📚 Year 9 SQA Maths: Vocabulary & Terminology Memory Guide | Year 9 SQA 数学：词汇术语速记指南
Mastering the language of mathematics is half the battle. This guide breaks down essential SQA Year 9 terms into easy-to-remember chunks, with quick mnemonics and bilingual explanations to sharpen your recall and boost your confidence.
掌握数学语言是成功的一半。这份指南将 SQA Year 9 的核心术语分解成易于记忆的模块，提供助记窍门和双语解释，帮助你快速回忆、增强信心。
1. Numbers and Number Systems | 数字与数系
Numbers are the building blocks of maths. Knowing the precise names helps you follow instructions and spot patterns. Here are the key terms and some memory tricks.
数字是数学的基石。准确的名字能帮助你理解题意、发现规律。以下是关键术语和记忆技巧。
- Integer – a whole number that can be positive, negative, or zero. Think: 'integer' sounds like 'intact' – nothing broken off (no fractions).
整数 – 可以是正数、负数或零的完整数字，没有分数部分。“整”就像完整无缺。 - Prime number – a number with exactly two distinct factors: 1 and itself. Mnemonic: A prime minister has only one cabinet (1) and themselves.
质数（素数） – 只有两个不同因数的数：1 和它本身。助记：质数就像首相，只有 1（国家）和自己。 - Factor – a number that divides another exactly. Think: a 'factor' that helps build the number.
因数 – 能整除另一个数的数。联想：构建数字的“零件”。 - Multiple – the result of multiplying a number by an integer. The times table gives you multiples.
倍数 – 一个数乘整数的结果。乘法表里的都是倍数。 - Square number / square root – 4² = 16, so 16 is a square number, and √16 = 4. Picture a perfect square of dots.
平方数 / 平方根 – 4² = 16，16 是平方数，√16 = 4。想象一个正方形点阵。 - Cube number / cube root – 3³ = 27, so 27 is a cube number, and ∛27 = 3. Picture a cube built from smaller cubes.
立方数 / 立方根 – 3³ = 27，27 是立方数，∛27 = 3。想象由小立方体搭成的大立方体。 - Index (exponent) – the small raised number showing how many times to multiply the base. In 5³, 3 is the index.
指数（幂） – 写在右上角的小数字，表示底数乘几次。5³ 中的 3 是指数。 - Standard form – a way to write very large or small numbers as a × 10ⁿ, where 1 ≤ a < 10. e.g. 3.2 × 10⁵.
标准形式（科学记数法） – 用 a × 10ⁿ 表示极大或极小的数，其中 1 ≤ a < 10。如 3.2 × 10⁵。
2. Algebra Basics | 代数基础
Algebra is a language of symbols. Learn the vocabulary, and you will be able to translate word problems into expressions and equations fluently.
代数是符号的语言。掌握词汇，你就能流畅地把文字题翻译成表达式和方程。
- Variable – a letter that stands for an unknown number. 'Variable' means it can vary.
变量 – 代表未知数的字母，“可变”意味着它可以取不同值。 - Constant – a fixed number that does not change. Think: 'constant' like a fixed star.
常数 – 固定不变的数。像恒星一样恒定。 - Coefficient – the number multiplying a variable. In 5x, 5 is the coefficient. 'Co' means with, so it goes with the variable.
系数 – 乘在变量前面的数。5x 中 5 是系数。“系”表示关联。 - Term – a single number, variable, or product of numbers and variables. 4, x, 3x² are terms.
项 – 单个数字、变量或数字与变量的乘积。如 4，x，3x² 都是项。 - Expression – a combination of terms with no equals sign, like 2x + 5.
表达式 – 项的组合，没有等号。如 2x + 5。 - Equation – a statement that two expressions are equal, like 2x + 5 = 11.
方程 – 表示两个表达式相等的式子，含有等号。如 2x + 5 = 11。 - Like terms – terms with identical variable parts. You can add 3x and 5x, but not 3x and 5y.
同类项 – 变量部分完全相同的项。可以合并 3x 和 5x，但不能合并 3x 和 5y。 - Simplify / Expand / Factorise – simplify (combine like terms), expand (remove brackets by multiplying), factorise (put brackets back in by taking out a common factor). Remember the order: Sometimes Expand then Simplify, or Factorise to break down.
化简 / 展开 / 因式分解 – 化简（合并同类项），展开（乘法去括号），因式分解（提取公因式加回括号）。记住顺序：有时先展开再化简，或因式分解来拆分。
3. Equations and Inequalities | 方程与不等式
Solving means finding the unknown. Inequalities show a range of possible values. The symbols are compact messages – learn to read them instantly.
解方程就是求出未知数。不等式表示一个取值范围。这些符号是紧凑的信息——要学会立刻读懂它们。
- Solve an equation – find the value of the variable that makes the statement true. Think of a balance scale: do the same to both sides.
