📚 Year 7 OCR Further Maths: Key Vocabulary Quick-Memorisation Guide | Year 7 OCR 进阶数学：词汇术语速记指南
Mastering mathematical vocabulary is a powerful tool – it unlocks word problems, clarifies explanations, and boosts confidence during tests. In OCR Year 7 Further Mathematics, you will encounter a rich set of terms from number theory, algebra, geometry and statistics. This guide pairs each key term with its meaning and a simple memory hook, helping you build a bilingual bridge between English terminology and Chinese understanding. Read the English definition, then the Chinese equivalent, and watch your fluency grow.
掌握数学词汇就像拿到一把万能钥匙——它能帮你破解文字题、让解释更清晰，并在考试中增强信心。在 OCR Year 7 进阶数学中，你会遇到来自数论、代数、几何和统计的大量术语。本指南把每个核心术语与释义和简单记忆法配对，帮你架起英文术语和中文理解之间的双语桥梁。先读英文定义，再看中文对应，你的数学语言流利度会明显提升。
1. Number and Place Value | 数字与位值
Numbers are the building blocks of mathematics. Year 7 extends your understanding of integers, place value, and special number sets. Every digit has a position, and every position has a power of ten. Recognising these terms helps you read, write and manipulate numbers with precision.
数字是数学的基石。Year 7 加深你对整数、位值以及特殊数集的理解。每个数字都有一个位置，每个位置代表十的幂。识别这些术语能帮助你精确地读、写和处理数字。
Integer: A whole number that can be positive, negative or zero, e.g. -3, 0, 42. Think of "integral" pieces – no fractions allowed.
整数：可以是正数、负数或零的完整数字，如 -3、0、42。记住“完整”的部分——不含分数。
Digit: Any of the symbols 0, 1, 2, ... 9 used to write numerals. The number 507 has three digits.
数字（数码）：用来书写数的符号 0 到 9 中的一个。507 有三个数码。
Place value: The value of a digit based on its position. In 3.14, the digit 1 represents 1 tenth (10⁻¹).
位值：数码根据位置所拥有的值。在 3.14 中，数码 1 表示十分之一 (10⁻¹)。
Rounding: Rewriting a number to a given degree of accuracy. 37 rounded to the nearest 10 is 40.
四舍五入：按给定精度重写一个数。37 舍入到最近的十是 40。
Significant figure (s.f.): Each digit that carries meaning contributing to precision. 0.305 has three significant figures.
有效数字：对精确度有实际意义的每一个数码。0.305 有三个有效数字。
Prime number: A number greater than 1 with exactly two distinct factors, 1 and itself. 2, 3, 5, 7, 11 are primes.
素数（质数）：大于 1 且只有两个不同的因数（1 和它本身）的数。2、3、5、7、11 都是素数。
Composite number: A positive integer that has more than two factors. 8 is composite because it can be divided by 1, 2, 4, 8.
合数：有多于两个因数的正整数。8 是合数，因为它可以被 1、2、4、8 整除。
Factor: A whole number that divides exactly into another number. Factors of 12 are 1,2,3,4,6,12.
因数：能整除另一个数的整数。12 的因数有 1, 2, 3, 4, 6, 12。
Multiple: The product of a number and any integer. Multiples of 6 are 6, 12, 18, 24, ...
倍数：一个数与任意整数的乘积。6 的倍数有 6、12、18、24……
Square number The result when an integer is multiplied by itself. 49 is a square number because 7² = 49.
平方数：整数自乘的结果。49 是平方数，因为 7² = 49。
Cube number A number formed by multiplying an integer by itself twice. 64 is a cube number (4³ = 64).
立方数：整数自乘两次得到的数。64 是立方数（4³ = 64）。
Square root: A value that, when squared, gives the original number. √25 = 5.
平方根：平方后得到原数的值。√25 = 5。
Cube root: A value that, when cubed, gives the original number. ∛27 = 3.
立方根：立方后得到原数的值。∛27 = 3。
2. Algebra Essentials | 代数基础
Algebra uses letters and symbols to represent numbers and relationships. In OCR Further Maths, you start manipulating expressions, forming equations, and using substitution. Learning the vocabulary early prevents confusion when instructions say "expand" or "factorise".
代数使用字母和符号表示数字与关系。在 OCR 进阶数学中，你会开始操作表达式、建立方程并运用代入法。及早学会这些词汇，可以避免听到“展开”或“因式分解”时手忙脚乱。
Variable: A symbol, usually a letter, that represents an unknown or changing number. In 3x + 5, x is the variable.
变量：一个符号，通常是字母，代表未知或变化的数。在 3x + 5 中，x 是变量。
Coefficient: The number multiplying a variable. In 7y, 7 is the coefficient.
系数：与变量相乘的数字。在 7y 中，7 是系数。
Term: A single number, variable, or the product of numbers and variables. 2x², -5 and 3xy are all terms.
项：一个单独的数、变量，或数与变量的乘积。2x²、-5 和 3xy 都是项。
Expression: A combination of terms with operations but no equals sign. 4a + 2b - 7 is an expression.
