📚 CAIE Year 10 Maths Vocabulary & Terminology Quick-Memorisation Guide | Year 10 CAIE 数学：词汇术语速记指南
Mastering the language of mathematics is half the battle in CAIE Year 10. This guide breaks down essential terms into logical groups, pairing each with a memorable trick, visual clue, or word origin to help you lock them into long-term memory. From algebraic expressions to statistical measures, you will find the exact vocabulary that appears in exam questions and mark schemes, explained clearly in both English and Chinese.
掌握数学语言是攻克 CAIE Year 10 考试的关键。这份指南将核心术语按逻辑分组，每一项都配有记忆窍门、图像线索或词源解析，帮助你把这些词汇牢牢刻入长期记忆。从代数表达式到统计量数，所有出现在考题和评分标准中的重点词汇，这里都以中英双语清晰阐释。
1. Algebraic Expressions | 代数表达式术语
Term: A single number, variable, or product of numbers and variables (e.g., 5x², –3y). Think of it as one "piece" of an expression separated by + or – signs.
项 (Term)：一个单独的数、变量或者数与变量的乘积（如 5x²、–3y）。可以把它想象成表达式中被加号或减号隔开的“一小块”。
Coefficient: The number part multiplying a variable in a term. In –4a, the coefficient is –4. Memory aid: "co-" means together, the number that works together with the variable.
系数 (Coefficient)：一个项中乘以变量的数字部分。在 –4a 中，系数就是 –4。记住“co-”表示“共同”，系数就是和变量一起出现的数字。
Constant: A term with no variable; its value never changes. In 3x + 7, 7 is the constant. Visualise it as a number that "stands constantly still".
常数 (Constant)：不含变量的项，它的值永远不变。在 3x + 7 中，7 就是常数。想象一个始终站立不动的数字，就是它。
Like terms: Terms that have exactly the same variable part (letters and powers). 2x² and –5x² are like; 2x² and 3x are not. They must "look alike" to be combined.
同类项 (Like terms)：变量部分（字母及其指数）完全相同的项。2x² 和 –5x² 是同类项；2x² 和 3x 不是。要能够合并，它们必须“长相一样”。
2. Equations, Identities, and Formulae | 方程、恒等式与公式
Equation ng an equals sign. It is only true for specific values. Example: 2x + 1 = 7. Link the word "equa-" to "equal" and imagine a balance scale.
方程 (Equation)：表明两个表达式相等的数学语句，含有等号。它只在特定取值下成立。例如 2x + 1 = 7。把 “equa-” 与 “equal” 联系起来，想象一架天平。
Identity: An equation that is true for all values of the variable, often written with ≡ (triple bar). Example: (x+1)² ≡ x² + 2x + 1. Think "identical" – both sides are always identical.
恒等式 (Identity)：对变量的所有取值都成立的等式，经常用 ≡（三横线）书写。例如 (x+1)² ≡ x² + 2x + 1。联想“identical”，两边永远相同。
Formula : An equation that shows how to calculate a quantity, usually involving multiple variables. e.g., A = πr². It's a "recipe" – plug in values to get a result.
公式 (Formula)：展示如何计算某个量的等式，通常涉及多个变量。如 A = πr²。它就像一份“食谱”，代入数值就能算出结果。
Subject of a formula ngle variable isolated on one side of the equals sign. In V = IR, V is the subject. If you "change the subject", you rearrange to isolate another variable.
公式的主项 (Subject of a formula)：等号一侧被单独孤立出来的变量。在 V = IR 中，V 就是主项。如果你“更换主项”，就是重新整理公式，把另一个变量单独解出来。
3. Functions and Graphs | 函数与图像术语
Function 2x+3. Think of a vending machine: press one button (input) and you get exactly one item (output).
函数 (Function)：一种将每个输入 (x) 对应到唯一输出 (y) 的规则。写作 f(x)=2x+3。想象一台自动售货机：按下一个按钮（输入），就得到一个确定商品（输出），不会多给。
Domain: All the possible input values (x-values) a function can accept. For f(x)=√x, domain is x ≥ 0. It's the "do-main" – what x is allowed to do.
定义域 (Domain)：函数可以接受的所有可能输入值（x 值）。对 f(x)=√x，定义域是 x ≥ 0。记住“域”就是允许 x“活动”的范围。
Range : All the possible output values (y-values) that come out of a function. For f(x)=x², range is y ≥ 0. You can think "range of outputs" like a mountain range spread across the y-axis.
值域 (Range)：函数产生的所有可能输出值（y 值）。对 f(x)=x²，值域是 y ≥ 0。就像是输出值在 y 轴上绵延开来的“山脉”。
Gradient: The steepness of a line, measured as rise/run. Positive gradient means uphill; negative means downhill. The word "grad" is like a grade of a slope – how steep you have to climb.
斜率/坡度 (Gradient)：一条直线的陡峭程度，计算方式为 垂直升高/水平前进。正斜率表示上坡，负斜率表示下坡。“Grad”就像坡度等级，说明你爬得有多陡。
Intercept e : The point where a graph crosses an axis. y-intercept is where x=0; x-intercept is where y=0. "Intercept" sounds like "intercept the axis", the point where it gets caught by an axis.
截距 (Intercept)：图像与坐标轴相交的点。y轴截距在 x=0 处，x轴截距在 y=0 处。“Intercept” 有“拦截”的意思，就是被坐标轴拦截住的点。
4. Geometry: Lines and Angles | 几何：线与角
Acute angle: An angle less than 90°. Memory: "a cute little angle".
锐角 (Acute angle)：小于 90° 的角。可以把它想象成“一枚可爱的小角”。
Obtuse angle: Between 90° and 180°. It is "obtuse" (obese? no) – think "obtuse" as "obviously larger than 90", or imagine it as a big, open angle.
钝角 (Obtuse angle)：在 90° 到 180° 之间的角。可以用“钝”联想到“迟钝的大个子”，比直角大，比平角小。
Reflex angle: Between 180° and 360°. It "reflects" back past a straight line.
优角 (Reflex angle)：180° 到 360° 之间的角。它“反射”过直线，超出半圆。
Complementary angles: Two angles that add to 90°. They "complete" each other to make a right angle.
余角 (Complementary angles)：加起来等于 90° 的两个角。它们互相“补全”成一个直角。
Supplementary angles: Two angles that add to 180°. They "supply" the missing part to make a straight line.
补角 (Supplementary angles)：加起来等于 180° 的两个角。它们互为“补给”，拼成一条直线。
Vertically opposite angles: Angles opposite each other when two lines cross; they are always equal. "Vertically" here means at the vertex; they sit directly across from each other like an X.
对顶角 (Vertically opposite angles)：两条直线相交时彼此相对的角，总是相等。这里的“vertically”指顶点，它们像 X 那样直接面对面。
5. Triangles and Polygons | 三角形与多边形
Isosceles triangle: Two equal sides and two equal base angles. Greek "isos" (equal) + "skelos" (leg). Equal legs.
等腰三角形 (Isosceles triangle)：有两条相等的边和两个相等的底角。源自希腊语“isos”（相等）+“skelos”（腿）。两条腿等长。
Scalene triangle: All sides and angles different. "Scalene" sounds like "scalene" – think "scaly", uneven edges like a fish's scales.
不等边三角形 (Scalene triangle)：所有边和角都不同。“Scalene”听起来像“scaly”（有鳞的），边缘参差不齐，像鱼鳞一样各不相等。
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle. "Hypo-" (under) + "teinein" (stretch). It stretches under the right angle.
斜边 (Hypotenuse)：直角三角形中最长的边，对着直角。“Hypo-”表示“在下面”，“ teinein”表示“伸展”，它在直角下方向外伸展。
Perpendicular bisector: A line that cuts another line exactly in half at a 90° angle. "Perpendicular" = right angle, "bisector" = cuts into two equal parts.
垂直平分线 (Perpendicular bisector)：一条以 90° 角将另一条线段平分成两半的直线。“垂直”指直角，“平分”指分成相等的两部分。
Angle bisector: A line that cuts an angle into two equal halves. "Bi-" means two, "sector" means cutter.
角平分线 (Angle bisector)：把一个角分成两个相等角的线。“Bi-”意为二，“sector”意为切割器，切成两半。
6. Circles | 圆
Radius (plural: radii): Distance from the centre of a circle to its edge. Think "radius radiates from centre".
半径 (Radius，复数 radii)：从圆心到圆周的距离。想象它从圆心“辐射”出去。
Diameter: A straight line passing through the centre from side to side; twice the radius. "Dia-" (across) + "metron" (measure). Measure across.
直径 (Diameter)：穿过圆心、从圆的一边到另一边的直线段；是半径的两倍。“Dia-”表示“穿过”，加上“metron”（测量），即“穿过整个圆测量的长度”。
Circumference: The distance around the edge of a circle. "Circum-" (around) + "ferre" (carry). The perimeter that carries around the circle.
圆周 (Circumference)：圆边缘的长度。“Circum-”意为“环绕”，就像带着边界绕圈。
Arc: A part of the circumference. Think of an arch – a curved segment.
弧 (Arc)：圆周的一部分。“Arc”像拱门 (arch) 的形状，一段弯曲的路径。
Chord: A line segment joining two points on a circle without passing through the centre. Not a "cord", but a "chord" as in music? It's a line stretched across a circle.
