📚 Year 8 AQA Mathematics: Quick Vocabulary & Terminology Guide | Year 8 AQA 数学：词汇术语速记指南
Mastering mathematical vocabulary is a crucial step towards success in Year 8 and beyond. This guide walks you through the essential terms from the AQA curriculum, providing clear definitions across number, algebra, geometry, statistics and more. Use it to build confidence and fluency in every topic.
掌握数学词汇是在 Year 8 及以后取得优异成绩的关键一步。本指南将带你浏览 AQA 课程中的核心术语，涵盖数、代数、几何、统计等领域，并给出清晰的定义。用它来建立信心，让每个主题都变得流畅自如。
1. Number Types | 数类型
We begin with the very foundations: the different families of numbers you will work with throughout the year. Knowing their names and properties helps you recognise how they behave in operations.
我们从最基础的部分开始：你在整个学年中都会打交道的不同数家族。了解它们的名称和性质有助于你在运算中识别它们的行为。
Natural Numbers: The counting numbers starting from 1, 2, 3, 4, and so on. They do not include zero or negative numbers.
自然数：从 1、2、3、4 等开始的计数数字，不包括零和负数。
Whole Numbers: Natural numbers together with zero (0, 1, 2, 3, …). They are never negative and have no fractional part.
非负整数：包含零和所有自然数的集合（0, 1, 2, 3, …）。永不为负且没有小数部分。
Integers: The set of whole numbers and their negative counterparts, e.g., …, –3, –2, –1, 0, 1, 2, 3, …
整数：所有非负整数及其相反数的集合，例如 …，–3，–2，–1，0，1，2，3，…
Rational Numbers: Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. Examples: ½, 0.75 (which is ¾), –4 (which is –4/1). Terminating and recurring decimals are rational.
有理数：可以写成分数 a/b 形式的任何数，其中 a 和 b 是整数且 b ≠ 0。例如：½，0.75（即 ¾），–4（即 –4/1）。有限小数和循环小数都是有理数。
Irrational Numbers: on. Their decimal expansions go on forever without repeating. Examples include π (≈3.14159…) and √2 (≈1.4142…).
无理数：无法用简单分数表示的数。它们的小数展开无限不循环。例如 π（≈3.14159…）和 √2（≈1.4142…）。
2. Multiples, Factors and Primes | 倍数、因数和质数
These concepts are the building blocks of number theory. They help you simplify calculations, find common denominators, and break numbers down into their basic parts.
这些概念是数论的基石。它们帮助你简化计算、寻找公分母，并将数字分解成基本组成部分。
Multiple: The result of multiplying a whole number by any integer. The multiples of 3 are 3, 6, 9, 12, …
倍数：一个整数与另一个整数相乘的结果。3 的倍数有 3、6、9、12 …
Factor: A whole number that divides exactly into another number with no remainder. The factors of 12 are 1, 2, 3, 4, 6, 12.
因数：能整除另一个数且没有余数的整数。12 的因数有 1、2、3、4、6、12。
Prime Number: A whole number greater than 1 that has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 and 13 are prime numbers.
质数：大于 1 且恰好只有两个不同因数的整数：1 和它本身。2、3、5、7、11 和 13 都是质数。
Composite Number: A whole number greater than 1 that is not prime; it has at least one factor other than 1 and itself. 4, 6, 8, 9 are composite.
合数：大于 1 的非质数整数；它至少有一个除 1 和自身以外的因数。4、6、8、9 是合数。
Prime Factorisation: Expressing a number as a product of prime numbers. For example, 12 = 2 × 2 × 3 = 2² × 3.
质因数分解：将一个数表示为质数的乘积。例如，12 = 2 × 2 × 3 = 2² × 3。
Highest Common Factor (HCF): The largest factor that two or more numbers share. The HCF of 8 and 12 is 4.
最大公因数 (HCF)：两个或多个数共有的最大因数。8 和 12 的最大公因数是 4。
Lowest Common Multiple (LCM): The smallest multiple that two or more numbers have in common. The LCM of 4 and 6 is 12.
