📚 Year 9 SQA Advanced Mathematics: Vocabulary & Terminology Quick Memory Guide | Year 9 SQA 进阶数学：词汇术语速记指南
Mastering the language of mathematics is the first step to solving problems with confidence. This guide breaks down the essential vocabulary for Year 9 SQA Advanced Mathematics into bite‑sized definitions, memory tricks, and paired examples, helping you speak ‘maths’ fluently.
掌握数学语言是自信解题的第一步。这份指南将 Year 9 SQA 进阶数学的核心词汇拆解为简明定义、记忆窍门与配对示例，助你流利表达“数学语言”。
1. Algebraic Expressions | 代数表达式
An expression is a mathematical phrase containing numbers, variables and operations, but no equals sign. For example, 3x³ + 2x − 7 is an expression.
表达式是由数字、变量和运算符号组成的数学短语，不含等号。例如 3x³ + 2x − 7 是一个表达式。
A term is a single number, a variable, or numbers and variables multiplied together. In 4a²b + 5c − 9, there are three terms.
项是指单个数字、单个变量或数字与变量的乘积。在 4a²b + 5c − 9 中，共有三项。
The coefficient is the number part of a term that multiplies the variable. In −6y⁴, the coefficient is −6.
系数是项中与变量相乘的数字部分。在 −6y⁴ 中，系数是 −6。
Like terms have exactly the same variable part and can be combined. 7mn and −2mn are like terms, but 7m and 7n are not.
同类项拥有完全相同的变量部分，可以合并。7mn 和 −2mn 是同类项，但 7m 和 7n 不是。
2. Equations and Solving | 方程与求解
An equation states that two expressions are equal. It always contains an equals sign, such as 2x + 5 = 11.
方程表明两个表达式相等，总是含有等号，例如 2x + 5 = 11。
An inequality compares two expressions using <, >, ≤ or ≥. The solution set is a range of values, not just one number.
不等式用 <、>、≤ 或 ≥ 比较两个表达式。解集是一个数值范围，不只是一个数。
To solve means to find the value of the unknown that makes the equation true. Balancing both sides keeps the equality.
求解指找出使方程成立的未知数值。方程两边保持平衡即可维持等式。
When substituting, you replace a variable with a given number. Substitute x = 3 into 2x + 5 gives 2(3) + 5 = 11.
代入指用给定数字替换变量。将 x = 3 代入 2x + 5 得到 2(3) + 5 = 11。
3. Sequences and Patterns | 数列与规律
A sequence is a list of numbers that follows a rule. Each number is called a term, often written as Uₙ.
数列是按规则排列的一列数。每个数称为一项，常记为 Uₙ。
An arithmetic sequence has a constant difference d between consecutive terms. 5, 9, 13, 17,… has d = 4.
等差数列的相邻两项之差为常数 d。5, 9, 13, 17,… 中 d = 4。
The nth term formula lets you find any term without listing all before it. For 3n − 1, the 20th term is 59.
第 n 项公式让你无需列出前面所有项就能找到任一项。对于 3n − 1，第 20 项是 59。
A geometric sequence multiplies by a constant ratio r each step. 3, 6, 12, 24,… has r = 2.
等比数列每一步乘以常数比例 r。3, 6, 12, 24,… 的 r = 2。
4. Indices and Surds | 指数与根式
An index (or exponent) tells you how many times to multiply a base by itself. In 5³, the index is 3, so 5 × 5 × 5 = 125.
指数（或幂）表示底数自乘的次数。在 5³ 中，指数是 3，即 5 × 5 × 5 = 125。
The laws of indices include aᵐ × aⁿ = aᵐ⁺ⁿ and (aᵐ)ⁿ = aᵐⁿ. These simplify expressions like x⁴ × x² = x⁶.
指数法则包括 aᵐ × aⁿ = aᵐ⁺ⁿ 和 (aᵐ)ⁿ = aᵐⁿ。它们可以简化如 x⁴ × x² = x⁶ 的表达式。
A sur is an irrational root that cannot be simplified to a whole number, like √2 or ³√9.
根式是指无法化简为整数的无理数根，例如 √2 或 ³√9。
Negative indices give reciprocals: a⁻ⁿ = 1/aⁿ. So 2⁻³ = 1/8. Fractional indices represent roots: a½ = √a.
负指数表示倒数：a⁻ⁿ = 1/aⁿ。因此 2⁻³ = 1/8。分数指数表示根号：a½ = √a。
5. Graphs and Linear Functions | 图像与线性函数
A linear function produces a straight‑line graph. It is usually written as y = mx + c, where m is the gradient and c is the y‑intercept.
线性函数生成一条直线图像，通常写作 y = mx + c，其中 m 是斜率，c 是 y 轴截距。
The gradient measures steepness: m = (change in y) ÷ (change in x), often called rise over run.