表达式：由项和运算符号组合而成、没有等号的式子。4a + 2b - 7 是一个表达式。
Equation al statement that two expressions are equal, using the sign =. 3x - 2 = 10 is an equation.
方程：用等号表明两个表达式相等的数学陈述。3x - 2 = 10 是一个方程。
Like terms: Terms that contain the same variable raised to the same power. 2x and 5x are like terms; 2x and 2x² are not.
同类项：含有相同变量且相同指数的项。2x 和 5x 是同类项；2x 和 2x² 不是。
Simplify: To rewrite an expression in its most compact form, usually by collecting like terms. 2x + 3x simplifies to 5x.
化简：将表达式改写成最紧凑的形式，通常通过合并同类项。2x + 3x 化简为 5x。
Expand: To multiply out brackets. Expanding 3(x + 4) gives 3x + 12.
展开：将括号乘开。展开 3(x + 4) 得到 3x + 12。
Factorise: To insert brackets by taking out common factors. Factorising 6x + 9 gives 3(2x + 3).
因式分解：提取公因数后插入括号。对 6x + 9 进行因式分解得到 3(2x + 3)。
Substitution: Replacing a variable with a given number. If y = 4, then 3y + 1 becomes 13.
代入：用给定数值替换变量。如果 y = 4，则 3y + 1 变为 13。
Formula itten with symbols, often used to calculate a value. A = lw gives the area of a rectangle.
公式：用符号写出的规则，常用于计算值。A = lw 给出长方形的面积。
3. Fractions, Decimals and Percentages | 分数、小数与百分数
Fractions, decimals and percentages are three ways to express parts of a whole. In Year 7 you compare, convert and calculate with all three forms. Knowing the precise terms helps you switch confidently between formats.
分数、小数和百分数是表示部分与整体关系的三种方式。Year 7 中你需要对这三种形式进行比较、互化和计算。掌握精确术语能让你在三者之间自信转换。
Numerator: The top part of a fraction, showing how many parts we have. In ⅜, 3 is the numerator.
分子：分数的上部，表示有多少份。在 ⅜ 中，3 是分子。
Denominator: The bottom part of a fraction, showing the total number of equal parts. In ⅜, 8 is the denominator.
分母：分数的下部，表示总共分成的等份数。在 ⅜ 中，8 是分母。
Equivalent fractions: Fractions that represent the same amount. ½ = ²⁄₄ = ⁴⁄₈.
等值分数：表示相同数量的分数。½ = ²⁄₄ = ⁴⁄₈。
Simplest form: A fraction where the numerator and denominator have no common factor except 1. ⁴⁄₆ in simplest form is ⅔.
最简形式：分子和分母除了 1 以外没有其他公因数的分数。⁴⁄₆ 的最简形式是 ⅔。
Mixed number: A whole number combined with a fraction. 2½ is a mixed number.
带分数：一个整数与一个分数组合。2½ 是一个带分数。
Improper fraction: A fraction where the numerator is larger than or equal to the denominator. ⁷⁄₄ is improper.
假分数：分子大于或等于分母的分数。⁷⁄₄ 是假分数。
Decimal: A number written with a decimal point, based on tenths, hundredths, etc. 0.75 is a decimal.
小数：用小数点写出的数字，基于十分位、百分位等。0.75 是小数。
Percentage: A fraction out of 100, shown by the symbol %. 45% means 45 out of 100.
百分数：以 100 为分母的分数，用符号 % 表示。45% 表示百分之四十五。
Conversion: Changing between forms. 0.2 = 20% = ⅕.
转换：在形式之间变化。0.2 = 20% = ⅕。
Percentage change: The increase or decrease expressed as a percentage of the original amount. If a £50 item becomes £60, the percentage increase is 20%.
百分比变化：以原值为基数，用百分比表示的增减量。若 50 英镑的物品变为 60 英镑，则百分比增加为 20%。
4. Geometry: Shapes and Angles | 几何：图形与角度
Geometry is the study of shapes, sizes, positions and angles. OCR Year 7 extends into classifying polygons, recognising angle facts and using coordinate grids. Precise language helps you describe properties without ambiguity.
几何学研究形状、大小、位置和角度。OCR Year 7 课程扩展到多边形分类、角度规律识别以及坐标网格的运用。精确的语言能让你毫无歧义地描述图形性质。
Point: An exact location, represented by a dot, with no size.
点：一个精确位置，用点表示，没有大小。
Line: A straight one-dimensional figure that extends infinitely in both directions.
直线：两端无限延伸的一维图形。
Line segment: A part of a line with two endpoints.
线段：有两个端点的直线一部分。
Ray: A part of a line that starts at an endpoint and extends infinitely in one direction.
射线：从一个端点开始向一个方向无限延伸的线的部分。
Angle: The space between two intersecting lines, measured in degrees (°).
角：两条相交直线之间的空间，以度 (°) 为单位。
Acute angle: An angle less than 90°.
锐角：小于 90° 的角。
Right angle: An angle of exactly 90°, shown by a small square.
