📚 Year 8 CIE Further Maths: Glossary & Terminology Quick Guide | Year 8 CIE 进阶数学：词汇术语速记指南
Building a strong mathematical vocabulary is just as important as learning procedures. In Year 8 CIE Further Maths, you will meet many new terms. This quick guide groups essential terminology by topic so you can master definitions and recall them easily. Each term is explained in English and Chinese, with memory tricks where useful.
建立扎实的数学词汇与学习解题方法同样重要。在 Year 8 CIE 进阶数学中，你会遇到许多新术语。本速记指南将核心术语按主题分组，帮助你掌握定义并轻松回忆。每个术语均提供中英文解释，并附上实用的记忆技巧。
1. Number and Arithmetic | 数与算术
A secure grasp of number types and operations underpins all further maths topics. Memorise these fundamental words.
牢固掌握数的类型和运算是所有进阶数学主题的基础。请记住以下基本词汇。
Integer: An integer is any whole number that is not a fraction. It can be positive, negative, or zero. Examples: -5, 0, 12.
整数：整数是任何不是分数的完整数，可以是正数、负数或零。例如：-5, 0, 12。
Prime Number: A prime number has exactly two distinct factors: 1 and the number itself. 2 is the only even prime. Note: 1 is not prime.
质数（素数）：质数恰好有两个不同的因数：1 和它本身。2 是唯一的偶质数。注意：1 不是质数。
Factor: A factor of a number divides it exactly without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
因数：一个数的因数是可以整除该数而不留余数的数。例如，12 的因数有 1, 2, 3, 4, 6 和 12。
Multiple: A multiple of a number is the result of multiplying that number by an integer. Multiples of 4 include 4, 8, 12, 16, …
倍数：一个数的倍数是用某个整数乘该数得到的结果。4 的倍数包括 4, 8, 12, 16, …
Square Root a number is a value that, when multiplied by itself, gives the original number. Symbol: √. √25 = 5 because 5 × 5 = 25.
平方根：一个数的平方根是自乘后得到原数的值。符号：√。√25 = 5，因为 5 × 5 = 25。
Quick memory tip: "Prime" can remind you of "primary" or VIP – only two special guests (1 and itself) are allowed.
速记技巧：'Prime' 可联想到 '首要' 或 VIP——只允许两位特殊嘉宾（1 和它本身）入场。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Being fluent with different representations of parts of a whole is essential. Here are the key words to describe them.
熟练掌握整体一部分的不同表示方法非常重要。以下为描述它们的关键词汇。
Numerator: The top part of a fraction; it shows how many equal parts are taken. In 3/8, the numerator is 3.
分子：分数中位于上方的部分，表示取了多少个等份。如 3/8 中，分子为 3。
Denominator: The bottom part of a fraction; it indicates the total number of equal parts the whole is split into. In 3/8, the denominator is 8.
分母：分数中位于下方的部分，表示整体被等分的总份数。如 3/8 中，分母为 8。
Equivalent Fractions: Different fractions that represent the same value. For example, 1/2, 2/4, and 5/10 are equivalent.
等值分数：表示相同数值的不同分数。例如，1/2、2/4 和 5/10 是等值的。
Mixed Number: A whole number combined with a proper fraction, such as 2¾. It shows a quantity greater than one.
带分数：由整数和真分数组合而成的数，如 2¾，表示大于 1 的量。
Recurring Decimal: A decimal that repeats a digit or block of digits forever. Example: 0.333… = 0.3̅. Recurring decimals can be written with a dot above the repeating digit(s).
循环小数：小数部分永远重复一个或一段数字的小数。例：0.333… = 0.3̅。循环小数可在重复数字上方加点表示。
3. Ratio, Proportion and Rates | 比、比例与率
Comparing quantities is a core skill. Learn these terms to describe relationships between numbers accurately.
比较数量是一项核心技能。学习以下术语以准确描述数字之间的关系。
Ratio: A ratio compares two or more quantities, showing the relative sizes. It is written as a : b or a to b. Example: a drink mix of 1 part cordial to 4 parts water has ratio 1 : 4.
比：比较两个或多个数量，表示相对大小。写作 a : b 或 a 比 b。例如，1 份浓缩果汁兑 4 份水的饮料，其比为 1 : 4。
Proportion the quantities are in proportion. Cross-multiplication can be used to test for proportion.
比例：说明两个比相等的关系。如果 a/b = c/d，这些量就成比例。可以使用交叉相乘来检验是否成比例。
Unitary Method: A technique where you first find the value of one unit, then scale up to the required amount. For instance, if 5 apples cost £2, one apple costs £0.40, so 8 apples cost £3.20.
归一法：先求出单一单位的值，再按需求放大至所需数量的方法。例如，若 5 个苹果售价 £2，则 1 个苹果 £0.40，所以 8 个苹果 £3.20。
Direct Proportion: Two quantities are in direct proportion if an increase in one causes a proportional increase in the other (constant ratio). Graphically, this creates a straight line through the origin.