解方程 – 找到使等式成立的变量值。想象天平：两边做同样的操作。 - Root / Solution – the value you find. 'Root' is the same as solution.
根 / 解 – 求出的值。根就是解。 - Inequality symbols –
< means 'less than', > means 'greater than', ≤ means 'less than or equal to', ≥ means 'greater than or equal to', ≠ means 'not equal to'.
不等号 – < 小于，> 大于，≤ 小于等于，≥ 大于等于，≠ 不等于。记忆法：开口朝向较大的数，像鳄鱼的嘴巴。 - Inequality – a statement that compares two expressions using one of the symbols above. The solution is usually a range, like x > 3.
不等式 – 用不等号连接两个表达式的式子。解通常是一个范围，如 x > 3。 - Balance method – performing the same operation on both sides of an equation or inequality to keep it balanced.
平衡法 – 在方程或不等式两边执行相同运算，以保持平衡。
4. Fractions, Decimals and Percentages | 分数、小数与百分比
These three forms describe parts of a whole. Being able to switch between them is a core SQA skill.
这三种形式都描述整体的一部分。在它们之间灵活转换是 SQA 的核心技能。
- Fraction – has a numerator (top) and denominator (bottom). Denomin-ator gives the name (like 'fifths'), numer-ator counts how many.
分数 – 由分子（上）和分母（下）组成。分母命名（如“五分之”），分子计数。 - Mixed number – a whole number and a fraction together, like 2½. Improper fraction – numerator bigger than denominator, like 5/2.
带分数 – 整数和分数写在一起，如 2½。假分数 – 分子大于分母，如 5/2。 - Equivalent fractions – fractions that represent the same amount, found by multiplying or dividing numerator and denominator by the same number.
等值分数 – 表示相同大小的分数，通过分子分母同乘或同除得到。 - Decimal – a number written with a decimal point. Terminating decimals end; recurring decimals have a repeating pattern (e.g. 0.333... or 0.3̅).
小数 – 带小数点的数。有限小数会终止；循环小数有重复数字（如 0.333...）。 - Percentage – 'per cent' means out of 100. To convert a fraction to a percent, multiply by 100.
百分比 – per cent 表示每百。分数化百分比，乘 100。 - Convert between forms – ; decimal → percentage: multiply by 100; percentage → fraction: put over 100 and simplify.
形式转换 – 分数化小数：分子除以分母；小数化百分数：乘 100；百分数化分数：写成分母 100 再化简。
5. Ratio and Proportion | 比率与比例
Ratio compares quantities, while proportion describes how one quantity changes with another. These are common in recipe scaling and map reading.
比率比较两个量，比例描述一个量如何随另一个量变化。这在调配配方和阅读地图中很常见。
- Ratio – a comparison of two or more quantities, written as 3:2. The order matters.
比 – 两个或更多量的比较，写作 3:2。顺序很重要。 - Divide in a given ratio – share an amount into parts. Add the parts, find one part's value, then multiply.
按给定比分发 – 按份数分配总量。把总份数相加，算出一份的量，再乘以对应份数。 - Proportion – says two ratios are equal. Also used for direct proportion: as one doubles, the other doubles.
比例 – 表示两个比相等。也用于正比例：一个量翻倍，另一个也翻倍。 - Unitary method – find the value of one unit first, then scale up. Perfect for best-buy problems.
归一法 – 先求出单一单位的量，再放大。最适合解决“最划算”问题。 - Scale – the ratio of a length on a drawing or map to the real length. E.g. 1:100 means 1 cm represents 100 cm.
比例尺 – 图纸或地图上的长度与实际长度的比。如 1:100 表示 1 厘米代表实际 100 厘米。
6. Geometry and Measurement | 图形与测量
Shapes have specific names and formulas. Focus on the meaning of perimeter, area, and volume, and learn the language of circles.
图形有专门的名称和公式。要重点理解周长、面积和体积的含义，并学习圆的相关术语。
- Perimeter – the distance around the outside of a 2D shape. Think 'rim' inside perimeter.
周长 – 二维图形外边界的长度。周长的“周”就是绕一圈。 - Area – the amount of surface a shape covers, measured in square units (cm², m²).
面积 – 图形覆盖的表面大小，单位是平方单位。 - Volume – the space a 3D object occupies, in cubic units (cm³, m³).
体积 – 三维物体占据的空间，单位是立方单位。 - Surface area – the total area of all faces of a 3D shape.
表面积 – 立体所有面的总面积。 - Circumference – the perimeter of a circle. Formula: C = π × d or 2πr.
圆周长 – 圆的周长。公式：C = π × d 或 2πr。 - Radius, diameter, π (pi) – tre to circumference; diameter is across through centre (double radius). π ≈ 3.14 or 22/7.
