📚 Year 8 SQA Advanced Mathematics: Vocabulary Terminology Quick Reference Guide | Year 8 SQA 进阶数学：词汇术语速记指南
Mastering the language of advanced mathematics at Year 8 level is half the battle. This guide breaks down the essential English and Chinese terms you will encounter in SQA Advanced Mathematics, offering clear definitions and memory hooks to help you build confidence. Read on to turn unfamiliar jargon into useful tools.
掌握 Year 8 进阶数学的语言是成功的一半。本指南拆解了 SQA 进阶数学中你会遇到的核心英文与中文术语，提供清晰的定义和记忆窍门，帮助你建立自信。请继续阅读，把陌生术语变成实用工具。
1. Algebraic Terminology | 代数术语
Variable – A symbol, usually a letter like x or y, that stands for an unknown or changing number. Think of 'vary' — it can vary.
变量 – 常用字母如 x 或 y 表示的未知或变化的数。联想 "变化" 一词即可记住。
Constant – A fixed number that does not change. In 3x + 5, the number 5 is a constant.
常数 – 一个固定不变的数。例如 3x + 5 中，5 就是常数。
Coefficient – The number multiplying a variable. In 4y, 4 is the coefficient. 'Co' means 'together' — it works with the variable.
系数 – 乘以变量的数字。在 4y 中，4 是系数。"系" 有联结之意，系数与变量相连。
Term – A single number, variable, or product of numbers and variables. For example, 7, x, and -2ab are terms separated by + or - in an expression.
项 – 一个单独的数、字母或数与字母的乘积。如 7、x、-2ab 都是项，在表达式中用加号或减号隔开。
Expression – A combination of terms without an equals sign, e.g. 2a + 3b - 7. It's a phrase, not a full sentence.
表达式 – 不含等号的项的集合，如 2a + 3b - 7。它像一个短语，而不是完整的句子。
Equation – atical statement showing that two expressions are equal, using an equals sign: 2x + 1 = 9.
方程 – 用等号连接两个表达式的数学陈述，如 2x + 1 = 9，表示两边相等。
2. Operations and Simplifying | 运算与化简
Like terms – Terms that have exactly the same variable part. 3x and -5x are like terms; 3x and 3y are not.
同类项 – 含有完全相同的字母因数的项。3x 与 -5x 是同类项，而 3x 与 3y 不是。
Simplify – Combine like terms and reduce an expression to its shortest form. 2x + 3x simplifies to 5x.
化简 – 合并同类项，把表达式化成最简形式。2x + 3x 化简为 5x。
Expand – Multiply out brackets. Expanding 3(x + 2) gives 3x + 6.
展开 – 去掉括号并做乘法。展开 3(x + 2) 得到 3x + 6。
Factorise – The reverse of expanding: write an expression as a product of brackets. 4x + 8 factorises to 4(x + 2).
因式分解 – 展开的逆运算，把表达式写成括号的乘积。4x + 8 因式分解为 4(x + 2)。
Equivalent expressions – Expressions that always have the same value, however the variables are chosen. x + x and 2x are equivalent.
等价表达式 – 无论变量取何值，值都相等的表达式。x + x 和 2x 是等价表达式。
3. Equations and Inequalities | 方程与不等式
Solve – the value(s) of the variable that make the equation true. Solving x + 4 = 10 gives x = 6.
解（动词） – 找出使方程成立的变量的值。解 x + 4 = 10 得到 x = 6。
Solution (root) – The actual value that satisfies the equation. For 2x = 8, the solution is x = 4.
解（名词） – 满足方程的变量的具体数值。对于 2x = 8，解是 x = 4。
Inequality – A statement that compares two expressions using <, >, ≤ or ≥, such as y > 3.
不等式 – 使用 <、>、≤ 或 ≥ 比较两个表达式的式子，如 y > 3。
Balance method – A technique for solving equations: perform the same operation on both sides to keep the equation balanced.
平衡法 – 解方程的方法：在等号两边同时进行相同的运算，保持平衡。
Satisfy – sfies an equation or inequality if it makes the statement true. x = 7 satisfies x - 2 = 5.