直角：恰好 90° 的角，用小方格标记。
Obtuse angle: An angle between 90° and 180°.
钝角：大于 90° 小于 180° 的角。
Reflex angle: An angle greater than 180° but less than 360°.
优角：大于 180° 且小于 360° 的角。
Parallel lines: Lines in a plane that never meet, always the same distance apart.
平行线：同一平面内永不相交、距离始终相等的直线。
Perpendicular lines: Lines that intersect at a right angle (90°).
垂直线：相交成直角 (90°) 的直线。
Polygon: A closed 2D shape with straight sides. Triangles, quadrilaterals and pentagons are polygons.
多边形：由直线段构成的封闭二维图形。三角形、四边形和五边形都是多边形。
Regular polygon: A polygon with all sides equal and all angles equal. A square is regular.
正多边形：所有边等长且所有角相等的多边形。正方形是正四边形。
Congruent: Shapes that are exactly the same size and shape, though they may be rotated or reflected.
全等：大小和形状完全相同，即使经过旋转或反射的图形。
Symmetry: A property where one half is a mirror image of the other half (reflective symmetry) or looks the same after a rotation (rotational symmetry).
对称：一半是另一半的镜像（反射对称），或旋转后与原图形重合（旋转对称）。
5. Measurement and Units | 测量与单位
Measurement connects numbers to the real world through length, mass, capacity and time. Year 7 demands fluency with metric units, conversions and compound measures. Mastering the terms ensures you choose the correct unit and interpret questions accurately.
测量借助长度、质量、容量和时间把数字与现实世界连接起来。Year 7 要求熟练掌握公制单位、单位换算和复合单位。掌握术语能确保你选对单位并准确理解题意。
Length: The measurement of something from end to end. Common units: mm, cm, m, km.
长度：物体从一端到另一端的测量量。常用单位：毫米 (mm)、厘米 (cm)、米 (m)、千米 (km)。
Mass: The amount of matter in an object, often called weight in everyday language. Units: g, kg.
质量：物体所含物质的量，日常常称重量。单位：克 (g)、千克 (kg)。
Capacity: The amount a container can hold. Units: mL, L.
容量：容器能容纳的量。单位：毫升 (mL)、升 (L)。
Perimeter: The total distance around the outside of a 2D shape. For a rectangle: P = 2(l + w).
周长：二维图形外部边界总长度。长方形周长：P = 2(l + w)。
Area : The amount of surface a 2D shape covers, measured in square units. A = l × w for a rectangle.
面积：二维图形表面覆盖的大小，以平方单位计量。长方形面积 A = l × w。
Volume: The space taken up by a 3D object, measured in cubic units. V = l × w × h for a cuboid.
体积：三维物体所占空间，以立方单位计量。长方体体积 V = l × w × h。
Surface area: The total area of all faces of a 3D shape.
表面积：三维图形所有面的总面积。
Conversion factor multiplier used to change units. 1 km = 1000 m, so to convert 3 km to m, multiply by 1000.
换算因子：改变单位时使用的乘数。1 km = 1000 m，将 3 km 转换为米需乘以 1000。
Compound unit: A unit that combines two or more basic units, e.g. km/h for speed, m² for area.
复合单位：由两个或更多基本单位组合而成的单位，如速度单位 km/h、面积单位 m²。
6. Statistics: Data Handling | 统计：数据处理
Statistics is about collecting, organising and interpreting data. You will learn to calculate averages, draw charts and spot trends. Using the correct statistical language helps you present a clear argument and avoid common mistakes.
统计是关于收集、整理和解读数据。你将学习计算平均数、绘制图表并发现趋势。使用正确的统计语言有助于清晰论证、避开常见错误。
Data: A collection of facts, numbers or measurements. Can be categorical (colours) or numerical (heights).
数据：事实、数字或测量值的集合。可以是类别数据（如颜色），也可以是数值数据（如身高）。
Survey: A method of collecting data by asking questions.
调查：通过提问收集数据的方法。
Frequency: How often something appears. A frequency table records tallies and counts.
频数：某个项目出现的次数。频数表记录划记与计数。
Mean : The average found by adding all values and dividing by the number of values. Mean of 2, 3, 7 is (2+3+7)÷3 = 4.
平均数（均值）：将所有数值相加除以数值个数得到的平均值。2、3、7 的均值为 (2+3+7)÷3 = 4。
Median: The middle value when data is ordered. Median of 1, 3, 8 is 3.
中位数：数据排序后的中间值。1、3、8 的中位数为 3。
Mode: The most frequent value. In 2, 2, 5, 7, 7, 7, the mode is 7.
众数：出现频率最高的值。在 2, 2, 5, 7, 7, 7 中，众数为 7。
Range: The difference between the largest and smallest values. Range of 3, 7, 9 is 9 - 3 = 6.
极差：最大值与最小值之差。3、7、9 的极差为 9 - 3 = 6。
Bar chart: A graph with rectangular bars where the height represents frequency. Bars are separated for categorical data.
条形图：用矩形条高度表示频数的图形。类别数据条形之间有空隙。
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