Year 9 CAIE Further Maths: Vocabulary & Terminology Quick Memorisation Guide | Year 9 CAIE 进阶数学：词汇术语速记指南

📚 Year 9 CAIE Further Maths: Vocabulary & Terminology Quick Memorisation Guide | Year 9 CAIE 进阶数学：词汇术语速记指南

Welcome to this quick memorisation guide crafted for Year 9 learners who are building a strong foundation in CAIE Further Mathematics. Mathematical vocabulary is more than just words – it is the precise language that unlocks concepts, clarifies problem‑solving steps, and boosts exam confidence. In this article we present essential terms organised by topic, each with a clear definition and a memory tip to help you recall them effortlessly. Let’s turn complex terminology into simple, memorable ideas.

欢迎阅读为 Year 9 学生打造的 CAIE 进阶数学词汇速记指南。数学词汇不仅是单词，更是开启概念、理清解题思路、提升考试信心的精确语言。本文按主题归纳核心术语，每个术语都配有清晰定义和记忆窍门，帮助你轻松牢记。让我们一起把复杂的术语变成简单易记的点子。

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1. Algebraic Expressions and Polynomials | 代数表达式与多项式

A variable is a symbol, usually a letter, that represents an unknown or changeable value. In the expression 3x + 5, x is the variable. Memory tip: Think of a variable as a ‘varying’ quantity – it can vary.

变量是用符号（通常是字母）表示未知或变化的值。在表达式 3x + 5 中，x 是变量。记忆窍门：将变量看作“可变”的量——它可以变化。

A constant is a fixed numerical value that does not change. In 3x + 5, the number 5 is a constant. Memory tip: ‘Constant’ stays constant – it never shifts.

常数是不变的固定数值。在 3x + 5 中，5 是常数。记忆窍门：“常数”就是保持不变——它从不改变。

The coefficient is the numerical factor multiplying a variable. In the term 7y, 7 is the coefficient of y. Memory tip: Coefficient works together with the variable, almost like a ‘co‑worker’.

系数是乘以变量的数字因子。在项 7y 中，7 是 y 的系数。记忆窍门：系数与变量一起发挥作用，像是一个“合作者”。

A term is a single number, variable, or product of numbers and variables. For example, 4a²b is a term. Memory tip: Separate terms by plus or minus signs when you look at an expression.

项是单个数字、变量或数字与变量的乘积。例如 4a²b 是一个项。记忆窍门：观察表达式时，通过加减号来区分不同的项。

An expression is a combination of terms without an equals sign, like 2p² − pq + 7. Equations contain an equals sign, while expressions do not.

表达式是不含等号的项的集合，如 2p² − pq + 7。方程含有等号，而表达式没有。

An equation states that two expressions are equal using '=' − 1 = 4x + 2. Solving an equation means finding the value(s) that make the statement true.

方程用等号表示两个表达式相等，如 3x − 1 = 4x + 2。解方程就是找出使等式成立的数值。

A polynomial is an algebraic expression with non‑negative integer exponents. Examples: 5x³ − 2x + 9 is a polynomial; x⁻² + 2 is not a polynomial.

多项式是各项指数为非负整数的代数表达式。例如 5x³ − 2x + 9 是多项式；x⁻² + 2 不是多项式。

The degree of a polynomial is the highest exponent of the variable. In 5x⁴ − x² + 3, the degree is 4. Memory tip: The degree tells you the ‘power’ of the whole polynomial.

多项式的次数是变量的最高指数。在 5x⁴ − x² + 3 中，次数为 4。记忆窍门：次数告诉你多项式的“最高次幂”。

Like terms have identical variable parts and can be combined by addition or subtraction. 3xy and −5xy are like terms, while 3xy and 3x are not.

同类项具有相同的变量部分，可以通过加法或减法合并。3xy 与 −5xy 是同类项，而 3xy 与 3x 不是。

A binomial is a polynomial with exactly two unlike terms, e.g., x² − 4. A trinomial has three terms, e.g., x² − 5x + 6. Memory tip: ‘Bi-’ means two, ‘tri-’ means three.

二项式是恰好含有两项的多项式，如 x² − 4。三项式含有三项，如 x² − 5x + 6。记忆窍门：“二”表示两个，“三”表示三个。

Expansion means multiplying out brackets to write an expression without any grouping symbols. For instance, (x+2)(x−3) expands to x² − x − 6.

展开指执行乘法运算去括号，得到不含括号的表达式。例如 (x+2)(x−3) 展开为 x² − x − 6。

Factorisation is the reverse process: writing an expression as a product of its factors. x² − x − 6 factorises to (x+2)(x−3).

因式分解是展开的逆过程：将表达式写成因式的乘积。x² − x − 6 分解为 (x+2)(x−3)。

A factor is an expression that divides another without a remainder. (x+2) is a factor of x² − x − 6. Memory tip: Think of factors as ‘building blocks’ that multiply to form the original expression.

