Year 8 OCR Further Maths: Quick Vocabulary and Terminology Guide | Year 8 OCR 进阶数学：词汇术语速记指南

📚 Year 8 OCR Further Maths: Quick Vocabulary and Terminology Guide | Year 8 OCR 进阶数学：词汇术语速记指南

Mastering mathematical vocabulary is like learning the grammar of a new language. This guide delivers a structured, bilingual approach to the key terms you will meet in Year 8 OCR Further Maths. By connecting each term with a clear definition, a useful example, and a memory tip, you can build a solid mental dictionary that will support problem-solving, reasoning, and exam success. Tackle the word bank section by section, and soon you will read, speak, and think mathematically with confidence.

掌握数学词汇就像学习一门新语言的语法。本指南采用结构化的双语方式，为你梳理 Year 8 OCR 进阶数学中会遇到的关键术语。每个术语都配有清晰的定义、实用的例子和记忆技巧，帮助你建立牢固的心理词典，提升解题能力、推理能力和考试成绩。逐节攻克这些词汇库，你很快就能自信地阅读、表达和思考数学问题。

1. Number Types and Sets | 数字类型与集合

Natural numbers are the counting numbers starting from 1: 1, 2, 3, … . They do not include zero, fractions, or decimals. Think 'nature's way' of counting whole objects.

自然数是从 1 开始的计数数字：1, 2, 3, … 。它不包括零、分数或小数。你可以联想“自然界中数数的方式”。

Integers are the set of whole numbers and their negatives, including zero: … , -2, -1, 0, 1, 2, … . The word 'integer' means 'whole' — no bits missing.

整数是全体正整数、负整数和零的集合：… , -2, -1, 0, 1, 2, … 。'integer'一词本身就带有“完整”的含义——没有零头。

Rational numbers can be written as a fraction of two integers, where the denominator is not zero. For example, ½, -3, 0.75 (which is ¾) are all rational. Remember the 'ratio' in rational.

有理数是可以写成两个整数之比的数，且分母不为零。例如 ½、-3、0.75 (即 ¾) 都是有理数。记住 rational 里藏着 'ratio' (比)。

Irrational numbers cannot be expressed as a simple fraction. Famous examples are the square root of 2 (√2) and π . Their decimal expansions go on forever without repeating — 'irrational' means 'not a ratio'.

无理数不能表示为简单的分数。著名的例子有 2 的平方根 √2 和 π。它们的小数展开无限不循环——'irrational' 就是“不是比”的意思。

Real numbers include all rational and irrational numbers; essentially every number you can place on a number line. 'Real' vs 'imaginary' — you only need real numbers for now.

实数包含所有有理数和无理数；基本上就是你能在数轴上标出的所有数。“实数”对应“虚数”——目前你只需掌握实数。

2. Prime Factorisation and Number Theory | 质因数分解与数论

A prime number is a whole number greater than 1 that has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11… are primes. Visualise a prime as a 'brick' that cannot be divided evenly by any smaller number except 1.

质数是大于 1 且恰好只有两个不同因数的整数：1 和它本身。2, 3, 5, 7, 11… 都是质数。可以把质数看作不可再分的“砖块”。

Composite numbers have more than two factors. 4, 6, 8, 9, 10 are all composite because they can be built by multiplying smaller primes together. The word 'composite' hints at 'composed of parts'.

合数拥有两个以上的因数。4, 6, 8, 9, 10 都是合数，因为它们可以由更小的质数相乘得到。'composite' 暗示它由“组合”而成。

Prime factorisation only. For example, 36 = 2² × 3². Use a factor tree to break the number down systematically — the leaves will all be primes.

质因数分解就是把一个数写成仅含质数的乘积形式。例如，36 = 2² × 3²。使用因数树将数字系统分解，末端的“叶子”全是质数。

Highest Common Factor (HCF) is the largest whole number that divides exactly into two or more numbers. For 24 and 36, the HCF is 12. Memorise: 'the biggest shareable block'.

