📚 Year 7 AQA Further Maths Vocabulary Quick Memorisation Guide | Year 7 AQA 进阶数学：词汇术语速记指南
Mastering the language of mathematics is the first step towards confident problem solving. This guide breaks down the essential terms you will encounter in Year 7 AQA Further Maths, pairing each English definition with its Chinese equivalent to help you learn faster and retain longer. Use it as a quick reference, a revision checklist, or a daily flashcard companion.
掌握数学语言是自信解题的第一步。这份指南拆解了你在 Year 7 AQA 进阶数学中将遇到的核心术语，为每条英文定义配上中文对应，帮助你更快学习、更持久记忆。你可以把它当作快速参考、复习清单或每日闪卡伴侣。
1. Algebraic Expressions and Equations | 代数表达式与方程
An algebraic expression is a combination of numbers, letters (variables), and operation symbols without an equals sign, such as 3x + 2.
代数表达式是由数字、字母（变量）和运算符号组成的式子，没有等号，例如 3x + 2。
An equation that shows two expressions are equal, always containing an equals sign, e.g. 5y − 3 = 12.
方程是表示两个表达式相等的数学陈述，总是包含等号，例如 5y − 3 = 12。
A variable is a symbol, usually a letter, that stands for an unknown number.
变量是一个符号，通常是字母，代表一个未知数。
A coefficient is the number in front of a variable, for instance in 7a the coefficient is 7.
系数是变量前面的数字，例如在 7a 中系数是 7。
A constant term is a number on its own with no variable attached, like the 4 in 2x + 4.
常数项是单独的数字，不带有变量，比如 2x + 4 中的 4。
Like terms have exactly the same variable part (same letter and same exponent); 3n and -5n are like terms.
同类项具有完全相同的变量部分（相同字母且指数相同）；3n 和 -5n 是同类项。
2. Number and Place Value | 数字与位值
An integer is any whole number, positive or negative, including zero.
整数是任何整数，包括正数、负数和零。
Place value tells you the value of a digit based on its position in a number, such as units, tens, hundreds, and tenths.
位值根据数字在数中的位置告诉你该数码的值，例如个位、十位、百位和十分位。
A factor of a number divides exactly into that number with no remainder; factors of 12 are 1, 2, 3, 4, 6, 12.
一个数的因数可以整除该数而没有余数；12 的因数有 1, 2, 3, 4, 6, 12。
A multiple is the result of multiplying a number by an integer; the first three multiples of 5 are 5, 10, 15.
倍数是把一个数乘以一个整数的结果；5 的前三个倍数是 5, 10, 15。
A prime number has exactly two distinct factors: 1 and itself; 7 is prime.
质数只有两个不同的因数：1 和它本身；7 是质数。
Square numbers are the product of multiplying an integer by itself, e.g. 4² = 16.
平方数是整数乘以自身的积，例如 4² = 16。
Cube numbers are obtained by multiplying an integer by itself twice, e.g. 3³ = 27.
立方数是将整数乘以自身两次得到的，例如 3³ = 27。
3. Fractions, Decimals and Percentages | 分数、小数与百分比
A numerator is the top number in a fraction; it shows how many parts we have.
分子是分数中上面的数，表示我们有多少份。
A denominator is the bottom number in a fraction; it shows the total number of equal parts the whole is divided into.
分母是分数中下面的数，表示整体被分成多少等份。
An equivalent fraction represents the same value even though it uses different numbers, e.g. ½ = 2/4.
等值分数尽管使用不同的数字，但表示相同的值，例如 ½ = 2/4。
A decimal point separates the whole number part from the fractional part, as in 3.75.
小数点将整数部分与小数部分分开，如 3.75。
Percentage means ‘out of 100’; the symbol is %.
百分比意思是“每100中的”；符号是 %。
Terminating decimals come to an end, like 0.25, while recurring decimals repeat a pattern forever, like 0.333… (denoted with a dot above the repeating digit).
终止小数会结束，如 0.25，而循环小数永远重复某个模式，如 0.333…（在重复数字上加一个点表示）。
A reciprocal of a number is 1 divided by that number; the reciprocal of 5 is ⅕.
一个数的倒数是 1 除以该数；5 的倒数是 ⅕。
4. Ratio and Proportion | 比与比例
A ratio compares two or more quantities, showing the relative size of one part to another. It is written with a colon, e.g. 3 : 2.
