📚 Year 8 Cambridge Maths: Vocabulary & Terminology Quick Memorisation Guide | Year 8 剑桥数学：词汇术语速记指南
A strong command of mathematical vocabulary is the foundation for success in Year 8 Cambridge Maths. This guide presents key terms grouped by topic, with memorable explanations in English and Chinese to help you quickly recall definitions, properties, and relationships. Use the mnemonics and visual links to lock each term into your long-term memory.
扎实的数学词汇是 Year 8 剑桥数学成功的基础。本指南按主题整理了关键术语，配以中英双语的助记解释，帮助你快速回忆定义、性质与关系。运用这些联想和图像技巧，把每一个术语刻入长期记忆。
1. Number Types and Properties | 数字类型与属性
This section covers the essential labels we give to numbers, from whole units to irrational constants. Learning the precise words helps you follow problems correctly.
本节涵盖赋予数字的基本标签，从完整单位到无理常数。掌握精确词汇能帮你正确理解题意。
Integer: A whole number with no fractional or decimal part. Memory tip: 'in-te-ger' sounds like 'in-tact', meaning whole and unbroken.
整数：没有分数或小数部分的完整数字。速记：'integer' 听起来像“完整的”，没有碎片。
Rational number: Any number that can be written as a fraction a/b, where a and b are integers and b ≠ 0. Think 'ratio'-nal – it can be expressed as a ratio.
有理数：任何可以写成分数 a/b 的数，a 和 b 是整数且 b ≠ 0。速记：'rational' 来自 ratio (比率)，可表示为比例。
Irrational number: A number that cannot be written as a simple fraction. Its decimal goes on forever without repeating. Examples: π and √2. Think 'ir-' as 'not' rational.
无理数：不能写成分数的数，小数无限不循环。例如 π 和 √2。速记：'irrational' 就是“非有理”。
Prime number: A whole number greater than 1 that has exactly two factors: 1 and itself. Think of 'prime' as 'first in importance', only divisible by trivial divisors.
质数（素数）：大于 1 且只有 1 和自身两个因数的整数。速记：“质” 是原始，只能被平凡因数整除。
Square number: ultiplying a number by itself. Example: 4² = 4×4 = 16. Visualise a perfect square of dots.
平方数：一个数自乘的结果，如 4² = 16。想象排列成一个正方形点阵。
Cube number: y itself twice more. Example: 2³ = 2×2×2 = 8. Think of stacking cubes in three dimensions.
立方数：一个数自乘两次，如 2³ = 8。想象三维立方体堆积。
2. Operations and Order of Operations | 运算与运算顺序
Words for calculations and the correct sequence are vital. Misreading 'product' or forgetting BODMAS can cost marks.
运算词汇和正确顺序至关重要。误读“积”或忘记运算法则都会丢分。
Sum: The result of addition. Memory: 'sum' sounds like 'some', putting some amounts together.
和：加法得到的结果。速记：把数量堆到一起。
Difference: The result of subtraction. Think of 'different' lengths – one minus the other.
差：减法得到的结果。想象两条不同长度相差的部分。
Product: The result of multiplication. Memory: 'pro-duct' is what you produce when you multiply.
积：乘法得到的结果。联想“产出”——相乘就产出了积。
Quotient: The result of division. It shares the root 'quot' with 'quote', as in sharing a portion.
商：除法得到的结果。“quotient” 和 “quote” 同源，意味分配份额。
BODMAS/BIDMAS: Brackets, Orders (Indices), Division, Multiplication, Addition, Subtraction. Mnemonic phrase: 'Big Old Dogs Must Always Sit'.
BODMAS/BIDMAS法则：括号、指数、乘除、加减。口诀：“冰糖葫芦打门牙，酸爽”。
3. Fractions, Decimals, and Percentages | 分数、小数和百分数
These three forms represent parts of a whole. Quick conversion and correct naming of parts are key skills.
这三种形式表示整体的部分。快速转换和正确命名各部分名称是关键技能。
Numerator: The top number in a fraction, showing how many parts we have. Memory: 'Num-' like 'number' up top, counting the pieces.
分子：分数线上的数，表示我们有多少份。速记：“子”在上面点数。
Denominator: The bottom number, showing the size of each equal part. Think 'de'-nominator, naming the kind of pieces, always down under.
