📚 Year 7 OCR Mathematics: Vocabulary & Terminology Quick Guide | Year 7 OCR 数学：词汇术语速记指南
Mastering mathematical vocabulary is the first step to success in Year 7 OCR Mathematics. This quick guide provides clear English definitions alongside Chinese translations for every essential term, helping you build confidence and fluency in both languages.
掌握数学词汇是学好七年级 OCR 数学的第一步。本速记指南为每一个关键术语提供了清晰的英文定义和中文翻译，帮助你在双语环境下建立信心、提升流利度。
1. Number Basics | 数字基础
An integer is any whole number, including zero, positive and negative numbers like −5, 0, 12. A positive number is greater than zero, written with or without a '+' sign. A negative number is less than zero and always written with a '−' sign. On a number line, negatives lie to the left of zero, positives to the right.
整数 (Integer) 包括零、正整数和负整数，例如 −5、0、12。正数 (Positive number) 大于零，可带 '+' 号或不带。负数 (Negative number) 小于零，必须带 '−' 号。在数轴 (Number line) 上，负数位于零的左侧，正数位于右侧。
A digit is a single symbol from 0 to 9. Place value tells us the worth of a digit based on its position: in 427, the 4 means four hundreds. Whole numbers are non‑negative integers (0, 1, 2, …), while natural numbers start from 1. Ordering numbers uses symbols <, > and =.
数字 (Digit) 是 0–9 的单个符号。位值 (Place value) 取决于位置：在 427 中，4 表示 400。整数 (Whole number) 是非负整数，自然数 (Natural number) 从 1 开始。数字大小比较使用 <、> 和 =。
2. Factors, Multiples and Primes | 因数、倍数与质数
A factor divides a number exactly, leaving no remainder. The highest common factor (HCF) is the largest factor shared by two or more numbers. A multiple is obtained by multiplying a number by an integer; the lowest common multiple (LCM) is the smallest positive multiple shared by numbers.
因数 (Factor) 能整除一个数。最大公因数 (HCF) 是几个数共有的最大因数。倍数 (Multiple) 由该数乘整数得到；最小公倍数 (LCM) 是共有的最小正倍数。
A prime number has exactly two distinct factors: 1 and itself (e.g., 2, 3, 5, 7). A composite number has more than two factors. Prime factors are factors that are prime, and we find them using a factor tree. The number 1 is neither prime nor composite.
质数 (Prime number) 只有两个不同的因数：1 和它本身（如 2、3、5、7）。合数 (Composite number) 有超过两个因数。质因数 (Prime factor) 是质数的因数，可用因数树 (Factor tree) 找出。数字 1 既不是质数也不是合数。
3. Fractions, Decimals and Percentages | 分数、小数与百分比
A fraction represents part of a whole. The numerator (top) shows how many parts we have; the denominator (bottom) shows the total equal parts. A proper fraction has a numerator smaller than the denominator; an improper fraction has a numerator equal to or larger than the denominator. A mixed number combines a whole number and a proper fraction.
分数 (Fraction) 表示整体的一部分。分子 (Numerator) 在上方，分母 (Denominator) 在下方。真分数 (Proper fraction) 分子小于分母；假分数 (Improper fraction) 分子大于或等于分母；带分数 (Mixed number) 由整数和真分数组成。
Equivalent fractions have the same value; you simplify by dividing numerator and denominator by their HCF. A decimal uses a decimal point to show tenths, hundredths, etc. Converting a fraction to a decimal uses numerator ÷ denominator. A percentage is a number out of 100, symbol %.
等价分数 (Equivalent fractions) 值相等，化简 (Simplify) 需分子分母同除 HCF。小数 (Decimal) 用小数点表示十分位、百分位，分数转小数用分子 ÷ 分母。百分比 (Percentage) 表示每百分之几，符号为 %。
4. Algebraic Expressions | 代数表达式
In algebra, variables (letters) stand for unknown numbers. A term is a single number, variable or product like 5y. The coefficient is the number part (in 5y, 5 is the coefficient). A constant is a term without a variable. An expression is a combination of terms and operations, e.g., 3x + 2 − y.
代数中，变量 (Variable) 用字母表示未知数。项 (Term) 是单个数字、字母或乘积，如 5y。系数 (Coefficient) 是项的数字部分。常数 (Constant) 不含变量。表达式 (Expression) 由项和运算组成，如 3x + 2 − y。
Like terms have identical variable parts (e.g., 4a and 7a) and can be simplified by adding or subtracting the coefficients. Substitution means replacing a variable with a given number and working out the value.
