📚 Year 11 CAIE Mathematics: Vocabulary and Terminology Memorisation Guide | Year 11 CAIE 数学：词汇术语速记指南
Mastering the specific vocabulary in CAIE IGCSE Mathematics is just as important as learning the procedures. A precise understanding of terms such as ‘integer’, ‘perpendicular’, or ‘histogram’ can mean the difference between full marks and a misinterpreted question. This guide organises essential terminology by topic, pairing each English term with a clear definition and its Chinese equivalent, along with simple memory hooks to help bilingual learners quickly absorb the language of mathematics.
在CAIE IGCSE数学中，精准掌握专业词汇与掌握解题步骤同样关键。对 ‘integer’（整数）、’perpendicular’（垂直）或 ‘histogram’（直方图）等术语的准确理解，常常决定着解题的正误。本指南将核心词汇按主题分类，每个英文术语均配以清晰的定义和中文对应，并附上便于牢记的联想提示，帮助双语学习者高效吸收数学用语。
1. Number and Operations | 数与运算词汇
Integer – a whole number that can be positive, negative, or zero, with no fractional or decimal part. Examples: -3, 0, 14.
整数 – 可正可负或为零的完整数字，不含分数或小数部分。例如 -3, 0, 14。记忆技巧：联想 ‘integer’ 与 ‘integral’（完整的），凡是不零碎的数是 ‘integer’。
Rational number – any number that can be expressed as a fraction a/b where a and b are integers and b ≠ 0. This includes terminating and repeating decimals.
有理数 – 均可表示为分数 a/b 的数，其中 a, b 为整数且 b ≠ 0，包含有限小数和循环小数。速记法：’rational’ 源自 ‘ratio’（比率），即能写成比值的数。
Significant figure (sf) – the digits in a number that carry meaningful information about its precision, counting from the first non-zero digit. In CAIE, answers are often required to 3 significant figures.
有效数字 – 指从首个非零数字起计、反映数值精度的数字。CAIE考试常要求保留3位有效数字。记忆诀窍：’significant’ 意味着真正重要的数字，忽略前导零。
Standard form – a way of writing very large or very small numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. E.g., 4.2 × 10⁵.
标准形式（科学记数法） – 将极大或极小的数写成 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。例如 4.2 × 10⁵。记法：联想到把小数点移动到只剩一位非零数字，再乘以10的幂。
2. Algebra: Expressions, Equations, and Inequalities | 代数：表达式、方程与不等式
Expression – a combination of numbers, variables, and operation symbols without an equals sign. For instance, 3x² – 2x + 5 is an algebraic expression.
表达式 – 由数字、变量和运算符号组成的式子，不含等号。例如 3x² – 2x + 5 是一个代数表达式。记忆：’expression’ 没有 ‘equals’，只是表示一种式子。
Equation – a mathematical statement that two expressions are equal, connected by ‘=’. Solving an equation means finding the value(s) that make it true.
方程 – 表示两个表达式相等的数学陈述，用 ‘=’ 连接。解方程就是找出使其成立的未知数值。对比：’equ-‘ 前缀意为相等（如 equal）。
Inequality – a relation between two expressions that are not equal, using symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
不等式 – 用不等号连接的两个表达式的关系，符号包括 （大于）、≤（不大于）、≥（不小于）。记忆：’inequality’ 中的 ‘in-‘ 表否定，表示不相等。
Like terms – terms that contain exactly the same variables raised to the same powers. Only like terms can be combined by addition or subtraction.
同类项 – 变量及其指数完全相同的项。仅同类项可以相加或相减。速记：’like’ 意思是相似，同类项长相相同。
3. Graphs and Functions | 图形与函数
Gradient (slope) – a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise / run). Formula: m = (y₂ – y₁) / (x₂ – x₁).
斜率 – 表示直线的倾斜程度，计算为纵坐标变化量除以横坐标变化量。公式：m = (y₂ – y₁) / (x₂ – x₁)。形象记忆：’gradient’ 像爬坡的倾斜度。
Intercept – the point where a line crosses an axis. The y-intercept is the value of y when x = 0.
截距 – 直线与坐标轴的交点。y 截距是当 x = 0 时 y 的值。’intercept’ 可分解为 inter（在……之间）+ cept（取），即线与轴相截之处。
Function – a rule that assigns each input exactly one output. Often written as f(x). The graph of a function passes the vertical line test.
函数 – 将一个输入唯一对应到一个输出的规则，常写作 f(x)。函数的图像能通过垂直线检验。联想：’function’ 像一台机器，每个输入产生确定输出。
Parabola – the U-shaped curve of a quadratic function y = ax² + bx + c. It has a vertex and an axis of symmetry.
