Year 10 AQA Further Maths: Key Terminology Quick-Memorisation Guide | AQA十年级进阶数学核心词汇速记指南

📚 Year 10 AQA Further Maths: Key Terminology Quick-Memorisation Guide | AQA十年级进阶数学核心词汇速记指南

Mastering the precise vocabulary of AQA Level 2 Further Mathematics is a powerful shortcut to exam confidence. This guide brings together the essential terms from algebra, functions, calculus, matrices, trigonometry and more, with clear definitions and memorable tips in both English and Chinese to speed up your learning.

精确掌握 AQA Level 2 进阶数学的词汇是提升考试信心的有力捷径。本指南汇集了代数、函数、微积分、矩阵、三角学等各个板块的核心术语，每个术语都配有清晰的中英定义和记忆妙招，帮助您双倍速吸收。

1. Algebraic Fundamentals | 代数基础术语

Variable – A letter or symbol that stands for a number which can change. In the equation y = 3x + 7, 'x' and 'y' are variables. Memory aid: A variable can 'vary' – it is not fixed.

变量 – 用来表示一个可以改变的数字的字母或符号。在等式 y = 3x + 7 里，'x' 和 'y' 就是变量。记忆法：变量会'变'——它不是固定的。

Constant – A fixed, unchanging number. In 5x + 2, the number 2 is a constant term. Tip: Think of something 'constant' that stays the same all the time.

常数 – 一个固定不变的数字。在 5x + 2 中，数字 2 就是常数项。窍门：想到'恒定'一词就不容易忘记。

Coefficient – The number that multiplies a variable. In 7x³ − 4x + 9, the coefficient of x³ is 7, and the coefficient of x is −4. Quick linker: 'Co-' means together – it works together with the variable.

系数 – 乘在变量前面的数字。在 7x³ − 4x + 9 中，x³ 的系数是 7，x 的系数是 −4。联想记忆：'系'表示联系，系数总是和变量绑在一起。

Term – A single mathematical product of numbers and variables, separated by '+' or '−' in an expression. For example, 3x², −5y and 7 are separate terms in 3x² − 5y + 7.

项 – 由数字和变量的乘积构成的一个独立部分，在表达式中用 '+' 或 '−' 分隔。例如在 3x² − 5y + 7 中，3x²、−5y 和 7 都是独立的项。

Expression – A combination of terms without an equals sign, such as 2a + 3b − 5. It cannot be solved – only simplified. Memory hook: An expression is like a phrase, while an equation is like a complete sentence.

表达式 – 由若干项组合而成且没有等号的数学片段，比如 2a + 3b − 5。它不能'解'，只能化简。巧记：表达式好比一个词组，方程才是完整的一句话。

Equation – A mathematical statement that two expressions are equal, containing an equals sign '='. For instance, 4x − 3 = 9 can be solved to find x. Hint: Equal-ity means equation.

方程 – 用等号 '=' 连接两个表达式，断言它们相等的数学陈述。例如 4x − 3 = 9 可以通过解方程求出 x。提示：看到等号就想到方程。

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2. Equations and Inequalities | 方程与不等式

Linear equation – riable appears only to the power of 1, giving a straight-line graph. Example: 2x + 3 = 11. Visual clue: 'Linear' → line.

一元一次方程（线性方程） – 变量只出现 1 次幂的方程，其图像是一条直线。例如 2x + 3 = 11。图像线索：'Linear' 联想到直线。

Quadratic equation – = 0 where a ≠ 0. Its graph is a parabola. Solving it may yield two, one or no real roots.

二次方程 – 形如 ax² + bx + c = 0 且 a ≠ 0 的方程，图像为抛物线。解方程可能得到两个、一个实数根或无实数根。

Simultaneous equations – A set of two (or more) equations that share the same variables and are solved together. Methods include elimination and substitution. Tip: 'Simultaneous' means happening at the same time.

联立方程 – 共用相同变量的两个（或多个）方程，需要同时求解。常用方法有消元法和代入法。提示：'联立'意为同时成立。

Root / Solution – variable that makes an equation true. For x² − 5x + 6 = 0, x = 2 and x = 3 are the roots. Idea: A root is where the graph touches the x-axis.

根 / 解 – 能使方程成立的变量取值。在 x² − 5x + 6 = 0 中，x = 2 和 x = 3 都是根。形象化：根就是图像与 x 轴交点的横坐标。

Inequality – A relation showing that one side is less than, greater than, or not equal to the other, using symbols <, >, ≤, ≥ or ≠. Example: 2x + 1 > 5. Note: Multiplying or dividing by a negative flips the sign.

不等式 – 用 <、>、≤、≥ 或 ≠ 表示两边大小关系的数学式。例如 2x + 1 > 5。注意：乘或除以负数时要反转不等号。

Number line & interval notation – Solutions to inequalities are often shown on a number line or written in interval form, e.g. x > 3 is written as (3, ∞) with a hollow circle at 3. Memory: Hollow for strict, solid for inclusive.

数轴与区间表示 – 不等式的解常用数轴展示或用区间符号书写，比如 x > 3 表示为 (3, ∞)，在 3 处画空心圆。记忆：空心表示严格不等，实心表示包含等号。

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3. Functions and Graphs | 函数与图像

Function – ssigns exactly one output for each input. Often written as f(x) = ..., e.g. f(x) = x² + 1. Key test: A vertical line cuts a function graph at most once.

函数 – 每个输入对应唯一输出的对应规则，常写作 f(x) = ...，例如 f(x) = x² + 1。关键检验：垂直线与函数图像至多相交一次。

Domain and Range – The domain is the set of all possible input values (x); the range is the set of all possible output values (f(x)). Mnemonics: Domain = 'x goes in', range = 'results out'.

定义域与值域 – 定义域是所有允许输入值 (x) 的集合；值域是所有可能输出值 ( f(x) ) 的集合。顺口溜：定义域看 x 的取值范围，值域看 y 的结果。

Composite function – the input of the other, written as fg(x) = f(g(x)). Always apply the inner function first. Phrase: 'g then f'.

复合函数 Published by TutorHao | Year 10 进阶数学 Revision Series | aleveler.com

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