📚 Year 11 SQA Maths: Key Terminology Quick Reference Guide | SQA 数学核心术语速记指南
Mastering the essential vocabulary of SQA National 5 Mathematics is a powerful shortcut to better exam performance. This guide provides clear, concise definitions of the most important terms you will encounter across algebra, geometry, trigonometry, statistics and more. Each term is explained in both English and Chinese to reinforce your understanding and help you interpret questions with confidence.
掌握 SQA National 5 数学的核心词汇是提升考试成绩的有效捷径。本指南提供了你在代数、几何、三角学、统计等领域会遇到的最重要术语的清晰简明定义。每个术语均以中英双语解释，帮助你加深理解，自信地解读题目。
1. Algebraic Expressions | 代数表达式
Variable: A symbol, usually a letter, that represents a number which can change or vary, e.g. x in 3x + 7.
变量：一个符号，通常是字母，代表可以变化或取不同值的数，例如 3x + 7 中的 x。
Constant: A fixed number that does not change, e.g. 7 in 3x + 7.
常数：固定不变的数字，例如 3x + 7 中的 7。
Coefficient: The number that multiplies a variable, e.g. 3 is the coefficient of x in 3x.
系数：乘以变量的数字，例如 3x 中 3 是 x 的系数。
Term: A single number, variable or a product of numbers and variables, separated by + or − signs in an expression.
项：由数字、变量或它们的乘积构成的独立部分，在表达式中通过加号或减号分隔。
Expression: A combination of terms without an equals sign, such as 4x² − 2x + 9.
表达式：不含等号的项的集合，例如 4x² − 2x + 9。
Simplify: To combine like terms and reduce an expression to its simplest possible form.
化简：合并同类项，将一个表达式化为最简形式。
Expand: s by : To remove brackets by multiplying each term inside the bracket by the term outside, e.g. 3(x + 2) = 3x + 6.
展开：通过将括号内的每一项乘以外面的项来去掉括号，例如 3(x + 2) = 3x + 6。
Factorise: To write an expression as a product of its factors, e.g. x² + 5x + 6 = (x + 2)(x + 3).
因式分解：把一个表达式写成其因式的乘积，例如 x² + 5x + 6 = (x + 2)(x + 3)。
2. Equations and Inequalities | 方程与不等式
Equation: s the equality of two expressions, often containing an unknown variable, e.g. 3x − 5 = 10.
方程：表明两个表达式相等的数学陈述，通常包含未知变量，例如 3x − 5 = 10。
Solve: To find the value(s) of the variable(s) that make an equation true.
求解：找出使方程成立的变量的值。
Inequality: tement that compares two expressions using symbols <, >, ≤ or ≥, e.g. 2x + 1 > 7.
不等式：用 <、>、≤ 或 ≥ 符号比较两个表达式的陈述，例如 2x + 1 > 7。
Solution set: All values of the variable that satisfy an equation or inequality.
解集：满足方程或不等式的变量的所有值。
Balancing method: A technique for solving equations by performing the same operation on both sides to isolate the variable.
平衡法：通过在等式两边进行相同的运算来隔离变量，从而求解方程的方法。
Number line representation: A visual way of showing solutions of inequalities, using open or closed circles and arrows.
数轴表示：用开圆或闭圆及箭头直观表示不等式解集的方法。
3. Straight Line | 直线
Gradient (slope): A measure of the steepness of a line, calculated as vertical change divided by horizontal change (rise/run), typically denoted by m.
斜率（坡度）：衡量直线陡峭程度的量，用垂直变化除以水平变化（纵差/横差）计算，通常用 m 表示。
y-intercept: The point where a straight line crosses the y-axis; in the equation y = mx + c, it is c.
y 截距：直线与 y 轴相交的点；在方程 y = mx + c 中为 c。
Equation of a straight line: Usually written as y = mx + c, where m is the gradient and c is the y-intercept.
直线方程：一般写作 y = mx + c，其中 m 是斜率，c 是 y 截距。
Midpoint: The point exactly halfway between two points; its coordinates are the averages of the x-values and y-values.
中点：两点间正中间的点；其坐标为两点 x 坐标的平均值和 y 坐标的平均值。
Parallel lines: Lines that never meet and have the same gradient (m₁ = m₂).
平行线：永不相交且斜率相同的直线 (m₁ = m₂)。
Perpendicular lines: Lines that intersect at 90°; the product of their gradients is −1 (m₁ × m₂ = −1).
垂直线：以 90° 角相交的直线；其斜率之积为 −1 (m₁ × m₂ = −1)。
4. Quadratic Functions and Graphs | 二次函数与图像
Quadratic function: A function of the form f(x) = ax² + bx + c where a ≠ 0. Its graph is a parabola.
二次函数：形如 f(x) = ax² + bx + c 的函数，其中 a ≠ 0，图像为抛物线。
Parabola: The smooth, symmetric U-shaped curve
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