抛物线 – 二次函数 y = ax² + bx + c 的U形曲线。有一个顶点和一条对称轴。记忆：’para-‘ 旁边，’bola’ 抛，想象抛体轨迹。
4. Geometry: Angles, Lines, and Shapes | 几何：角、线与形状
Perpendicular – two lines that intersect at a right angle (90°). The symbol is ⊥. In coordinate geometry, perpendicular lines have gradients that multiply to -1.
垂直 – 相交成直角（90°）的两条直线。符号为 ⊥。在坐标几何里，垂直线的斜率乘积为 -1。记法：’perpendicular’ 里含有 ‘pend’（悬挂），像铅垂线一样直。
Parallel – lines in a plane that never meet, however far they are extended. They have the same gradient.
平行 – 在同一平面内永不相交的直线，无论怎样延长都不相遇。它们斜率相等。想一想 ‘parallel’ 中两个 ‘l’ 像平行轨道。
Angle bisector – a line or ray that divides an angle into two equal parts. In a triangle, the angle bisectors meet at the incentre.
角平分线 – 将一个角平分为两个相等角的射线或线段。在三角形中，三条角平分线交于内心。’bisect’ 的 ‘bi-‘ 是二，’sect’ 是切，平分两半。
Perpendicular bisector – a line that cuts a segment into two equal parts at exactly 90°.
垂直平分线 – 将线段垂直平分成两等份的直线。记忆：’perpendicular’ 表明角度，’bisector’ 表明平分。
5. Mensuration: Length, Area, and Volume | 度量：长度、面积与体积
Perimeter – the total distance around the outside of a 2D shape. For a rectangle, P = 2(l + w).
周长 – 平面图形边界一周的总长度。例如矩形周长 P = 2(l + w)。可联想 ‘peri-‘ 是周围，’meter’ 是测量，测一周之长。
Area – the amount of space inside a flat shape, measured in square units. Common formulas: rectangle = l × w, triangle = ½bh, circle = πr².
面积 – 平面图形内部所占空间的大小，单位是平方单位。常见公式：矩形：长×宽，三角形：½bh，圆：πr²。记忆：’area’ 与面积都是指表面覆盖范围。
Volume – the amount of space occupied by a 3D object, measured in cubic units. Prism volume = area of cross-section × length.
体积 – 立体图形所占空间的大小，单位是立方单位。棱柱体积 = 截面积 × 长。’volume’ 和容量相关。
Surface area – the total area of all the faces of a 3D solid. For a cube of edge a, SA = 6a².
表面积 – 立体图形所有面的总面积。边长为 a 的立方体，表面积 = 6a²。拆字：’surface’ 表面 + ‘area’ 面积。
6. Trigonometry | 三角学
Hypotenuse – the longest side of a right-angled triangle, opposite the right angle. It is always the side used in the denominator of sine and cosine ratios.
斜边 – 直角三角形中最长的边，对着直角。它总是在正弦和余弦比的分母中出现。记忆：’hypo-‘ 在下，’tenuse’ 伸展，像斜撑的边。
Sine, cosine, tangent – the three primary trigonometric ratios. In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
正弦、余弦、正切 – 三个基本三角比。直角三角形中：sin θ = 对边/斜边，cos θ = 邻边/斜边，tan θ = 对边/邻边。记忆口诀 SOH CAH TOA 对应 sin=O/H, cos=A/H, tan=O/A。
Angle of elevation – the angle measured upwards from the horizontal to a line of sight. Angle of depression is measured downwards.
仰角 – 从水平线向上测量至视线的夹角。俯角为向下测量的角。’elevation’ 意为上升，视线抬高；’depression’ 为下降。
Sine rule – a/sin A = b/sin B = c/sin C, used for finding sides or angles in non-right triangles.
正弦定理 – a/sin A = b/sin B = c/sin C，用于非直角三角形求边或角。记忆为两边与其对角正弦成正比。
7. Vectors and Transformations | 向量与变换
Vector – a quantity that has both magnitude (size) and direction. Represented by a column vector (x, y) or a directed line segment. Scalar is only magnitude.
向量 – 既有大小又有方向的量。可用列向量 (x, y) 或有向线段表示。标量仅有大小。联想 ‘vector’ 与 ‘vehicle’（交通工具）同源，都有移动方向。
Translation – a transformation that moves every point of a shape the same distance in the same direction. Described by a vector.
平移 – 将图形每个点按相同方向移动相同距离的变换。用向量来描述。’trans-‘ 跨越，’lation’ 携带，整体平动。
Rotation – turning a shape about a fixed point (centre of rotation) through a given angle and direction. Size and shape are invariant.