正比例：如果一个量增加，另一个量按相同倍率增加（比值恒定），就称这两个量成正比例。图像为一条过原点的直线。
4. Algebraic Expressions | 代数表达式
Algebra gives us a language to express general mathematical ideas. These terms will help you manipulate symbols confidently.
代数为我们提供了表达通用数学思想的语言。以下术语将助你自信地处理符号。
Variable: A letter or symbol that stands for an unknown value or a value that can change. Common variables are x, y, and t.
变量：代表未知值或可改变值的字母或符号。常用变量有 x、y 和 t。
Coefficient: The number multiplying a variable in a term. In 5x², the coefficient is 5. If no number is written, the coefficient is 1 (e.g., x means 1x).
系数：单项式中与变量相乘的数字。如 5x² 中系数为 5。若未写数字，则系数为 1（例如 x 表示 1x）。
Term: A single mathematical entity that can be a number, a variable, or numbers and variables multiplied together. In 7y³ + 2y − 9, there are three terms.
项：可以是一个数、一个变量或数与变量的乘积构成的单一数学实体。在 7y³ + 2y − 9 中，有三项。
Like Terms: Terms that contain exactly the same variables raised to the same powers, only their coefficients may differ. 3x² and −5x² are like terms; 3x² and 3x are not.
同类项：所含变量及其指数完全相同的项，仅系数可能不同。3x² 和 −5x² 是同类项；3x² 和 3x 则不是。
Expand: To remove brackets in an expression by multiplying each term inside by the factor outside. Example: 3(a + 4) expands to 3a + 12.
展开：通过用括号外的因式乘以括号内的每一项来消去括号。例如：3(a + 4) 展开为 3a + 12。
Factorise: The reverse of expanding; write an expression as a product of its factors. e.g., 6x + 9 factorises to 3(2x + 3).
因式分解：与展开相反，将表达式写成其因式的乘积。例如，6x + 9 因式分解为 3(2x + 3)。
5. Equations and Inequalities | 方程与不等式
Solving equations means finding unknown values; dealing with inequalities introduces ranges of possible answers. Here is the vocabulary you need.
解方程意味着求出未知数的值；处理不等式则会引入可能的数值范围。以下是你需要掌握的词汇。
Equation ing that two expressions are equal, connected by an equals sign (=). Example: 2x + 3 = 11.
方程：用等号（=）连接，表明两个表达式相等的数学陈述。例：2x + 3 = 11。
Inequality ecessarily equal, using symbols like <, >, ≤, ≥. Example: x > 5 means x is greater than 5.
不等式：使用 <、>、≤、≥ 等符号表示两个表达式未必相等的关系。例：x > 5 表示 x 大于 5。
Solution (Root) e value of the variable that makes an equation true. For x + 4 = 7, the solution is x = 3.
解（根）：使方程成立的变量的值。对于 x + 4 = 7，解为 x = 3。
Balance Method: An approach to solving equations where you keep both sides balanced by performing the same operation on each side (add, subtract, multiply, divide).
平衡法：解方程的一种方法，通过对等式两边进行相同运算（加减乘除）来维持平衡。
Unknown: A letter or symbol representing an as yet unsearched number. In many equations, we solve for the unknown.
未知数：代表尚未确定数值的字母或符号。在许多方程中，我们求解未知数。
6. Sequences | 数列
Patterns are everywhere in mathematics. These terms will help you describe and predict the next terms in a sequence.
规律在数学中无处不在。以下术语将帮助你描述并预测数列中的后续项。
Sequence: A list of numbers or objects in a particular order, often following a rule. Example: 3, 6, 9, 12, … is a sequence.
数列（序列）：按特定顺序排列的一列数或对象，通常遵循某一规则。例：3, 6, 9, 12, … 为一个数列。
Term: Each individual number or item in a sequence. The first term is often denoted as a₁ or T₁. In 5, 9, 13, 17, the 3rd term is 13.
项：数列中的每一个数或元素。第一项常记作 a₁ 或 T₁。在 5, 9, 13, 17 中，第 3 项为 13。
nth Term: A formula that lets you calculate any term of a sequence using its position number n. For the sequence 7, 10, 13, 16, … the nth term is 3n + 4.
第 n 项：允许你利用位置编号 n 计算数列中任意一项的公式。对于数列 7, 10, 13, 16, …，第 n 项为 3n + 4。
Arithmetic Sequence s is constant. This fixed amount is called the common difference, d. Example: 2, 5, 8, 11, … (d = 3).
等差数列：相邻两项的差恒定的数列。这个固定的差值称为公差 d。例如：2, 5, 8, 11, … （d = 3）。
Geometric Sequence revious term by a fixed non-zero number called the common ratio, r. Example: 3, 6, 12, 24, … (r = 2).
