📚 Year 10 AQA Mathematics: Vocabulary Quick-Memorisation Guide | Year 10 AQA 数学：词汇术语速记指南
Mastering key mathematical vocabulary is essential for success in Year 10 AQA Mathematics. This guide presents a structured, bilingual approach to help you memorise the most important terms quickly, using clear definitions, comparisons, and memory hooks. Each section pairs English explanations with Chinese translations so you can strengthen your understanding in both languages.
掌握关键的数学词汇是在AQA Year 10数学考试中取得成功的基础。本指南以结构化的双语方式，通过清晰的定义、对比和记忆线索，帮助你快速记住最重要的术语。每个小节都将英文解释与中文翻译配对，助你同时巩固双语的数学理解。
1. Expressions, Equations, Identities and Formulae | 表达式、方程、恒等式与公式
An expression is a mix of numbers, letters and operation symbols without an equals sign, e.g. 3x² + 2x − 5. You cannot solve it, only simplify or substitute values into it.
表达式是由数字、字母和运算符号组成的式子，没有等号，例如 3x² + 2x − 5。表达式不能求解，只能化简或代入求值。
An equation qual, using an equals sign, e.g. 2x + 3 = 11. Equations are solved to find unknown values.
方程用等号连接两个表达式，表示它们相等，例如 2x + 3 = 11。方程可以通过求解找到未知数的值。
An identity is always true for every possible value of the variable and is written with a triple bar ≡, e.g. (x + 1)² ≡ x² + 2x + 1. Think 'identical' – it's identically true.
恒等式对于变量的每一个可能取值都成立，使用三横线符号 ≡ 表示，例如 (x + 1)² ≡ x² + 2x + 1。联想“恒”字表示永远成立，恒等式就是永远正确的等式。
A formula tities, e.g. A = lw for the area of a rectangle. It often contains more than one variable.
公式是一种表示不同量之间关系的方程，例如矩形面积 A = lw。公式中通常包含多个变量，用于计算。
2. Terms, Coefficients and Constants | 项、系数与常数
A term is a single number, variable, or product of numbers and variables, separated by + or − in an expression. In 5x³ − 2x + 7, the terms are 5x³, −2x and 7.
项是单个数字、变量或数字与变量的乘积，在表达式中由加号或减号分隔。在 5x³ − 2x + 7 中，项分别是 5x³、−2x 和 7。
The coefficient is the number factor that multiplies a variable in a term. In 5x³, 5 is the coefficient. Remember: 'co' + 'efficient' – the number that works efficiently with the variable.
系数是项中与变量相乘的数字部分。在 5x³ 中，5 是系数。可以这样记忆：“系”就像系在变量前面的数字。
A constant is a term that has a fixed value, with no variable part. In 5x³ − 2x + 7, the number 7 is the constant. It stays constant while x changes.
常数是值固定不变的项，不含变量。在 5x³ − 2x + 7 中，7 就是常数。无论变量如何变化，常数始终保持不变。
3. Expanding and Factorising | 展开与因式分解
Expanding means removing brackets by multiplying each term inside the bracket by the factor outside. For example, expanding 3(x + 2) gives 3x + 6. Think of 'expanding' as spreading out the terms.
展开是指将括号外的因式乘以括号内的每一项，从而去掉括号。例如，将 3(x + 2) 展开得到 3x + 6。可以想象把手风琴拉开——把式子“展开”来。
Factorising is the reverse of expanding: it rewrites an expression as a product of its factors by identifying a common factor. For example, 6x + 9 factorises to 3(2x + 3). Look for the highest common factor (HCF).
因式分解是展开的逆过程：通过找出公因式，将表达式写成几个因式的乘积。例如 6x + 9 分解为 3(2x + 3)。找出最大公因式是关键。
In Year 10, you also encounter factorising quadratic expressions of the form x² + bx + c into (x + p)(x + q). Remember to find two numbers that multiply to c and add to b.
在 Year 10 中，你还会遇到将 x² + bx + c 形式的二次表达式分解为 (x + p)(x + q)。记住寻找两个数，它们的乘积等于 c，和等于 b。
4. Linear Equations and Inequalities | 线性方程与不等式
A linear equation est power of the variable is 1, such as 2x + 3 = 7. Its graph forms a straight line, hence 'linear'. Solving involves isolating the variable using inverse operations.
线性方程是指变量的最高次幂为 1 的方程，如 2x + 3 = 7。它的图像是一条直线，因此称为“线性”。解方程需要使用逆运算将变量分离出来。
An inequality han or equal to). e.g. x + 4 > 10. The solution is a range of values, not a single number.
