📚 Year 10 CAIE Mathematics: Quick Vocabulary Memorisation Guide | Year 10 CAIE 数学：词汇术语速记指南
Mastering mathematical terminology is the key to understanding questions and communicating solutions clearly. This guide highlights the essential vocabulary you will encounter in Year 10 CAIE Mathematics, grouped by topic, with concise explanations and mnemonic tips to help you learn faster and recall with confidence.
准确理解数学用语是解题的基础，更是用英文清晰表达思路的前提。本速记指南精选 Year 10 CAIE 数学核心术语，按主题分类，配合简明释义与记忆口诀，帮助你快速内化、考试不慌。
1. Number Types and Operations | 数的类型与运算
Integer – A whole number that can be positive, negative, or zero, with no fractional or decimal part. Examples: −5, 0, 12.
整数 – 没有小数或分数部分的正数、负数或零。如 −5, 0, 12。
Rational Number – Any number that can be expressed as a fraction p/q where p and q are integers and q ≠ 0. Terminating and recurring decimals are rational.
有理数 – 能用分数 p/q 表示的数，其中 p、q 为整数且 q ≠ 0。有限小数和循环小数都是有理数。
Irrational Number – A number that cannot be written as a simple fraction; its decimal expansion is non‑terminating and non‑recurring. √2 and π are classic examples.
无理数 – 不能表示为简单分数的数，小数展开无限不循环。典型例子如 √2、π。
Reciprocal – The reciprocal of a non‑zero number a is 1/a. Multiplying a number by its reciprocal always gives 1. For a fraction, simply swap numerator and denominator.
倒数 – 非零数 a 的倒数是 1/a。一个数与其倒数相乘恒为 1。分数的倒数只需将分子分母颠倒即可。
Significant Figures (s.f.) – Digits that carry meaning contributing to the precision of a number. The first non‑zero digit is the first significant figure.
有效数字 – 对数值精确度有意义的数字。第一个非零数字即为第一个有效数字。
2. Fractions, Decimals and Percentages | 分数、小数和百分比
Improper Fraction – A fraction where the numerator is greater than or equal to the denominator, e.g., 9/4. It can be converted into a mixed number.
假分数 – 分子大于或等于分母的分数，如 9/4。可转化为带分数。
Mixed Number – A number consisting of an integer and a proper fraction, e.g., 2 ¼.
带分数 – 由一个整数和一个真分数组成的数，如 2 1/4。
Percentage Increase – tity expressed as a percentage of the original value. Formula: (increase ÷ original) × 100%.
百分比增加 – 用原值的百分比表示的相对增长量。公式：(增加量 ÷ 原值) × 100%。
Multiplier – A decimal factor used to apply a percentage change directly. For a 15% increase, the multiplier is 1.15; for a 15% decrease, it is 0.85.
乘数因子 – 用于直接计算百分比变化的小数因子。增加 15% 用 1.15，减少 15% 用 0.85。
3. Algebraic Expressions and Manipulation | 代数表达式与化简
Variable – A symbol, usually a letter, that represents an unknown or changeable quantity. In 3x + 5, x is the variable.
变量 – 表示未知或可变化数量的符号，通常是字母。在 3x + 5 中，x 是变量。
Coefficient – The numerical factor multiplying a variable in a term. In 7y, the coefficient is 7.
系数 – 项中乘在变量前面的数字因子。如 7y 中的系数是 7。
Like Terms – Terms that contain exactly the same variable(s) raised to the same power(s). Only like terms can be combined through addition or subtraction.
同类项 – 包含完全相同的变量且次数相同的项。只有同类项才能通过加减合并。
Expansion – the term outside, e.g., 4(a + 3) = 4a + 12. The distributive law underlies all expansion.
展开 – 将括号外的项乘以括号内的每一项，如 4(a + 3) = 4a + 12。乘法分配律是所有展开的基础。
Factorisation – The reverse process of expansion: writing an expression as a product of its factors. The highest common factor is often extracted first.
因式分解 – 展开的逆运算：把表达式写成其因式的乘积。通常优先提取最大公因式。
4. Linear Equations and Inequalities | 线性方程与不等式
Equation – A mathematical statement showing that two expressions are equal, containing an equals sign. Solving an equation means finding the value(s) of the unknown that make the equality true.
方程 – 含有等号、表明两个表达式相等的数学陈述。解方程就是找出使等式成立的未知数的值。
Inequality – t;, >, ≤ or ≥. The solution set is often a range of values rather than a single number.
不等式 – 使用 <、>、≤ 或 ≥ 比较两个表达式的陈述。解集通常是一个范围而非单个数值。
Unknown – The variable whose value needs to be determined. In 2x − 7 = 11, x is the unknown.
未知数 – 需要求解的变量。在 2x − 7 = 11 中，x 是未知数。
Solve – To find the value or set of values that satisfy an equation or inequality. Maintain balance by performing the same operation on both sides.