比比较两个或更多数量，显示一部分相对于另一部分的大小。用冒号书写，例如 3 : 2。
Proportion describes how much of a total is taken up by a part; it can be expressed as a fraction or percentage.
比例描述部分占整体的多少；可以用分数或百分比表示。
A unitary method works by finding the value of one part first, then scaling up or down.
单一单位法先求出一份的值，然后进行放大或缩小。
When quantities are in direct proportion, as one increases, the other increases at the same rate.
当量成正比例时，一个量增加，另一个也以相同的速率增加。
5. Geometry: Lines and Angles | 几何：线与角
A line segment is a part of a line with two endpoints.
线段是一条线上有两个端点的部分。
A ray starts at a point and extends infinitely in one direction.
射线从一个点开始，无限延伸到一个方向。
Parallel lines are straight lines that never meet, remaining the same distance apart.
平行线是永不相交、距离保持相等的直线。
Perpendicular lines meet or intersect at a right angle (90°).
垂直线以直角（90°）相遇或相交。
An acute angle is less than 90°, an obtuse angle is between 90° and 180°, and a reflex angle is between 180° and 360°.
锐角小于 90°，钝角在 90° 和 180° 之间，优角在 180° 和 360° 之间。
Vertically opposite angles are equal and are formed when two lines cross.
对顶角相等，由两条直线相交形成。
Angles at a point sum to 360°, while angles on a straight line sum to 180°.
绕点一周角之和为 360°，而平角（直线上各角）之和为 180°。
6. 2D Shapes and Their Properties | 平面图形及其性质
A polygon is a closed 2D shape with straight sides. A regular polygon has all sides and all angles equal.
多边形是由直线段围成的封闭平面图形。正多边形的所有边和所有角都相等。
A quadrilateral is a polygon with four sides. Special quadrilaterals include the square, rectangle, parallelogram, rhombus, trapezium and kite.
四边形是有四条边的多边形。特殊的四边形包括正方形、矩形、平行四边形、菱形、梯形和筝形。
A circle is the set of all points at a fixed distance from the centre. The circumference is the distance around the circle, the radius is the distance from centre to edge, and the diameter passes through the centre connecting two points on the edge (d = 2r).
圆是到定点距离等于定长的所有点的集合。周长是绕圆一周的长度，半径是从圆心到圆周的距离，直径是通过圆心连接圆周上两点的线段（d = 2r）。
Area measures the space inside a 2D shape; perimeter measures the total distance around the shape.
面积度量平面图形内部的空间大小；周长度量图形边界线的总长。
Congruent shapes are identical in shape and size; similar shapes have the same shape but may be different in size.
全等图形形状和大小完全相同；相似图形形状相同但大小可能不同。
7. 3D Shapes and Measures | 立体图形与度量
A 3D solid has faces (flat surfaces), edges (where two faces meet) and vertices (corners).
立体图形有面（平的表面）、棱（两个面相交的线段）和顶点（角）。
A prism has a uniform cross-section along its length; a cylinder is a special curved prism.
棱柱沿其全长具有相同的横截面；圆柱体是一种特殊的曲面棱柱。
A net is a 2D arrangement that folds to make a 3D shape.
展开图是折叠后形成一个立体图形的平面排列。
Volume measures the space inside a 3D solid; surface area is the total area of all its faces.
体积度量立体图形内部的空间；表面积是所有面的总面积。
m), centimetre (cm), metre (m), kilometre (km). 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
长度公制单位：毫米 (mm)、厘米 (cm)、米 (m)、千米 (km)。1 cm = 10 mm，1 m = 100 cm，1 km = 1000 m。
8. Statistics and Data Handling | 统计与数据处理
Data is a collection of facts or numbers. Qualitative data describes qualities (e.g. colour), while quantitative data is numerical.
数据是事实或数字的集合。定性数据描述特征（如颜色），而定量数据是数值型的。
The mean is the average found by adding all values and dividing by how many there are.
平均数（均值）是通过将所有数值相加再除以个数得到的平均值。
The median is the middle value when data is ordered; the mode is the value that appears most often, and the range is the difference between the largest and smallest values.
