📚 Year 11 WJEC Maths: Quick Guide to Vocabulary and Terms | Year 11 WJEC 数学：词汇术语速记指南
Mathematics is not only about numbers; it is also a language. In the WJEC Year 11 Mathematics specification, examiners expect you to read a question, recognise the precise mathematical instruction it contains, and then respond in the correct form. A student who can solve a quadratic equation but does not know that "factorise" means "write as a product of brackets" may still drop marks, while a student who understands that "interquartile range" describes the spread of the middle 50% of the data can pick up marks quickly and confidently.
数学不仅仅是数字，它更是一门语言。在 WJEC 11 年级数学考试大纲中，考官期望你读题时能准确识别其中的数学指令，并以正确的形式作答。一个会解二次方程、却不知道 "factorise"（因式分解）意为"写成括号乘积形式"的学生仍可能失分；而一个明白 "interquartile range"（四分位距）描述数据中间 50% 离散程度的学生，则能快速而自信地拿到分数。
This expanded glossary collects the essential vocabulary of the WJEC Year 11 course - from number types and algebra, through geometry and trigonometry, to statistics, probability and graph work - and pairs every term with a clear definition, a typical exam context and a common trap to avoid. Use it as a checklist before each mock paper and as a final read-through on the night before the real exam.
这份扩充版词汇指南汇集了 WJEC 11 年级课程的核心术语——从数的类型与代数，到几何与三角，再到统计、概率与图像——并为每个术语配上清晰定义、典型考题情境与常见陷阱。你可以把它当作每次模拟考前的清单，也可以在大考前夜做最后一次通读。
1. Number Types and Operations | 数的类型与运算
WJEC questions often use set notation to describe numbers, so you must know exactly which set a value belongs to. Natural numbers (ℕ) are the counting numbers {1, 2, 3, ...}; integers (ℤ) include negatives and zero, {..., −2, −1, 0, 1, 2, ...}; rational numbers (ℚ) can be written as p/q where p and q are integers and q ≠ 0, which covers terminating and recurring decimals; irrational numbers cannot be written as simple fractions, for example π and √2; real numbers (ℝ) are all numbers on the continuous number line, rational and irrational together.
WJEC 题目常用集合记号描述数，因此你必须清楚一个数究竟属于哪个集合。自然数（ℕ）是计数数 {1, 2, 3, ...}；整数（ℤ）包含负数与零 {..., −2, −1, 0, 1, 2, ...}；有理数（ℚ）可写成 p/q，其中 p、q 为整数且 q ≠ 0，涵盖有限小数与循环小数；无理数无法写成分数，例如 π 与 √2；实数（ℝ）是连续数轴上的所有数，有理数与无理数合在一起。
| Symbol | Set | 中文 | Example |
| ℕ | Natural numbers | 自然数 | 7 |
| ℤ | Integers | 整数 | −12 |
| ℚ | Rational numbers | 有理数 | 0.75, ⅔ |
| ℝ | Real numbers | 实数 | π, √5, −3 |
A prime number has exactly two distinct factors, 1 and itself, so 1 is not prime and 2 is the only even prime. Factors divide exactly into a number, while multiples are produced by multiplying a number by an integer. The highest common factor (HCF) is the largest factor shared by two or more numbers, and the lowest common multiple (LCM) is the smallest positive number that is a multiple of each of them. The reciprocal of a number is 1 divided by that number, so the reciprocal of 5 is 0.2 and the reciprocal of ⅔ is 1.5.
质数恰好有两个不同因数：1 与它本身，因此 1 不是质数，而 2 是唯一的偶质数。因数能整除某数，倍数则是该数乘以整数所得。最大公因数（HCF）是两个或多个数共有的最大因数，最小公倍数（LCM）是同时为各数倍数的最小正整数。一个数的倒数是用 1 除以它，因此 5 的倒数是 0.2，⅔ 的倒数是 1.5。
The index laws must be memorised as vocabulary as well as algebra: m and n here stand for any powers of the same base a.
指数法则不仅要当作代数来学，也要当作词汇来记：下面的 m 与 n 表示同一个底数 a 的任意指数。
aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ ÷ aⁿ = aᵐ⁻ⁿ (aᵐ)ⁿ = aᵐⁿ a⁰ = 1 a⁻ⁿ = 1/aⁿ a1/n = ⁿ√a
ered as BIDMAS: Brackets, Indices, Division and Multiplication, Addition and Subtraction. A very common WJEC trap is treating a negative number squared as negative, when in fact (−3)² = 9 but −3² = −9.
有向数（directed numbers）是带正负号的数；加上一个负数等同于减去它。运算顺序记作 BIDMAS：括号、指数、乘除、加减。WJEC 一个非常常见的陷阱是把负数的平方当成负值，实际上 (−3)² = 9，而 −3² = −9。
2. Algebra: Expressions, Equations, Formulae and Identities | 代数：表达式、方程、公式与恒等式
These four words look similar but mean very different things, and WJEC examiners use them deliberately. A term is a single part of an algebraic expression, such as 5x or −3y². A coefficient is the number multiplying a variable, so in 7x the coefficient is 7. A constant is a fixed value with no variable attached, such as the 4 in 3x + 4. A variable is a letter representing an unknown or changing quantity.