最大公因数 (HCF) 是能同时整除两个或多个数的最大整数。对于 24 和 36，HCF 是 12。记住：它是“可分享的最大整块”。

Lowest Common Multiple (LCM) is the smallest number that is a multiple of two or more given numbers. For 4 and 6, the LCM is 12. Connecting picture: the first time their multiplication 'clocks' chime together.

最小公倍数 (LCM) 是两个或多个数共有的倍数中最小的一个。对于 4 和 6，LCM 是 12。想象成它们的“倍数时钟”第一次同时敲响的时刻。

Indices (powers or exponents) ultiplied by itself. In 5³, 3 is the index, meaning 5 × 5 × 5. The tiny raised number is a ‘super-shorthand’ for repeated multiplication.

指数（幂）表示一个基数自乘的次数。在 5³ 中，3 是指数，表示 5 × 5 × 5。这个小小的上标数字就是重复相乘的“超级缩写”。

3. Algebraic Expressions | 代数表达式

An algebraic expression , but no equals sign. 3x + 2, a² - 5ab, and 4(y - 1) are all expressions. Think of it as a 'recipe' that can take different values.

代数表达式是由数字、变量（字母）和运算符号 (+, -, ×, ÷) 组成但没有等号的数学短语。3x + 2, a² - 5ab, 4(y - 1) 都是表达式。可以把它看作一种可根据变量而变化的“配方”。

A term is each part of an expression separated by + or - signs. In 5x² + 3x - 7, the terms are 5x², 3x, and -7. 'Term' sounds like 'term-in-al' and marks one member of a little gang of addends.

项是表达式中由 + 或 - 号分隔的每个部分。在 5x² + 3x - 7 中，项是 5x², 3x 和 -7。可以把“项”想象成加法帮派的一位成员。

The coefficient is the number factor in front of a variable. In 7y, the coefficient is 7. It tells you how many copies of that variable you have — like a pack size.

系数是变量前面的数字因子。在 7y 中，系数是 7。它告诉你有多少份那个变量——就像一个包装盒的规格。

A constant is a term with no variable part; its value never changes. In 2x + 5, the number 5 is the constant. Picture it as the firm, unchanging foundation of the expression.

常数是没有变化部分的项；它的值永不改变。在 2x + 5 中，数字 5 就是常数。可以把它想象成表达式中稳固不变的基石。

Like terms have exactly the same variable raised to the same power; they can be combined. 4ab and -2ab are like terms, but 4ab and 4a²b are not. 'Like attracts like' when simplifying.

同类项具有完全相同的变量及其幂次；它们可以合并。4ab 和 -2ab 是同类项，但 4ab 和 4a²b 不是。化简时“物以类聚”。

Expand means to multiply out brackets to remove them. Expanding 3(b + 2) gives 3b + 6. Imagine the number outside 'high-fiving' each term inside.

展开是指通过乘法去掉括号。将 3(b + 2) 展开得到 3b + 6。想象括号外的数字依次与括号内的每一项“击掌”相乘。

Factorise is the reverse of expanding — inserting brackets by taking out a common factor. 6x + 9 factorises to 3(2x + 3). The trick is to ask: what is the biggest thing both terms share?

因式分解是展开的逆运算——通过提取公因数插入括号。6x + 9 分解为 3(2x + 3)。问自己：这两项能共享的最大东西是什么？

4. Equations and Inequalities | 方程与不等式

An equation states that two expressions are equal, using an equals sign '=' a balanced scale; whatever you do to one side, you must do to the other to keep it level.

方程用等号 '=' 表示两个表达式相等。2x + 3 = 11 是一个方程。它就像一个平衡的天平，对一边做的任何操作，必须在另一边做同样的操作以保持平衡。

A formula ip between different quantities. A = l × w gives the area of a rectangle. Think of it as a 'rule written in maths'.