等比数列：从第二项起，每一项都是前一项乘以一个固定的非零数得到的数列，该固定数称为公比 r。例如：3, 6, 12, 24, … （r = 2）。
7. Graphs and Coordinates | 图与坐标
Graphs turn algebraic relationships into visual stories. Make sure you can talk about axes, lines, and gradients.
图像将代数关系转化为视觉故事。确保你能描述坐标轴、直线和斜率。
Coordinate Plane: A two-dimensional surface formed by two perpendicular number lines, the x-axis (horizontal) and y-axis (vertical). Points are located using ordered pairs.
坐标平面：由两条互相垂直的数轴——x 轴（水平）和 y 轴（垂直）构成的二维平面。用有序对确定点的位置。
Origin: The point where the x-axis and y-axis intersect. Its coordinates are (0, 0).
原点：x 轴与 y 轴的交点。其坐标为 (0, 0)。
Ordered Pair: A pair of numbers written as (x, y) that gives the horizontal and vertical position of a point. (3, −2) means 3 units right and 2 units down from the origin.
有序对：形如 (x, y) 的一对数，表示点的水平与垂直位置。(3, −2) 表示从原点向右 3 个单位、向下 2 个单位。
Gradient (Slope): A measure of steepness of a line, often calculated as rise/run or change in y ÷ change in x. A larger gradient means a steeper line.
斜率（坡度）：衡量直线陡峭程度的量，通常用纵差/横差或 y 的变化量 ÷ x 的变化量计算。斜率越大，直线越陡。
Intercept the line cuts the y-axis (x = 0), and the x-intercept is where it cuts the x-axis (y = 0).
截距：直线与坐标轴的交点。y 轴截距是直线与 y 轴（x = 0）相交的位置，x 轴截距是直线与 x 轴（y = 0）相交的位置。
8. Angles and Lines | 角与线
Geometry begins with lines and angles. These terms set the stage for shapes, constructions, and proofs.
几何学始于线与角。这些术语为图形、作图和证明奠定了基础。
Acute Angle: An angle that measures more than 0° and less than 90°.
锐角：度量大于 0° 且小于 90° 的角。
Obtuse Angle: An angle greater than 90° but less than 180°.
钝角：大于 90° 但小于 180° 的角。
Reflex Angle: An angle greater than 180° and less than 360°.
优角（反角）：大于 180° 且小于 360° 的角。
Parallel Lines: Lines in a plane that are always the same distance apart and never meet. They are marked with identical arrow symbols.
平行线：同一平面内始终等距且永不相交的直线。用相同箭头符号标记。
Perpendicular Lines: Lines that intersect at a right angle (90°). The symbol is ⊥.
垂线：相交成直角（90°）的直线。符号为 ⊥。
Transversal: A line that cuts across two or more other lines, typically parallel lines. It creates pairs of corresponding, alternate, and co-interior angles.
截线：横穿两条或多条（通常平行）直线的线。截线会产生同位角、内错角和同旁内角。
9. Polygons and Symmetry | 多边形与对称
Shapes have names and properties that you must recall quickly. Symmetry helps describe a shape's balance.
图形有你需要快速回忆的名称和性质。对称帮助描述图形的平衡性。
Polygon: A closed 2D shape with three or more straight sides. Triangles, quadrilaterals, pentagons, and hexagons are all polygons.
多边形：由三条或以上线段围成的封闭二维图形。三角形、四边形、五边形、六边形都属于多边形。
Regular Polygon: A polygon where all sides are equal in length and all interior angles are equal. Example: a square, an equilateral triangle, a regular hexagon.
正多边形：所有边等长且所有内角相等的多边形。例如：正方形、等边三角形、正六边形。
Quadrilateral: A polygon with exactly four sides. Special types include square, rectangle, parallelogram, rhombus, trapezium, and kite.
四边形：恰好有四条边的多边形。特殊类型包括正方形、矩形、平行四边形、菱形、梯形和筝形。
Line of Symmetry: A line that divides a shape into two identical halves that are mirror images of each other. A rectangle has two lines of symmetry.
对称轴：将图形分成两个互为镜像的相同半边的直线。矩形有两条对称轴。
Rotational Symmetry: A shape has rotational symmetry if it looks the same more than once during a full 360° turn. Order of symmetry tells you how many matches there are.
旋转对称：如果一个图形在绕中心旋转 360° 的过程中出现多于一次的自身重合，则具有旋转对称。对称阶表示重合的次数。
10. Mensuration | 测量与计量
Measuring length, area, and volume is a practical side of further maths. These definitions will keep your units and formulas straight.
测量长度、面积和体积是进阶数学的实践部分。这些定义将帮助你理清单位与公式。
Perimeter tance around the outside of a 2D shape. For a rectangle, perimeter = 2 × (length + width).
周长：二维图形外边界的总长度。对矩形，周长 = 2 ×（长 + 宽）。
Area: The amount of space inside a 2D shape, measured in
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