中位数是数据排序后的中间值；众数是出现次数最多的值，极差是最大值与最小值的差。
A frequency table lists data values alongside how many times each occurs.
频数表列出数据值以及每个值出现的次数。
A bar chart uses rectangular bars to show frequencies; a pictogram uses pictures or symbols to represent data.
条形图用矩形条表示频数；象形图用图片或符号表示数据。
A pie chart represents data as slices of a circle where each slice’s angle is proportional to the frequency.
饼图将数据表示为圆的扇形，每个扇形的角度与频数成正比。
9. Probability Language | 概率术语
Probability measures how likely an event is to happen. It can be written as a fraction, decimal or percentage between 0 (impossible) and 1 (certain).
概率度量某个事件发生的可能性大小。可以用 0（不可能）到 1（必然）之间的分数、小数或百分比表示。
An outcome is a possible result of a trial, like rolling a 3 on a die. A sample space lists all possible outcomes.
结果是试验的一个可能出现的情况，比如抛骰子得到 3。样本空间列出所有可能的结果。
An event is a set of one or more outcomes. The probability of an event not happening is 1 minus the probability of it happening.
事件是一个或一组结果的集合。一个事件不发生的概率等于 1 减去它发生的概率。
Equally likely outcomes have the same chance of occurring, such as the sides of a fair coin.
等可能的结果具有相同发生的机会，例如一枚公平硬币的两面。
10. Coordinates and Graphs | 坐标与图像
The coordinate plane is formed by a horizontal x-axis and a vertical y-axis, which intersect at the origin (0,0).
坐标平面由水平的 x 轴和竖直的 y 轴组成，两轴交于原点 (0,0)。
A coordinate pair (x, y) gives the horizontal position first, then the vertical position.
坐标对 (x, y) 首先给出水平位置，然后给出垂直位置。
A scatter graph shows the relationship between two sets of data using plotted points. Correlation describes the trend: positive, negative or none.
散点图用描点来显示两组数据之间的关系。相关性描述趋势：正相关、负相关或无相关。
rawn from an equation like y = 2x + 1 by generating a table of values and plotting points.
可以通过生成数值表并描点，由类似 y = 2x + 1 这样的方程画出直线图像。
Gradient = mx + c, m is the gradient and c is the y-intercept (where the line crosses the y-axis).
斜率（梯度）度量一条直线的陡峭程度；在直线方程 y = mx + c 中，m 是斜率，c 是 y 轴截距（直线与 y 轴的交点）。
11. Sequences and Patterns | 数列与规律
A sequence is a list of numbers that follow a rule. Each number is a term.
数列是按照某种规则排列的一列数。每一个数叫作项。
A linear sequence increases or decreases by a constant amount, called the common difference.
线性数列以一个恒定的量增加或减少，这个量叫作公差。
The term-to-term rule tells you how to get from one term to the next; the position-to-term rule (nth term rule) gives a formula for finding any term based on its position n.
相邻项规则告诉你如何从一项得到下一项；第 n 项规则（通项公式）给出一个基于位置 n 求任意项的公式。
A Fibonacci-type sequence is formed by adding the two previous terms to get the next term.
斐波那契型数列由前两项相加得到下一项。
12. Key Command Words in Exam Questions | 考试题关键指令词
Simplify means to write an expression in its most compact form by collecting like terms; do not solve.
化简意味着通过合并同类项将表达式写成最紧凑的形式；不要解方程。
Evaluate means to find the numerical value of an expression by substituting given values.
求值意味着通过代入给定数值求出表达式的数值结果。
Solve means to find the unknown value(s) that make an equation true, usually presenting the answer as x = …
求解意味着找出使方程成立的未知数的值，通常答案写成 x = … 的形式。
Expand means to multiply out brackets, e.g. 3(x + 2) becomes 3x + 6.
展开意味着用乘法去掉括号，例如 3(x + 2) 变为 3x + 6。
Factorise anding; it means to rewrite an expression as a product of factors, e.g. 4x + 8 = 4(x + 2).
因式分解是展开的逆运算；意味着将表达式重写为因式的乘积，例如 4x + 8 = 4(x + 2)。
Show that questions require you to demonstrate a given result step by step, often using logical reasoning or algebraic manipulation.
证明（Show that）题型要求你逐步展示出一个给定结果，通常使用逻辑推理或代数操作。
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