📚 Year 7 OCR Further Maths: Vocabulary & Terminology Quick Memorisation Guide | Year 7 OCR 进阶数学：词汇术语速记指南
Welcome to your quick memorisation guide for Year 7 OCR Further Maths! Mastering mathematical vocabulary is like learning a new language — once you know the key terms, you can understand problems, communicate your reasoning, and boost your confidence. This article breaks down essential terminology into bite-sized sections, each with clever memory tricks to make revision fast and fun.
欢迎使用 Year 7 OCR 进阶数学词汇术语速记指南！掌握数学词汇就像学习一门新语言——一旦熟悉了关键术语，你就能理解题目、清晰表达推理过程，并增强自信。本文将核心术语拆分为若干小节，每节都配有巧妙的记忆技巧，让复习变得快速又有趣。
1. Algebraic Expressions: The Building Blocks | 代数表达式：基本构件
Algebra uses letters and symbols to generalise numbers. An expression is a combination of these symbols without an equals sign, like 3x + 2.
代数用字母和符号来表示数字。表达式就是这些符号的组合，没有等号，例如 3x + 2。
A variable is a symbol, usually a letter such as x or y, that represents an unknown or changeable number. Think of it as a 'mystery box' holding a value you might need to find.
变量是一个符号，通常是字母（如 x 或 y），代表未知或可变的数字。可以把它想象成一个“神秘盒子”，里面藏着你需要找出的数值。
A constant is a fixed number that never changes its value, like 5, −3, or ½. It stands alone, steady as a rock.
常量是一个固定不变的数值，如 5、−3 或 ½。它独自挺立，像岩石一样稳固。
A coefficient is the number multiplying a variable. In 7y, 7 is the coefficient. Memory trick: coefficient sounds like 'co-pilot' — it sits right beside the variable, flying together.
系数是乘以变量的那个数字。在 7y 中，7 就是系数。记忆妙招：coefficient 读起来像“co-pilot（副驾驶）”——它紧挨着变量，齐驱并进。
A term is a single mathematical entity, which can be a number, a variable, or a product of both. Like terms have exactly the same variable part: 2a and 5a are like terms, but 2a and 3a² are not.
项是一个独立的数学单元，可以是数字、变量或两者的乘积。同类项具有完全相同的变量部分：2a 和 5a 是同类项，但 2a 和 3a² 不是。
2. Equations and Inequalities: Balancing Acts | 方程与不等式：平衡的艺术
als sign =. Solving an equation means finding the value of the unknown that makes it true.
方程是表明两个表达式相等的陈述，用等号 = 连接。解方程就是要找出使等式成立的未知数的值。
Think of an equation as a balanced seesaw: whatever you do to one side, you must do to the other to keep it level.
把方程想象成一个平衡的跷跷板：对一边做了什么，另一边也必须做同样的事，以保持水平。
r equal to) and ≥ (greater than or equal to). The open side always faces the larger number — imagine a hungry crocodile's mouth opening towards the bigger meal.
不等式使用 <（小于）、>（大于）、≤（小于等于）和 ≥（大于等于）等符号比较两个值。开口永远朝向较大的数字——想象一只饥饿鳄鱼的嘴巴张向更丰盛的大餐。
(or values) that satisfy an equation or inequality. For x + 4 = 9, the solution is x = 5.
解是满足方程或不等式的那个（或那些）值。对于 x + 4 = 9，解就是 x = 5。
An identity is a special type of equation that is true for all values of the variable, often written with a ≡ symbol. For example, 2(x + 3) ≡ 2x + 6.
恒等式是一种特殊的方程，对变量的所有取值都成立，常用 ≡ 符号表示。例如 2(x + 3) ≡ 2x + 6。
3. Integers and Number Properties: The Number Toolkit | 整数与数的性质：数字工具箱
Integers are whole numbers that can be positive, negative, or zero. They are the 'stepping stones' on the number line.
整数是正整数、负整数和零。它们是数轴上的“铺路石”。
A prime number is an integer greater than 1 that has exactly two factors: 1 and itself. 2, 3, 5, 7, 11 are primes. Remember: 1 is not prime — it only has one factor.
质数是大于 1 且恰好只有两个因数（1 和它本身）的整数。2、3、5、7、11 都是质数。记住：1 不是质数——它只有一个因数。
A factor is a whole number that divides exactly into another number, leaving no remainder. A multiple is the product of a number and any integer. To remember which is which: factors are the 'parents' that make the number, multiples are the 'children' that grow from it.