同类项 (Like terms) 变量部分相同（如 4a 和 7a），可通过加减系数合并。代入 (Substitution) 是用数值替换变量并计算出结果。
5. Solving Equations | 解方程
An equation is a statement that two expressions are equal; it has an equals sign. The unknown is the variable we aim to find. To solve an equation, we use inverse operations: addition ↔ subtraction, multiplication ↔ division. The balance method keeps the equation equal by performing the same operation on both sides. The solution is the value that makes the equation true.
方程 (Equation) 表示两个表达式相等，包含等号。未知数 (Unknown) 是我们要求解的变量。求解 (Solve) 方程需使用逆运算 (Inverse operations)：加 ↔ 减，乘 ↔ 除。天平法 (Balance method) 通过在等式两边进行相同运算来保持平衡。解 (Solution) 是使方程成立的数值。
6. Geometry: Shapes and Angles | 几何：图形与角度
A polygon is a closed 2D shape with straight sides. A triangle has 3 sides; a quadrilateral has 4 sides. Special quadrilaterals include: square (4 equal sides, 4 right angles), rectangle (opposite sides equal, 4 right angles), parallelogram (opposite sides parallel), rhombus (4 equal sides, opposite angles equal) and trapezium (at least one pair of parallel sides). A regular polygon has all sides and angles equal.
多边形 (Polygon) 是由直线边围成的封闭二维图形。三角形 (Triangle) 有 3 条边；四边形 (Quadrilateral) 有 4 条边。特殊四边形包括：正方形 (Square)（四边相等、四个直角）、长方形 (Rectangle)（对边相等、四个直角）、平行四边形 (Parallelogram)（对边平行）、菱形 (Rhombus)（四边相等、对角相等）和梯形 (Trapezium)（至少一对平行边）。正多边形 (Regular polygon) 各边各角均相等。
An angle measures a turn and is given in degrees (°). Acute angles are < 90°; a right angle is exactly 90°; an obtuse angle is between 90° and 180°; a straight angle is 180°; a reflex angle is > 180° but < 360°. Angles are classified by size.
角 (Angle) 度量旋转量，单位为度 (°)。锐角 (Acute) 小于 90°；直角 (Right angle) 等于 90°；钝角 (Obtuse) 在 90° 至 180° 之间；平角 (Straight angle) 为 180°；优角 (Reflex) 大于 180° 且小于 360°。
7. Symmetry and Transformations | 对称与变换
Line symmetry (or reflection symmetry) means one half of a shape mirrors the other. The line of symmetry is the fold line. Rotational symmetry occurs when a shape looks the same after a turn of less than 360°. The order of rotational symmetry is the number of times it matches itself in a full turn.
线对称 (Line symmetry) 指图形一半可以镜像另一半，对称轴 (Line of symmetry) 即折叠线。旋转对称 (Rotational symmetry) 指旋转小于 360° 后与原图重合。旋转对称的阶 (Order) 指旋转一周重合的次数。
A reflection flips a shape over a mirror line; a translation slides a shape without turning or flipping; a rotation turns a shape around a fixed centre. Two shapes are congruent if they have the same size and shape, even if rotated or flipped.
反射 (Reflection) 沿镜面翻转图形；平移 (Translation) 移动位置而不旋转翻转；旋转 (Rotation) 绕定点转动。若两图形形状大小相同（不论是否旋转或翻转），则它们全等 (Congruent)。
8. Measures and Units | 度量与单位
Metric units for length: millimetre (mm), centimetre (cm), metre (m), kilometre (km). For mass: gram (g) and kilogram (kg). For capacity ). Relationships: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m; 1 kg = 1000 g; 1 l = 1000 ml.
公制长度单位：毫米 (mm)、厘米 (cm)、米 (m)、千米 (km)。质量单位：克 (g)、千克 (kg)。容量单位：毫升 (ml)、升 (l)。换算：1 cm = 10 mm，1 m = 100 cm，1 km = 1000 m；1 kg = 1000 g；1 l = 1000 ml。
Perimeter is the total distance around a 2D shape, found by adding all side lengths. Area is the amount of space inside a shape, measured in square units (cm², m²). For rectangles, area = length × width. Volume is the space a 3D object occupies, measured in cubic units (cm³, m³).
周长 (Perimeter) 是二维图形边界的总长，将各边长相加。面积 (Area) 是图形内部区域的大小，单位为平方单位 (cm², m²)。长方形面积 = 长 × 宽。体积 (Volume) 是三维物体占据的空间，单位为立方单位 (cm³, m³)。
9. Statistics Basics | 统计基础
Data is a collection of facts or numbers. The mean is the average: sum of values ÷ number of values. The median is the middle value when data
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