📚 Year 8 OCR Maths: Vocabulary & Terminology Quick-Reference Guide | Year 8 OCR 数学：词汇术语速记指南
Mastering the language of mathematics is just as important as solving the problems themselves. In Year 8 OCR Mathematics, a clear understanding of key terms can turn a confusing question into a straightforward task. This guide covers the essential vocabulary you need to know, organised by topic, with both English definitions and Chinese translations to support bilingual learners and reinforce memory through side‑by‑side explanations.
掌握数学的语言与解决问题本身同样重要。在 Year 8 OCR 数学课程中，清楚地理解关键术语能将令人困惑的问题变成简单的任务。本指南涵盖了你需要掌握的基本词汇，按主题分类，提供英文定义与中文译文，通过中英对照解释帮助双语学习者加深记忆。
1. Number Types & Place Value | 数字类型与位值
Integer: A whole number that can be positive, negative, or zero, with no fractional or decimal part.
整数： 可以是正数、负数或零的整数，没有分数或小数部分。
Negative number: A number less than zero, written with a minus sign (−) in front, e.g. −5.
负数： 小于零的数，前面写有负号 (−)，例如 −5。
Place value: The value of a digit depending on its position in a number, such as ones, tens, hundreds, or tenths, hundredths.
位值： 数字中某个数码根据其位置所具有的值，如个位、十位、百位，或十分位、百分位。
Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers.
数码： 用于书写数字的任一符号 0、1、2、3、4、5、6、7、8、9。
Rounding: Replacing a number with an approximate value that has fewer digits, often to a given place value or decimal place.
四舍五入 / 取整： 用一个位数较少且接近原数的近似值来代替原数，通常精确到指定的位值或小数位。
2. Fractions, Decimals & Percentages | 分数、小数与百分数
Fraction: A way of representing a part of a whole, written as a/b where a is the numerator and b is the denominator.
分数： 表示整体一部分的方式，写作 a/b，其中 a 是分子，b 是分母。
Equivalent fractions: Different fractions that represent the same value, e.g. 1/2 and 2/4.
等值分数： 表示相同数值的不同分数，例如 1/2 和 2/4。
Decimal: A number written with a decimal point to separate the whole part from the fractional part, e.g. 3.75.
小数： 用小数点分隔整数部分与小数部分的数，例如 3.75。
Percentage: A fraction expressed as a part of 100, using the symbol %, e.g. 25% means 25 out of 100.
百分数： 以 100 为分母的分数，用符号 % 表示，例如 25% 表示百分之二十五。
Terminating decimal: A decimal that has a finite number of digits after the decimal point, like 0.4 or 1.25.
有限小数： 小数点后数字位数有限的小数，如 0.4 或 1.25。
Recurring decimal: A decimal with a pattern of digits that repeats forever, often shown with a dot or bar notation, e.g. 0.\u03073 (meaning 0.333...).
循环小数： 数字模式无限重复的小数，常用点或杠表示，例如 0.\u03073 (即 0.333...)。
3. Algebraic Expressions | 代数表达式
Variable: A symbol, usually a letter, that represents an unknown or changeable number.
变量： 通常用字母表示未知或可变化数的符号。
Coefficient: The number multiplying a variable in an algebraic term, e.g. in 4x the coefficient is 4.
系数： 代数项中与变量相乘的数，例如在 4x 中系数是 4。
Term: A single number, variable, or product of numbers and variables separated by + or − signs, e.g. 5y or 3ab.
项： 单个数字、变量，或数字与变量的乘积，在表达式中由加号或减号分隔，如 5y 或 3ab。
Expression: A combination of terms without an equals sign, e.g. 3x + 2.
表达式： 不含等号的项的集合，例如 3x + 2。
Like terms: Terms that contain exactly the same variables raised to the same powers, only their coefficients may differ (e.g. 2x and −5x).
同类项： 含有完全相同变量且次数相同的项，只有系数可能不同 (例如 2x 和 −5x)。
Simplify: To combine like terms and perform arithmetic operations to make an expression as short as possible.
化简： 合并同类项并进行算术运算，使表达式尽可能简短。
4. Equations & Inequalities | 方程与不等式
Equation: hematical statement that two expressions are equal, shown by the = sign, e.g. 2x + 3 = 11.
