📚 Year 10 SQA Maths: Vocabulary Quick Reference Guide | Year 10 SQA 数学：词汇术语速记指南
Mastering the specific vocabulary used in SQA maths exams is just as important as knowing the methods. This guide breaks down essential terms by topic, pairing each English definition with its Chinese equivalent, so you can build confidence in both languages and learn exactly what examiners expect you to do.
掌握 SQA 数学考试中使用的专业词汇与掌握解题方法同样重要。本指南按主题梳理关键术语，为每个英文定义配上对应的中文解释，帮助你建立双语信心，准确理解题目要求。
1. Number and Algebra | 数与代数
Integer: A whole number that can be positive, negative, or zero, such as −3, 0, 7.
整数：可正、可负或为零的整数，例如−3、0、7。
Rational number: Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0.
有理数：任何可以写成分数 a/b 形式的数，其中 a 和 b 为整数且 b ≠ 0。
Surd: An irrational root, such as √2 or ³√5, left in exact root form.
根式（无理根）：无理数形式的根，如 √2 或 ³√5，保留精确根号形式。
Index (exponent): The small superscript number showing how many times a base is multiplied by itself; e.g., in 5³, 3 is the index.
指数：表示底数自乘次数的小型上标数字；例如在 5³ 中，3 是指数。
Laws of indices: Rules for multiplying, dividing, and raising powers, such as aᵐ × aⁿ = aᵐ⁺ⁿ.
指数运算法则：关于幂的乘、除和乘方的规则，如 aᵐ × aⁿ = aᵐ⁺ⁿ。
Scientific notation (standard form): Writing numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
科学记数法（标准形式）：将数字写成 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。
Percentage: A fraction out of 100; often used to compare quantities or express change.
百分比：分母为 100 的分数；常用于比较数量或表示变化。
Ratio: A comparison of two or more quantities of the same kind, written as a : b.
比：同类两个或多个量之间的比较，写作 a : b。
2. Expressions, Equations and Formulae | 表达式、方程与公式
Expression: A combination of terms using operations (e.g., 3x + 2y) but with no equals sign.
表达式：用运算符号连接的若干项的组合（例如 3x + 2y），没有等号。
Equation: A mathematical statement that two expressions are equal, containing an equals sign.
方程：表示两个表达式相等的数学陈述，包含等号。
Expand: Multiply out brackets to rewrite an expression; e.g., 2(x + 3) = 2x + 6.
展开：去括号以重写表达式；例如 2(x + 3) = 2x + 6。
Factorise: Write an expression as a product of its factors; e.g., x² − 9 = (x + 3)(x − 3).
因式分解：把表达式写成它的因式之积；例如 x² − 9 = (x + 3)(x − 3)。
Simplify: Collect like terms and reduce an expression to its simplest form.
化简：合并同类项，将表达式化为最简形式。
Solve: Find the value(s) of the variable that make an equation true.
解（求解）：求出使方程成立的变量的值。
Subject of the formula: Rearranging a formula so that a chosen variable stands alone on one side.
公式的主项：重新整理公式，使选定的变量单独位于等式一边。
Quadratic equation: An equation of the form ax² + bx + c = 0, where a ≠ 0.
二次方程：形如 ax² + bx + c = 0 的方程，其中 a ≠ 0。
Inequality: A statement comparing expressions using <, >, ≤, or ≥.
不等式：用 <, >, ≤ 或 ≥ 连接表达式的比较语句。
3. Functions and Graphs | 函数与图像
Function: A relationship where each input has exactly one output, often written as f(x).
函数：每个输入恰好对应一个输出的关系，常写作 f(x)。
Gradient (slope): The steepness of a line, calculated as change in y divided by change in x.
斜率（梯度）：直线的倾斜程度，用 y 的变化量除以 x 的变化量计算。
y-intercept: The point where a line crosses the y-axis; for y = mx + c, it is c.
y轴截距：直线与 y 轴相交的点；对于 y = mx + c，它是 c。
Straight-line equation: Usually written in the form y = mx + c, where m is the gradient and c is the y-intercept.
直线方程：通常写为 y = mx + c 的形式，其中 m 是斜率，c 是 y轴截距。
Quadratic graph (parabola): The U-shaped curve representing y = ax² + bx + c, with a turning point at its vertex.
二次函数图像（抛物线）：表示 y = ax² + bx + c 的 U 形曲线，其顶点为转折点。
Roots of an equation: The x-values where the graph crosses the x-axis (y = 0).
方程的根：图像与 x 轴 (y = 0) 交点的 x 值。
Turning point: The point on a quadratic graph where the curve changes direction (maximum or minimum).