满足 – 如果一个值使方程或不等式成立，就说它满足该式。x = 7 满足 x - 2 = 5。
4. Sequences | 序列
Sequence – An ordered list of numbers following a rule. Example: 2, 5, 8, 11, ... is a sequence.
序列（数列） – 按照某种规律排列的一列数。例如：2, 5, 8, 11, ... 是一个序列。
Term-to-term rule – A rule that tells how to get from one term to the next, e.g. 'add 3'.
逐项规则 – 描述如何从一项得到下一项的规则，如 "加 3"。
Position-to-term rule (nth term) – A rule that uses the position n to calculate the value of the term directly. For the sequence above, the nth term is 3n - 1.
第 n 项规则（通项公式） – 利用位置 n 直接计算该项值的规则。上面序列的通项公式是 3n - 1。
Arithmetic sequence – A sequence where the difference between consecutive terms is constant. 5, 9, 13, 17 has common difference 4.
等差数列 – 相邻两项的差保持不变的序列。5, 9, 13, 17 的公差为 4。
Geometric sequence – A sequence where each term is multiplied by a constant to get the next. 2, 6, 18, 54 has common ratio 3.
等比数列 – 每一项乘以固定倍数得到后一项的序列。2, 6, 18, 54 的公比为 3。
5. Coordinates and Straight-Line Graphs | 坐标与直线图
Coordinate – A pair of numbers (x, y) that shows a point's position on a grid. The first number is the x-coordinate, the second the y-coordinate.
坐标 – 用一对数字 (x, y) 表示点在网格上的位置。第一个数是 x 坐标，第二个是 y 坐标。
Axes – The two perpendicular number lines on a graph. The horizontal axis is the x-axis, the vertical axis is the y-axis.
坐标轴 – 图上互相垂直的两条数线。水平的是 x 轴，垂直的是 y 轴。
Origin – The point where the axes intersect, labelled (0, 0).
原点 – 坐标轴相交的点，记为 (0, 0)。
Gradient – A measure of steepness of a line, calculated as rise/run or (change in y)/(change in x). A line with gradient 2 goes up 2 units for every 1 unit right.
斜率 – 直线的倾斜程度，用 纵向变化/横向变化 计算。斜率为 2 的直线每向右 1 单位，上升 2 单位。
y-intercept – The point where a line crosses the y-axis. In y = 2x + 3, the y-intercept is 3.
y 截距 – 直线与 y 轴的交点。在 y = 2x + 3 中，y 截距是 3。
6. Geometry Basics | 几何基础
Point – An exact location in space, often labelled with a capital letter. It has no size.
点 – 空间中的一个确切位置，通常用大写字母标注，没有大小。
Line – A straight one-dimensional figure that extends infinitely in both directions. It has no thickness.
直线 – 向两端无限延伸的一维图形，没有粗细。
Line segment – A part of a line with two endpoints. Think of a segment as a piece of a line.
线段 – 有两个端点的直线的一部分。
Ray – A part of a line that starts at one point and extends infinitely in one direction.
射线 – 从一个点出发向一个方向无限延伸的线。
Angle – The figure formed by two rays sharing a common endpoint, measured in degrees.
角 – 由两条有公共端点的射线组成的图形，以度为单位。
Perpendicular – Two lines that meet at a right angle (90°).
垂直 – 两条相交成直角（90°）的直线。
Parallel – Lines in a plane that never meet, however far they are extended. They always stay the same distance apart.
平行 – 在同一平面内永不相交的直线，它们之间的距离处处相等。
7. Triangles and Pythagoras | 三角形与毕达哥拉斯
Triangle – A polygon with three sides and three angles. The sum of interior angles is always 180°.
三角形 – 有三条边和三个角的多边形，内角和总是 180°。
Right-angled triangle – A triangle that has one 90° angle. The side opposite the right angle is the longest side.
直角三角形 – 有一个角是 90° 的三角形。直角所对的边是最长边。
Hypotenuse – The side opposite the right angle in a right-angled triangle. It is always the longest side.
斜边 – 直角三角形中直角所对的边，总是最长的一边。
Legs – The two shorter sides that form the right angle in a right-angled triangle.