最小公倍数 (LCM)：两个或多个数共有的最小倍数。4 和 6 的最小公倍数是 12。
3. Fractions, Decimals and Percentages | 分数、小数和百分数
Interchanging between these three representations is a core Year 8 skill. A strong command of the vocabulary makes conversions and comparisons much easier.
在这三种表示形式之间灵活切换是 Year 8 的一项核心技能。牢固掌握这些词汇能让换算和比较变得容易得多。
Numerator: The top number in a fraction; it tells how many parts we have.
分子：分数中上面的数字，表示我们取了多少份。
Denominator: The bottom number in a fraction; it tells the total number of equal parts the whole is divided into.
分母：分数中下面的数字，表示整体被等分成了多少份。
Proper Fraction: A fraction where the numerator is smaller than the denominator, e.g., ⅗. Its value is between 0 and 1.
真分数：分子小于分母的分数，例如 ⅗。其值介于 0 和 1 之间。
Improper Fraction: A fraction where the numerator is equal to or larger than the denominator, e.g., ⅞ or ⁹⁄₄.
假分数：分子等于或大于分母的分数，例如 ⅞ 或 ⁹⁄₄。
Mixed Number: A number consisting of a whole part and a proper fraction part, e.g., 2⅓.
带分数：由一个整数部分和一个真分数部分组成的数，例如 2⅓。
Equivalent Fractions: Different fractions that represent the same value, e.g., ½ = ²⁄₄ = ⁴⁄₈.
等值分数：表示相同值的不同分数，例如 ½ = ²⁄₄ = ⁴⁄₈。
Recurring Decimal: A decimal with a digit or block of digits that repeats forever, often written with a dot notation, e.g., 0.333… or 0.16̇.
循环小数：小数部分有一位或几位数字无限重复，常用点标记表示，例如 0.333… 或 0.16̇。
Percentage: A quantity out of 100; symbol %. To convert a fraction to a percentage, find an equivalent fraction with denominator 100.
百分数：表示占 100 份中的多少；符号为 %。将分数转换为百分数，可寻找分母为 100 的等值分数。
4. Ratio and Proportion | 比和比例
Ratio and proportion describe how quantities compare to each other. They are used in recipes, maps, and scale drawings.
比和比例描述数量之间如何相互比较。它们用于食谱、地图和比例图。
Ratio: A way of comparing two or more quantities, written as a : b. The order matters.
比：一种比较两个或多个数量的方式，写作 a : b。顺序很重要。
Simplify a Ratio: Divide each part by the highest common factor to get the simplest whole-number ratio. 8 : 12 simplifies to 2 : 3.
化简比：用每个部分除以它们的最大公因数，得到最简单的整数比。8 : 12 化简为 2 : 3。
Proportion: A statement that two ratios are equal, or a comparative part of a whole. Often seen in direct proportion problems.
比例：表示两个比相等，或某量在整体中所占的比较份额。常见于正比例问题。
Unitary Method: A technique where you first find the value of one unit, then multiply to find the required amount. Used in best-buy and recipe scaling.
单位法：一种先求一个单位的值，再相乘得到所需数量的方法。用于最佳购买和食谱调整。
Direct Proportion: A relationship where two quantities increase or decrease at the same rate. Graphically it gives a straight line through the origin. y ∝ x.
正比例：两个量以相同速率增加或减少的关系。图像为一条通过原点的直线。y ∝ x。
5. Algebraic Expressions | 代数表达式
Algebra generalises arithmetic using letters for unknown or changing numbers. Mastering the language of algebra is the key to solving problems efficiently.
代数用字母代表未知或变化的数，推广了算术。掌握代数学的语言是高效解题的关键。
Variable: A letter or symbol that stands for an unknown or changeable number, e.g., x, y, n.
变量：代表未知或可变数字的字母或符号，例如 x, y, n。
Constant: A fixed value, a number on its own. In the expression 3x + 5, 5 is the constant.
常量：一个固定的值，即单独的一个数。在表达式 3x + 5 中，5 是常量。
Term: A single number, variable, or the product of numbers and variables. In 4x² – 2y + 7, the terms are 4x², –2y and 7.
项：单个的数、变量，或数与变量的乘积组成的部分。在 4x² – 2y + 7 中，项为 4x², –2y 和 7。
Coefficient: The number factor multiplying a variable. In –5a, the coefficient is –5.
