Year 9 AQA Further Maths: Vocabulary & Terminology Quick Reference Guide | Year 9 AQA 进阶数学：词汇术语速记指南

📚 Year 9 AQA Further Maths: Vocabulary & Terminology Quick Reference Guide | Year 9 AQA 进阶数学：词汇术语速记指南

Understanding mathematical vocabulary is the first step to mastering Year 9 AQA Further Maths. This guide provides quick, bilingual explanations of essential terms to boost your confidence and exam performance.

理解数学词汇是掌握 Year 9 AQA 进阶数学的第一步。本指南提供核心术语的双语快速解释，帮助你提升信心和考试成绩。

1. Algebraic Expressions | 代数表达式

Algebra is the language of generalised arithmetic. Firmly grasping the building blocks of expressions will help you manipulate and solve problems efficiently.

代数是广义算术的语言。牢牢掌握表达式的构建模块，能帮助你高效地处理并解决问题。

• Variable: A symbol, usually a letter, that stands for an unknown or changeable number. Example: in 4x – 7, x is the variable.

  变量：代表未知或可变数值的符号，通常是一个字母。例如在 4x – 7 中，x 是变量。

• Constant: A fixed value that does not change. In the expression 3y + 5, the number 5 is a constant.

  常数：固定的、不变的数值。在表达式 3y + 5 中，数字 5 是常数。

• Term: A single number, variable, or product of numbers and variables separated by + or – signs. In 2a + 3b – c, the terms are 2a, 3b, and c.

  项：由加号或减号分隔的单个数字、变量或数与变量的乘积。在 2a + 3b – c 中，项分别为 2a, 3b 和 c。

• Coefficient: The numerical factor multiplying a variable in a term. In 7p², 7 is the coefficient of p².

  系数：项中乘以变量的数字因数。在 7p² 中，7 是 p² 的系数。

• Expression: A mathematical phrase made up of numbers, variables and operation symbols, without an equals sign. E.g., 5n + 4, 3(x – 2).

  表达式：由数字、变量和运算符号组成的数学短语，不含等号。例如 5n + 4, 3(x – 2)。

• Equation: A statement that two expressions are equal, using the equals sign. Example: 2x + 1 = 9.

  方程：使用等号表示两个表达式相等的陈述。例如 2x + 1 = 9。

• Identity: An equation that is true for all values of the variables, often shown with the ≡ symbol. Example: a(b + c) ≡ ab + ac.

  恒等式：对所有变量取值都成立的等式，常用符号 ≡ 表示。例如 a(b + c) ≡ ab + ac。

• Simplify: To collect like terms and perform arithmetic to write an expression in its simplest form. E.g., 2x + 3x simplifies to 5x.

  化简：合并同类项并进行算术运算，将表达式写成最简形式。例如 2x + 3x 化简为 5x。

• Expand: To multiply out brackets by distributing each term. For instance, expanding 3(y + 4) gives 3y + 12.

  展开：利用分配律去掉括号。例如展开 3(y + 4) 得到 3y + 12。

• Factorise: The reverse of expanding; rewriting an expression as a product of its factors. E.g., 6x – 9 factorises to 3(2x – 3).

  因式分解：展开的逆过程；将表达式写成其因式的乘积。例如 6x – 9 分解得到 3(2x – 3)。

• Substitute To replace a variable with a numerical value. If x = 2, substituting into x² + 1 gives 5.

  代入：用数值替换变量。若 x = 2，代入 x² + 1 得到 5。

2. Equations and Inequalities | 方程与不等式

Equations set up relationships, while inequalities define ranges of possible values. Knowing these terms makes solving more systematic.

方程建立了相等关系，而不等式则定义了可能的取值范围。熟悉这些术语会让求解过程更加条理化。

• Linear equation : An equation where the highest power of the variable is 1, producing a straight line graph. Example: 2x – 3 = 7.