弦 (Chord)：连接圆上两点但不经过圆心的线段。就像绷紧的一根弦，横跨在圆内。
Tangent: A straight line that touches a circle at exactly one point. "Tangere" (to touch) – it just "touches" and does not cross.
切线 (Tangent)：一条只在一个点上刚好接触圆的直线。源自拉丁语“tangere”（触碰），它仅仅“触碰”而不穿过。
7. Trigonometry | 三角学
Sine (sin), Cosine (cos), Tangent (tan): Ratios of sides in right-angled triangles. Use the mnemonic: SOH CAH TOA – acent/Hypotenuse, Tan = Opposite/Adjacent. It sticks because it sounds like a funny chant.
正弦 (sin)、余弦 (cos)、正切 (tan)：直角三角形中各边的比值。用记忆口诀：SOH CAH TOA – Sin = 对边/斜边, Cos = 邻边/斜边, Tan = 对边/邻边。念起来像一句有趣的咒语，不容易忘。
Angle of elevation: The angle formed upward from a horizontal line to a line of sight. Imagine you "elevate" your eyes to look up.
仰角 (Angle of elevation)：从水平线向上看向物体时形成的角。想象你“抬起”视线望高处。
Angle of depression: The angle formed downward from a horizontal line. You "depress" your gaze to look down.
俯角 (Angle of depression)：从水平线向下看时形成的角。你“压低”目光看向下面。
Pythagoras' theorem: In a right-angled triangle, a² + b² = c², where c is the hypotenuse. Think "Pythag" – the "pi-thag" rule always holds, and you can remember 3-4-5 as a classic triplet.
勾股定理 (Pythagoras' theorem)：直角三角形中，a² + b² = c²，c 是斜边。记住 3-4-5 这一组经典勾股数，就能联想到这个定理。
8. Statistics and Data | 统计与数据
Mean: The average, sum of all values divided by the number of values. It is "mean" because it balances the data – think of it as the "fair share".
平均数 (Mean)：所有数值的总和除以数值的个数。它像是让数据达到平衡的“公平份额”。
Median: The middle value when data is ordered. "Median" is like "medium" – right in the middle, like a central strip on a road.
中位数 (Median)：将数据排序后处于中间位置的值。“Median”和“medium”同源，就是正中间，像马路中间隔离带。
Mode: The value that appears most often. "Mode" sounds like "most" – the most frequent.
众数 (Mode)：出现次数最多的值。英文里“Mode”和“most”相近，就是最频繁的那个。
Range (statistics): The difference between the largest and smallest values. It measures the "spread" – like a mountain range stretching from low to high.
极差/范围 (Range)：最大值与最小值之差。它衡量数据的“散布宽度”，就像山脉从低到高的跨度。
Quartile: Values that divide an ordered data set into four equal parts. Lower quartile (Q₁), median (Q₂), upper quartile (Q₃). "Quart-" means four.
四分位数 (Quartile)：把排序后的数据分成四等份的值。下四分位数 Q₁，中位数 Q₂，上四分位数 Q₃。“Quart-”就是四的意思。
Interquartile range (IQR): Q₃ – Q₁, the spread of the middle 50% of data. It ignores outliers, giving a robust measure of spread.
四分位距 (Interquartile range, IQR)：Q₃ – Q₁，中间 50% 数据的散布范围。它不受极端值影响，是比较稳健的离散程度度量。
9. Probability | 概率
Outcome: A possible result of a probability experiment. Flipping a coin has two outcomes: heads and tails.
结果 (Outcome)：概率实验的一种可能结果。抛硬币有两种结果：正面和反面。
Event: A set of one or more outcomes. Rolling a die and getting an even number is an event consisting of {2,4,6}.
事件 (Event)：一个或多个结果组成的集合。掷骰子得到偶数是一个事件，包含 {2,4,6}。
Sample space: The set of all possible outcomes. Often listed in a table or list. Think of it as the "space of all samples" you can get.
样本空间 (Sample space)：所有可能结果的集合。经常用表格或列表表示。想象这是你可以抽取的“所有样本的空间”。
Mutually exclusive events: Events that cannot happen at the same time. "Mutually exclusive" – if one is included, the other is excluded.
互斥事件 (Mutually exclusive events)：不可能同时发生的事件。互相排斥，发生一个就排除了另一个。
Independent events: The outcome of one event does not affect the probability of the other. Think "independent" as "not dependent" on each other, like two separate dice rolls.
独立事件 (Independent events)：一个事件的结果不影响另一个事件发生的概率。“独立”就是互不依赖，像两次独立的抛骰子。
10. Measures and Units | 测量与单位
Metric prefixes (×1000), centi- (÷100), milli- (÷1000). Remember from smallest to largest: milli- is like "millionth" y = 100 years), kilo- is 1000 (kilogram). The prefixes are consistent across all SI units.