求解 – 找出满足方程或不等式的数值或集合。始终在等号两边执行相同运算以保持平衡。
5. Sequences and Patterns | 数列与规律
Arithmetic Sequence – A sequence where the difference between consecutive terms is constant. This constant is called the common difference, d.
等差数列 – 相邻两项之差为常数的数列。这个常数称为公差 d。
Common Difference – (or subtracted) to go from one term to the next in an arithmetic sequence. d = aₙ − aₙ₋₁.
公差 – 等差数列中从前一项到后一项所加（或减）的固定量。d = aₙ − aₙ₋₁。
nth Term – A formula that generates any term of a sequence based on its position n. For arithmetic sequences, the nth term is a + (n − 1)d where a is the first term.
第 n 项 – 根据位置 n 生成数列中任意一项的公式。等差数列的第 n 项为 a + (n − 1)d，其中 a 是首项。
Term‑to‑Term Rule – A rule that describes how to move from one term to the next. For example, “add 3 and then multiply by 2”.
递推规则 – 描述如何从一项得到下一项的规则。例如“加 3 然后乘以 2”。
6. Coordinates and Graphs | 坐标与图形
Cartesian Plane – A plane defined by a horizontal x‑axis and a vertical y‑axis meeting at the origin (0,0). Points are located using ordered pairs (x, y).
笛卡尔平面 – 由水平 x 轴和垂直 y 轴相交于原点 (0,0) 所确定的平面。用有序数对 (x, y) 定位点。
Gradient (Slope) – A measure of the steepness of a line, calculated as (change in y) ÷ (change in x). Positive gradient slopes upward, negative slopes downward.
斜率 – 描述直线倾斜程度的量，计算为 y 的变化量 ÷ x 的变化量。正斜率向上倾斜，负斜率向下。
Intercept – The point where a graph crosses an axis. The y‑intercept is where x = 0, and the x‑intercept is where y = 0. In y = mx + c, c is the y‑intercept.
截距 – 图形与坐标轴的交点。y 截距在 x = 0 处，x 截距在 y = 0 处。在 y = mx + c 中，c 是 y 截距。
Midpoint – The point exactly halfway between two given points. Its coordinates are the averages of the x‑coordinates and y‑coordinates respectively.
中点 – 两点正中间的点的坐标，其 x 坐标和 y 坐标分别是两点坐标的平均值。
7. Geometry: Angles and Shapes | 几何：角与形状
Acute Angle – An angle measuring less than 90°. Think “a cute little angle”.
锐角 – 小于 90° 的角。可联想“尖锐的小角”。
Obtuse Angle – An angle greater than 90° but less than 180°. Picture a wide, “obese” opening.
钝角 – 大于 90° 但小于 180° 的角。可想象成“胖胖的钝角”。
Reflex Angle – An angle greater than 180° but less than 360°. It “reflects” the remainder of a full turn.
优角 – 大于 180° 但小于 360° 的角。它是周角减去相应劣角的余角。
Regular Polygon – A polygon where all sides are equal in length and all interior angles are equal. Examples: equilateral triangle, square, regular pentagon.
正多边形 – 所有边等长、所有内角相等的多边形。如等边三角形、正方形、正五边形。
Interior Angle Sum – les of a convex polygon with n sides is (n − 2) × 180°. Each interior angle of a regular n‑gon is this sum divided by n.
内角和 – n 边形内角和为 (n − 2) × 180°。正 n 边形的每个内角等于内角和除以 n。
8. Mensuration: Perimeter, Area, Volume | 测量：周长、面积、体积
Perimeter – The total distance around the outer edge of a 2D shape. It is the sum of all side lengths.
周长 – 围绕二维图形外缘的总距离，等于所有边长之和。
Area – cm², m², etc.). Common formulas: rectangle = length × width, triangle = ½ × base × height.
面积 – 二维图形边界内的空间大小。单位为平方单位（cm²、m² 等）。常用公式：矩形 = 长 × 宽，三角形 = ½ × 底 × 高。
Volume – ace occupied by an object, measured in cubic units (cm³, m³). Prism volume = area of cross‑section × length.
体积 – 物体所占据的三维空间大小，单位为立方单位（cm³、m³）。棱柱体积 = 截面面积 × 长度。
Surface Area – The total area of all faces (or surfaces) of a 3D solid. For a cylinder it equals 2πr² + 2πrh.
表面积 – 三维立体所有面（或表面）的总面积。圆柱的表面积等于 2πr² + 2πrh。
π (pi) – to its diameter, approximately 3.14159. It appears in circumference = 2πr and area = πr².
π（圆周率） – 圆的周长与直径之比，约等于 3.14159。常用于周长 = 2πr 和面积 = πr²。
9. Trigonometry Basics | 三角学基础
Hypotenuse – The longest side of a right‑angled triangle, always opposite the right angle.
