📚 Year 8 WJEC Advanced Maths: Glossary Quick-Reference Guide | Year 8 WJEC 进阶数学：词汇术语速记指南
Mastering the language of mathematics is the first step towards confident problem-solving. This glossary brings together the key terms you will meet in Year 8 WJEC Advanced Maths, with clear explanations and relevant examples to help you memorise and use them accurately.
掌握数学语言是迈向自信解题的第一步。这份词汇指南汇集了你在 Year 8 WJEC 进阶数学中将遇到的关键术语，配有清晰的解释和相关示例，帮助你准确记忆并使用它们。
1. Algebraic Terms and Expressions | 代数术语与表达式
Variable: A symbol, usually a letter such as x or y, that stands for an unknown number or a quantity that can change. In the expression 4n + 7, n is the variable.
变量：一个符号，通常用 x 或 y 之类的字母表示，代表未知的数或可以变化的量。在表达式 4n + 7 中，n 就是变量。
Constant: A fixed number on its own that does not change value. In 3x + 5, the number 5 is a constant term.
常数：一个本身固定不变的数值。在 3x + 5 中，数字 5 是一个常数项。
Term: A single number, a variable, or the product of numbers and variables inside an expression, separated by '+' or '−' signs. For example, in 2a² − 5b + 9, the three terms are 2a², −5b and 9.
项：表达式中的一个单独的数、一个变量或数与变量的乘积，各项之间由 '+' 或 '−' 分隔。例如，在 2a² − 5b + 9 中，三个项为 2a²、−5b 和 9。
Expression: A combination of terms without an equals sign. 3p + 2q − 8 is an expression; it is not an equation because it does not state that two things are equal.
表达式：几个项的组合，不含等号。3p + 2q − 8 是一个表达式；它不是一个方程，因为它没有表示两端相等。
2. Simplifying and Expanding | 化简与展开
Like terms: Terms that contain exactly the same variable part, including the same exponent. For instance, 7y and −2y are like terms, but 4x² and 4x are not like terms because the exponents differ.
同类项：含有完全相同的变量部分（包括相同的指数）的项。例如，7y 和 −2y 是同类项，但 4x² 和 4x 不是同类项，因为指数不同。
Simplify: To reduce an expression to its shortest form by collecting like terms. Simplifying 2x + 5y + 3x − y gives 5x + 4y.
化简：通过合并同类项将表达式化为最简形式。化简 2x + 5y + 3x − y 得到 5x + 4y。
Expand term in the first bracket by each term in the second, such as (x + 2)(x + 5) = x² + 7x + 10.
展开：用括号外的项乘以括号内的每一项，从而去除括号。展开 4(m + 3) 得到 4m + 12。对于两个括号，需要用第一个括号中的每一项分别乘以第二个括号中的每一项，如 (x + 2)(x + 5) = x² + 7x + 10。
Factorise: The reverse of expanding; to write an expression as a product of its factors by identifying a common factor. 6a + 9 can be factorised to 3(2a + 3).
因式分解：展开的逆运算：找出公因式，将表达式写成它的因式的乘积。6a + 9 可以因式分解为 3(2a + 3)。
3. Solving Equations and Inequalities | 解方程与不等式
Equation t that two expressions are equal, connected by an equals sign. 3n − 4 = 11 is an equation.
方程：表示两个表达式相等的数学陈述，由等号连接。3n − 4 = 11 就是一个方程。
Solve ue (or values) of the variable that makes an equation true. Solving y/4 = 5 yields y = 20.
解（方程）：求出使方程成立的变量的值。解 y/4 = 5 得到 y = 20。
Inequality (less than or equal to). For example, 2x + 1 ≤ 7 means 2x + 1 is less than or equal to 7.
不等式：使用符号比较两个表达式的语句：> (大于), < (小于), ≥ (大于或等于), ≤ (小于或等于)。例如，2x + 1 ≤ 7 表示 2x + 1 小于或等于 7。
Solution set: The collection of all values that satisfy an inequality. The solution set for x ≥ 4 is 'all numbers greater than or equal to 4'.
解集：满足不等式的所有值的集合。x ≥ 4 的解集是“所有大于或等于 4 的数”。
4. Number Types and Properties | 数的类型与性质
Integer: Any whole number that can be positive, negative or zero, including −3, 0, 8 and 150. Integers do not include fractions or decimals.
整数：任何正整数、负整数或零，如 −3、0、8 和 150。整数不包括分数或小数。
Prime number: A whole number greater than 1 that has exactly two distinct factors: 1 and itself. The first few primes are 2, 3, 5, 7, 11 and 13. Note that 1 is not prime.
质数（素数）：大于 1 且只有两个不同因数的整数：1 和它本身。最小的几个质数是 2、3、5、7、11 和 13。注意 1 不是质数。
Factor y, leaving no remainder. 4 and 6 are both factors of 24 because 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
因数：能整除另一个数而不留余数的数。4 和 6 都是 24 的因数，因为 24 ÷ 4 = 6 且 24 ÷ 6 = 4。
Square number and cube number of 2, e.g. 5² = 25. A cube number multiplies a number by itself twice more, e.g. 3³ = 27.
