📚 Year 9 CCEA Further Mathematics: Vocabulary Terminology Quick Memorisation Guide | Year 9 CCEA 进阶数学：词汇术语速记指南
Welcome to your Year 9 CCEA Further Mathematics vocabulary and terminology quick memorisation guide. Mastering the language of mathematics is the first step to understanding advanced concepts and solving problems with confidence. This guide covers essential terms across algebra, geometry, trigonometry, statistics and probability, presented in a bilingual English–Chinese format to aid memorisation for CCEA students.
欢迎使用 Year 9 CCEA 进阶数学词汇术语速记指南。掌握数学语言是理解高级概念和自信解题的第一步。本指南涵盖代数、几何、三角学、统计与概率中的核心术语，以中英双语呈现，帮助 CCEA 考生记忆。
1. Algebraic Expressions and Terms | 代数表达式与术语
An algebraic expression is a mathematical phrase that can contain numbers, variables and operation symbols, but no equals sign. For example, 5x² − 3x + 7 is an expression.
代数表达式是一个可以包含数字、变量和运算符号但没有等号的数学短语。例如，5x² − 3x + 7 是一个表达式。
A variable is a symbol, usually a letter, that stands for an unknown number. In the expression 4y + 9, y is the variable.
变量是一个符号，通常是一个字母，代表未知的数。在表达式 4y + 9 中，y 是变量。
A constant is a fixed number that does not change. In 2x + 6, 6 is the constant term.
常数是一个不改变的固定数字。在 2x + 6 中，6 是常数项。
A term is a single number, variable, or product of numbers and variables, separated by + or − signs. In 3a²b − 7a + 5, the terms are 3a²b, −7a, and 5.
项是单个数字、变量或数字与变量的乘积，由加号或减号分隔。在 3a²b − 7a + 5 中，项是 3a²b、−7a 和 5。
The coefficient is the numerical factor of a term that contains a variable. In the term 8m³, 8 is the coefficient.
系数是含有变量的项的数字因子。在项 8m³ 中，8 是系数。
Like terms have exactly the same variable parts (same variables raised to the same powers). 4x² and −2x² are like terms, but 4x² and 4x are not.
同类项具有完全相同的变量部分（相同的变量和相同的指数）。4x² 和 −2x² 是同类项，但 4x² 和 4x 不是。
A polynomial is an algebraic expression with one or more terms, where each variable has a non‑negative integer exponent. 2x³ + x − 1 is a polynomial.
多项式是含有一个或多个项的代数表达式，其中每个变量的指数都是非负整数。2x³ + x − 1 是一个多项式。
The degree of a polynomial is the highest power of the variable in the expression. The polynomial 5x⁴ − 2x² + 7 has degree 4.
多项式的次数是表达式中变量的最高次幂。多项式 5x⁴ − 2x² + 7 的次数是 4。
Memory tip: 'Coefficient' shares the root 'co‑' meaning 'together'. The number works together with the variable.
记忆技巧：'Coefficient（系数）' 的词根 'co‑' 意为 '共同'，这个数字与变量共同起作用。
2. Exponents and Roots | 指数与根
The base is the number or variable being raised to a power. In 3², 3 is the base.
底数是被进行乘方运算的数字或变量。在 3² 中，3 是底数。
The exponent mes the base is multiplied by itself. In 2⁵, the exponent is 5, meaning 2 × 2 × 2 × 2 × 2.
指数（亦称幂或指数）表示底数自乘的次数。在 2⁵ 中，指数是 5，表示 2 × 2 × 2 × 2 × 2。
A square number is the result of multiplying a number by itself. 49 is a square number because 7² = 49.
平方数是一个数自乘的结果。49 是平方数，因为 7² = 49。
A cube number is the result of raising a number to the power of three. 8 is a cube number (2³ = 8).
立方数是一个数的三次方的结果。8 是立方数（2³ = 8）。
The square root of a number is a value that, when multiplied by itself, gives the original number. √25 = 5 because 5² = 25.
一个数的平方根是自乘后得到原数的值。√25 = 5，因为 5² = 25。
The cube root is the inverse operation of cubing. ∛27 = 3 because 3³ = 27.