因数是能够整除另一个数且无余数的整数。倍数是一个数与任意整数的乘积。记法：因数是制造数字的“父母”，倍数是数字繁衍出的“孩子”。
The highest common factor (HCF) of two numbers is the largest factor they share. The lowest common multiple (LCM) is the smallest multiple they have in common. HCF helps with simplifying fractions; LCM helps with finding common denominators.
两个数的最大公因数（HCF）是它们共有的最大因数。最小公倍数（LCM）是它们共有的最小倍数。HCF 用在分数化简；LCM 用在通分求公分母。
4. Fractions, Decimals and Percentages: Three Faces of the Same Number | 分数、小数和百分数：同一个数的三张面孔
A fraction represents a part of a whole, written as numerator over denominator. The denominator shows how many equal parts the whole is divided into; the numerator shows how many parts we have.
分数表示整体的一部分，写成分母分之分子。分母表示整体被分成了多少等份；分子表示我们取了多少份。
An equivalent fraction is a fraction that has the same value as another, created by multiplying or dividing the numerator and denominator by the same number. Visualise slicing a pizza: ½ is the same as ²⁄₄.
等值分数是值相同的分数，通过分子和分母同乘或同除一个数得到。想象切披萨：½ 和 ²⁄₄ 是一样的。
A decimal uses a decimal point to separate the whole number part from the fractional part. Terminating decimals end, like 0.75; recurring decimals have a repeating pattern, like 0.333...
小数用小数点将整数部分和小数部分分隔开。有限小数会结束，如 0.75；循环小数有重复的数字模式，如 0.333...
A percentage means 'out of 100'. To convert a fraction to a percentage, make the denominator 100 or multiply by 100%. The symbol % helps you think: per-cent = per hundred.
百分数表示“每百”。将分数转换为百分数，可使分母变成 100 或乘以 100% 。符号 % 助记：per-cent 就是每百。
5. Sequences and Patterns: Order in Numbers | 数列与规律：数字中的秩序
ce is called a term. The position of a term is often called n, so the first term is n = 1.
数列是按一定规律排列的一串数。数列中的每个数称为项。项的位置常表示为 n，因此第一项对应 n = 1。
An arithmetic sequence is a sequence where the difference between consecutive terms is constant. This difference is called the common difference. For example, in 2, 5, 8, 11... the common difference is +3.
等差数列是相邻两项的差恒定的数列。这个差称为公差。例如在 2, 5, 8, 11... 中，公差为 +3。
The nth term of an arithmetic sequence gives a formula to find any term without listing all previous ones. It often looks like: an + b, where a is the common difference and b is the adjustment to reach the first term.
等差数列的第 n 项提供了一个公式，无需列出前面所有项即可求出任意一项。它通常形如 an + b，其中 a 是公差，b 是使首项成立的调整量。
nth term = a + (n − 1)d
记忆技巧：想象一个梯子，每一步上升的高度都是公差 d。第 n 级的高度 = 第一级高度 + (n−1) 个台阶。
6. Geometry: Angles and Shapes | 几何：角度与图形
An angle measures the turn between two lines meeting at a point. It is measured in degrees (°). Acute angles are less than 90°, right angles are exactly 90°, obtuse angles are between 90° and 180°, and reflex angles are greater than 180°.
角衡量两条线在一点相交时的旋转量，以度（°）为单位。锐角小于 90°，直角恰好为 90°，钝角在 90° 到 180° 之间，优角大于 180°。
A polygon is a closed 2D shape with straight sides. Naming polygons uses Greek prefixes: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8).
多边形是由直边围成的封闭二维图形。多边形的命名使用希腊语前缀：三角形（3）、四边形（4）、五边形（5）、六边形（6）、七边形（7）、八边形（8）。
A regular polygon has all sides and all angles equal. An irregular polygon does not. Symmetry means a shape can be reflected or rotated and still look the same. A line of symmetry divides a shape into two mirror-image halves.
正多边形所有边和所有角都相等。不规则多边形则不然。对称指的是图形经过反射或旋转后看起来仍然一样。对称轴将图形分成两个镜像的部分。
A transformation changes the position or size of a shape. Translation slides a shape without turning; rotation turns it around a centre; reflection flips it over a line; enlargement changes its size by a scale factor.
变换改变图形的位置或大小。平移是滑动图形而不转动；旋转是绕一个中心转动；反射是沿一条线翻转；放大是按比例因子改变大小。
7. Perimeter, Area and Volume: Measuring Space | 周长、面积与体积：空间的度量
Perimeter is the total distance around the outside of a 2D shape. It is found by adding all side lengths. Think of it as the 'fence' around a garden.
周长是二维图形外边界的总长度，通过将所有边长相加得到。可以想成是花园周围的“栅栏”。
in square units (e.g., cm², m²). For a rectangle, area = length × width. Area is like the 'carpet' covering a floor.
