📚 Year 8 CCEA Further Mathematics: Quick Vocabulary Memorization Guide | Year 8 CCEA 进阶数学：词汇术语速记指南
Mastering mathematical vocabulary is the first step to solving problems with confidence. This guide breaks down the essential terms for Year 8 CCEA Further Mathematics and provides simple memory tricks to help you remember them quickly. Each term is explained in English and Chinese so you can learn with clarity.
掌握数学词汇是自信解题的第一步。本指南分解了 Year 8 CCEA 进阶数学的关键术语，并提供简单的记忆技巧帮助你快速记住它们。每个术语都配有中英文解释，让你学得清清楚楚。
1. Number System Terms | 数字系统术语
An integer is any whole number that can be positive, negative, or zero. Think of 'int' as in 'intact' – a number that is not broken into fractions.
整数（integer）是任何正数、负数或零的整数。把 'int' 想作 'intact（完整）' – 一个不包含分数的完整数。
A rational number is any number that can be written as a fraction or ratio of two integers. The word 'rational' contains 'ratio'.
有理数（rational number）是任何可以写成分数或两整数之比的数。单词 'rational' 里包含 'ratio（比）'。
Place value tells us the value of a digit based on its position, such as units, tens, hundreds. Remember that the 'place' gives value.
位值（place value）根据数字所在的位置告诉我们该数字的值，如个位、十位、百位。记住 'place（位置）' 决定 value（值）。
A positive number is greater than zero; a negative number is less than zero. On a number line, positives go right, negatives go left.
正数（positive number）大于零；负数（negative number）小于零。在数轴上，正数向右，负数向左。
Decimal numbers use a decimal point to separate the whole part from the fractional part. The word comes from 'decem', Latin for ten, because it is based on powers of ten.
小数（decimal）使用小数点将整数部分与小数部分分开。这个词源自拉丁语 'decem'（十），因为它基于十的幂。
Digits are the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write numbers. 'Digit' also means finger – we once counted on our fingers!
数字（digits）是用于书写数的符号 0–9。'Digit' 也有手指的意思 – 我们曾经用手指计数！
2. Factors and Multiples | 因数与倍数
A factor is a whole number that divides exactly into another number. Think of a 'factory' that produces the number through multiplication.
因数（factor）是可以整除另一个数的整数。想象一下 'factory（工厂）' 通过乘法生产出那个数。
A multiple is the result of multiplying a number by an integer. Multiples are like the multiplication table outputs.
倍数（multiple）是一个数乘以整数得到的结果。倍数就像乘法表的输出。
The highest common factor (HCF) the largest factor shared by two or more numbers. HCF = Highest Common Friend they share.
最大公因数（HCF）是两个或更多数共有的最大的因数。HCF 就像它们分享的最大的共同朋友。
The lowest common multiple (LCM) is the smallest multiple that two or more numbers have in common. LCM: the Lowest Common Meeting point.
最小公倍数（LCM）是两个或更多数共有的最小的倍数。LCM：最小的共同会合点。
A prime number has exactly two distinct factors: 1 and itself. Prime numbers are the building blocks of all whole numbers.
质数（prime number）恰好有两个不同的因数：1 和它本身。质数是所有整数的积木块。
A composite number has more than two factors. Composite means 'made up of parts', just like composite materials.
合数（composite number）有多于两个因数。Composite 意为“由部分构成的”，就像复合材料。
Prime factorisation breaks a number into a product of prime factors. You can use a factor tree to find it. 'Prime factors' are the prime numbers that multiply to make the original.
质因数分解（prime factorisation）将一个数分解成质因数的乘积。你可以用因子树来找到它。'Prime factors' 是乘起来得到原数的质数。
3. Fractions and Decimals | 分数与小数
The numerator is the top part of a fraction, indicating how many parts we have. Remember: Numerator is Up (look for the 'u' in numerator).
分子（numerator）是分数的上部分，表示我们有多少份。记忆法：Numerator 向上（字母中有 u，代表 up）。
The denominator is the bottom part, showing the total number of equal parts. Denominator is Down (look for the 'd' in denominator).
分母（denominator）是下部分，表示总等份数。记忆法：Denominator 向下（字母中有 d，代表 down）。
A proper fraction numerator smaller than the denominator (value less than 1). Proper = polite, stays small.
真分数（proper fraction）分子小于分母（值小于 1）。Proper 意为适当的、保持较小。
An improper fraction numerator larger than or equal to the denominator (value 1 or more). Improper = top-heavy.