立方根是立方的逆运算。∛27 = 3，因为 3³ = 27。
A surd is an irrational root that cannot be simplified to remove the root symbol. √2 and 5√3 are surds.
根式（无理根式）是一个无法化简去掉根号的无理数。√2 和 5√3 都是根式。
An expression can be written with rational exponents: a1/2 is the same as √a, and a1/3 equals ∛a. (Note: In Unicode this is written as a¹’² and √a.)
表达式可以用有理指数表示：a¹’² 等同于 √a，a¹’³ 等同于 ∛a。
Key: bⁿ → b is the base, n is the exponent / 关键：bⁿ → b 是底数，n 是指数
3. Equations and Inequalities | 方程与不等式
An equation showing that two expressions are equal, using an equals sign. 2x + 5 = 11 is an equation.
方程是表明两个表达式相等的数学语句，使用等号。2x + 5 = 11 是一个方程。
The solution value of the variable that makes the equation true. For x + 3 = 10, the solution is x = 7.
方程的解（或根）是使方程成立的变量的值。对于 x + 3 = 10，解是 x = 7。
Solving an equation means finding all values that satisfy it. The balance method keeps both sides equal by applying inverse operations.
解方程意味着找出所有满足方程的值。平衡法通过使用逆运算保持等号两边始终相等。
A linear equation a variable raised only to the power 1. Its graph is a straight line. y = 3x − 2 is linear.
线性方程中的变量指数仅为 1，其图像是一条直线。y = 3x − 2 是线性的。
A quadratic equation contains a variable squared as its highest power. x² − 4x + 3 = 0 is quadratic.
二次方程的最高次幂为变量的平方。x² − 4x + 3 = 0 是二次方程。
Simultaneous equations are a set of equations with common variables, solved together to find the values that satisfy all equations at once.
联立方程组是一组含有共同变量的方程，需一起求解，找出同时满足所有方程的值。
An inequality compares two expressions using symbols <, >, ≤ or ≥. x > 4 means x is greater than 4.
不等式使用符号 <、>、≤ 或 ≥ 比较两个表达式。x > 4 表示 x 大于 4。
Memory tip: The inequality symbol opens towards the larger number, like a hungry mouth. / 记忆技巧：不等号的大口朝向较大的数，像一张饥饿的嘴。
4. Factorising and Expanding | 因式分解与展开
To expand an expression means to remove brackets by multiplying each term inside. Expanding 3(x + 4) gives 3x + 12.
展开是指通过乘法去除括号。展开 3(x + 4) 得到 3x + 12。
To factorise is the reverse process: writing an expression as a product of its factors. 6x + 9 factorises to 3(2x + 3).
因式分解是展开的逆过程：将一个表达式写成其因子的乘积。6x + 9 因式分解为 3(2x + 3)。
The highest common factor (HCF) is the largest factor shared by all terms. For 12x² and 8x, the HCF is 4x.
最大公因式（HCF）是所有项共有的最大因子。对于 12x² 和 8x，最大公因式是 4x。
The difference of two squares is a pattern: a² − b² = (a + b)(a − b). Example: x² − 49 = (x + 7)(x − 7).
平方差是一种模式：a² − b² = (a + b)(a − b)。例如：x² − 49 = (x + 7)(x − 7)。
A trinomial is an expression with three terms. Expanding (x + 2)(x − 5) gives the trinomial x² − 3x − 10.
三项式是含有三项的表达式。展开 (x + 2)(x − 5) 得到三项式 x² − 3x − 10。
A perfect square ult of squaring a binomial: (x + a)² = x² + 2ax + a². For example, (x + 3)² = x² + 6x + 9.
完全平方三项式是二项式平方的结果：(x + a)² = x² + 2ax + a²。例如 (x + 3)² = x² + 6x + 9。
5. Sequences | 数列
A sequence is an ordered list of numbers following a rule. Each number is called a term. Example: 5, 8, 11, 14, …
数列是按照某种规则排列的有序数字列表。每个数字称为项。例如：5, 8, 11, 14, …
An arithmetic sequence has a constant common difference (d) between consecutive terms. In 2, 7, 12, 17, …, d = 5.