半径、直径、圆周率 π – 半径是圆心到圆周；直径是穿过圆心的线段（两倍半径）。π 约等于 3.14。 - Prism, cylinder, polygon – a prism has a constant cross-section; cylinder is a prism with circular cross-section; polygon is a many-sided closed figure.
棱柱、圆柱、多边形 – 棱柱横截面不变；圆柱是以圆为横截面的棱柱；多边形是多条边组成的封闭图形。
7. Angles and Lines | 角度与线条
Angles are classified by size and by their position when lines intersect. Memorising these pairs will unlock angle problems.
角可以按大小分类，也可以按直线相交的位置关系分类。记住这些角对的名字，就能解决角度问题。
- Acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), reflex (between 180° and 360°).
锐角（小于 90°），直角（90°），钝角（90° 到 180° 之间），优角（180° 到 360° 之间）。 - Complementary angles – two angles that add up to 90°. Come together to 'complete' a right angle.
互余角 – 和为 90° 的两个角。互补就像凑成一个直角。 - Supplementary angles – two angles that add up to 180°. 'S' for straight line.
互补角 – 和为 180° 的两个角。“补”成一条直线。 - Vertically opposite angles – formed when two lines cross; they are equal.
对顶角 – 两直线相交形成的相对的两角，它们相等。 - Parallel and transversal – a transversal cuts parallel lines. Then corresponding angles are equal (F shape), alternate angles are equal (Z shape), interior (co-interior) angles sum to 180° (C shape).
平行与截线 – 截线穿过平行线。那么同位角相等（F 形），内错角相等（Z 形），同旁内角互补（C 形）。 - Perpendicular – lines that meet at a right angle.
垂直 – 相交成直角的直线。
8. Data Handling | 数据处理
Collecting and interpreting data requires knowing averages, spread, and chart types. These terms appear in every data question.
收集和解读数据需要了解平均数、分散程度和图表类型。这些术语出现在每道数据题中。
- Data – information. Primary data: collected by you. Secondary data: collected by someone else.
数据 – 信息。一手数据：自己收集的；二手数据：别人收集的。 - Frequency – how often something occurs. A tally is a counting method (groups of five).
频数 – 某事件发生的次数。划记是计数方法（五笔一组）。 - Mean – sum of values divided by the number of values. 'Mean' is the average teacher – adds all scores and divides.
平均数（均值） – 总和除以个数。想象“平均分配”。 - Median – the middle value when data is ordered. Think: median on a motorway – the central strip.
中位数 – 排序后正中间的数值。像高速公路的中央分隔带。 - Mode – the most frequent value. Mode = 'most'.
众数 – 出现次数最多的值。众就是多。 - Range – difference between largest and smallest. Tells you spread.
极差（范围） – 最大值减最小值，反映分散程度。 - Outlier – a value far from the others. Might be a mistake or surprising result.
异常值 – 远离其他数据的值。可能是错误或特殊现象。 - Discrete vs continuous data – discrete data can only take certain values (e.g. number of students); continuous data can take any value in a range (e.g. height).
离散数据 vs 连续数据 – 离散数据只能取特定值（如学生人数）；连续数据在一个区间内可以取任意值（如身高）。
9. Probability | 概率
Probability is the chance of something happening. The vocabulary ranges from impossible to certain, with a numerical scale from 0 to 1.
概率是事件发生的可能性。词汇从不可能会到必然，对应 0 到 1 的数值尺度。
- Probability scale – 0 (impossible), ½ (even chance), 1 (certain).
概率尺度 – 0（不可能），½（等可能），1（必然）。 - Event, outcome – an event is something you are interested in; an outcome is a single possible result.
事件、结果 – 事件是感兴趣的事情；结果是单个可能的情况。 - Sample space – the set of all possible outcomes. Often listed or shown in a diagram.
样本空间 – 所有可能结果的集合。通常用列表或图表表示。 - Theoretical probability – what should happen in theory, e.g. P(heads) = ½.
理论概率 – 理论上应发生的概率，如 P(正面) = ½。 - Experimental probability (relative frequency) – from an actual experiment or trial: number of successes / total trials.
实验概率（相对频率） – 通过实际实验得到的频率：成功次数 / 总试验次数。 - Frequency tree – a diagram showing frequencies of combined events, often used in probability calculations.
频率树 – 展示组合事件频数的树形图，常用于概率计算。
10. Patterns and Sequences | 模式与数列
Sequences follow a rule. Being able to describe the rule and find the nth term gives you power to predict any term.
数列遵循某种规则。能够描述规则并找出第 n 项，就能预测任意项。
- Sequence – an ordered list of numbers. Each number is a term.
数列 – 按顺序排列的一列数。每个数叫一项。 - Arithmetic sequence – a sequence with a constant difference between terms, like 3, 7, 11, 15 (+4).
等差数列 – 相邻两项的差恒定的数列，如 3, 7, 11, 15（差 4）。 - Common difference – the amount added (or subtracted) each time.
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