方程： 用等号表示两个表达式相等的数学语句，例如 2x + 3 = 11。
Solution: The value of the variable that makes an equation true.
解： 使方程成立的变量的值。
Inverse operation: The operation that reverses the effect of another, e.g. addition and subtraction, or multiplication and division.
逆运算： 与原运算效果相反的运算，例如加法与减法，或乘法与除法。
Inequality: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
不等式： 用 < (小于)、> (大于)、≤ (小于等于)、≥ (大于等于) 等符号比较两个表达式的语句。
Balance method: Solving an equation by doing the same operation on both sides to keep it balanced.
平衡法： 通过对方程两边进行相同运算来求解，保持方程平衡。
5. Geometry: Lines & Angles | 几何：线与角
Acute angle: An angle measuring less than 90°.
锐角： 小于 90° 的角。
Obtuse angle: An angle measuring more than 90° but less than 180°.
钝角： 大于 90° 且小于 180° 的角。
Right angle: An angle of exactly 90°, often marked with a small square.
直角： 正好等于 90° 的角，通常用小方格标记。
Parallel lines: Lines that are always the same distance apart and never meet.
平行线： 始终等距且永不相交的直线。
Perpendicular lines: Lines that intersect at a right angle (90°).
垂直线： 相交成直角 (90°) 的直线。
Vertically opposite angles: Angles opposite each other when two lines cross; they are equal.
对顶角： 两条直线相交时相对的两个角，它们相等。
Angles on a straight line: The sum of angles on a straight line is 180°.
平角 / 直线上的角： 一条直线上的角之和为 180°。
6. Properties of 2D Shapes | 二维图形的性质
Polygon: A closed, flat shape with straight sides, e.g. triangle, quadrilateral, pentagon, hexagon.
多边形： 由直线段围成的封闭平面图形，如三角形、四边形、五边形、六边形。
Regular polygon: A polygon with all sides equal in length and all angles equal in size.
正多边形： 所有边等长、所有角相等的多边形。
Quadrilateral: A polygon with four sides. Special types include square, rectangle, rhombus, parallelogram, trapezium and kite.
四边形： 有四条边的多边形。特殊类型包括正方形、长方形、菱形、平行四边形、梯形和筝形。
Rotational symmetry: The number of times a shape looks exactly the same during a full 360° turn; the order of rotational symmetry.
旋转对称： 图形在旋转 360° 的过程中与自身重合的次数，即旋转对称的级数。
Line of symmetry: A line that divides a shape into two identical mirrored halves.
对称轴： 将图形分成两个镜像相同部分的直线。
7. Perimeter, Area & Volume | 周长、面积与体积
Perimeter: The total distance around the outside of a 2D shape.
周长： 二维图形外边线的总长度。
Area: The amount of surface inside a 2D shape, measured in square units (e.g. cm², m²).
面积： 二维图形内部表面的大小，以平方单位计量 (如 cm²、m²)。
Volume: The amount of space a 3D object occupies, measured in cubic units (e.g. cm³, m³).
体积： 三维物体所占空间的大小，以立方单位计量 (如 cm³、m³)。
Compound shape: A shape made by combining two or more simpler shapes; its area or perimeter is found by splitting it into known parts.
组合图形： 由两个或多个简单图形组合而成的图形；可通过拆分求面积或周长。
Prism: A 3D shape with a constant cross‑section along its length, e.g. triangular prism, cuboid.
柱体： 沿长度方向横截面保持不变的立体图形，如三棱柱、长方体。
8. Coordinates & Graphs | 坐标与图像
Coordinate plane (Cartesian plane): A grid defined by a horizontal x‑axis and a vertical y‑axis, used to locate points with pairs (x, y).
坐标平面 (笛卡尔平面)： 由水平 x 轴和垂直 y 轴构成的网格，用于用数对 (x, y) 确定点的位置。
Origin: The point (0, 0) where the x‑axis and y‑axis intersect.
原点： x 轴与 y 轴的交点 (0, 0)。
Quadrant: One of the four regions of the coordinate plane, numbered I to IV anticlockwise starting from the top right.
象限： 坐标平面被轴分成的四个区域，从右上角开始逆时针编号 I 至 IV。
Coordinates: An ordered pair (x, y) that shows a point's horizontal (x) and vertical (y) position.
