📚 Year 11 SQA Maths: Essential Terms Guide | SQA 数学词汇术语速记指南
Mastering the language of mathematics is half the battle in SQA National 5 Maths. Whether you are tackling algebra, geometry, or statistics, a clear understanding of key terms can prevent silly mistakes and boost your problem‑solving confidence. This guide collects the must‑know vocabulary, explained in plain English and Chinese, so you can quickly recall what ‘simultaneous equations’ or ‘standard deviation’ actually means when it matters most — in the exam hall.
在 SQA National 5 数学中，掌握数学语言就等于成功了一半。无论你面对的是代数、几何还是统计，对关键术语的清晰理解都能避免粗心错误，提升解题信心。本指南汇集了必学的核心词汇，用平实的英文和中文解释，让你在考场上能够迅速回想起 ‘simultaneous equations’ 或 ‘standard deviation’ 到底是什么意思。
1. Number and Arithmetic Basics | 数与算术基础
Integer: A whole number that can be positive, negative, or zero, without any fractional or decimal part.
整数： 可以是正数、负数或零，没有分数或小数部分的完整数字。
Factor: A whole number that divides exactly into another number with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 exactly.
因数： 能整除另一个整数而没有余数的数。例如，3 是 12 的因数，因为 12 ÷ 3 = 4。
Prime number: A positive integer greater than 1 that has exactly two distinct factors — 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13…
质数（素数）： 大于 1 的正整数，且恰好只有两个不同的因数——1 和它本身。前几个质数是 2, 3, 5, 7, 11, 13……
Least Common Multiple (LCM): The smallest positive integer that is a multiple of two or more numbers. For 4 and 6, the LCM is 12.
最小公倍数： 两个或多个数的倍数中最小的那个正整数。对于 4 和 6，最小公倍数是 12。
Highest Common Factor (HCF) / Greatest Common Divisor (GCD): The largest positive integer that divides two or more numbers without a remainder. For 12 and 18, the HCF is 6.
最大公因数： 能同时整除两个或多个数的最大正整数。对于 12 和 18，最大公因数是 6。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Numerator: The top part of a fraction, indicating how many parts we have.
分子： 分数线上方的部分，表示我们拥有多少份。
Denominator: The bottom part of a fraction, showing how many equal parts the whole is divided into.
分母： 分数线下方的部分，表示整体被等分成多少份。
Recurring decimal: A decimal with a digit or group of digits that repeats forever, such as 0.333… or 0.142857142857… – often written with a dot or line above the repeating part.
循环小数： 有一个或一组数字无限重复的小数，例如 0.333…… 或 0.142857142857…… ——通常在循环部分上方加点或横线表示。
Percentage increase: The change in value expressed as a percentage of the original amount. Formula: (increase ÷ original) × 100%.
百分数增加： 用原始数量的百分数表示的数值变化。公式：(增加量 ÷ 原值) × 100%。
3. Algebra Essentials | 代数基础
Expression: A combination of numbers, variables, and operation signs (+, −, ×, ÷) that represents a value, but does not contain an equals sign. Example: 3x + 5y − 2.
表达式： 由数字、变量和运算符号（+、−、×、÷）组成的式子，表示一个值，但不含等号。例如：3x + 5y − 2。
Coefficient: The numerical factor placed in front of a variable in a term. In 7a, 7 is the coefficient of a.
系数： 项中写在变量前面的数字因子。在 7a 中，7 是 a 的系数。
Term: A single part of an algebraic expression separated by + or − signs. In 2x + 3y − 4, the terms are 2x, 3y, and −4.
项： 代数表达式中用 + 或 − 分隔的单个部分。在 2x + 3y − 4 中，各项为 2x、3y 和 −4。
Simplify: To rewrite an expression in its most compact form by collecting like terms, carrying out operations, and applying algebraic rules.
化简： 通过合并同类项、执行运算并应用代数规则，将表达式改写成最紧凑的形式。
4. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement that two expressions are equal, shown by the equals sign (=). It can be solved to find unknown values.