假分数（improper fraction）分子大于或等于分母（值大于或等于 1）。Improper 意为上重下轻。
A mixed number contains a whole number and a proper fraction. It is a 'mix' of two forms.
带分数（mixed number）包含一个整数和一个真分数。它是两种形式的“混合”。
Equivalent fractions have the same value but different numerators and denominators. You can find them by multiplying or dividing the top and bottom by the same number.
等值分数（equivalent fractions）有相同的值但分子分母不同。你可以通过将上下同乘或同除以一个数来得到。
A terminating decimal has a finite number of digits after the decimal point, like 0.25. It terminates (stops).
有限小数（terminating decimal）小数点后位数有限，例如 0.25。它会终止（停止）。
A recurring decimal ts a digit or a block of digits forever, shown with a dot or bar. Recur = to happen again.
循环小数（recurring decimal）永远重复一个或多个数字，用点或横线表示。Recur 意为再次发生。
4. Ratio and Proportion | 比率与比例
A ratio compares two or more quantities, showing their relative sizes. It can be written as a : b or a/b. Think 'relationship' in numbers.
比（ratio）比较两个或多个数量，显示它们的相对大小。可以写成 a : b 或 a/b。想象数字间的“关系”。
Proportion states that two ratios are equal. When things are in proportion, they are balanced. 'Proportion' contains 'portion'.
比例（proportion）表示两个比相等。当事物成比例时，它们是平衡的。'Proportion' 包含 'portion（部分）'。
To simplify a ratio, divide all parts by their common factor. Just like simplifying a fraction.
化简比 是将比的所有项除以它们的公因数。就像化简分数一样。
A scale factor is the multiplier used to enlarge or reduce a shape while keeping proportions the same. Scale changes size.
比例因子（scale factor）是用于放大或缩小图形同时保持形状比例的乘数。Scale 改变大小。
The unitary method finds the value of one unit first, then multiples to find the required value. Unit first, then scale up.
归一法（unitary method）先求出一单位的值，再乘以倍数求所需值。先算 unit（单位），再放大。
We can divide a quantity into a given ratio by finding the total number of parts and sharing accordingly.
我们可以按给定比分一个量，先求出总份数，然后按份分配。
5. Algebra Basics | 代数基础
A variable ol (often a letter) that represents a number that can change or vary. Variable = can vary.
变量（variable）是一个符号（通常是字母），代表可以变化或变动的数。Variable = 可以变化。
A constant is a fixed value that does not change, such as the number 3. Constant stays constant.
常量（constant）是一个固定的值，不改变，例如数字 3。Constant 保持恒定。
A coefficient is the number multiplied by a variable in a term, e.g., in 5x, 5 is the coefficient. It 'co-works' with the variable.
系数（coefficient）是项中与变量相乘的数，例如 5x 中，5 是系数。它与变量“协同工作”。
A term is a single number, variable, or the product of numbers and variables, separated by + or − signs. Think of a 'term' as one piece of an expression.
项（term）是单个数、变量或数与变量的乘积，由加号或减号分开。将“项”想像成表达式的一个片段。
An expression is a combination of terms without an equals sign, like 2x + 5. It expresses a calculation.
表达式（expression）是项的集合，没有等号，如 2x + 5。它表达了一个计算。
An equation is a mathematical statement that two expressions are equal, using an equals sign. E-quality – two sides have equal value.
方程（equation）是说明两个表达式相等的数学语句，使用等号。E-quality – 两边具有相等值。
Like terms have exactly the same variable part, such as 3a and 5a. Only like terms can be combined.
同类项（like terms）具有完全相同的字母部分，如 3a 和 5a。只有同类项才能合并。
To substitute means to replace a variable with a given number. Substitute means to swap in.
代入（substitute）意为用给定的数替换变量。Substitute 就是换入。
6. Equations and Expressions | 方程与表达式
To solve an equation means to find the value(s) of the variable that make the equation true. The solution is the answer.
解方程（solve an equation）意为求出使方程成立的变量的值。解就是答案。
Inverse operations are opposite operations: addition and subtraction, multiplication and division. Use inverses to undo operations.
逆运算（inverse operations）是相反的运算：加法与减法，乘法与除法。用逆运算来还原操作。
The balance method keeps an equation balanced by doing the same operation to both sides. Like a scale in balance.
平衡法（balance method）通过对两边进行相同的运算来保持方程平衡。就像天平保持平衡。
Expanding brackets means multiplying each term inside the bracket by the factor outside. The brackets expand out.
展开括号（expanding brackets）意为将括号外的因数乘以括号内的每一项。括号向外展开。
Factorising is the reverse of expanding: writing an expression as a product of factors. Think of putting back into brackets.
