📚 Year 11 CAIE Maths: Essential Terminology Memorisation Guide | Year 11 CAIE 数学：词汇术语速记指南
Mastering mathematical vocabulary is key to understanding exam questions and communicating solutions clearly. This guide groups CAIE Year 11 maths terminology by topic and provides quick memory hooks to help you recall definitions, properties and operations faster.
掌握数学词汇是理解考题和清晰表达解答的关键。本指南按主题整理了CAIE Year 11数学术语，并提供快速记忆挂钩，帮助你更快地回忆定义、性质和运算。
1. Number Types and Notation | 数字类型与符号
Numbers are the building blocks of mathematics. In the CAIE exam, you need to recognise and use different number categories instantly.
数字是数学的基础。在CAIE考试中，你需要立即识别并使用不同的数字类别。
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Integer: A whole number that can be positive, negative or zero (e.g. -3, 0, 42). Think of 'integer' as a number that can be counted on your 'fingers' without breaking them into fractions.
整数: 可正可负或为零的完整数字（如 -3, 0, 42）。'整数'意味着没有分数部分，就像完整的一根手指。
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Natural Numbers: The counting numbers starting from 1 (1, 2, 3, ...). Remember 'natural' because you naturally count from 1.
自然数: 从1开始用于计数的数（1, 2, 3, ...）。记法：你自然地从1开始数数。
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Rational Number: Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. Rhyme trick: 'Rational is fractional' – it's a ratio.
有理数: 可以写成 a/b 形式的数，其中 a、b 为整数且 b ≠ 0。速记：有理数就是可以写成“比”的数。
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Irrational Number: A number that cannot be expressed as a simple fraction, e.g. π, √2. 'Irrational' starts with 'I' like 'Infinite non-repeating decimal'.
无理数: 不能表示为简单分数的数，如 π、√2。联想到“无理” – 没有理性的比，所以不能写成分数。
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Prime Number number greater than 1 with exactly two factors: 1 and itself (2, 3, 5, 7, 11, ...). Think 'prime' = 'primary' – only divisible by the primary 1 and itself.
质数（素数）: 大于1且只有两个因数1和它本身的自然数。记忆：'质' 强调本质，只有最基本的两个因数。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
Fractions, decimals and percentages appear everywhere in IGCSE Maths, from probability to ratio problems. Memorise the terminology to switch between forms effortlessly.
分数、小数和百分数在IGCSE数学中无处不在，从概率到比例问题都需要。记住术语，以便在不同形式之间轻松转换。
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Numerator / Denominator: In 3/4, 3 is the numerator (top) and 4 is the denominator (bottom). Mnemonic: 'Numerator is Up' shares U; 'Denominator is Down' shares D.
分子 / 分母: 在 3/4 中，3是分子（上），4是分母（下）。口诀：分子在上，母在下。
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Improper Fraction: A fraction where numerator ≥ denominator, e.g. 7/4. It is 'top-heavy' – think of it being improperly heavy.
假分数: 分子大于或等于分母的分数，如 7/4。称为“假”因为看起来头重脚轻。
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Mixed Number: A whole number and a proper fraction combined, e.g. 1 3/4. It's a 'mix' of an integer and a fraction.
带分数: 一个整数与一个真分数的组合，如 1 3/4。它是整数和分数的混合体。
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Significant Figures aning contributing to precision. Rule: start counting from the first non-zero digit. Think 'sig fig' = 'significant digits that figure in the measurement'.
有效数字: 对精度有意义的数字。规则：从第一个非零数字开始数。联想“有效” – 真正有意义的数字。
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Standard Form: Writing numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer. Handy hook: 'Standard form makes giant and tiny numbers standardly short'.
标准形式: 写为 a × 10ⁿ，其中 1 ≤ a < 10。记忆：标准形式让极大或极小的数字变得标准简洁。
3. Algebra – Expressions and Equations | 代数 – 表达式与方程
Algebraic terminology is often mixed up. Knowing the precise meaning of 'expression', 'equation' and 'formula' saves marks in the exam.
代数术语常常被混淆。了解“表达式”、“方程”和“公式”的确切含义可以在考试中避免失分。
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Expression: A combination of terms with no equals sign, e.g. 3x + 2y - 5. 'Expression expresses a value' – it shows a relationship but does not state an equality.