旋转 – 图形绕定点（旋转中心）按给定角度和方向转动。大小和形状不变。记忆：车轮旋转。
Enlargement – a transformation that changes the size of a shape by a scale factor relative to a centre of enlargement. A negative scale factor produces an inverted image.
放大 – 以放大中心为基准，按比例因子改变图形大小的变换。负比例因子产生倒立图像。’enlargement’ 含 ‘large’，表示大小的改变。
8. Statistics | 统计
Mean – the sum of all values divided by the number of values. Often called the average, but can be affected by extreme values.
平均数（均值） – 所有数值之和除以数值个数。通常称为平均值，但易受极端值影响。’mean’ 表示平均位置。
Median – the middle value when the data are arranged in order. For an even number of values, it is the average of the two middle numbers.
中位数 – 数据排序后正中间的数值。偶数个数据时是中间两数的平均值。’median’ 像一条中间线 (medium)。
Mode – the value that appears most frequently in a data set. A set can have no mode, one mode, or more than one mode.
众数 – 数据中出现次数最多的值。一组数据可以没有众数、有一个或多个众数。联想 ‘mode’ 和 ‘most’ 发音相近。
Histogram – a diagram that displays grouped continuous data, where the area of each bar is proportional to the frequency. Unlike a bar chart, bars touch each other.
直方图 – 展示连续分组数据的图，每个柱形的面积与频数成比例。与条形图不同，柱条之间没有空隙。’histo-‘ 源自组织，’gram’ 图表。
9. Probability | 概率
Probability – a measure of the chance that an event will occur, expressed as a number between 0 and 1 or as a fraction, decimal, or percentage.
概率 – 衡量事件发生可能性的尺度，用0到1之间的数、分数、小数或百分数表示。记法：’probable’ 意为可能。
Sample space – the set of all possible outcomes of an experiment. For rolling a die, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间 – 试验所有可能结果的集合。掷骰子的样本空间为{1, 2, 3, 4, 5, 6}。’sample’ 示例，’space’ 空间，即所有结果的“房间”。
Mutually exclusive events – events that cannot happen at the same time. If A and B are mutually exclusive, P(A or B) = P(A) + P(B).
互斥事件 – 不可能同时发生的事件。若A和B互斥，则P(A或B) = P(A) + P(B)。’mutually exclusive’ 意为你排除我，我排除你。
Tree diagram – a branching diagram used to list all possible outcomes of two or more events, with probabilities written on the branches.
树形图 – 用分支列出两件或多件事所有可能结果的图，分支上标注概率。像树枝分叉一样，直观展示概率相乘相加。
10. Quick Memory Techniques for Mathematical Terms | 数学术语速记技巧
Use prefixes and suffixes: Many terms come from Latin or Greek roots. ‘Poly-‘ means many (polygon, polynomial). ‘Equi-‘ means equal (equilateral, equation). ‘-gon’ refers to angles (pentagon, hexagon). Recognising these halves unlocks dozens of words.
利用前后缀：大量术语来自拉丁或希腊词根。’poly-‘ 表示多（多边形、多项式）。’equi-‘ 表示相等（等边、方程）。’-gon’ 指角（五边形、六边形）。识别这些部分能解锁大量词汇。
Link to everyday English: ‘Gradient’ shares the root with ‘grade’ (slope). ‘Parallel’ is like ‘parallel lines’ in railway tracks. ‘Correlation’ sounds like ‘co-relation’, meaning two things moving together.
与日常英语挂钩：’Gradient’ 与 ‘grade’（坡度）同源。’Parallel’ 像铁路的平行铁轨。’Correlation’ 可记作 ‘co-relation’（共同关系），表示两事物联动。
Create bilingual acronyms: For trigonometry, remember ‘SOH CAH TOA’ – Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. For order of operations, BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction) or its Chinese equivalent: 括号、指数、乘除、加减。
编双语口诀：三角比用 ‘SOH CAH TOA’ 记忆。运算顺序用 BIDMAS（括号、指数、乘除、加减）。这些首字母歌谣能帮你在考场上迅速调取规则。
Visualise with shape: Associate ‘vertical’ with the upright letter ‘V’. ‘Horizontal’ aligns with the horizon. Draw a small picture next to the word in your revision notes; the dual coding reinforces memory.
图形化记忆：把 ‘vertical’ 和直立的字母 ‘V’ 联系起来。’Horizontal’ 则联想到地平线。复习时在词语旁画个小图，这种双重编码能强化记忆。
Repeat in context, not isolation: Write a full sentence using the term, e.g., ‘The gradient of the line y = 2x + 3 is 2.’ This builds both language and mathematical fluency.
在语境中复述，而非孤立背诵：用该术语写一个完整句子，例如 ‘The gradient of the line y = 2x + 3 is 2.’ 这能同时提升语言和数学流畅度。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply