📚 Year 11 AQA Maths: Essential Vocabulary Fast-Track Guide | AQA 数学：词汇术语速记指南
Mastering the language of mathematics is half the battle in your AQA GCSE exam. This guide will walk you through the high-frequency terms you must know, grouped by topic, with clear definitions and memory aids. Use it as a checklist to boost your confidence and precision.
掌握数学语言是攻克 AQA GCSE 考试的一半。本指南将带你梳理必须掌握的高频术语，按主题分组，附有清晰的定义和记忆技巧。把它用作自查清单，提升你的信心和答题准确性。
1. Number & Place Value | 数与位值术语
Integer refers to any whole number that can be positive, negative, or zero. Always remember that fractions and decimals are not integers. The term significant figure is used when rounding to a specific number of digits, starting from the first non-zero digit.
整数 (Integer) 指任何正、负或零的完整数字。记住分数和小数都不是整数。当你按特定数位四舍五入，并从第一个非零数字开始计数时，就用到了有效数字 (Significant figure)。
Standard form is a way of writing very large or very small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. The reciprocal of a number is 1 divided by that number; for a fraction, simply flip it.
标准形式 (Standard form) 是将极大或极小数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10，n 是整数。倒数 (Reciprocal) 就是 1 除以那个数；对于分数，直接上下颠倒即可。
Factor, multiple, and prime number are foundational: a factor divides exactly into a number; a multiple is in its times table; a prime number has exactly two distinct factors. The highest common factor (HCF) and lowest common multiple (LCM) will always come up in wordy problems.
因数 (Factor)、倍数 (Multiple) 和质数 (Prime number) 是基础：因数是能整除某数的数；倍数是某数乘法表中的数；质数恰好有两个不同的因数。最大公因数 (HCF) 和最小公倍数 (LCM) 必定出现在文字题中。
2. Fractions, Decimals & Percentages | 分数、小数与百分比
Numerator and denominator describe the top and bottom parts of a fraction. The word equivalent means equal in value, even if the fractions look different. When we say terminating decimal, we mean a decimal that stops, like 0.75. A recurring decimal has a repeating pattern, shown with a dot notation.
分子 (Numerator) 和分母 (Denominator) 描述分数的上部和下部。等值 (Equivalent) 表示数值相等，即使分数看起来不同。有限小数 (Terminating decimal) 指会停止的小数，如 0.75。循环小数 (Recurring decimal) 有重复的数字模式，用点标记表示。
Percentage increase and decrease compare the change to the original amount, usually calculated using a multiplier. The phrase compound interest is when interest is added to the principal, and then itself earns interest. Depreciation is the opposite – a repeated percentage decrease in value.
百分比增加 (Percentage increase) 和减少 (Percentage decrease) 将变化与原量比较，通常用乘数计算。复利 (Compound interest) 指利息加入本金后也产生利息。贬值 (Depreciation) 则相反——价值的重复百分比减少。
3. Ratio, Proportion & Rates | 比、比例与比率
A ratio compares part to part, while a proportion compares a part to the whole. The word unitary method means finding the value of one unit first. Direct proportion means as one amount increases, the other increases at the same rate; inverse proportion means one quantity increases as the other decreases.
比 (Ratio) 比较部分与部分，而比例 (Proportion) 比较部分与整体。单位法 (Unitary method) 是先求出一个单位的值。正比例 (Direct proportion) 指一个量增加时，另一个以相同速率增加；反比例 (Inverse proportion) 指一个量增加时另一个减少。
You must also recognise scale factor – the multiplier linking corresponding lengths in similar shapes – and gradient as a rate of change. In conversion graphs, gradient gives the exchange rate or speed.
你还须识别比例因子 (Scale factor)——连接相似形状对应长度所用的乘数——以及作为变化率的梯度 (Gradient)。在换算图中，梯度给出汇率或速度。
4. Algebraic Expressions & Manipulation | 代数表达式与运算
The word expression is a collection of terms with no equals sign; an equation has an equals sign and shows balance; an identity is true for all values and uses the ≡ symbol. The coefficient is the number part of a term, e.g. in 5x, 5 is the coefficient.
表达式 (Expression) 是没有等号的项的集合；方程 (Equation) 含有等号并表示平衡；恒等式 (Identity) 对所有值都成立，使用 ≡ 符号。系数 (Coefficient) 是一项中的数字部分，例如在 5x 中，5 是系数。
Expanding means multiplying out brackets; factorising is putting back into brackets by finding common factors. A quadratic is an expression where the highest power is 2, usually written as x² + bx + c. The term completing the square rewrites a quadratic in the form (x + p)² + q.
展开 (Expanding) 指脱去括号相乘；因式分解 (Factorising) 是找出公因数后放回括号。二次式 (Quadratic) 是最高次幂为 2 的式子，通常写作 x² + bx + c。配方法 (Completing the square) 将二次式写成 (x + p)² + q 的形式。
5. Equations, Inequalities & Sequences | 方程、不等式与数列
A linear equation produces a straight-line graph and involves variables with power 1. When the variable is raised to power 2, it becomes a quadratic equation. Simultaneous equations require you to find values that satisfy two (or more) equations at once.
线性方程 (Linear equation) 产生直线图，变量次数为 1。变量次数为 2 时，成为二次方程 (Quadratic equation)。联立方程 (Simultaneous equations) 要求找出同时满足两个（或多个）方程的值。
Inequality signs (, ≤, ≥) show a range of solutions. Remember ‘integer solutions‘ to an inequality must be whole numbers. A sequence is a list of numbers following a rule; the nth term formula lets you find any term without listing from the beginning. The word arithmetic means the same difference is added each time; geometric means multiplied.
不等式 (Inequality) 符号 (, ≤, ≥) 表示解的范围。记住不等式的整数解 (Integer solutions) 必须是完整数字。数列 (Sequence) 是按规则排列的一系列数；第 n 项 (nth term) 公式让你不必从头排起就能找到任一项。等差 (Arithmetic) 意味着每次加上相同的差；等比 (Geometric) 则是乘以相同比率。
6. Graphs & Functions | 图形与函数
Coordinates are written (x, y) and the origin is (0,0). The y-intercept is where a line crosses the y-axis; gradient (m) measures steepness as rise over run. In y = mx + c, m is gradient and c is y-intercept. A function is a special relation with one output for each input; you will see notation f(x).
坐标 (Coordinates) 写作 (x, y)，原点 (Origin) 是 (0,0)。y 轴截距 (y-intercept) 是直线与 y 轴的交点；梯度 (Gradient) (m) 用纵增量除以横增量来度量倾斜度。在 y = mx + c 中，m 是梯度，c 是 y 轴截距。函数 (Function) 是一种每个输入对应一个输出的特殊关系；你会见到 f(x) 的记法。
Turning point of a quadratic graph is the maximum or minimum point. Roots are the x-values where the graph crosses the x-axis (y = 0). Exponential growth curves use a constant multiplier, often written as y = a × bˣ.
二次图像的转折点 (Turning point) 是极大或极小点。根 (Roots) 是图像与 x 轴交点处的 x 值 (y = 0)。指数增长 (Exponential growth) 曲线采用固定的乘数，常写作 y = a × bˣ。
7. Geometry: Angles & Lines | 几何：角与线
Acute, obtuse, and reflex describe angles less than 90°, between 90° and 180°, and over 180° respectively. Perpendicular lines meet at 90°; parallel lines never meet. Know the angle rules on parallel lines: corresponding, alternate, and co-interior (allied) angles.
锐角 (Acute)、钝角 (Obtuse) 和优角 (Reflex) 分别描述小于 90°、介于 90° 与 180° 之间以及超过 180° 的角。垂线 (Perpendicular) 相交成 90°；平行线 (Parallel) 永不相交。熟记平行线角度规则：同位角 (Corresponding)、内错角 (Alternate) 和同旁内角 (Co-interior)。
Bearings are measured clockwise from north, always given as three digits. A locus is a path traced by a point obeying a rule. Bisect means cut exactly in half; you must know how to bisect a line or angle using compasses.
方位角 (Bearings) 从北顺时针测量，总以三位数字给出。轨迹 (Locus) 是一个点遵循规则所描出的路径。平分 (Bisect) 指切成完全相等的两半；你必须会使用圆规平分线段或角。
8. Perimeter, Area & Volume | 周长、面积与体积
Perimeter is the total distance around the outside of a shape. Area is measured in square units; you must recall formulas for triangle (½ × base × height), parallelogram, trapezium and circle (πr²). The circumference of a circle is πd.
周长 (Perimeter) 是形状外沿的总长度。面积 (Area) 以平方单位度量；你必须记住三角形 (½ × 底 × 高)、平行四边形、梯形和圆 (πr²) 的公式。圆的周长 (Circumference) 是 πd。
Volume of a prism is area of cross-section × length. A surface area is the total area of all faces. For curved solids, recognise cone and sphere. The term capacity is often used for the volume a container can hold, usually in millilitres or litres.