系数：与变量相乘的因数。在 –5a 中，系数为 –5。
Expression: A combination of terms formed using operations but without an equals sign. 2x + 3 and a² – 4b are expressions.
表达式：用运算符号组合项构成，但不含等号。2x + 3 和 a² – 4b 是表达式。
Like Terms: Terms that contain exactly the same variables raised to the same powers. 5x and –3x are like terms; 2x and 2x² are not.
同类项：含有完全相同的变量且指数相同的项。5x 和 –3x 是同类项，但 2x 和 2x² 不是。
Simplify: To reduce an expression by collecting like terms or performing operations. 2x + 3x simplifies to 5x.
化简：通过合并同类项或执行运算将表达式缩减。2x + 3x 化简为 5x。
6. Equations and Inequalities | 方程和不等式
Equations and inequalities set conditions that allow you to find specific values for variables. Understanding the vocabulary helps you follow each step of the solution.
方程和不等式设定条件，让你为变量找到特定的值。理解这些词汇有助于你跟上解题的每一步。
Equation: atical statement showing two expressions are equal, containing an equals sign. Example: 3x – 1 = 8.
方程：一个数学陈述，表示两个表达式相等，包含等号。例如：3x – 1 = 8。
Solution (or Root): value of the variable that makes the equation true. For x + 4 = 10, the solution is x = 6.
解：使方程成立的变量的值。对于 x + 4 = 10，解为 x = 6。
Solve: To find the value(s) of the variable that satisfy the equation.
解方程：求出满足方程的变量的值。
Inequality: e quantity is greater or less than another, using symbols <, >, ≤, ≥. x > 3 means 'x is greater than 3'.
不等式：表示一个量大于或小于另一个量的陈述，使用符号 <、>、≤、≥。x > 3 表示 'x 大于 3'。
Balance Method: A technique for solving equations where the same operation is applied to both sides to keep the equation balanced.
天平法：一种解方程的方法，对等式两边施加相同运算以保持平衡。
Integer Solution: A solution that is a whole number. Not all equations have integer solutions, but Year 8 problems often do.
整数解：为整数的解。并非所有方程都有整数解，但 Year 8 的题目常常有。
7. Sequences | 序列
Sequences are ordered lists of numbers that follow a rule. Working with them develops pattern-spotting and algebraic thinking.
序列是按规则排列的有序数字列表。处理序列培养发现规律和代数思维能力。
Sequence: A list of numbers or objects in a special order. Example: 2, 4, 6, 8, …
序列：按特定顺序排列的一列数字或对象。例如：2, 4, 6, 8, …
Term: Each individual number or object in a sequence. The first term is often labelled T₁.
项：序列中的每一个数字或对象。第一项常标记为 T₁。
Nth Term: A formula that allows you to find any term in a sequence using its position number n. For 3, 5, 7, …, the nth term is 2n + 1.
第 n 项：一个公式，利用位置编号 n 可以求出序列中的任意项。对于 3, 5, 7, …，第 n 项为 2n + 1。
Arithmetic (Linear) Sequence: A sequence where the difference between consecutive terms is constant. This difference is called the common difference.
算术（线性）序列：相邻两项的差恒定的序列。这个差称为公差。
Common Difference: The amount added or subtracted to get from one term to the next in an arithmetic sequence. In 7, 11, 15, … the common difference is +4.
公差：在算术序列中，从一项到下一项所加上或减去的量。在 7, 11, 15, … 中，公差为 +4。
Term-to-term Rule: A descriptive rule connecting each term to the next, e.g., 'add 3' or 'multiply by 2'.
项间规则：描述相邻项如何联系的规则，例如“加 3”或“乘以 2”。
8. Angles and Lines | 角与线
Shapes and spaces are built from lines and angles. Learning the correct names and properties is essential for solving problems in geometry and reasoning about figures.
图形和空间由线和角构成。学习正确的名称和性质对解决几何问题和图形推理至关重要。
Acute Angle: An angle greater than 0° and less than 90°.
锐角：大于 0° 且小于 90° 的角。
Right Angle: Exactly 90°, often shown by a small square in the corner.