斜边 – 直角三角形中最长的边，总对着直角。
Opposite Side – In a right‑angled triangle, the side that is opposite to the angle of interest (θ).
对边 – 直角三角形中，与所选角 (θ) 相对的边。
Adjacent Side – The side that forms the angle of interest together with the hypotenuse, excluding the opposite side.
邻边 – 与斜边一起构成所研究角的边，不包括对边。
Sine (sin) – Trigonometric ratio: sin θ = opposite ÷ hypotenuse. Memorise with SOH.
正弦 (sin) – 三角比：sin θ = 对边 ÷ 斜边。可用 SOH 记忆。
Cosine (cos) – Trigonometric ratio: cos θ = adjacent ÷ hypotenuse. CAH is the reminder.
余弦 (cos) – 三角比：cos θ = 邻边 ÷ 斜边。可用 CAH 记忆。
Tangent (tan) – Trigonometric ratio: tan θ = opposite ÷ adjacent. TOA completes the set: SOH‑CAH‑TOA.
正切 (tan) – 三角比：tan θ = 对边 ÷ 邻边。TOA 与 SOH‑CAH 构成完整的口诀：SOH‑CAH‑TOA。
10. Statistics: Averages and Spread | 统计：平均数与离散程度
Mean – The arithmetic average, calculated by summing all data values and dividing by the number of values. Sensitive to extreme values.
平均数（均值） – 所有数据值的总和除以个数。易受极端值影响。
Median – The middle value when data is arranged in order. For an even number of values, it is the average of the two middle numbers.
中位数 – 数据按序排列后位于中间的数值。数据个数为偶数时取中间两数的平均值。
Mode – The value or category that appears most frequently. A data set can have one mode, more than one mode, or no mode at all.
众数 – 出现频率最高的数值或类别。数据集可以有单众数、多众数或无众数。
Range – A simple measure of spread: largest value minus smallest value. It shows the interval over which the data vary.
极差 – 最简单的离散程度度量：最大值减去最小值。反映数据变动的跨度。
Quartiles – Values that divide an ordered data set into four equal parts. The first quartile (Q1) is the median of the lower half, the third quartile (Q3) is the median of the upper half.
四分位数 – 将有序数据分成四等份的值。第一四分位数 (Q1) 是下半部分的中位数，第三四分位数 (Q3) 是上半部分的中位数。
11. Probability Terminology | 概率术语
Experiment – A repeatable process that produces a set of outcomes, such as tossing a coin or rolling a die.
试验 – 产生一组结果的可重复过程，如抛硬币或掷骰子。
Outcome – A possible result of a probability experiment. For a six‑sided die, the outcomes are 1, 2, 3, 4, 5, 6.
结果 – 概率试验的可能结果。掷六面骰子的结果有 1, 2, 3, 4, 5, 6。
Event – A set of one or more outcomes. “Rolling an even number” is an event containing outcomes {2, 4, 6}.
事件 – 一个或多个结果的集合。“掷出偶数”是一个事件，包含结果 {2, 4, 6}。
Probability Scale – A scale from 0 to 1 that measures the likelihood of an event occurring, where 0 means impossible and 1 means certain.
概率尺度 – 测量事件发生可能性的 0 到 1 的尺度，0 表示不可能，1 表示必然。
Mutually Exclusive Events – cannot occur at the same time. P(A or B) = P(A) + P(B) if A and B are mutually exclusive.
互斥事件 – 不可能同时发生的事件。如果 A 和 B 互斥，则 P(A 或 B) = P(A) + P(B)。
12. Transformations | 变换
Translation – Sliding a shape without turning, flipping, or resizing it. Described by a column vector giving horizontal and vertical movement.
平移 – 只滑动图形而不转动、翻转或改变大小。用列向量描述水平和垂直移动量。
Reflection – Mirroring a shape over a line (the mirror line). Each point on the image is the same perpendicular distance from the mirror as the original point.
反射（镜射） – 以一条线（镜线）为轴翻转图形。像上的每一点与镜线的垂直距离等于原图形对应点的距离。
Rotation – Turning a shape around a fixed centre point through a specified angle and direction (clockwise or anticlockwise).
旋转 – 围绕一个固定中心点按指定角度和方向（顺时针或逆时针）转动图形。
Enlargement – Changing the size of a shape by a scale factor from a centre of enlargement. A scale factor greater than 1 increases size; between 0 and 1 reduces size.
放大 – 以放大中心为基准，按比例因子改变图形大小。比例因子大于 1 放大，介于 0 和 1 之间缩小。
Scale Factor – The multiplier that determines how much each side length of a shape is enlarged or reduced. Corresponding distances between images are multiplied by the scale factor.
比例因子 – 决定图形每条边被放大或缩小倍数的乘数。像与原像对应距离均乘以该比例因子。
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