面积是图形所覆盖的表面大小，以平方单位（如 cm², m²）计量。对于矩形，面积 = 长 × 宽。面积好比铺在地板上的“地毯”。
. The height must be perpendicular to the base. Imagine the triangle is half of a rectangle folded along the diagonal.
Area (triangle) = ½ × b × h
三角形的面积 = ½ × 底 × 高，高必须垂直于底。可以想象三角形是矩形沿对角线剪开的一半。
a cuboid, volume = length × width × height. Volume is like how much water a box can hold.
体积衡量三维物体所占空间，以立方单位（cm³, m³）计量。对于长方体，体积 = 长 × 宽 × 高。体积好比一个盒子能装多少水。
8. Statistics: Averages and Spread | 统计：平均数与离散程度
Statistics is the study of collecting, analysing, and presenting data. Three common averages summarise a data set: mean, median, and mode.
统计学是研究数据的收集、分析和呈现的学科。三种常见的平均数用于概括一组数据：均值、中位数和众数。
The mean is calculated by adding all values and dividing by the number of values. Think: 'mean' is the 'average' you usually meet — it shares the total equally.
均值的计算方法是把所有数值相加，再除以数值的个数。联想：“均值”是你最常碰到的平均数——它把总和均摊给每个人。
The median is the middle value when data are ordered. If there are two middle numbers, take their mean. 'Median' sounds like 'medium' — it sits in the central position.
中位数是将数据排序后位于中间的值。如果有两个中间数，就取它们的平均数。median 听起来像 medium——它位居中央。
The mode is the value that appears most often. Memory trick: 'mode' starts with 'mo' as in 'most'. A set can have more than one mode or no mode at all.
众数是出现次数最多的值。记忆法：mode（众数）和 most（最多）都以 "mo" 开头。一组数据可能有多于一个众数，也可能没有众数。
sures how spread out the data is. Range = largest value − smallest value. It tells you the 'stretch' of the data.
极差衡量数据的分散程度。极差 = 最大值 − 最小值。它告诉你数据的“伸展”范围。
9. Probability Basics: The Language of Chance | 概率基础：机会的语言
Probability is the chance that a particular event will happen. It is a number between 0 and 1 (or 0% and 100%). 0 means impossible; 1 means certain.
概率是特定事件发生的可能性大小，它是一个介于 0 和 1（或 0% 到 100%）之间的数值。0 表示不可能；1 表示必然发生。
pace is the list of all possible outcomes. For a fair coin, sample space = {Heads, Tails}.
事件是一个结果或一组结果的集合。样本空间是所有可能结果的列表。对于一枚均匀硬币，样本空间 = {正面, 反面}。
le outcomes / total number of possible outcomes. Always check that all outcomes are equally likely.
理论概率为：P(事件) = 有利结果数 / 所有可能结果总数。务必检查所有结果是否等可能。
P(Event) = favourable / total
记忆：将概率想象成一张馅饼，有利结果占了几片。
10. Coordinates and Graphs: Mapping Relationships | 坐标与图像：描绘关系
Coordinates are pairs of numbers (x, y) that pinpoint a location on a grid. The x-coordinate (abscissa) comes first and tells you how far to move horizontally; the y-coordinate (ordinate) comes second and moves vertically. 'Along the corridor, then up the stairs.'
坐标是成对的数字 (x, y)，用来在网格中精确定位。x 坐标（横坐标）在前，指示水平方向移动多远；y 坐标（纵坐标）在后，指示垂直方向移动。“先沿着走廊走，再上楼梯”。
The origin is the point (0, 0) where the x-axis and y-axis intersect. Quadrants divide the grid into four regions. In the first quadrant, both x and y are positive.
原点是 x 轴和 y 轴的交点 (0, 0)。坐标系分为四个象限。在第一象限中，x 和 y 均为正值。
ts equation often appears as y = mx + c, where m is the gradient and c is the y-intercept.
方程的图像展示了两个变量之间的关系。变化速率恒定的直线图称为线性图像。其方程常表示为 y = mx + c，其中 m 是斜率，c 是 y 轴截距。
in y) / (change in x). A positive gradient goes uphill; a negative gradient goes downhill.
斜率衡量一条线的倾斜程度：m = 上升高度 / 水平距离 = (y 的变化量) / (x 的变化量)。正斜率向上爬升；负斜率向下滑落。
Use these terms to talk about graphs with precision — you are not just drawing a line, you are describing a relationship.
使用这些术语精准地谈论图像——你不是在随便画线，而是在描述一种数学关系。
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