等差数列的相邻两项之间的差是常数，称为公差（d）。在 2, 7, 12, 17, … 中，d = 5。
A geometric sequence has a constant common ratio (r) between consecutive terms. In 3, 6, 12, 24, …, r = 2.
等比数列的相邻两项之比是常数，称为公比（r）。在 3, 6, 12, 24, … 中，r = 2。
The nth term s formula allows you to find any term in a sequence without listing all previous terms. For 5, 9, 13, 17, …, the nth term is aₙ = 4n + 1.
第 n 项公式使你能直接求出数列中任意一项，而无需列出前面所有项。对于 5, 9, 13, 17, …，第 n 项公式为 aₙ = 4n + 1。
A recurrence relation defines the next term by referring to previous terms. aₙ₊₁ = aₙ + 3 with a₁ = 2 generates 2, 5, 8, 11, …
递推关系通过前一项或几项来定义后一项。aₙ₊₁ = aₙ + 3，其中 a₁ = 2，可生成 2, 5, 8, 11, …
Arithmetic nth term: aₙ = a₁ + (n−1)d / 等差数列第 n 项：aₙ = a₁ + (n−1)d
6. Functions | 函数
A function is a rule that assigns each input exactly one output. It can be written as f(x) = 2x + 1. 'Input' is the x‑value, 'output' is the resulting value.
函数是一种将每个输入恰好对应一个输出的规则，可写成 f(x) = 2x + 1。'输入' 是 x 值，'输出'是得到的结果值。
The domain et of is the set of all possible input values for a function. For f(x) = 1/x, the domain excludes x = 0.
定义域是函数所有可能输入值的集合。对于 f(x) = 1/x，定义域不能包含 x = 0。
The range is the set of all possible output values. For f(x) = x², the range is all numbers ≥ 0.
值域是所有可能输出值的集合。对于 f(x) = x²，值域是所有 ≥ 0 的数。
Function notation f(x) means 'the function of x'. It does not mean f multiplied by x. If f(x) = 3x − 4, then f(2) = 2.
函数记号 f(x) 表示 'x 的函数'，不是 f 乘以 x。若 f(x) = 3x − 4，则 f(2) = 2。
The inverse function ) reverses the effect of the original function. If f(x) = 2x + 3, then f⁻¹(x) = (x − 3)/2.
反函数 f⁻¹(x) 逆转原函数的效果。若 f(x) = 2x + 3，则 f⁻¹(x) = (x − 3)/2。
Memory tip: Think of a function as a machine: you put in an input, the machine applies the rule, and an output comes out.
记忆技巧：把函数想象成一台机器：你放入一个输入，机器应用规则，然后输出一个结果。
7. Coordinate Geometry | 坐标几何
The coordinate plane is formed by a horizontal x‑axis and a vertical y‑axis. Their intersection, (0,0), is called the origin.
坐标平面由水平的 x 轴和垂直的 y 轴构成，它们的交点 (0,0) 称为原点。
An ordered pair (x, y) gives the position of a point. The first number is the x‑coordinate, the second is the y‑coordinate.
有序数对 (x, y) 表示点的位置。第一个数是 x 坐标，第二个数是 y 坐标。
The gradient pness: gradient = change in y / change in x. A higher absolute value means a steeper line.
直线的梯度（斜率）衡量其倾斜程度：梯度 = y 的变化量 / x 的变化量。绝对值越大，直线越陡。
The y‑intercept is the point where a line crosses the y‑axis (x = 0). The x‑intercept is where the line crosses the x‑axis (y = 0).
y 轴截距是直线与 y 轴的交点（x = 0）；x 轴截距是直线与 x 轴的交点（y = 0）。
The equation of a straight line is often written as y = mx + c, where m is the gradient and c is the y‑intercept. For y = 2x − 5, m = 2 and c = −5.
直线方程常写成 y = mx + c，其中 m 是梯度，c 是 y 轴截距。对于 y = 2x − 5，m = 2，c = −5。
gradient. Perpendicular lines have gradients that are negative reciprocals (product = −1).
平行线梯度相同；垂直线梯度互为负倒数（乘积为 −1）。
8. Geometry and Measures | 几何与测量
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