公式是一类特殊的方程，展示了不同量之间的关系。A = l × w 给出了矩形面积。可以把它看作“用数学写成的规则”。

An identity is an equation that is true for all values of the variable, often written with the symbol '≡' (triple bar). For instance, a + a ≡ 2a. The triple bar triple-confirms it works every time.

恒等式是对变量所有取值都成立的等式，常用符号 '≡' 表示。例如，a + a ≡ 2a。三重等号“三重确认”它永远成立。

An inequality compares two expressions using symbols: less than "<", greater than ">", less than or equal to "≤", greater than or equal to "≥". The open side always faces the larger amount — like a hungry crocodile eating the bigger number.

不等式使用符号比较两个表达式：小于 "<", 大于 ">", 小于等于 "≤", 大于等于 "≥"。开口总是朝向较大的数——就像一头饥饿的鳄鱼要吃更大的数字。

Solving an equation (s) of the variable that make the equation true. For x + 5 = 9, the solution is x = 4. You 'isolate' the letter by performing inverse operations.

解方程就是找出使方程成立的变量值。对于 x + 5 = 9，解是 x = 4。通过逆运算将字母“隔离”出来。

5. Sequences and Patterns | 数列与规律

A sequence is an ordered list of numbers that follow a rule. 3, 6, 9, 12… is a sequence with a rule of 'add 3'. The commas show order, just like a queue follows a trail.

数列是按规则排列的有序数字列表。3, 6, 9, 12… 是一个数列，规则是“加 3”。逗号展示了顺序，就像排队前行的轨迹。

The term of a sequence refers to a number in the sequence, described by its position. The first term is often called T₁ or u₁. Position is power — know the number's place.

数列的项是指数列中的某个数字，由它的位置来描述。第一项通常记作 T₁ 或 u₁。位置就是力量——要知道数字的排位。

The nth term of a linear sequence is a formula that lets you find any term using its position n. For 5, 8, 11, 14… the nth term is 3n + 2. 'n' stands for 'number of the term', a direct ticket to any term without listing all previous ones.

线性数列的第 n 项公式可以让你利用位置 n 找到对应项。对于 5, 8, 11, 14…，第 n 项是 3n + 2。'n' 代表“项数编号”，是直达任意项的快捷票。

An arithmetic sequence changes by adding or subtracting a constant difference each time. 7, 10, 13, 16… has a common difference of +3. 'Arithmetic' here points to addition as the key engine.

等差数列通过每次加上或减去一个常数差值得到。7, 10, 13, 16… 的公差是 +3。这里的 'arithmetic' 提示加法是核心引擎。

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A geometric sequence changes by multiplying by a constant ratio each time. 2, 6, 18, 54… has a common ratio of ×3. 'Geo-metric' suggests multiplying by the same 'measure' each step.

等比数列通过每次乘以一个常数比值得到。2, 6, 18, 54… 的公比是 ×3。'Geo-metric' 暗示每一步乘以相同的“尺度”。

6. Coordinates and Graphs | 坐标与图形

Coordinates combine an x-value and a y-value in the form (x, y) to pinpoint a location on a grid. The origin is (0, 0), where the axes cross. 'Along the corridor, up the stairs' — x first, then y.

坐标以 (x, y) 的形式组合 x 值和 y 值，精确定位网格上的点。原点是 (0, 0)，即坐标轴交汇处。记忆口诀：“先沿走廊走横轴，再爬楼梯上纵轴”。

The x-axis is the horizontal number line, and the y-axis is the vertical number line. They split the plane into four quadrants. Think 'x to the left and right, y to the sky and ground'.

x 轴是水平的数轴，y 轴是垂直的数轴。它们将平面分成四个象限。联想“左右为 x，天地为 y”。

Gradient measures the steepness of a line. It is calculated as (change in y) ÷ (change in x), often called 'rise over run'. A steep hill has a large gradient; a flat road has gradient zero.