棱柱的体积 (Volume) 是横截面积 × 长。表面积 (Surface area) 是所有面的总面积。对于曲面体，要认出圆锥 (Cone) 和球体 (Sphere)。容积 (Capacity) 常指容器能容纳的体积，通常以毫升或升为单位。
9. Transformations & Similarity | 变换与相似
Translation slides a shape by a vector; the shape stays congruent. Rotation requires centre, angle and direction. Reflection flips the shape over a mirror line; enlargement changes size and needs a centre and scale factor. If the scale factor is negative, it appears inverted through the centre.
平移 (Translation) 用向量滑动图形，形状保持全等。旋转 (Rotation) 需要中心、角度和方向。反射 (Reflection) 将图形翻过一条镜线；放大 (Enlargement) 改变大小，需要中心和比例因子。若比例因子为负，图形将通过中心反向呈现。
Congruent shapes are identical in size and shape, no matter their orientation. Similar shapes have the same angles and proportional sides; the scale factor links corresponding lengths, and area scale factor is the square of length scale factor.
全等 (Congruent) 图形无论朝向如何，形状和大小完全相同。相似 (Similar) 图形拥有相同角度和成比例的边；比例因子连接对应长度，面积比例因子是长度比例因子的平方。
10. Pythagoras, Trigonometry & Vectors | 毕达哥拉斯、三角与向量
Pythagoras’ theorem applies only to right-angled triangles: a² + b² = c², where c is the hypotenuse (longest side opposite the right angle). The three trigonometric ratios are sine (opposite/hypotenuse), cosine (adjacent/hypotenuse), and tangent (opposite/adjacent). You must label sides correctly from a given angle.
毕达哥拉斯定理 (Pythagoras’ theorem) 仅适用于直角三角形：a² + b² = c²，其中 c 是斜边（直角所对的最长边）。三种三角比是正弦 (Sine) (对/斜)、余弦 (Cosine) (邻/斜) 和正切 (Tangent) (对/邻)。你必须从给定角正确标出各边。
A vector has both magnitude and direction, usually written as a column or using i and j. Magnitude of a vector is its length, found by Pythagoras. Resultant vector is the sum of two or more vectors. Parallel vectors are scalar multiples of one another.
向量 (Vector) 具有大小和方向，通常写作列向量或使用 i 和 j。向量的模 (Magnitude) 是其长度，用毕达哥拉斯定理求得。合向量 (Resultant vector) 是两个或多个向量之和。平行向量彼此是标量倍数。
11. Probability & Statistics | 概率与统计
Probability is a measure of chance, always between 0 and 1, or 0% and 100%. An outcome is a possible result; an event is a set of outcomes. The sample space lists all possible outcomes. Mutually exclusive events cannot happen at the same time; for them, P(A or B) = P(A) + P(B).
概率 (Probability) 是对机会的衡量，总在 0 到 1 或 0% 到 100% 之间。结果 (Outcome) 是一个可能的结果；事件 (Event) 是一组结果。样本空间 (Sample space) 列出所有可能结果。互斥 (Mutually exclusive) 事件不能同时发生；对它们，P(A 或 B) = P(A) + P(B)。
Mean, median, mode, and range are measures of average and spread. Cumulative frequency adds up frequencies as you go; plot on a graph to find median and quartiles. Box plot shows minimum, lower quartile, median, upper quartile and maximum.
平均数 (Mean)、中位数 (Median)、众数 (Mode) 和极差 (Range) 是度量平均和离散的指标。累积频数 (Cumulative frequency) 是逐项累加频数；将其画成图可找出中位数和四分位数。箱形图 (Box plot) 显示最小值、下四分位数、中位数、上四分位数和最大值。
12. Exam Command Words | 考试指令词
Recognising command words like ‘evaluate’, ‘solve’, ‘prove’, and ‘show that’ is vital. Evaluate means to carry out the calculation and give a numerical result. Solve is often used with equations; prove demands a logical chain of reasoning. Show that means you must demonstrate the steps leading to the given answer.
识别指令词如 “evaluate (求值)”、“solve (求解)”、“prove (证明)” 和 “show that (说明…” 极为关键。Evaluate 指执行计算并给出数值结果。Solve 常用于方程；prove 要求逻辑推理链条。Show that 意指你必须展示通往给定答案的步骤。
Estimate means round numbers before calculating to get an approximate answer. Factorise completely means take out the highest common factor and then check if there is any further factorisation possible. Sketch a graph means show the general shape and key points, not a plot on graph paper.
Estimate (估算) 指在计算前对数字取整获得近似答案。Factorise completely (完全因式分解) 意味着先提出最大公因数，再检查能否进一步分解。Sketch (草图) 指绘出大致形状和关键点，并非在坐标纸上精确绘制。
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