直角：恰好 90°，常在角内用一个小方块表示。
Obtuse Angle: Greater than 90° but less than 180°.
钝角：大于 90° 但小于 180° 的角。
Straight Angle: Exactly 180°, forming a straight line.
平角：恰好 180°，形成一条直线。
Reflex Angle: Greater than 180° but less than 360°.
优角：大于 180° 但小于 360° 的角。
Parallel Lines: Straight lines that never meet, no matter how far they are extended. They are always equidistant.
平行线：无论怎样延长都不相交的直线。它们始终保持等距。
Perpendicular Lines: Lines that intersect at a right angle (90°).
垂直线：以直角（90°）相交的直线。
Corresponding Angles: Angles in matching positions when a line crosses parallel lines; they are equal.
同位角：一条截线与平行线相交时，位于相同位置的一对角；它们相等。
Alternate Angles: Angles on opposite sides of the transversal and inside the parallel lines; they are equal.
内错角：在截线两侧且位于平行线内侧的角；它们相等。
Supplementary Angles: Two angles that add up to 180°.
补角：两个角之和为 180°。
Complementary Angles: Two angles that add up to 90°.
余角：两个角之和为 90°。
9. 2D Shapes | 二维图形
From triangles to quadrilaterals, knowing the vocabulary of 2D shapes lets you describe properties such as sides, angles, and symmetries accurately.
从三角形到四边形，掌握二维图形的词汇让你能准确地描述边、角、对称性等属性。
Polygon: A closed 2D shape with straight sides. Triangle (3 sides), quadrilateral (4), pentagon (5), hexagon (6), and so on.
多边形：由直线段围成的封闭二维图形。三角形（3 边）、四边形（4 边）、五边形（5 边）、六边形（6 边）等。
Regular Polygon: A polygon with all sides equal and all angles equal. A square is a regular quadrilateral.
正多边形：所有边等长且所有角相等的多边形。正方形是正四边形。
Scalene Triangle: A triangle with no equal sides and no equal angles.
不等边三角形：没有边等长、没有角相等的三角形。
Isosceles Triangle: A triangle with at least two equal sides and two equal base angles.
等腰三角形：至少有两条边相等、两个底角相等的三角形。
Equilateral Triangle: All three sides equal, and all three angles 60°.
等边三角形：三条边全等，三个角均为 60°。
Parallelogram: A quadrilateral with both pairs of opposite sides parallel. Opposite sides are equal, opposite angles are equal.
平行四边形：两组对边分别平行的四边形。对边相等，对角相等。
Rhombus: A parallelogram with all four sides equal. A square is a special rhombus with right angles.
菱形：四条边都相等的平行四边形。正方形是有直角的特殊菱形。
Trapezium (UK): A quadrilateral with at least one pair of parallel sides.
梯形（英国定义）：至少有一组对边平行的四边形。
Perimeter: The total distance around the outside of a 2D shape.
周长：二维图形外沿的总距离。
Area: measured in square units. Commonly used: A = l×w for rectangles, A = ½×b×h for triangles.
面积：图形覆盖的表面大小，以平方单位计。常用：长方形 A = 长×宽，三角形 A = ½×底×高。
10. 3D Shapes and Volume | 三维图形和体积
Moving into three dimensions, we consider faces, edges, vertices, and the space inside a solid. Correct terminology helps when drawing nets and calculating volumes.
进入三维空间，我们考虑面、棱、顶点以及立体内部的容积。正确的术语有助于绘制展开图和计算体积。
Face: A flat surface on a 3D shape. A cube has 6 square faces.
面：三维图形上的平面表面。立方体有 6 个正方形面。
Edge: The line where two faces meet. A cube has 12 edges.
棱：两个面相交的线。立方体有 12 条棱。
Vertex (plural: Vertices): A corner where three or more edges meet. A cube has 8 vertices.
顶点：三条或更多棱相交的角点。立方体有 8 个顶点。
Prism: A 3D shape with two parallel congruent faces and rectangular faces joining them. The cross-section is constant along its length.
棱柱：有两个平行且全等的底面、侧面均为矩形的三维图形。其横截面沿长度方向不变。
Pyramid: A 3D shape with a polygonal base and triangular faces that meet at a common apex.
棱锥：底面为
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