的意思，角张得比较开。
Reflex angle: An angle that measures between 180° and 360°. A reflex is a ‘bending back’ – the angle is bent beyond a straight line.
优角（反角）：度数在 180° 到 360° 之间。‘反射’有折回的意思，角超过了直线，像回弯了。
Supplementary angles: Two angles that add up to 180°. Use ‘S’ for straight line – supplementary angles form a straight angle together.
补角：两个角的和为 180°。可以借助‘补’联想到补成一条直线（平角）。
Vertically opposite angles: When two lines intersect, the angles directly across from each other are equal. They share a vertex and are opposite.
对顶角：两直线相交时，相对的两个角相等。它们共用一个顶点且位置相对，因此‘对顶’互相对着。
Corresponding angles: When a transversal crosses parallel lines, the angles in matching corners are equal. Think of them as ‘copies’ in the same position.
同位角：一条截线穿过平行线时，处于相同位置角落的角相等。可以联想‘同位’就是在同一个位置上，像复制拷贝。
7. Geometry: Polygons and Circles | 几何：多边形与圆
Polygon: A closed 2D shape with straight sides. The word comes from ‘poly‑’ (many) and ‘‑gon’ (angles). Triangle, quadrilateral, pentagon are all polygons.
多边形：由直线段围成的封闭二维图形。‘多边’意味着多条边，三角形、四边形、五边形都是多边形。
Regular polygon: A polygon where all sides and all interior angles are equal. A square is a regular quadrilateral, an equilateral triangle is a regular triangle.
正多边形：所有边等长且所有内角相等的多边形。正方形是正四边形，等边三角形是正三角形。
Quadrilateral: Any polygon with exactly four sides. Common types include square, rectangle, parallelogram, trapezium and kite.
四边形：有且仅有四条边的多边形。常见类型有正方形、长方形、平行四边形、梯形和风筝形。
Circle: The set of all points in a plane that are a fixed distance (radius) from a centre. The boundary is called the circumference.
圆：平面内到定点（圆心）的距离等于定长（半径）的所有点的集合。这个边线称为圆周。
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。从圆心到切点的半径垂直于切线。
Sector: The region enclosed by two radii and an arc, like a slice of pizza. The angle between the radii is the sector angle.
扇形：由两条半径和一条弧围成的区域，就像一块比萨饼。两条半径之间的角就是扇形角。
8. Measures: Perimeter, Area and Volume | 测量：周长、面积与体积
Perimeter: The total distance around the outside of a 2D shape. Simply add all the side lengths; for a circle it is called circumference.
周长：二维图形外边界的总长度。把所有边长加起来；圆的周界称为圆周。
Area: The amount of space inside a 2D shape, measured in square units (cm², m²). Think of covering the shape with unit squares and counting them.
面积：二维图形内部空间的大小，单位为平方单位（cm², m²）。可以想象用单位正方形铺满图形再计数。
Volume: The amount of space a 3D solid occupies, measured in cubic units (cm³, m³). For prisms, volume = cross‑sectional area × length.
体积：三维立体所占空间的大小，单位为立方单位（cm³, m³）。对于棱柱，体积 = 横截面积 × 长度。
Prism: A 3D shape with a constant cross‑section along its length. Both ends are identical polygons. Cylinders are a special type of prism with circular cross‑section.
棱柱（柱体）：沿长度方向横截面保持不变的立体。两端是全等的多边形。圆柱是具有圆形横截面的特殊柱体。
Surface area: The total area of all faces (or surfaces) of a 3D object. For a cube of side a, surface area = 6a². Unfold the net in your mind.
表面积：三维物体所有面（或曲面）的总面积。边长为 a 的立方体，表面积 = 6a²。想象把立体拆成展开图就容易理解。
9. Ratio, Proportion and Rates of Change | 比、比例与变化率
Ratio: A way to compare two or more quantities, showing the relative size. Written as a : b or in simplest form. Order matters – 1:2 is very different from 2:1.
比：比较两个或多个量相对大小的方法，写作 a : b 并化为最简。顺序很重要，1:2 和 2:1 天差地别。
Proportion: A statement that two ratios are equal. If a/b = c/d, then the quantities are in proportion. Cross‑multiplying helps to check.
比例：表明两个比相等的陈述。若 a/b = c/d，则这些量成比例。可用交叉相乘来验证。
Direct proportion: A relationship where two quantities increase (or decrease) at the same rate. If y is directly proportional to x, we write y ∝ x, so y = kx.
正比例：两个量以相同速率增大（或减下）的关系。若 y 与 x 成正比，记作 y ∝ x，即 y = kx。
Percentage: A fraction with denominator 100; ‘per cent’ means ‘out of a hundred’. Use multipliers such as 1.25 for a 25 % increase.
百分比：分母为 100 的分数，‘百分之’意思就是每一百份中的数量。计算增减时可使用乘数，如增长 25 % 用 1.25。
Scale factor: The number that all lengths of an original shape are multiplied by to produce an enlarged or reduced similar shape. Enlargements can be fractional for reduction.
比例因子（缩放倍率）：原图形所有长度乘以该数得到相似扩大或缩小图形。缩小用小于 1 的分数。
10. Statistics: Averages and Spread | 统计：平均与离散
Mean: The sum of all data values divided by the number of values. Often called the ‘average’, but it is just one type. Think ‘mean’ = ‘fair share’ if you split everything equally.
平均数（均值）：所有数据值之和除以数据个数。通常说的‘平均’多指均值，可联想成把总量平均分配。
Median: The middle value when the data is placed in order. For an odd‑sized list, it’s the centre item; for an even‑sized list, take the mean of the two middle numbers.
中位数：数据排序后位于正中的值。奇数个数据时取正中项；偶数个数据时取中间两项的均值。
Mode: The value that appears most often. A dataset can have one mode (unimodal), more than one (multimodal) or none at all. Think ‘mode = most’.
众数：出现次数最多的数据值。可以有单一众数、多个众数或没有。可以联‘众’就是人多势众，出现频率最高。
Range: The difference between the largest and smallest data values. It is a simple measure of spread. Range = max − min.
极差（范围）：数据最大值与最小值的差。它是衡量离散程度最简便的指标，极差 = 最大值 − 最小值。
Interquartile range (IQR): The range of the middle 50 % of data, found as upper quartile (Q₃) minus lower quartile (Q₁). IQR ignores extreme outliers.
四分位距（IQR）：位于中间 50 % 数据的范围，即上四分位数 (Q₃) 减下四分位数 (Q₁)。IQR 不受极端离群值影响。
11. Statistics: Data Representation | 统计：数据表示
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