因式分解（factorising）是展开的逆过程：将表达式写成因式的乘积。想象把它放回括号里。
A linear equation has the variable to the power of 1 only, like 2x + 3 = 7. Its graph is a straight line.
线性方程（linear equation）变量的指数仅为 1，如 2x + 3 = 7。它的图像是直线。
7. Sequences | 序列
A sequence is an ordered list of numbers that follow a pattern. 'Sequence' suggests order.
序列（sequence）是按模式排列的有序数列。'Sequence' 暗示顺序。
Each number in a sequence is called a term. The first term is often denoted as a₁.
序列中的每个数称为项（term）。第一项通常记作 a₁。
An arithmetic sequence has a constant difference between consecutive terms, called the common difference (d). Arithmetic – add the same each time.
等差数列（arithmetic sequence）相邻项之间的差恒定，这个差称为公差（common difference, d）。算术级数 – 每次加上相同的数。
A geometric sequence has a constant ratio between consecutive terms, called the common ratio (r). Geometric – multiply by the same each time.
等比数列（geometric sequence）相邻项之间的比值恒定，这个比称为公比（common ratio, r）。几何级数 – 每次乘以相同的数。
A linear sequence is another name for an arithmetic sequence, because its terms grow linearly. It can be described by the nth term formula: a + (n − 1)d.
线性序列（linear sequence）是等差数列的别称，因为其项线性增长。可以用第 n 项公式来描述：a + (n − 1)d。
The nth term of a sequence is a formula that lets you find any term by substituting the position number n. It is the 'rule' of the sequence.
序列的第 n 项（nth term）是一个公式，让你代入位置数 n 就能找到任意一项。它是序列的“规则”。
To generate a sequence, apply the rule repeatedly from a starting value. Generate means to produce.
生成（generate）序列是从起始值开始，重复应用规则。Generate 意为产生。
8. Angles and Lines | 角度与线条
An angle is the space between two intersecting lines, measured in degrees (°). The corner is the vertex.
角（angle）是两条相交线之间的空间，以度数（°）衡量。转角处是顶点。
An acute angle measures between 0° and 90°. Acute = 'a cute' little angle, small and sharp.
锐角（acute angle）介于 0° 到 90° 之间。Acute 像 'a cute（可爱的小）' 角，小而尖。
A right angle is exactly 90°, often marked with a square corner. Right = perfectly upright.
直角（right angle）恰好是 90°，通常用方形角标记。Right 意为正好的、直立的。
An obtuse angle is greater than 90° but less than 180°. Obtuse sounds like 'obese' – a fat angle!
钝角（obtuse angle）大于 90° 且小于 180°。Obtuse 听起来像 'obese（肥胖的）' – 一个大角！
A reflex angle is greater than 180° but less than 360°. Reflex means bent back – it bends past a straight line.
优角（reflex angle）大于 180° 且小于 360°。Reflex 意为反折 – 它折过了直线。
Parallel lines are straight lines that never meet, staying the same distance apart. Think of the two l's in 'parallel' running side by side.
平行线（parallel lines）是永不相交、保持等距的直线。想象 'parallel' 里的两个 l 并排跑。
Perpendicular lines intersect at a right angle (90°). 'Perpendicular' contains the symbol ⟂ if you look closely.
垂直线（perpendicular lines）相交成直角（90°）。'Perpendicular' 一词如果仔细看，里面含有 ⟂。
A transversal is a line that crosses at least two other lines. Trans- means across.
截线（transversal）是穿过至少两条线的线。Trans- 意为横穿。
Alternate angles are equal angles on opposite sides of the transversal, inside the parallel lines. They form a 'Z' shape.
内错角（alternate angles）在截线两侧且在平行线内侧的等角。它们形成 'Z' 形。
Corresponding angles are equal angles on the same side of the transversal, both above or both below the parallel lines. They form an 'F' shape.
同位角（corresponding angles）在截线同侧且在平行线同侧（上或下）的等角。它们形成 'F' 形。
Vertically opposite angles are equal angles opposite each other when two lines cross. They make an 'X'.
对顶角（vertically opposite angles）是两条直线相交时相对的等角。它们形成 'X'。
9. 2D Shapes | 二维图形
A polygon is a closed 2D shape with straight sides. 'Poly' means many, 'gon' means angle – many angles.
多边形（polygon）是由直边围成的封闭二维图形。'Poly' 意为许多，'gon' 意为角 – 许多角。
A triangle has 3 sides and 3 angles. Tri- means three.
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