表达式: 没有等号的项的组合，如 3x + 2y - 5。“表示”一个值，但没有陈述相等关系。
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Equation: A statement that two expressions are equal, containing an equals sign, e.g. 2x + 3 = 11. 'Equa-tion' has 'equa' like 'equal'.
方程: 陈述两个表达式相等的式子，含有等号，如 2x + 3 = 11。“方程”意味着“左右相等”。
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Formula: A rule written with symbols, often with multiple variables, e.g. A = πr². Think 'formula' sounds like 'form' – a standard form to calculate something.
公式: 用符号写出的规则，常含多个变量，如 A = πr²。记法：“公”式，大家都用的计算式。
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Coefficient: The number multiplying a variable, e.g. in 5x, 5 is the coefficient. Visual: co-efficient means 'efficient number that works with' the variable.
系数: 乘以变量的数字，如 5x 中的 5。“系”在变量前面，像纽带一样相乘。
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Identity: An equation true for all values, often using the ≡ symbol, e.g. x² - 1 ≡ (x+1)(x-1). Memory: 'Identity is identical' – always true.
恒等式: 对所有值都成立的等式，常使用 ≡ 符号，如 x² - 1 ≡ (x+1)(x-1)。“恒” – 永远成立。
4. Graphs and Functions | 图表与函数
Function notation and graph vocabulary are crucial for coordinate geometry questions. Grasp these terms to interpret sketches and draw accurate graphs.
函数记号和图形词汇对坐标几何题至关重要。掌握这些术语以解读草图并绘制准确图形。
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Function: A relation where each input has exactly one output, often written f(x). Think of a 'function machine': input goes in, exactly one output comes out.
函数: 每个输入恰好有一个输出的关系，常写为 f(x)。想象一台“函数机”：一个输入进去，只有一个输出出来。
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Domain / Range is : Domain is the set of possible inputs (x-values), range is the set of possible outputs (y-values). 'Domain = x, Range = y' – think alphabetically: D before R, x before y.
定义域 / 值域: 定义域是可能的输入集(x值)，值域是可能的输出集(y值)。按字母顺序：D在R前，x在y前。
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Gradient / Slope: The steepness of a line, calculated as rise/run or Δy/Δx. 'Gradient is how fast you go up as you go across'.
斜率/坡度: 直线的倾斜程度，计算为 Δy/Δx。记忆：斜率就是横着走时竖着爬升的比率。
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Intercept: The point where a line crosses an axis. y-intercept is where x = 0. 'Intercept' = 'inter-' (between) + '-cept' (taken) – where the line is taken by the axis.
截距: 直线与坐标轴的交点。y截距即 x = 0 时的 y 值。截距就是直线被坐标轴截住的地方。
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Quadratic Function: A function of the form f(x) = ax² + bx + c, graph is a parabola. 'Quad' means 4, but here 'quadratic' comes from square (area), like a four-sided square’s area is side².
二次函数: 形如 f(x) = ax² + bx + c 的函数，图像是抛物线。“二次”指最高次为2，联想正方形的面积是边长的平方。
5. Geometry – Lines, Angles and Shapes | 几何 – 线、角与形状
Geometry terms describe shapes, positions and relationships. Precise vocabulary ensures you don't confuse 'parallel' with 'perpendicular'.
几何术语描述形状、位置和关系。精确的词汇确保你不会把“平行”和“垂直”搞混。
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Parallel: Lines that never meet, staying the same distance apart. Look at the parallel 'll' in 'parallel' – two parallel lines.
平行: 永不相交、保持等距的线。看看“平行”二字都有“二”的部分，像两条平行线。
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Perpendicular: Lines that intersect at a right angle (90°). Mnemonic: a 'perpendicular' line looks like a perfect 'L'.
垂直: 相交成直角(90°)的线。联想“垂” – 下垂的线总是垂直地面；垂直就像一个大写L的形状。
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Bisector: A line that cuts something exactly into two equal parts. 'Bi' means two, 'sect' means cut – so bisector cuts into two equal parts.