斜率衡量一条线的陡峭程度，计算为 (y 的变化) ÷ (x 的变化)，常称作“纵差比横差”。陡峭的山坡斜率大；平坦的道路斜率为零。

The y-intercept the point where the line crosses the y-axis. In y = 2x + 3, the y-intercept is (0, 3). It is the starting value when x = 0 — the launch pad of the graph.

y 轴截距是直线与 y 轴相交的点。在 y = 2x + 3 中，y 轴截距为 (0, 3)。它是当 x = 0 时的起始值——图像的发射台。

Parallel lines have the same gradient and never meet. Their equations look identical except for the y-intercept. Perpendicular lines meet at right angles and have gradients that multiply to give -1.

平行线具有相同的斜率且永不相交。它们的方程除截距外看起来相同。垂直线相交成直角，且它们的斜率乘积为 -1。

A linear graph ht line and follows the form y = mx + c, where m is the gradient and c is the y-intercept. 'Line' and 'linear' share the same root — simple and straight.

线性图像呈现为一条直线，遵循形式 y = mx + c，其中 m 是斜率，c 是 y 轴截距。“line”和“linear”同源——简单且笔直。

7. Geometry Vocabulary | 几何术语

Acute angles measure between 0° and 90° and look sharp. Right angles are exactly 90°, marked with a small square. Obtuse angles are between 90° and 180° — think 'obtuse' meaning blunt or rounded. Reflex angles are greater than 180° but less than 360°.

锐角在 0° 到 90° 之间，看起来尖尖的。直角恰好 90°，用一个小方块标示。钝角在 90° 到 180° 之间——想想“钝”表示不锋利。优角大于 180° 但小于 360°。

Perpendicular lines intersect at right angles. A flagpole is perpendicular to the ground. 'Perpendicular' contains the word 'perpendicular', but just remember two lines crossing like a perfect 'plus' sign.

垂直线以直角相交。旗杆与地面垂直。垂线就像完美的“加号”交汇。

Polygons are closed 2D shapes with straight sides. Triangles (3 sides), quadrilaterals (4), pentagons (5), hexagons (6)… The prefix tells the number of sides — 'poly' means many, 'gon' means angle.

多边形是封闭的二维直线图形。三角形 (3 边)、四边形 (4)、五边形 (5)、六边形 (6)……前缀表示边数——“poly”意为多，“gon”意为角。

Symmetry in a shape means one half mirrors the other. A line of symmetry divides the shape into two identical halves. Rotational symmetry means the shape looks the same after part of a full turn.

对称指形状的一半与另一半成镜像。对称轴将图形分为两个完全相同的部分。旋转对称意味着图形绕中心旋转某一角度后与原图重合。

Pythagoras' theorem otenuse (longest side, opposite the right angle). The theorem says the squares on the two legs add up to the square on the longest side.

勾股定理描述了直角三角形三边的关系：a² + b² = c²，其中 c 是斜边（最长边，对着直角）。定理表明两条直角边上的正方形面积之和等于斜边上的正方形面积。

8. Measures and Units | 测量与单位

Perimeter is the total distance around the edge of a 2D shape. Think 'rim' distance, or 'peri'-meter — the measure around. For a rectangle, add all four side lengths.

周长是二维图形边缘的总长度。联想法：“周”就是四周，“长”就是长度。计算长方形周长时将所有边长相加。

Area rectangle = length × width. It is like laying square tiles to cover the floor completely.

面积测量图形内部表面的大小，以平方单位 (cm², m²) 记录。矩形面积 = 长 × 宽。就像用方形地砖完全铺满地面。

Volume in cube units (cm³, m³). Volume of a cuboid = length × width × height. Stack layers: think 'area of the base times height'.

体积测量立体图形占据的空间，以立方单位 (cm³, m³) 记录。长方体体积 = 长 × 宽 × 高。分层堆积：“底面积乘以高”。

Metric prefixes help scale units: kilo- (×1000), centi- (÷100), milli- (÷1000). 'King Henry Died By Drinking Chocolate Milk' can recall the order: kilo-, hecto-, deca-, base, deci-, centi-, milli-.