转折点：二次函数图像上曲线改变方向的点（最大值或最小值）。
4. Geometry and Trigonometry | 几何与三角学
Pythagoras’ theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
勾股定理：在直角三角形中，斜边的平方等于两直角边的平方和：a² + b² = c²。
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
斜边：直角三角形中最长的边，位于直角对面。
Trigonometric ratios (SOH CAH TOA): sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
三角比（SOH CAH TOA）：sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边。
Angle of elevation: The angle measured upwards from the horizontal to a line of sight.
仰角：从水平线向上测量到视线的角。
Angle of depression: The angle measured downwards from the horizontal to a line of sight.
俯角：从水平线向下测量到视线的角。
Bearing: A three-digit angle measured clockwise from North, e.g., 045°.
方位角：从正北方向顺时针测量的三位数角度，例如 045°。
Similar shapes: Figures with the same shape but possibly different sizes; corresponding angles are equal, and sides are in proportion.
相似图形：形状相同但大小可能不同的图形；对应角相等，对应边成比例。
Scale factor: The multiplier used to enlarge or reduce a shape. For similar figures, lengths are multiplied by the scale factor.
比例因子（缩放因子）：用于放大或缩小图形的乘数。对于相似图形，边长乘以比例因子。
5. Measurement and Units | 度量与单位
Area: The amount of space inside a 2D shape, measured in square units such as cm².
面积：平面图形内部的空间大小，以平方单位计量，如 cm²。
Perimeter: The total distance around the edge of a 2D shape.
周长：围绕一个平面图形边缘的总距离。
Volume: The amount of space inside a 3D object, measured in cubic units such as cm³.
体积：立体物体内部的空间大小，以立方单位计量，如 cm³。
Compound measure: A measurement formed by combining two or more base units, e.g., speed (km/h) or density (g/cm³).
复合计量：由两个或多个基本单位组合而成的量度，例如速度 (km/h) 或密度 (g/cm³)。
Arc length: The distance along the curved edge of a sector of a circle.
弧长：圆扇形弯曲边缘的长度。
Sector area: The area of the wedge-shaped part of a circle bounded by two radii and an arc.
扇形面积：由圆的两条半径和一段弧围成的楔形部分的面积。
6. Statistics | 统计
Mean: The arithmetic average, calculated as sum of values divided by the number of values.
平均数（均值）：算术平均值，由数值总和除以数值个数计算得到。
Median: The middle value when data is arranged in order. For an even number of data items, it is the mean of the two middle numbers.
中位数：将数据排序后位于中间的值。若数据个数为偶数，则取中间两个数的平均值。
Mode: The value that appears most frequently in a data set.
众数：数据集中出现频率最高的值。
Range: The difference between the largest and smallest values in a data set.
极差：数据集中最大值与最小值之差。
Quartiles (Q₁, Q₂, Q₃): Values that divide ordered data into quarters. Q₂ is the median.
四分位数 (Q₁, Q₂, Q₃)：把有序数据分成四等份的位置值，Q₂ 为中位数。
Interquartile range (IQR): A measure of spread, IQR = Q₃ − Q₁.
四分位距 (IQR)：一种离散程度的度量，IQR = Q₃ − Q₁。
Standard deviation: A measure of how spread out numbers are around the mean; a smaller standard deviation indicates data are clustered more closely.
标准差：衡量数据相对于均值的离散程度；标准差越小，数据越集中。
Box plot (box-and-whisker diagram): A diagram showing the minimum, Q₁, median, Q₃, and maximum to summarise a data set.
箱线图（盒须图）：通过显示最小值、Q₁、中位数、Q₃ 和最大值来概括数据集的图形。
Scatter graph: A plot of paired data (x, y) used to investigate possible relationships between two variables.
散点图：绘制成对数据 (x, y) 的图形，用于探究两个变量之间可能的关系。
Line of best fit: A straight line drawn on a scatter graph that best represents the trend of the data.
最佳拟合线：在散点图上绘制的一条最能代表数据趋势的直线。
Correlation: Describes the direction and strength of a relationship between two variables: positive, negative, or none.
相关性：描述两个变量之间关系的方向和强度：正相关、负相关或无相关。
7. Probability | 概率
Probability: A value between 0 and 1 (inclusive) measuring how likely an event is to happen; can be written as a fraction, decimal, or percentage.
概率：一个介于 0 和 1（含）之间的值，衡量事件发生的可能性；可用分数、小数或百分数表示。
Sample space: The set of all possible outcomes of an experiment, often shown as a list or table.
样本空间：试验所有可能结果的集合，常以列表或表格形式表示。
Mutually exclusive events: Two events that cannot occur at the same time; P(A or B) = P(A) + P(B).