公制词头：kilo- (×1000), centi- (÷100), milli- (÷1000)。从最小到最大记忆：milli- 听起来像“微小的”（千分之一，千足虫有很多小节），centi- 是百分之一（一个世纪是100年），kilo- 是一千（千克是一千克）。所有国际单位制单位都共用这些词头。
Compound measures ssure are rates formed by dividing one quantity by another. E.g., speed = distance ÷ time. "Compound" because it combines two simple measures.
复合单位 (Compound measures)：速度、密度、压强等由两个量相除构成的比率。例如 速度 = 距离 ÷ 时间。“复合”是因为它把两个简单单位结合在了一起。
Perimeter: The total distance around the outside of a shape. "Peri-" (around) + "meter" (measure). Measure around.
周长 (Perimeter)：围绕图形外边缘的总长度。“Peri-”意为周围，“meter”是测量，绕一圈测量。
Area: The space inside a 2D shape, measured in square units. Think "a-rea" as "a region".
面积 (Area)：二维图形内部的空间，以平方单位计量。可以联想为“一片区域”。
Volume: The space inside a 3D object, measured in cubic units. Volume is the "voluminous" interior.
体积 (Volume)：三维物体内部的空间，以立方单位计量。Volume 有“大量、容积”的意思，就是里面能装多少。
Surface area: The total area of all surfaces of a 3D solid. Imagine peeling off the skin and laying it flat – the total area of that skin.
表面积 (Surface area)：三维立体所有表面的总面积。想象把外皮剥下来铺平，那一整张皮的面积就是表面积。
11. Sets | 集合
Set: A collection of distinct objects, enclosed in braces {}. Think of a set of trading cards – clear, well-defined, no duplicates.
集合 (Set)：一组明确、各不相同的对象，用大括号 { } 包围。就像一套交换卡片，界限清晰，没有重复。
Element: An object inside a set. Use the symbol ∈ to show membership. "Element" is an elementary member.
元素 (Element)：集合中的对象。用 ∈ 表示属于关系。它是集合的基本组成成员。
Universal set (ℰ): The set that contains all possible elements under consideration, usually depicted as a big rectangle in a Venn diagram. It is the "universe" for the problem.
全集 (Universal set, ℰ)：包含当前问题中所有可能元素的集合，在韦恩图中通常用大方框表示。它就是问题里的“世界”。
Intersection ( ∩ ): Elements common to both sets. Visualise two overlapping circles; the overlap is where they "intersect" each other.
交集 (Intersection, ∩)：同时属于两个集合的元素。想象两个相交的圆，交叠的部分就是它们“交集”之处。
Union ( ∪ ): All elements that are in either set or both. Think "united" – everything joined together.
并集 (Union, ∪)：属于任一集合或两个集合的所有元素。想象“联合”起来，把东西都合在一起。
Complement ( A' ): Everything not in set A (but still in the universal set). It "completes" the set A to the whole universe.
补集 (Complement, A' )：不在集合 A 中（但仍在全集中）的所有元素。它把集合 A “补全”成整个全集。
12. Sequences and Number Patterns | 数列与数字模式
Arithmetic sequence: A sequence where the difference between consecutive terms is constant (common difference d). Example: 3, 7, 11, 15... Think "arithmetic" – adding (or subtracting) the same amount each time, just like basic arithmetic operations.
等差数列 (Arithmetic sequence)：相邻两项的差为常数的数列（公差 d）。例如 3, 7, 11, 15... 每次加上（或减去）相同的数，就像做基本的算术一样。
Geometric sequence: A sequence where each term is found by multiplying the previous term by a constant (common ratio r). Example: 2, 6, 18, 54... "Geo-metric" relates to growth by multiplication, like geometrical scaling.
等比数列 (Geometric sequence)：每一项都是前一项乘以一个常数（公比 r）所得的数列。例如 2, 6, 18, 54... “几何”式增长通过乘法进行，就像图形按比例放大一样。
nth term: A formula for the term in position n. For arithmetic: a + (n–1)d. Often called the "general term" because it generates any term you want.
通项/第 n 项 (nth term)：计算第 n 个位置的项的公式。等差数列中为 a + (n-1)d。它也被称为“一般项”，因为你可以用它生成任意一项。
Fibonacci sequence , 8, 13... where each term is the sum of the two before it. It appears in nature; the name "Fibonacci" itself is memorable as a famous mathematician. You can link it to "Fibonacci = follow the two before".
斐波那契数列 (Fibonacci sequence)：1, 1, 2, 3, 5, 8, 13... 每一项是前两项之和。它在自然界中时常出现，数学家名字本身就很好记。可以记成“斐波那契 = 跟着前两个走”。
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