方程： 用等号（=）表示两个表达式相等的数学陈述。可以求解未知数的值。
Solving: Finding the value(s) of the variable that make an equation true. For x + 3 = 7, solving gives x = 4.
求解： 找出使方程成立的变量的值。对于 x + 3 = 7，求解得到 x = 4。
Simultaneous equations: A set of two or more equations with multiple unknowns that are true at the same time. At National 5 level, these usually involve two variables and can be solved by substitution or elimination.
联立方程组： 包含两个或多个未知数、且同时成立的两个或多个方程。在 National 5 层次，通常涉及两个变量，可用代入法或消元法求解。
Inequality: A statement comparing two expressions that are not equal, using symbols like , ≤, ≥. Example: 2x + 1 > 5.
不等式： 用 、≤、≥ 等符号比较两个不相等的表达式的陈述。例如：2x + 1 > 5。
5. Functions and Graphs | 函数与图像
Function: A rule that relates each input value to exactly one output value, often written as f(x). For f(x) = 2x + 1, when x = 3, f(3) = 7.
函数： 将每一个输入值对应到恰好一个输出值的规则，常写作 f(x)。对于 f(x) = 2x + 1，当 x = 3 时，f(3) = 7。
Gradient (slope): The measure of steepness of a line, calculated as change in y divided by change in x between two points. Often denoted by m.
斜率（坡度）： 衡量一条直线倾斜程度的量，由两点间的 y 变化量除以 x 变化量计算得出。通常用 m 表示。
y-intercept: The point where a line or curve crosses the y‑axis. For a straight line y = mx + c, c is the y‑intercept.
y 截距： 直线或曲线与 y 轴相交的点。对于直线 y = mx + c，c 就是 y 截距。
Quadratic function: A function that can be written in the form ax² + bx + c, where a ≠ 0. Its graph is a parabola.
二次函数： 可以写成 ax² + bx + c 形式的函数，其中 a ≠ 0。其图像是一条抛物线。
6. Geometry | 几何学
Angle: The figure formed by two rays sharing a common endpoint (vertex). Measured in degrees (°).
角： 由两条具有公共端点（顶点）的射线构成的图形。用度（°）来度量。
Right angle: An angle of exactly 90°.
直角： 恰好为 90° 的角。
Triangle: A polygon with three sides and three interior angles that sum to 180°. Types include equilateral (equal sides), isosceles (two equal sides), and scalene (no equal sides).
三角形： 有三条边和三个内角的多边形，内角和为 180°。类型包括等边三角形（三边相等）、等腰三角形（两边相等）和不等边三角形（各边都不等）。
Circle: radius, diameter, circumference: The radius is the distance from the centre to the edge. The diameter is twice the radius, passing through the centre. Circumference is the perimeter of the circle.
圆：半径、直径、周长： 半径是从圆心到圆周的距离。直径是通过圆心的线段，长度是半径的两倍。周长是圆的边界长度。
7. Trigonometry | 三角学
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，正对直角。
Sine (sin), Cosine (cos), Tangent (tan): Trigonometric ratios relating angles to side lengths in a right‑angled triangle. sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent.
正弦（sin）、余弦（cos）、正切（tan）： 将一个角度与直角三角形中各边长度关联起来的三角比。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之间的角度。
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之间的角度。
8. Statistics | 统计学
Mean: The average of a set of numbers, found by adding all values and dividing by the count of values.
平均数（均值）： 一组数的平均值，计算方法为将所有数值相加再除以数值的个数。
Median: The middle value when a data set is ordered from smallest to largest. If there are two middle values, the median is their mean.
中位数： 将数据集按从小到大的顺序排列后处于中间位置的值。如果中间有两个数，中位数就是它们的平均数。
Mode: The value that occurs most frequently in a data set. A set may have one mode, more than one mode, or no mode at all.