公制前缀帮助换算单位：千 (×1000)，厘 (÷100)，毫 (÷1000)。记忆口诀：“千克百十分厘毫”依次递进。

Significant figures (s.f.) are the digits in a number that carry meaning about its precision. In 0.00430, the first significant figure is 4. A number is rounded to a given number of significant figures by keeping the required digits from the left non-zero digit.

有效数字 (s.f.) 是一个数字中表示其精度的有意义的数位。在 0.00430 中，第一个有效数字是 4。将数字舍入到指定有效数字位时，从左边第一个非零数字开始保留所需位数。

9. Statistics and Data Handling | 统计与数据处理

The mean is the average found by adding all values and dividing by the number of values. It is the 'fair share' value. Median is the middle value when data are ordered; mode is the most frequent value; range = largest - smallest.

平均数是所有数值之和除以数值个数的结果，是“平均分配”所得。中位数是数据排序后位于中间的值；众数是出现次数最多的值；极差 = 最大值 - 最小值。

Discrete data can only take specific, separate values — often whole numbers, like number of students in a class. Continuous data can take any value within a range, like height or time.

离散数据只能取特定的、分开的值——通常是整数，比如班级人数。连续数据可以在某个范围内取任意值，比如身高或时间。

A frequency table organises data by listing values alongside how often they occur. Tally marks are often used before the frequencies are counted. The total of all frequencies gives the number of data items.

频数表通过列出数值及其出现的频率来整理数据。在统计频数前常使用划记符号。所有频数之和就是数据的总个数。

A bar chart uses rectangular bars to represent frequency; the height of each bar shows the count. A pie chart uses sectors of a circle to show proportions of a whole. Pie charts compare angles — 360° represents all data.

条形图用矩形条表示频数；条的高度对应计数。饼图用圆的扇形来表示各部分的占比。饼图比较角度——360° 代表全部数据。

A scatter graph shows the relationship between two sets of data points. Correlation describes the pattern: positive (both increase), negative (one increases while the other decreases), or no correlation.

散点图展示两组数据点之间的关系。相关性描述模式：正相关（同增）、负相关（一增一减）或无相关。

10. Probability Basics | 概率基础

Probability measures the likelihood that an event will happen. It is given as a fraction, decimal, or percentage between 0 and 1 (or 100%). 0 means impossible; 1 means certain. 'Probable' hints at 'likely'.

概率衡量一个事件发生的可能性大小。它用 0 到 1 (或 100%) 之间的分数、小数或百分数表示。0 表示不可能；1 表示必定发生。

A sample space is the set of all possible outcomes of an experiment. For a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. Write it out as a list or a table to see every possibility.

样本空间是一次试验所有可能结果的集合。对于一枚公平的六面骰子，样本空间是 {1, 2, 3, 4, 5, 6}。将它列为清单或表格，以便看到所有可能性。

Outcomes are equally likely qually likely, probability = (number of favourable outcomes) / (total number of outcomes).

若每个结果发生的机会相同，则称它们是等可能的。一枚公平硬币的正面和反面是等可能结果。此时概率 = (有利结果的数量) ÷ (总结果数量)。

Two events are mutually exclusive if they cannot happen at the same time. Rolling a 2 and rolling a 5 on a single die are mutually exclusive. 'Mutually exclusive' means they exclude each other — no overlap at all.

如果两个事件不能同时发生，则它们是互斥的。掷一次骰子得到 2 和得到 5 是互斥事件。“互斥”意味着它们互相排斥——完全没有交叠。

Relative frequency is an estimate of probability based on experiment: number of times an event occurs divided by total trials. As you do more trials, relative frequency tends to settle close to the theoretical probability.

相对频数是通过实验得到的概率估计值：事件发生的次数除以总试验次数。随着试验次数增加，相对频数会趋于理论概率。

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