  线性方程：变量的最高次幂为 1 的方程，其图像是一条直线。例如 2x – 3 = 7。

• Quadratic equation ntaining a term with the variable squared, e.g., x² + 5x + 6 = 0. Its graph is a parabola.

  二次方程：含有变量平方项的方程，如 x² + 5x + 6 = 0。它的图像是抛物线。

• Solution / Root: A value that makes an equation true. The solutions of (x – 1)(x + 4) = 0 are x = 1 and x = –4.

  解 / 根：使方程成立的数值。方程 (x – 1)(x + 4) = 0 的解为 x = 1 和 x = –4。

• Solve: To find the value(s) of the variable that satisfy the equation or inequality.

  求解：找出使方程或不等式成立的变量值。

• Simultaneous equations: A set of two or more equations with multiple variables that share the same solution. Often solved by elimination or substitution.

  联立方程组：包含两个或多个方程，并且含有多个变量且共用同一组解的方程组。通常用消元法或代入法求解。

• Inequality ment comparing two expressions using symbols <, >, ≤, or ≥. Example: 3x + 1 < 10.

  不等式：使用符号 <、>、≤ 或 ≥ 比较两个表达式大小的数学陈述。例如 3x + 1 < 10。

• Strict inequality: Inequalities using < or > that exclude the boundary value. x > 4 means 4 is not included.

  严格不等式：使用 < 或 > 的不等式，不包含边界值。x > 4 表示 4 不取。

• Inclusive inequality qualities using ≤ or ≥ that include the boundary value. x ≤ 7 means 7 is a valid solution.

  非严格不等式：使用 ≤ 或 ≥ 的不等式，包含边界值。x ≤ 7 表示 7 是合格解。

• Balance method: A solving technique where the same operation is applied to both sides of an equation to maintain equality.

  平衡法：一种求解技巧，对方程两边同时进行相同运算以保持相等关系。

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3. Numbers and Sets | 数与集合

Classifying numbers and using set language builds a strong foundation for number theory and logic in Further Maths.

对数字进行分类并使用集合语言，能为进阶数学中的数论与逻辑打下坚实基础。

• Natural numbers (ℕ): Positive whole numbers from 1 upwards: 1, 2, 3, … Some definitions include 0.

  自然数 (ℕ)：从 1 开始的正整数：1, 2, 3, … 有些定义也包括 0。

• Integers (ℤ): All positive and negative whole numbers including zero: … –2, –1, 0, 1, 2, …

  整数 (ℤ)：所有正整数、负整数以及零：… –2, –1, 0, 1, 2, …

• Rational numbers (ℚ): Numbers that can be expressed as a fraction a/b where a and b are integers, b ≠ 0. E.g., ½, 0.75, –3.

  有理数 (ℚ)：可以表示为分数 a/b (a, b 为整数且 b ≠ 0) 的数。例如 ½, 0.75, –3。

• Irrational numbers: Numbers that cannot be written as a simple fraction. Their decimal expansions are non‑terminating and non‑repeating, e.g., √2, π.

  无理数：不能写成简单分数的数，其小数部分无限不循环，如 √2, π。

• Real numbers (ℝ): The set of all rational and irrational numbers, representing every point on the number line.

  实数 (ℝ)：所有有理数和无理数的集合，代表数轴上的每一个点。

• Prime number: An integer greater than 1 with exactly two distinct factors: 1 and itself. Example: 2, 3, 5, 7, 11.

  质数：大于 1 且只有 1 和自身两个不同因数的整数。例如 2, 3, 5, 7, 11。

• Composite number: A positive integer that has more than two factors. 12 is composite because its factors are 1, 2, 3, 4, 6, 12.

  合数：有超过两个因数的正整数。12 是合数，因为它的因数为 1, 2, 3, 4, 6, 12。

• Factor: A whole number that divides exactly into another number. 3 is a factor of 15.