众数： 数据集中出现次数最多的值。一个数据集可能有一个众数、多个众数，或者没有众数。
Range: A measure of spread, calculated as maximum value minus minimum value.
极差（范围）： 衡量数据分散程度的统计量，等于最大值减去最小值。
Standard deviation: A measure of how spread out numbers are from the mean. A small standard deviation means data points are close to the mean; a large one indicates they are more spread.
标准差： 衡量数值相对于平均值的分散程度。标准差小表示数据点靠近平均值；标准差大表示数据点更加分散。
9. Probability | 概率
Probability: The chance of an event happening, expressed as a number between 0 (impossible) and 1 (certain). Often written as a fraction, decimal or percentage.
概率： 某个事件发生的可能性，用一个介于 0（不可能）和 1（必然发生）之间的数字表示。常写成分数、小数或百分数。
Outcome: A possible result of a probability experiment, such as getting a ‘4’ when rolling a die.
结果： 概率实验中可能出现的一个结果，比如掷骰子得到“4”。
Sample space: The set of all possible outcomes of an experiment, often listed in a diagram or table.
样本空间： 一次实验所有可能结果的集合，通常用图表或表格列出。
Mutually exclusive events: Events that cannot happen at the same time. For example, a coin toss cannot be both heads and tails simultaneously.
互斥事件： 不能同时发生的事件。例如，掷一枚硬币不可能同时出现正面和反面。
10. Measurement and Units | 度量与单位
Perimeter: The total distance around the outside of a 2D shape. Found by adding all side lengths.
周长： 二维图形外边界的总长度。通过将所有边长相加求得。
Area: The amount of surface inside a 2D shape, measured in square units (cm², m², etc.).
面积： 二维图形内部表面的大小，用平方单位（cm²、m² 等）度量。
Volume: The amount of space enclosed by a 3D object, measured in cubic units (cm³, m³, etc.).
体积： 三维物体所包围的空间量，用立方单位（cm³、m³ 等）度量。
Surface area: The total area of all the faces of a 3D solid.
表面积： 三维立体所有面的总面积。
11. Coordinate Geometry Key Words | 坐标几何关键词
Midpoint: The exact middle point of a line segment, found by averaging the x‑coordinates and the y‑coordinates of the endpoints.
中点： 线段正中间的点，通过求端点 x 坐标和 y 坐标的平均值得到。
Distance formula: Used to find the length between two points (x₁, y₁) and (x₂, y₂). Derived from Pythagoras’ theorem: √[(x₂ − x₁)² + (y₂ − y₁)²].
距离公式： 用于求两点 (x₁, y₁) 和 (x₂, y₂) 之间的长度。由勾股定理推导而来：√[(x₂ − x₁)² + (y₂ − y₁)²]。
Pythagoras’ theorem: In a right‑angled triangle, a² + b² = c², where c is the hypotenuse. Essential for finding missing side lengths.
勾股定理： 在直角三角形中，a² + b² = c²，其中 c 是斜边。是求未知边长的基础。
12. Exam Command Words | 考试指令词
Evaluate: Work out the numerical value. For ‘evaluate 3x + 2 when x = 4’, the answer is 14.
求值： 计算出数值结果。对 ‘当 x = 4 时，计算 3x + 2 的值’，答案是 14。
Factorise: Write an expression as a product of its factors, e.g., x² − 9 = (x + 3)(x − 3).
因式分解： 把表达式写成其因式的乘积，例如 x² − 9 = (x + 3)(x − 3)。
Expand: Multiply out brackets, e.g., 2(x + 4) = 2x + 8.
展开： 将括号乘开，例如 2(x + 4) = 2x + 8。
Justify / Explain: Give a mathematical reason for your answer, often quoting a theorem, definition, or property.
证明 / 解释： 用数学理由支撑你的答案，通常需要引用某个定理、定义或性质。
Hence: Use the previous result to answer the next part of the question.
由此： 利用前一步的结果来回答问题的下一部分。
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