分母：分数线下的数，表示每份的大小。速记：“母”在下面给整体命名。
Equivalent fractions: ominators, e.g. ½ = 2/4. Visualise cutting the same cake into different numbers of slices.
等值分数：值相等但分子分母不同的分数，如 ½ = 2/4。想象同一块蛋糕分成的块数不同。
Percentage: A ratio per hundred, symbol %. Memory: 'per cent' means 'for each hundred'. Always link the symbol to the ×(1/100) operation.
百分数：每一百份中的比率，符号 %。速记：'percent' 就是“每百”，总是与除以 100 挂钩。
4. Algebraic Expressions and Equations | 代数表达式与方程
Algebra uses letters for unknowns. Understanding the vocabulary of expressions and equations is essential before you start simplifying or solving.
代数用字母表示未知量。在化简或解方程之前，先要理解表达式与方程的相关词汇。
Variable: A symbol, usually a letter, that represents an unknown value. Memory: 'vary-able' – its value can vary.
变量：一个符号（常为字母），代表未知数。速记：“可以变化”的量。
Coefficient: The number multiplies a variable. Example: in 3x, 3 is the coefficient. Think 'co-' together + 'efficient' helper – it works with the variable.
系数：乘在变量前的数。如 3x 中 3 是系数。速记：与变量合在一起的数字伙伴。
Constant: A fixed number that does not change. Imagining a constant friend – always there, never varying.
常数：固定不会改变的数。速记：像忠实的常量朋友，永远不变。
Expression: A combination of numbers, variables and operators, without an equals sign. Example: 5x + 2. Think of expressing a calculation but not comparing.
表达式：由数、变量和运算符组成，没有等号。如 5x + 2。它只是表达一个算式，不进行比较。
Equation: A mathematical statement showing two expressions are equal, always containing an '=' sign. Memory: 'equ-' means equal; equation has equality.
方程：表示两个表达式相等的数学陈述，必有等号。速记：'equation' 里有 equal，两边平衡。
5. Geometry: Angles and Lines | 几何：角与线
Angle vocabulary can be tricky, but once you link each term to a visual image, they stick. Lines and their relations describe most shapes.
角的词汇可能有些难记，但一旦每个词联系上一个视觉图像，就能牢而不忘。线和线的关系描述了大多数图形。
Acute angle: Less than 90°. Memory: 'a cute' small angle, like a cute tiny puppy – sharp and little.
锐角：小于 90°。速记：'acute' 像“a cute”（可爱），小巧锐利。
Right angle: Exactly 90°, marked with a square corner. Think of a perfect upright corner, 'right' as correct and straight.
直角：恰好 90°，用小方格标识。联想端正的角落，“正”确的角。
Obtuse angle: Greater than 90° but less than 180°. Memory: think 'obese' angle – it looks wide and heavy.
钝角：大于 90° 小于 180°。速记：'obtuse' 想成肥胖的角，宽大钝重。
Reflex angle: Greater than 180° but less than 360°. Memory: a reflex angle 'reflects' around beyond a straight line.
优角：大于 180° 小于 360°。速记：'reflex' 像光线反射回来，超过了半圆。
Perpendicular lines: Lines that intersect at right angles. Memory: the symbol '⊥' looks like a right angle; 'perpendicular' sounds like 'perfect angle'.
垂直线：相交成直角的线。速记：符号 ⊥ 就像直角；完美交成直角。
Parallel lines: Lines that never meet, maintaining a constant distance. Memory: the two 'll's in parallel look like two parallel tracks.
平行线：永不相交、保持等距的线。速记：'parallel' 里的两个 l 像是两条铁轨。
6. Triangles and Quadrilaterals | 三角形与四边形
Triangles are named by side lengths or angles. Quadrilaterals are classified by parallel sides and side lengths. Mnemonics can prevent mix-ups.
三角形按边或角命名，四边形按平行边和边长分类。巧记可以防止混淆。
Equilateral triangle: All three sides equal, all angles 60°. Memory: 'equal-lateral' – equal sides. Think of a perfect uniform triangle.
等边三角形：三条边都相等，每个角 60°。速记：'equilateral' 就是“等边”。
Isosceles triangle: Two equal sides and two equal base angles. Memory: say 'I-sos-e-leez' like 'I saw sausages' – two sausages of the same length!