平分线: 把图形恰好分成两等份的线。“平”分意味着平均分割。
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Chord: A line segment joining two points on a circle. A chord is like a 'cord' stretched across the circle – the diameter is the longest chord.
弦: 连接圆上两点的线段。弦像一根拉在圆内的绳子，直径是最长的弦。
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Tangent: A line that touches a circle at exactly one point. Think of a bike tyre touching the road at a single point – tangent just 'touches'.
切线: 与圆只在一个点接触的线。联想“切” – 轻轻接触，像车轮擦过地面。
6. Area, Volume and Mensuration | 面积、体积与测量
These terms relate to measuring space. The ability to recall mensuration formulas often depends on knowing the correct name for each quantity.
这些术语与测量空间有关。回忆测量公式的能力通常取决于知道每个量的正确名称。
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Area: The amount of surface a shape covers, measured in square units (cm², m²). Think 'A-rea' – 'A' flat surface.
面积: 形状所覆盖的平面大小，以平方单位（cm², m²）计。面积就是“面”的积。
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Volume: The amount of space a solid occupies, in cubic units (cm³, m³). Volume and 'voluminous' share the idea of filling space.
体积: 立体物体所占空间大小，以立方单位（cm³, m³）计。体积 – 物体的积。
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Surface Area: The total area of all faces of a solid. 'Surface area' literally means the area of every surface.
表面积: 立体所有面的总面积。字面意思就是所有表面的面积之和。
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Prism: A solid with a constant cross-section. Example: triangular prism. Mnemonic: 'prism' sounds like 'prison' – the cross-section is kept 'imprisoned' throughout.
棱柱: 具有恒定横截面的立体。例如三棱柱。联想：棱柱的横截面始终如一，被“锁”住不变。
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Hemisphere: Exactly half of a sphere. 'Hemi' means half. A hemisphere of the Earth is a perfect example.
半球体: 恰好是球体的一半。'Hemi' 即一半的意思，地球的半球就是一个例子。
7. Trigonometry and Bearings | 三角学与方位角
Trigonometry and bearing problems need you to label sides and angles correctly. These terms appear in right-angled triangles and navigation.
三角学和方位角问题要求你正确标注边和角。这些术语出现在直角三角形和导航中。
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Hypotenuse: The longest side of a right-angled triangle, opposite the right angle. Hypotenuse rhymes with 'hypoten-use'? Think 'high-potential' – it's the biggest side.
斜边: 直角三角形中最长的边，直角对边。“斜” – 倾斜，是直角所对的斜着的边。
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Opposite / Adjacent adjacent is the side next to the angle (not the hypotenuse). Label relative to the angle: 'Opposite = Opposite the angle, Adjacent = Attached to the angle'.
对边 / 邻边: 对边是给定角的对面那条边；邻边是紧挨着该角的边（不是斜边）。联想：对边正对着角，邻边紧挨着角。
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Sine (sin), Cosine (cos), Tangent (tan): Ratios of sides in right triangles: SOH CAH TOA. Memorise the mnemonic: 'Some Old Horses Can Always Hear Their Owners Approaching'.
正弦(sin), 余弦(cos), 正切(tan): 直角三角形边长的比。记忆口决：SOH CAH TOA – 对/斜、邻/斜、对/邻。
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Angle of Elevation / Depression: Elevation is the angle looking up from horizontal; depression is looking down. 'Elevation' = 'Elevate' (raise); 'Depression' goes downwards.
仰角 / 俯角: 仰角是从水平线向上看的角；俯角是向下看的角。仰 – 抬头，俯 – 低头。
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Bearing: A direction measured clockwise from North, given as three digits (e.g. 045°, 230°). 'Bearing' guides you like a compass – always from North.
方位角: 从正北顺时针测量的方向，用三位数表示，如045°、230°。“方位”像指南针一样指示方向，始终以北为起点。
8. Statistics and Data Representation | 统计与数据表示
Statistical terms describe data sets. Clear understanding of 'mean', 'median' and 'mode' is essential for any data-handling question.
统计术语描述数据集。清晰理解“平均数”、“中位数”和“众数”对任何数据处理题都至关重要。
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Mean: The average, sum of values divided by the number of values. 'Mean' is what most people 'mean' by average.