这四个词看起来相似，含义却大不相同，WJEC 考官会有意区分使用。项（term）是代数式的一个组成部分，如 5x 或 −3y²。系数（coefficient）是乘在变量前的数，因此 7x 的系数是 7。常数（constant）是没有变量的固定值，如 3x + 4 中的 4。变量（variable）是代表未知量或变化量的字母。
sign and can be solved to find a value, for example 4x + 3 = 15. A formula is a rule connecting two or more variables, for example A = πr²; it can be rearranged to change the subject. An identity is true for every value of the variable and uses the symbol ≡, for example 2(x + 3) ≡ 2x + 6. An inequality uses <, ≤, > or ≥ instead of an equals sign.
表达式（expression）是由若干项组成、不含等号的式子，例如 4x² − 3x + 1；它只能被化简，不能被求解。方程（equation）含等号，可以解出数值，例如 4x + 3 = 15。公式（formula）是连接两个或多个变量的规则，例如 A = πr²；它可以被变形以改变主元。恒等式（identity）对变量的所有取值都成立，使用记号 ≡，例如 2(x + 3) ≡ 2x + 6。不等式（inequality）用 <、≤、> 或 ≥ 代替等号。
The command verbs are just as important. To simplify means to collect like terms and write the expression in its shortest form. To evaluate or work out means to substitute given numbers and calculate a value. To substitute means to replace a letter with a number. To solve means to find the value or values of the unknown that make the equation true. To rearrange, or change the subject, means to rewrite a formula so that a different letter stands alone on one side.
指令动词同样重要。Simplify（化简）指合并同类项，把式子写成最简形式。Evaluate 或 work out（求值/算出）指代入给定数值并计算出一个结果。Substitute（代入）指用数字替换字母。Solve（求解）指找出使方程成立的一个或多个未知数值。Rearrange 或 change the subject（变形/改变主元）指重新整理公式，让另一个字母单独出现在等号一侧。
Typical WJEC contexts include forming equations from word problems, solving simultaneous equations by elimination or substitution, and solving linear inequalities where the inequality sign reverses if you multiply or divide by a negative number. Always check whether the question asks for an integer answer, a value in a given form, or a solution set.
WJEC 常见题型包括：由文字应用题列方程、用消元法或代入法解联立方程、解一元一次不等式（若乘除负数，不等号方向要反转）。务必检查题目要求的是整数答案、指定形式的答案，还是解集。
3. Expanding, Factorising and Quadratic Vocabulary | 展开、因式分解与二次式词汇
To expand, or multiply out, means to remove brackets by multiplying every term inside by the term outside, or by using the grid method for two brackets. To factorise means the opposite: to rewrite an expression as a product of factors, usually brackets. Factorising is a favourite WJEC instruction because it tests both fluency and understanding of structure.
Expand（展开）或 multiply out（去括号）指用括号外的项乘括号内每一项从而去掉括号，两个括号相乘时可用网格法。Factorise（因式分解）正好相反：把一个式子改写成若干因子的乘积，通常是括号形式。因式分解是 WJEC 偏爱的指令，因为它同时考查运算熟练度与对结构的理解。
- Common factor 公因式：taking out the highest common factor of every term, e.g. 6x² + 9x = 3x(2x + 3).
- Difference of two squares 平方差：a² − b² = (a + b)(a − b), e.g. x² − 25 = (x + 5)(x − 5).
- Quadratic trinomial 二次三项式：x² + bx + c factorises as (x + p)(x + q) where p + q = b and pq = c.
- Completing the square 配方法：x² + bx + c = (x + b/2)² − (b/2)² + c, giving the minimum point of the curve.
wn shape when a < 0. The roots, solutions or zeros of a quadratic are the values where the curve crosses the x-axis, and they are the same as the solutions of ax² + bx + c = 0.
二次式（quadratic expression）的形式为 ax² + bx + c，其中 a ≠ 0，a 是 x² 的系数。它的图像是抛物线：当 a > 0 时开口向上，当 a < 0 时开口向下。二次式的根（roots）、解（solutions）或零点（zeros）就是曲线与 x 轴相交处的取值，与方程 ax² + bx + c = 0 的解完全相同。
eal roots there are: two if Δ > 0, one repeated root if Δ = 0, and no real roots if Δ < 0.
若二次式无法因式分解，就使用求根公式。判别式 Δ 告诉你实数根的个数：Δ > 0 时有两个根，Δ = 0 时有一个重根，Δ < 0 时没有实数根。
x = (−b ± √b² − 4ac) / 2a Δ = b² − 4ac
eans where a graph crosses an axis: the y-intercept is the value of y when x = 0, which for ax² + bx + c is simply c.
转折点（turning point）、顶点（vertex）或驻点（stationary point）是曲线的最高点或最低点，它位于对称轴 x = −b/2a 上。截距（intercept）指图像与坐标轴相交处：y 截距是 x = 0 时的 y 值，对 ax² + bx + c 而言就是 c。
4. Sequences, nth Term and Series Vocabulary | 数列、第 n 项与级数词汇
A sequence is an ordered list of numbers called terms. The first term is written as the first value, sometimes labelled a or u₁, and the nth term is the general rule that generates any term from its position number n. A term-to-term rule moves from one term to the next, for example "add 4"; a position-to-term rule links the term directly to n, for example 4n + 1. WJEC questions often ask you to find the nth term, use it to predict a large term, or decide whether a given number is a member of the sequence.
数列（sequence）是一列有序的数，其中的每个数称为项（term）。第一项
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