等腰三角形：两条边相等，两底角相等。速记：发音像“I saw sausages”——两根等长的香肠！
Scalene triangle: All sides different lengths. Memory: 'sca-lene' suggests 'scales' are different; no equal sides.
不等边三角形：各边长度都不同。速记：'scalene' 让人想到刻度不同，没有等边。
Parallelogram: A quadrilateral with opposite sides parallel and equal. Memory: 'parallel-ogram' – a shape built from parallel lines.
平行四边形：对边平行且相等的四边形。速记：含有“平行”的形状。
Rhombus: A parallelogram with all four sides equal. Memory: think of a 'diamond' shape; 'rhombus' rhymes with 'rom-bus' – a bus of equal sides.
菱形：四边相等的平行四边形。速记：像钻石形状，四边相等。
Trapezium: A quadrilateral with at least one pair of parallel sides. Memory: 'tra-pe-zium' sounds like 'trap-ease' – one pair of lines trapped in parallel.
梯形：至少有一对边平行的四边形。速记：一对平行线像被“陷阱”困住。
7. Measurement: Perimeter, Area, Volume | 测量：周长、面积、体积
Measurement terms describe the size of objects. Learning the exact meaning of each word avoids common errors in applying formulas.
测量术语描述物体的大小。学习每个词的精确含义可以避免应用公式时出错。
Perimeter: The total distance around the outside of a shape. Memory: 'peri-' around, like a perimeter fence; think 'meter' measures around.
周长：围绕形状外边缘的总长度。速记：想象沿着边界的栅栏走一圈测量。
Area: sured in square units. Formula for rectangle: length × width. Imagine painting the surface – the paint needed is the area.
面积：形状所覆盖表面的大小，以平方单位计量。矩形公式：长 × 宽。联想刷墙需要用多少涂料。
Volume: ic units. For a cuboid: length × width × height. Memory: think of filling a box with cubes – the number of cubes is the volume.
体积（容积）：立体物体占据的空间，以立方单位计量。长方体公式：长 × 宽 × 高。想象用单位立方体填满箱子。
Capacity: The maximum amount a container can hold, often in litres or millilitres. Memory: 'cap-acity' – how much a cap-like container holds.
容量：容器能容纳的最大量，常用升或毫升。罐头能装多少液体。
Metric unit conversions: km - hm - dam - m - dm - cm - mm. Use 'King Henry Died By Drinking Chocolate Milk' to remember the order.
公制单位换算：千米、百米、十米、米、分米、厘米、毫米。可用口诀“千爸十米分厘毫”辅助排序。
8. Statistics: Data Handling | 统计：数据处理
Statistics words describe data sets. Distinguishing between mean, median and mode is a classic exam requirement.
统计词汇描述数据集。区分平均数、中位数和众数是考试的经典要求。
Mean: The average, found by summing values and dividing by the count. Memory: 'mean' is what you typically mean by average.
平均数（均值）：所有数据之和除以数据个数。速记：通常说的“平均”就是指均值。
Median: The middle value when data are ordered. Memory: think of the 'median strip' in a road – it sits in the middle.
中位数：排序后处于中间位置的值。速记：像公路的中央隔离带，位于正中。
Mode: The value that appears most often. Memory: 'mode' sounds like 'most' – the most frequent value.
众数：出现次数最多的值。速记：'mode' 听起来像 most，出现最多的那个。
Range: The spread of data: maximum minus minimum. Memory: 'mountain range' goes from low valley to high peak – cover the distance.
范围（极差）：数据最大值减最小值。速记：如山脉从低谷到高峰覆盖的距离。
Probability: The likelihood of an event happening, on a scale from 0 (impossible) to 1 (certain). Memory: 'prob-able' – how probable it is, expressed as a fraction.
概率：事件发生的可能性，从 0 (不可能) 到 1 (必然)。速记：'probable' 表示可能性，常写成分数。
9. Ratios and Proportions | 比与比例
Ratio and proportion compare parts and wholes. Knowing the difference keeps your working clear in sharing and scaling problems.
比和比例比较部分与整体。清楚它们的区别有助于在分配和缩放问题中理清思路。
Ratio: A comparison of two or more quantities, often written as a : b. Memory: 'ratio' relates to 'recipe' – mixing ingredients in a specific ratio.
比：
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