斜率衡量陡峭程度：m = (y 的变化量) ÷ (x 的变化量)，常称为纵升与横增之比。
The y‑intercept is where the line crosses the y‑axis (x = 0). The x‑intercept is where it crosses the x‑axis (y = 0).
y 轴截距是直线与 y 轴的交点（x = 0）。x 轴截距是直线与 x 轴的交点（y = 0）。
Parallel lines have the same gradient. Perpendicular lines have gradients that multiply to −1 (m₁ × m₂ = −1).
平行线斜率相等。垂直线的斜率乘积为 −1（m₁ × m₂ = −1）。
6. Quadratic Foundations | 二次基础
A quadratic expression contains a variable squared, like x² + 5x + 6. Its graph is a parabola, a U‑shaped curve.
二次表达式含有变量的平方项，例如 x² + 5x + 6。其图像为抛物线，一条 U 形曲线。
To factorise means to write an expression as a product of brackets. x² + 5x + 6 = (x + 2)(x + 3).
因式分解指将表达式写成括号乘积的形式。x² + 5x + 6 = (x + 2)(x + 3)。
Expanding brackets reverses factorisation: (x + 4)(x − 1) = x² + 3x − 4. Use FOIL (First, Outer, Inner, Last) to remember the order.
展开括号是因式分解的逆运算：(x + 4)(x − 1) = x² + 3x − 4。可用“首先、外侧、内侧、最后”（FOIL）记忆顺序。
The roots of a quadratic are the values of x that make the expression zero. They are also the x‑intercepts of the parabola.
二次式的根是使表达式为零的 x 值，也是抛物线与 x 轴的交点横坐标。
7. Geometry Terms | 几何术语
An acute angle is less than 90°. An obtuse angle is between 90° and 180°. A reflex angle is greater than 180°.
锐角小于 90°，钝角在 90° 到 180° 之间，优角大于 180°。
Congruent shapes are identical in size and shape. Similar shapes have the same shape but may differ in size; corresponding angles are equal and sides are in proportion.
全等形状大小和形状完全相同。相似形状形状相同但大小可不同；对应角相等，对应边成比例。
When two lines intersect, vertically opposite angles are equal. Alternate angles and corresponding angles on parallel lines are also equal.
两直线相交时，对顶角相等。平行线上的内错角和同位角也相等。
A polygon is regular if all sides and angles are equal. The sum of interior angles of an n‑sided polygon is (n − 2) × 180°.
各边和角均相等的多边形是正多边形。n 边多边形的内角和为 (n − 2) × 180°。
8. Measurement and Formulae | 度量与公式
Perimeter is the total distance around a 2D shape. Area measures the surface inside, typically in square units.
周长是二维图形一周的总长度。面积衡量内部的表面大小，单位通常为平方单位。
The area of a triangle is ½ × base × height. Always use the perpendicular height, not a slant side.
三角形面积为 ½ × 底 × 高。务必使用垂直高度，而非斜边。
Volume measures the space a 3D shape occupies. A prism’s volume is area of cross‑section × length.
体积衡量三维物体占据的空间。棱柱的体积 = 横截面积 × 长度。
Pythagoras’ theorem states that in a right‑angled triangle, a² + b² = c², where c is the hypotenuse.
勾股定理指出，在直角三角形中，a² + b² = c²，其中 c 是斜边。
The diameter of a circle is twice the radius. Circumference = π × diameter, or 2πr.
圆的直径是半径的两倍。周长 = π × 直径，即 2πr。
9. Data and Statistics | 数据与统计
The mean is the average: add all values and divide by how many there are. The median is the middle value when data is ordered.
平均数是所有数值之和除以个数。中位数是数据排序后正中间的值。
The mode is the most frequent value. The range is the difference between the highest and lowest values, showing spread.
众数是出现频率最高的值。极差是最大值与最小值之差，反映离散程度。
A frequency table tallies how often each value occurs. A grouped frequency table is used for continuous data or large data sets.
频数表记录每个值出现的次数。分组频数表用于连续数据或大数据集。
A scatter graph shows the relationship between two variables. Correlation describes the direction and strength of that relationship, not causation.
散点图展示两个变量间的关系。相关性描述该关系的方向和强度，并非因果性。
10. Probability Language | 概率语言
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). It is often written as a fraction, decimal or percentage.
概率衡量事件发生的可能性，介于 0（不可能）到 1（必然）之间，常写成分数、小数或百分比。
An outcome is a possible result of an experiment. The sample space is the set of all possible outcomes.
结果是试验的一个可能情况。样本空间是所有可能结果的集合。
An event is a specific set of outcomes. For a fair six‑sided die, the event ‘even number’ includes outcomes 2, 4 and 6.
事件是一组特定的结果。对一个均匀六面骰子，“偶数”事件包含 2、4 和 6 等结果。
A tree diagram helps list all possible outcomes for two or more stages. Multiply along branches to find probabilities of combined events.
树状图帮助列出两阶段或更多阶段的所有可能结果。沿分支相乘可得组合事件的概率。
Mutually exclusive events cannot happen at the same time. Independent events do not affect each other’s probabilities.
互斥事件不能同时发生。独立事件彼此的概率互不影响。
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