直角边 – 直角三角形中构成直角的两条较短的边。
Pythagoras' theorem: a² + b² = c²
Pythagoras' theorem – In a right-angled triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b).
勾股定理（毕达哥拉斯定理） – 直角三角形中，斜边的平方等于两直角边的平方和。公式为 a² + b² = c²。
8. Angles and Polygons | 角与多边形
Acute angle – An angle less than 90°. Imagine a cute, small angle.
锐角 – 小于 90° 的角。可以联想尖锐锋利。
Obtuse angle – An angle greater than 90° but less than 180°. It looks 'obtuse' or blunt.
钝角 – 大于 90° 且小于 180° 的角。显得钝钝的、不尖锐。
Reflex angle – An angle greater than 180° but less than 360°. Think of a reflex action going beyond a straight line.
优角 – 大于 180° 且小于 360° 的角，超过了平角。
Polygon – A closed 2D shape with straight sides. Triangles, quadrilaterals, pentagons are all polygons.
多边形 – 由线段围成的封闭二维图形。三角形、四边形、五边形都是多边形。
Interior angle – ide a polygon at a vertex. The sum of interior angles of an n-sided polygon is (n-2)×180°.
内角 – 多边形顶点处内部的角。n 边形内角和为 (n-2)×180°。
Exterior angle – The angle formed outside a polygon when one side is extended. The exterior angles of any polygon add up to 360°.
外角 – 延长多边形的一条边后在外面形成的角。任意多边形的外角和均为 360°。
9. Measurement and Units | 测量与单位
Perimeter – The total distance around a 2D shape. For a rectangle, perimeter = 2(length + width).
周长 – 二维图形外边界的总长度。矩形周长 = 2×(长+宽)。
Area – f space inside a 2D shape, measured in square units. Area of a rectangle = length × width.
面积 – 二维图形内部的空间大小，以平方单位计量。矩形面积 = 长×宽。
Volume – 3D object occupies, measured in cubic units. Volume of a cuboid = length × width × height.
体积 – 三维物体占据的空间，以立方单位计量。长方体体积 = 长×宽×高。
Capacity – mount a container can hold, usually measured in litres or millilitres. 1 litre = 1000 cm³.
容量 – 容器可容纳的液体量，常用升或毫升。1 升 = 1000 立方厘米。
Unit conversion – Changing a measurement from one unit to another, e.g. 1 m = 100 cm, 1 kg = 1000 g.
单位换算 – 把度量从一种单位转换成另一种，如 1 米 = 100 厘米，1 千克 = 1000 克。
Compound shape – A shape made up of two or more simple shapes. Find its area by splitting it into rectangles, triangles, etc.
组合图形 – 由两个或多个简单图形拼成的图形。可分割成矩形、三角形等求面积。
10. Statistics | 统计
Data – A collection of facts, numbers, or information. Data can be discrete (counted) or continuous (measured).
数据 – 收集到的事实、数字或信息。离散数据是可以数的，连续数据是需要测量的。
Mean – The average of a set of numbers, found by dividing the sum by how many numbers there are. Also called arithmetic mean.
平均数（均值） – 一组数的总和除以个数，常称为算术平均。
Median – The middle value when the data is ordered from smallest to largest. If there are two middle numbers, it's their average.
中位数 – 将数据从小到大排列后处于中间的数；若有两个中间数则取其平均值。
Mode – The value that appears most often. A set of data can have one mode, more than one mode, or no mode.
众数 – 出现次数最多的数据。一组数据可能有一个众数、多个众数或没有众数。
Range – The difference between the largest and smallest values in a data set. It measures spread.
极差 – 数据中最大值与最小值的差值，衡量数据的分散程度。
Frequency – How often a particular value occurs. A frequency table records counts.
频数（频率） – 某个数值出现的次数。频数表用于记录计数。
11. Probability | 概率
Probability – A measure of how likely an event is, on a scale from 0 (impossible) to 1 (certain). Often expressed as a fraction, decimal or percentage.
概率 – 衡量事件发生可能性的数值，范围从 0（不可能）到 1（必然），常用分数、小数或百分比表示。
Experiment – A repeatable process with a set of possible outcomes, such as rolling a die.
试验 – 可重复的、
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