互斥事件：不可能同时发生的两个事件；P(A 或 B) = P(A) + P(B)。
Independent events: Events where the outcome of one does not affect the probability of the other; P(A and B) = P(A) × P(B).
独立事件：一个事件的结果不影响另一个事件概率的事件；P(A 且 B) = P(A) × P(B)。
Tree diagram: A branching diagram showing all possible outcomes and probabilities for multi-stage events.
树形图：显示多阶段事件所有可能结果及其概率的分支图。
Expected frequency: The number of times an event is predicted to occur, calculated as probability × number of trials.
期望频数：预计事件发生的次数，用 概率 × 试验次数 计算。
8. Key Verbs in Exam Questions | 考试题目关键动词
Calculate: Work out the answer, showing steps where necessary. You may use a calculator unless told otherwise.
计算：求出答案，必要时展示步骤。除非另有说明，可使用计算器。
Evaluate: Find the numerical value of an expression, e.g., evaluate 2x + 5 when x = 3.
求值：求表达式的数值，例如当 x = 3 时，求 2x + 5 的值。
Simplify: Reduce an expression to its shortest, neatest form, collecting like terms and cancelling where appropriate.
化简：将表达式化为最简短、最整洁的形式，合并同类项并在适当处约分。
Expand: Remove brackets by multiplying out, e.g., 3(a + 4) = 3a + 12.
展开：通过乘法去括号，例如 3(a + 4) = 3a + 12。
Factorise: Write an expression as a product of its factors; look for common factors first.
因式分解：将表达式写成它的因式之积；首先寻找公因式。
Solve: Find the value(s) of the variable(s) that satisfy an equation or inequality.
解（求解）：找出满足方程或不等式的变量的值。
Hence / Hence or otherwise: Use the result found in the previous part to help answer this question; if you cannot, use an alternative method.
由此 / 由此或其他方法：利用上一部分得到的结果回答本题；若无法使用，可采用其他方法。
Show that: Prove that a given expression or statement is true, usually by working through the steps and arriving at the given answer.
证明（说明）：通过逐步演算，验证给定的表达式或陈述成立，最终得出所给的结果。
Justify: Give a reason or explanation for your answer, often using mathematical properties or definitions.
解释理由：为你的答案提供原因或解释，通常运用数学性质或定义。
9. Common Confusions and Tips | 常见混淆与提示
Expression vs. Equation: An expression does not have an equals sign (e.g., 4x + 1), while an equation does (e.g., 4x + 1 = 9). You simplify an expression and solve an equation.
表达式与方程：表达式没有等号（如 4x + 1），方程则有等号（如 4x + 1 = 9）。表达式要化简，方程要求解。
Factorising vs. Expanding: Expanding removes brackets; factorising puts brackets back in. They are reverse processes.
因式分解与展开：展开是去括号，因式分解是重新加入括号。两者互为逆运算。
Gradient vs. Rate of change: In many contexts these mean the same thing: how quickly y changes with respect to x. For a line, it is constant; for a curve, it changes.
斜率与变化率：在许多语境下含义相同：y 相对于 x 变化的快慢。对于直线，它为常数；对于曲线，它是变化的。
Radius vs. Diameter: A common mistake is confusing the two. Diameter = 2 × radius.
半径与直径：常见错误是混淆两者。直径 = 2 × 半径。
Square root vs. Square: Square means multiplying a number by itself (n²). Square root (√) is the reverse: finding the number that was squared.
平方根与平方：平方是指一个数自乘 (n²)，平方根 (√) 是其逆运算：寻找被平方的原数。
Direct proportion vs. Inverse proportion: In direct proportion, y = kx; as x increases, y increases at a constant rate. In inverse proportion, y = k/x; as x increases, y decreases.
正比例与反比例：正比例中 y = kx，x 增大时 y 以恒定速率增大；反比例中 y = k/x，x 增大时 y 减小。
10. Quick Reference Table | 速查表
The table below summarises a selection of high-frequency SQA maths terms with their direct Chinese translations, useful for quick revision.
下表汇总了部分高频 SQA 数学术语及其直译，便于快速复习。
| English Term | 中文术语 |
|---|---|
| Simplify | 化简 |
| Factorise | 因式分解 |
| Expand | 展开 |
| Solve | 解（求解） |
| Subject of the formula | 公式的主项 |
| Gradient | 斜率 |
| y-intercept | y轴截距 |
| Hypotenuse | 斜边 |
| Bearing | 方位角 |
| Interquartile range | 四分位距 |
| Standard deviation | 标准差 |
| Mutually exclusive | 互斥 |
| Tree diagram | 树形图 |
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