不等式使用符号 <（小于）、≤（小于或等于）、>（大于）、≥（大于或等于）来比较两个表达式，例如 x + 4 > 10。解是一个范围，而不是一个具体的数。
When multiplying or dividing an inequality by a negative number, you must reverse the inequality sign. This is a classic pitfall – flip the sign to keep the truth.
当不等式两边乘以或除以一个负数时，必须反转不等号。这是一个经典易错点——记住要“调转方向”才能保持正确。
5. Quadratic Expressions and Equations | 二次表达式与二次方程
A quadratic expression is an algebraic expression where the highest power of the variable is 2, e.g. x² + 5x + 6. The word 'quadratic' comes from the Latin 'quadratus' meaning square.
二次表达式是变量最高次幂为 2 的代数表达式，例如 x² + 5x + 6。'quadratic'一词源自拉丁语“quadratus”，意为正方形，与平方有关。
A quadratic equation 0. You can solve it by factorising, completing the square, or using the quadratic formula.
二次方程是将二次表达式设为等于零的方程，例如 x² + 5x + 6 = 0。可以通过因式分解、配方法或求根公式来求解。
The quadratic formula is x = [−b ± √b² − 4ac] / 2a. For memory, sing it to the tune of 'Pop Goes the Weasel'. Note: 'Roots' are the solutions, also called 'x-intercepts' on a graph.
求根公式为 x = [−b ± √b² − 4ac] / 2a。可以用熟悉的旋律帮助记忆。注意：“根”就是方程的解，在图像上也称为“x轴截距”。
6. Simultaneous Equations | 联立方程组
Simultaneous equations + y = 10 and x − y = 2. You need to find values that satisfy all equations simultaneously.
联立方程组是指包含两个或多个未知数的两个或更多方程，它们同时成立，例如 2x + y = 10 和 x − y = 2。你需要找到同时满足所有方程的值。
Two main solution methods are elimination (add or subtract equations to remove one variable) and substitution (rearrange one equation and substitute into the other). Elimination is often quicker when coefficients align neatly.
主要的两种解法是消元法（通过加减方程消去一个变量）和代入法（将一个方程变形后代入另一个）。当系数对齐时，消元法通常更快捷。
Remember to check your solution by substituting the values back into the original equations. A common AQA question asks whether a given pair solves the system.
记住要把求得的值代入原方程组检验。AQA考试中经常出现判断某一对数值是否为方程组解的题目。
7. Coordinate Geometry: Gradient and Intercept | 坐标几何：斜率与截距
The gradient ange: m = Δy / Δx. A positive gradient slopes upward, a negative gradient slopes downward.
直线的斜率（m）衡量其倾斜程度和方向。计算方法为竖直变化量除以水平变化量：m = Δy / Δx。正斜率向上倾斜，负斜率向下倾斜。
The y-intercept -axis. In the slope-intercept form y = mx + c, m is the gradient and c is the y-intercept.
y轴截距（c）是直线与 y 轴相交的点。在斜截式 y = mx + c 中，m 是斜率，c 是 y 轴截距。
Two lines are parallel if they have the same gradient. They are perpendicular if the product of their gradients is −1 (e.g. 2 and −½).
如果两条直线的斜率相等，它们平行。如果它们的斜率之积为 −1（例如 2 和 −½），则它们垂直。
To find the midpoint x₂, y₂), use the average: M = ((x₁ + x₂)/2, (y₁ + y₂)/2). It is the point exactly halfway.
求连接 (x₁, y₁) 和 (x₂, y₂) 两点线段的中点，使用平均数：M = ((x₁ + x₂)/2, (y₁ + y₂)/2)。它恰好是正中间的点。
8. Angles and Polygons | 角与多边形
Acute angle: less than 90°. Right angle: exactly 90°, often marked with a small square. Obtuse angle: between 90° and 180°. Reflex angle: greater than 180° but less than 360°.
锐角：小于 90°。直角：恰好 90°，常以一个小方格标示。钝角：介于 90° 和 180° 之间。优角：大于 180° 但小于 360°。
Angles on a straight line sum to 180°. Angles around a point sum to 360°. Vertically opposite angles are equal.
平角（直线上的角）之和为 180°。绕点一周的角之和为 360°。对顶角相等。
A polygon erior angles. The sum of interior angles = (n − 2) × 180°, where n is the number of sides.
多边形是由直边组成的封闭二维图形。正多边形的各边相等，各内角也相等。内角和 = (n − 2) × 180°，其中 n 为边数。
Exterior angles of any polygon always sum to 360°. For a regular polygon, one exterior angle = 360° / n.