  因数：能整除另一个数的整数。3 是 15 的因数。

• Multiple: The product of a number and any integer. Multiples of 5 are 5, 10, 15, 20, …

  倍数：一个数与任意整数的乘积。5 的倍数有 5, 10, 15, 20, …

• HCF / LCM: Highest Common Factor (largest factor shared by two or more numbers) and Lowest Common Multiple (smallest multiple shared by two or more numbers).

  最大公因数 / 最小公倍数：最大公因数（两数或多个数共有的最大因数）和最小公倍数（两数或多个数共有的最小倍数）。

• Set: A well‑defined collection of distinct objects, written with curly brackets. E.g., A = {2, 4, 6}.

  集合：一组明确、互异对象的整体，用花括号表示。例如 A = {2, 4, 6}。

• Element: A member of a set. For set A = {a, b, c}, we write a ∈ A. If an item is not in the set, we write d ∉ A.

  元素：集合中的成员。对于集合 A = {a, b, c}，可写作 a ∈ A；若某项不属于该集合，则记作 d ∉ A。

• Subset: A set B is a subset of A (B ⊆ A) if every element of B is also in A. ⊂ denotes a proper subset where B is smaller.

  子集：若集合 B 的每个元素都属于集合 A，则 B ⊆ A。⊂ 表示真子集，即 B 较小且不相等。

• Union and intersection: The union A ∪ B contains all elements in A or B. The intersection A ∩ B contains only elements in both A and B.

  并集与交集：并集 A ∪ B 包含所有属于 A 或 B 的元素。交集 A ∩ B 仅包含同时属于 A 和 B 的元素。

• Empty set: The set with no elements, denoted by {} or ∅.

  空集：没有任何元素的集合，记作 {} 或 ∅。

• Complement: The complement of set A, written A', is all elements in the universal set that are not in A.

  补集：集合 A 的补集记为 A'，表示全集中所有不属于 A 的元素。

4. Geometry Basics | 基础几何

Geometry terminology describes shapes, angles and properties. Accurate vocabulary is crucial for reasoning and proofs.

几何术语描述了形状、角度及其性质。准确的词汇对推理和证明至关重要。

• Angle: The measure of turn between two lines meeting at a common vertex, measured in degrees.

  角：两条线汇聚在同一顶点处的旋转量，以度为单位。

• Acute angle: An angle less than 90°.

  锐角：小于 90° 的角。

• Obtuse angle: An angle greater than 90° but less than 180°.

  钝角：大于 90° 且小于 180° 的角。

• Reflex angle: An angle greater than 180° but less than 360°.

  优角：大于 180° 且小于 360° 的角。

• Right angle: An angle of exactly 90°, often marked with a small square.

  直角：恰好 90° 的角，通常用小方格标记。

• Perpendicular lines: Two lines that intersect at a right angle.

  垂直线：相交成直角的两条直线。

• Parallel lines: Lines in a plane that never meet, remaining the same distance apart.

  平行线：同一平面内永不相交且保持相等距离的直线。

• Polygon: A closed 2D shape with straight sides. Triangles, quadrilaterals and pentagons are polygons.

  多边形：由直线段构成的封闭二维图形。三角形、四边形和五边形都是多边形。

• Regular polygon: A polygon with all sides equal and all interior angles equal, e.g., a square or an equilateral triangle.

  正多边形：所有边长相等且所有内角相等的多边形，例如正方形或等边三角形。

• Sum of interior angles: For a polygon with n sides, the sum is (n – 2) × 180°.

  内角和：对于 n 边形，内角和为 (n – 2) × 180°。

• Pythagoras' theorem: In a right‑ uare of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².

  勾股定理：在直角三角形中，斜边的平方等于两条直角边的平方和：a² + b² = c²。

• Hypotenuse: The longest side of a right‑angled triangle, opposite the right angle.

  斜边：直角三角形中最长的边，

  Published by TutorHao | Year 9 进阶数学 Revision Series | aleveler.com

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