因式是能整除另一表达式而不留余数的式子。(x+2) 是 x² − x − 6 的因式。记忆窍门：把因式想象成组装成原式的“积木块”。

In division, the quotient is the result, and the remainder is what is left. When 23 ÷ 5, the quotient is 4 and the remainder is 3.

在除法中，商是结果，余数是剩余部分。23 ÷ 5 时，商为 4，余数为 3。

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2. Equations, Inequalities and Modulus | 方程、不等式与绝对值

an equation is a value that makes the equation true. Roots are solutions, often seen as x‑intercepts on a graph. For 2x = 6, x = 3 is the solution.

方程的解是使方程成立的数值。根也是解，常表现为图像与 x 轴的交点。对于 2x = 6，x = 3 是解。

. A quadratic equation has degree 2 and graphs as a parabola in the form ax² + bx + c = 0.

线性方程的次数为 1，图像是一条直线，如 y = 2x + 1。二次方程的次数为 2，图像是抛物线，形如 ax² + bx + c = 0。

The quadratic formula gives the solutions of ax² + bx + c = 0: x = (−b ± √b² − 4ac) / (2a). The discriminant Δ = b² − 4ac determines the nature of the roots.

求根公式给出 ax² + bx + c = 0 的解：x = (−b ± √b² − 4ac) / (2a)。判别式 Δ = b² − 4ac 决定根的性质。

, there is one repeated real root. If Δ < 0, there are no real roots (only complex roots). Memory tip: Delta ‘discriminates’ between root types.

若 Δ > 0，二次方程有两个不等实根；Δ = 0，有一个重根；Δ < 0，无实根（只有复根）。记忆窍门：Delta 负责“辨别”根的类型。

Simultaneous equations are two or more equations solved together. Methods include substitution, elimination, and graphical intersection. The solution is the pair (x, y) that satisfies all equations.

方程组是需同时求解的两个或多个方程，解法包括代入法、消元法和图像交点法。解是满足所有方程的 (x, y) 对。

An inequality uses symbols <, >, ≤, ≥ to compare expressions. The solution set is a range of values, often shown on a number line with open or closed circles.

不等式使用 <、>、≤、≥ 比较表达式，解集是一段数值范围，常在数轴上用空心或实心圆点表示。

The modulus (or absolute value) |x| gives the distance of x from zero on the number line, always non‑negative. |−3| = 3 and |3| = 3. Memory tip: Modulus ignores the sign and looks at magnitude.

绝对值 |x| 表示数轴上 x 到零的距离，总是非负的。|−3| = 3，|3| = 3。记忆窍门：绝对值忽略符号，只看数值大小。

A compound inequality combines two inequalities, e.g., 1 < x ≤ 5 means x is greater than 1 and at most 5. Solve and graph each part carefully.

复合不等式将两个不等式合并，如 1 < x ≤ 5 表示 x 大于 1 且不超过 5。求解时要分别处理并准确作图。

To solve an equation or inequality means to find all values that satisfy it. Graphical solutions rely on intersection points of graphs.

求解方程或不等式就是找出所有满足条件的值。图像解法依赖于图形交点的坐标。

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3. Indices and Surds | 指数与根式

An index (or exponent) tells how many times a base is multiplied by itself. In aⁿ, n is the index, a is the base, and the whole expression is called a power. Memory tip: The index sits up high and ‘points’ to the repeated multiplication.

指数表示底数自乘的次数。在 aⁿ 中，n 是指数，a 是底数，整个式子称为幂。记忆窍门：指数高高在上，“指示”重复相乘的次数。

Key laws of indices simplify calculations: aᵐ × aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ, a^m/n = ⁿ√aᵐ (the nth root of a raised to the m).

基本指数法则能简化计算： aᵐ × aⁿ = aᵐ⁺ⁿ， (aᵐ)ⁿ = aᵐⁿ， a⁻ⁿ = 1/aⁿ， a^m/n = ⁿ√aᵐ（a 的 m 次方的 n 次方根）。

Square root √x returns the non‑negative value whose square is x. Cube root ³√x is the number that when cubed gives x. The nth root ⁿ√a is the inverse of the nth power. Memory tip: The root symbol √ looks a bit like a tree root.

平方根 √x 指平方后等于 x 的非负值。立方根 ³√x 是立方后得到 x 的数。n 次方根 ⁿ√a 是 n 次幂的逆运算。记忆窍门：根号 √ 看起来有点像树根的形状。

A surd is an irrational root that cannot be simplified to a rational number, e.g., √2, ³√5. Surds are left in root form to keep exact values.

根式是无法化简为有理数的无理方根，如 √2、³√5。根式保留根号形式以维持精确值。

Rationalising the denominator means removing a surd from the bottom of a fraction. To rationalise 1/√2, multiply numerator and denominator by √2 to obtain √2/2. Memory tip: Rationalise makes the denominator ‘rational’.

分母有理化是指把分数分母中的根号消去。对 1/√2 有理

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