任何多边形的外角和始终为 360°。对于正多边形，一个外角 = 360° / n。
9. Area, Perimeter and Volume | 面积、周长与体积
Perimeter is the total distance around the outside of a 2D shape. Add all side lengths. Area is the amount of flat space inside the shape, measured in square units like cm².
周长是二维图形外部边界的总长度，将各边长度相加即可。面积是图形内部平坦空间的大小，以平方单位（如 cm²）计量。
le circumference = 2πr or πd; Circle area = πr². For π, use the button on your calculator.
主要公式：矩形面积 = 长 × 宽；三角形面积 = ½ × 底 × 高；圆的周长 = 2πr 或 πd；圆的面积 = πr²。记住使用计算器上的 π 键。
Volume ts like cm³. For a cuboid: V = l × w × h. For a prism: V = area of cross-section × length.
体积衡量三维形状内部的空间大小，以立方单位（如 cm³）表示。长方体：V = 长 × 宽 × 高。棱柱：V = 横截面积 × 长度。
Surface area is the total area of all faces on a 3D solid. Imagine 'unwrapping' the shape and adding up the areas of every face.
表面积是三维立体所有面的总面积。可以想象将立体“展开”成平面，然后将每个面的面积相加。
10. Statistics: Averages and Range | 统计：平均数与极差
The mean is the sum of all data values divided by the number of values. It is the arithmetic average, sensitive to extreme values.
平均数（均值）是所有数据值之和除以数据个数。它代表算术平均值，容易受极值影响。
The median is the middle value when the data is arranged in order. If there are two middle numbers, take their mean. The median is not affected by outliers.
中位数是将数据按顺序排列后位于中间的值。如果有两个中间数，则取它们的平均数。中位数不受异常值影响。
The mode is the value that appears most frequently. A data set can have one mode, more than one mode (bimodal), or no mode at all.
众数是出现频率最高的值。一组数据可以有一个众数、多个众数（双峰），或没有众数。
The range is a measure of spread: largest value minus smallest value. It gives a quick sense of how spread out the data is.
极差是衡量分散程度的指标：最大值减去最小值。它能快速反映数据的分散情况。
11. Probability Terms | 概率术语
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). It is written as a fraction, decimal or percentage.
概率衡量事件发生的可能性，数值范围从 0（不可能）到 1（必然）。可以用分数、小数或百分比表示。
An experiment or trial is an action that produces results. An outcome is a single possible result, and an event is a set of one or more outcomes.
实验/试验是产生结果的活动。结果是单个可能的结果，而事件是一个或多个结果的集合。
The sample space , 6}. Probability of event = (number of favourable outcomes) / (total number of outcomes).
样本空间列出了所有可能的结果。对于一枚公正的六面骰子，样本空间为 {1, 2, 3, 4, 5, 6}。事件的概率 =（有利结果数）/（总结果数）。
Mutually exclusive events cannot happen at the same time, e.g. tossing Heads and Tails on one coin. Their probabilities add up when combined.
互斥事件不可能同时发生，如掷一枚硬币不可能既正面又反面。它们的概率可以直接相加。
12. Indices and Standard Form | 指数与标准形式
Indices (or powers) show how many times a number is multiplied by itself. In aⁿ, a is the base and n is the index/exponent. A negative index like a⁻² means 1/a². A fractional index a1/2 is √a.
指数（也称幂）表示一个数自乘的次数。在 aⁿ 中，a 是底数，n 是指数。负指数如 a⁻² 表示 1/a²。分数指数 a1/2 等同 √a。
aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ. Memorise these with simple examples like 2² × 2³ = 2⁵.
关键指数定律：aᵐ × aⁿ = aᵐ⁺ⁿ；aᵐ ÷ aⁿ = aᵐ⁻ⁿ；(aᵐ)ⁿ = aᵐⁿ。通过简单例子如 2² × 2³ = 2⁵ 来记忆。
Standard form × 10ⁿ, where 1 ≤ A < 10 and n is an integer. e.g. 4 500 = 4.5 × 10³; 0.0032 = 3.2 × 10⁻³.
标准形式（科学记数法）将极大或极小的数写作 A × 10ⁿ，其中 1 ≤ A < 10 且 n 为整数。例如 4 500 = 4.5 × 10³；0.0032 = 3.2 × 10⁻³。
n, left → positive n. AQA expects you to enter and read standard form on your calculator.
转换时，数小数点左右移动的位数：右移则 n 为负，左移则 n 为正。AQA 考试要求你能在计算器中输入并读懂标准形式。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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