平均数（均值）: 总和除以项数。平均数就是大家通常说的“平均”。
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Median: The middle value when data is ordered. 'Median' sounds like 'medium' – the middle.
中位数: 数据排序后居中的值。“中”位 – 中间位置。
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Mode: The most frequently occurring value. 'Mode' and 'most' both start with 'mo'.
众数: 出现频率最高的值。众 – 人数最众，出现最多。
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Range: The difference between the maximum and minimum values. Range tells you the 'range' of data spread.
极差（范围）: 最大值与最小值的差。范围表示数据伸展的宽度。
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Interquartile Range (IQR): Upper quartile (Q3) minus lower quartile (Q1), the spread of the middle 50%. Think 'inter' (between) quartiles – the range between the quartiles.
四分位距 (IQR): 上四分位数(Q3)减去下四分位数(Q1)，即中间50%数据的跨度。“四分位距”就是四分位之间的差距。
9. Probability and Sets | 概率与集合
Probability questions demand precise language – 'event', 'outcome', 'mutually exclusive' etc. Correct vocabulary avoids misinterpretation.
概率题目要求精确的语言——“事件”、“结果”、“互斥”等。正确的词汇避免误解。
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Experiment: A repeatable process that gives outcomes, e.g. tossing a coin. In probability, an experiment is any trial with random results.
试验: 一个可重复并产生结果的程序，如抛硬币。在概率中，试验就是任何会产生随机结果的尝试。
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Outcome: A possible result of an experiment, e.g. heads. 'Outcome' = what comes out of the experiment.
结果: 试验可能出现的一种情况，如正面。结果就是试验“得出”的东西。
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Event: A set of one or more outcomes, e.g. getting an even number on a die. An event is something that can 'eventuate'.
事件: 一个或多个结果的集合，如掷骰子得到偶数。事件就是可能发生的事情。
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Mutually Exclusive: Events that cannot happen at the same time, e.g. getting a head and tail on one coin toss. 'Mutually exclusive' means they exclude each other.
互斥事件: 不可能同时发生的事件，如一次抛硬币同时得正反面。互斥就是互相排斥。
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Independent Events: The outcome of one does not affect the other, e.g. rolling two dice. 'Independent' means each event acts freely, no dependence.
独立事件: 一个事件的结果不影响另一个，如掷两枚骰子。独立就是不互相依赖。
10. Vectors and Transformations | 向量与变换
Vectors describe movement, and transformations change shapes. These terms often appear together in matrix and geometry papers.
向量描述运动，变换改变形状。这些术语常一起出现在矩阵和几何试卷中。
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Vector: A quantity with both magnitude and direction, often written as a column [x over y] or as bold a. 'Vector' sounds like 'direction'? Think of a vector as an arrow pointing somewhere.
向量: 既有大小又有方向的量，常写为列向量 [x 上 y] 或粗体 a。向量像一支指向某处的箭。
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Magnitude: The length or size of a vector, calculated using Pythagoras' theorem. 'Magnitude' = 'how big' – think of magnitude of an earthquake.
模（大小）: 向量的长度，用勾股定理计算。“模”就是大小，想象地震的震级(magnitude)。
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Translation: Sliding a shape without rotation or reflection, described by a column vector. 'Trans' means across, 'late' carries – carrying a shape across a plane.
平移: 将形状不旋转、不翻转地滑动，用列向量描述。“平移”就是平着移动。
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Reflection: Flipping a shape over a mirror line to produce a mirror image. Think of your reflection in a mirror – same shape, reversed.
反射（翻折）: 将形状沿一条镜线翻转，产生镜像。照镜子时你看到的正是反射。
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Rotation: Turning a shape about a centre through a given angle. 'Rotation' means spinning around. Remember: 'rotate' needs a centre and an angle.
旋转: 将形状绕某个中心转动一定角度。旋转需要指定旋转中心和角度。
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Enlargement: Changing the size of a shape by a scale factor from a centre. 'Enlarge' literally means make larger, but can also reduce if 0 < scale factor < 1.
放大（位似）: 以某中心按比例因子改变形状的大小。放大不一定是变大，比例因子小于1则是缩小。
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