平方数和立方数：平方数是一个数自乘的结果，写成指数 2，如 5² = 25。立方数是一个数自乘三次，如 3³ = 27。
5. Fractions, Decimals and Percentages | 分数、小数与百分比
Numerator and denominator: The numerator is the top part of a fraction, showing the number of parts considered. The denominator is the bottom part, showing the total number of equal parts. In 3/8, 3 is the numerator and 8 is the denominator.
分子与分母：分子是分数上面的部分，表示考虑的部分数量。分母是下面的部分，表示整体被分成多少等份。在 3/8 中，3 是分子，8 是分母。
Equivalent fractions: Fractions that represent the same amount, even though they use different numerators and denominators. 1/2, 2/4 and 5/10 are all equivalent.
等价分数：表示同样大小但使用不同分子和分母的分数。1/2、2/4 和 5/10 都是等价分数。
Decimal: A number written with a decimal point to show tenths, hundredths and so on. 0.75 is a decimal that is equivalent to 3/4.
小数：用小数点表示十分位、百分位等的数。0.75 是一个小数，等价于 3/4。
Percentage: A way of expressing a number as a fraction of 100, using the symbol %. 35% means 35 out of 100, or 35/100 = 0.35.
百分比：用百分号 % 表示一个数占 100 的百分之多少。35% 表示每一百中有 35，即 35/100 = 0.35。
6. Ratio and Proportion | 比与比例
Ratio: A way of comparing two or more quantities using a colon. For example, if a recipe uses 3 cups of flour and 2 cups of sugar, the ratio of flour to sugar is 3:2.
比：用冒号比较两个或更多量的方法。例如，若一个食谱用 3 杯面粉和 2 杯糖，面粉与糖的比是 3:2。
Simplifying ratios: Ratios can often be reduced just like fractions, by dividing each part by a common factor. The ratio 12:8 simplifies to 3:2 by dividing both sides by 4.
化简比：比通常可以像分数一样约简，将每一部分除以公因数。比 12:8 缩小为 3:2，两边都除以 4。
Proportion ll bag and 6:15 in a large bag, then 2/5 = 6/15, showing the two ratios are in proportion.
比例：表示两个比相等的等式。若小袋中红球与蓝球的比是 2:5，大袋中是 6:15，则 2/5 = 6/15，说明两组比成比例。
Direct proportion , the other is multiplied by the same number. For y = 3x, y is directly proportional to x.
正比例：如果一个量乘以某数，另一个量也乘以相同的数，则这两个量成正比。对于 y = 3x，y 与 x 成正比。
7. Sequences and the nth Term | 数列与第 n 项
Sequence: An ordered list of numbers that follows a particular rule. For example, 5, 9, 13, 17, … is a linear sequence where the rule is 'add 4' each time.
数列：按一定规则排列的一列数。例如，5, 9, 13, 17, … 是一个线性数列，规律是每次“加 4”。
Term-to-term rule: A rule that tells you how to move from one term to the next in a sequence. In the sequence 3, 7, 11, 15, …, the term-to-term rule is 'add 4'.
项对项规则：说明如何从数列的一项得到下一项的规则。在数列 3, 7, 11, 15, … 中，项对项规则是“加 4”。
nth term: A formula that lets you find any term in a sequence directly, without knowing the previous term. For a sequence starting at 2 and increasing by 5 each time, the nth term is 5n − 3.
第 n 项：一个公式，让你直接找出数列中的任意一项，而无需知道前一项。对于从 2 开始每次增加 5 的数列，第 n 项是 5n − 3。
Arithmetic sequence: A sequence where the difference between consecutive terms is constant. 10, 6, 2, −2, … is arithmetic because the difference is −4 each step.
等差数列：相邻两项之间的差保持不变的数列。10, 6, 2, −2, … 是等差数列，因为每步的差为 −4。
8. Angles, Lines and Polygons | 角、线与多边形
Acute, obtuse and reflex angles: An acute angle measures between 0° and 90°. An obtuse angle is greater than 90° but less than 180°. A reflex angle is larger than 180° but smaller than 360°.
锐角、钝角与反角：锐角在 0° 到 90° 之间。钝角大于 90° 但小于 180°。反角大于 180° 但小于 360°。
Parallel lines: Lines that are always the same distance apart and never meet. On a diagram they are marked with arrow symbols. Perpendicular lines, in contrast, meet at a right angle (90°).
平行线：始终等距且永不相交的直线。在图中它们用箭头标记。与之相对，垂直线相交成直角（90°）。
Polygon: A closed 2D shape with three or more straight sides. Triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides) and hexagons (6 sides) are all polygons.
多边形：由三条或更多条直边围成的封闭二维图形。三角形（3 条边）、四边形（4 条边）、五边形（5 条边）和六边形（6 条边）
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