坐标： 表示点水平位置 (x) 和垂直位置 (y) 的有序数对 (x, y)。
Linear graph: A straight‑ h representing a relationship with a constant rate of change, often written as y = mx + c.
线性图像： 表示变化率恒定的关系的直线图像，常写作 y = mx + c。
9. Ratio & Proportion | 比与比例
Ratio: A way of comparing two or more quantities, written with a colon, e.g. 3 : 2.
比： 比较两个或多个数量的一种方式，用冒号书写，例如 3 : 2。
Equivalent ratios: Ratios that can be simplified or scaled to the same basic form, e.g. 2 : 4 and 1 : 2 are equivalent.
等比： 可化简或放大为相同基本形式的比，例如 2 : 4 与 1 : 2 等价。
Proportion: A statement that two ratios are equal, often solved using cross multiplication or a unitary method.
比例： 表示两个比相等的陈述，常用交叉相乘法或归一法求解。
Direct proportion: A relationship where two quantities increase or decrease at the same rate; y ∝ x.
正比例： 两个量以相同速率增加或减少的关系；y ∝ x。
Scale factor: The number you multiply by to enlarge or reduce a shape or ratio while keeping the same proportions.
比例因子： 放大或缩小图形或比时所乘的数，保持比例不变。
10. Statistics & Probability | 统计与概率
Mean: The average found by adding all values and dividing by the number of values.
平均数 (均值)： 将所有数值相加再除以数值个数得到的平均值。
Median: The middle value when data is ordered from smallest to largest.
中位数： 将数据从小到大排序后位于中间的值。
Mode: The value that appears most frequently in a data set.
众数： 数据集中出现频率最高的值。
Range: The difference between the largest and smallest values in a data set, a measure of spread.
极差： 数据中最大值与最小值之差，衡量离散程度。
Probability: A measure of the likelihood of an event, expressed as a number between 0 (impossible) and 1 (certain), or as a fraction, decimal or percentage.
概率： 事件发生可能性的度量，用 0 (不可能) 到 1 (必然) 之间的数字表示，或以分数、小数、百分数表示。
Sample space: The set of all possible outcomes of an experiment, often shown in a list or diagram.
样本空间： 试验所有可能结果的集合，常用列表或图表表示。
11. Units & Measurements | 单位与度量
Metric units: Standard units of measurement based on multiples of ten, such as millimetre (mm), centimetre (cm), metre (m), kilometre (km), gram (g), kilogram (kg), millilitre (mL) and litre (L).
公制单位： 基于十进倍数的标准计量单位，如毫米 (mm)、厘米 (cm)、米 (m)、千米 (km)、克 (g)、千克 (kg)、毫升 (mL) 和升 (L)。
Conversion: Changing a measurement from one unit to another, e.g. 1 km = 1000 m, 1 m = 100 cm.
单位换算： 将度量从一种单位转换为另一种单位，例如 1 km = 1000 m，1 m = 100 cm。
Time intervals: The difference between two times expressed in hours, minutes and seconds; often calculated using 24‑hour clock notation.
时间差： 两个时刻之间的时长，以小时、分钟和秒表示；常用 24 小时制计算。
Speed: travelled per unit of time; often given in m/s or km/h. Formula: speed = distance ÷ time.
速度： 单位时间内移动的距离，常用 m/s 或 km/h 表示。公式：速度 = 距离 ÷ 时间。
12. Averages & Data Representation | 平均值与数据表示
Discrete data: Data that can only take certain values, often counts (e.g. number of students).
离散数据： 只能取特定值的数据，通常是计数结果 (如学生数)。
Continuous data: Data that can take any value within a range, usually measurements (e.g. height, time).
连续数据： 在某个范围内可任意取值的数据，通常是测量值 (如身高、时间)。
Bar chart: A graph using bars of equal width to show frequencies of categories; the height of each bar represents the frequency.
条形图： 用等宽条柱显示类别频数的图表；每根柱子的高度代表频数。
Pictogram: A chart using pictures or symbols to represent data, where each symbol stands for a certain number of items.
象形图： 用图片或符号表示数据的图表，每个符号代表一定数量的项目。
Pie chart: A circular chart divided into sectors, where the angle of each sector is proportional to the frequency it represents.
饼状图： 将圆分成扇形的图表，每个扇形的圆心角与其代表的频数成正比。
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