Year 10 CCEA Maths: Key Terminology Revision Guide | 词汇术语速记指南

📚 Year 10 CCEA Maths: Key Terminology Revision Guide | 词汇术语速记指南

Mastering mathematical terminology is the key to unlocking problem-solving success in Year 10 CCEA Mathematics. This bilingual revision guide presents must-know terms with clear definitions, practical examples, and memory tricks to help you recall them quickly under exam pressure.

掌握数学术语是打开Year 10 CCEA数学解题之门的钥匙。这份双语复习指南列出必会术语，配以清晰定义、实例和记忆妙招，助你在考试压力下快速回想。

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1. Numbers & Number Sets | 数字与数系

Natural numbers (counting numbers) – the set of positive whole numbers starting from 1: {1, 2, 3, …}. They are used to count objects.

自然数（计数数） – 从1开始的正整数集合：{1, 2, 3, …}。用于数物体，就像数苹果不会数到0或半个苹果。

Whole numbers – all natural numbers together with zero: {0, 1, 2, 3, …}. They represent complete units.

非负整数 – 所有自然数加上零的集合：{0, 1, 2, 3, …}。表示完整的单位，没有分数。

Integers – the set of whole numbers and their negatives: {…, -3, -2, -1, 0, 1, 2, 3, …}. No fractional or decimal part.

整数 – 包括正整数、负整数和零，无分数或小数部分。联想：整 = 完整；integer 中的 “teg” 像 “tag” 标签，标记完整。

Rational numbers – any number that can be written as a fraction p/q where p and q are integers and q ≠ 0. Includes terminating and recurring decimals.

有理数 – 能写成分数 p/q 形式的数，p和q是整数且q≠0。小数有限或循环便是有理数。记住 “rational” 含 “ratio” 比例之意。

Irrational numbers – numbers that cannot be expressed as a simple fraction. Their decimal expansion goes on forever without repeating. Examples: π, √2.

无理数 – 无法表示为分数的数，小数无限不循环。如 π 和 √2。 “ir-” 是否定前缀，不是比例数。

Prime number – a natural number greater than 1 that has exactly two distinct factors: 1 and itself. e.g., 2, 3, 5, 7.

质数（素数） – 大于1的自然数，只有1和它本身两个因数。最小的质数是2。记忆：只能“质”与自己配对。

Composite number – a natural number greater than 1 that is not prime; it has more than two factors. e.g., 4 (1,2,4), 12.

合数 – 大于1且不是质数的自然数，有两个以上的因数。 “composite” 意为组合而成。

Factor – a number that divides another number exactly without leaving a remainder. e.g., factors of 12 are 1, 2, 3, 4, 6, 12.

因数（约数） – 能整除给定数的数。想象因子“配对”相乘得原数。

Multiple – the product of a number and any integer. e.g., multiples of 3: 3, 6, 9, 12, …

倍数 – 一个数与任何整数的积。乘法表里的数都是倍数。

Highest Common Factor (HCF) – the largest factor shared by two or more numbers.

最大公因数（HCF） – 几个数共有的最大因数。列出所有因数找最大。

Lowest Common Multiple (LCM) – the smallest multiple that is common to two or more numbers.

最小公倍数（LCM） – 几个数共有的最小倍数。写几个倍数圈出首个相同。

Square number – the product when a whole number is multiplied by itself. e.g., 5² = 25.

平方数 – 一个整数自乘的积。形象化为正方形面积。

Cube number – the product when a whole number is used as a factor three times. e.g., 3³ = 27.

立方数 – 整数乘三次的积。好比正方体体积。

Square root (√) – a value that, when multiplied by itself, gives the original number. √25 = 5.

平方根 – 自乘得原数的值。求边长反过来用。

Cube root (∛) – a value that, when used three times in a product, gives the original number. ∛27 = 3.

立方根 – 连乘三次得原数的值。

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2. Fractions, Decimals & Percentages | 分数、小数与百分数

Numerator – the top number in a fraction, indicating how many parts are taken.

分子 – 分数线上方的数，表示取了几份。记住“Numerator → North → 上方”。

Denominator – the bottom number in a fraction, showing the total number of equal parts the whole is divided into.

分母 – 分数线下方的数，表示整体被分成多少等份。 “Denominator → Down” 下。

Proper fraction – a fraction where the numerator is less than the denominator, e.g., 3/4. Its value is less than 1.

真分数 – 分子小于分母的分数，值小于1。

Improper fraction – a fraction where the numerator is greater than or equal to the denominator, e.g., 5/3. Its value is ≥1.

假分数 – 分子大于或等于分母的分数，值≥1。“不真”的分数。

Mixed number – a whole number combined with a proper fraction, e.g., 2½.

带分数 – 整数与真分数结合的形式。

Equivalent fractions – fractions that represent the same value, though they may look different, e.g., 1/2 = 2/4 = 3/6.

等值分数 – 分子分母成比例扩大或缩小，但数值相等。

Simplify (reduce) a fraction – divide numerator and denominator by their highest common factor to get an equivalent fraction in lowest terms.

约分 – 分子分母同除以最大公因数，化成最简分数。

Decimal – a number written with a decimal point to show parts of a whole. e.g., 0.75.

小数 – 用小数点表示部分整体的数。

Terminating decimal – a decimal that ends, or has a finite number of digits after the decimal point, e.g., 0.25, 1.8.

有限小数 – 小数点后位数有限，可以化作分母为10的幂的分数。

Recurring (repeating) decimal – a decimal with a pattern of digits that repeats forever, e.g., 0.333… or 1.272727…

循环小数 – 小数点后有一段数字无限重复。写为上方加点或短线。

Percentage – a number expressed as a fraction of 100, symbol %. e.g., 45% means 45 out of 100.

百分数（百分比） – 以100为分母的分数，用%表示。 “per cent” 每百。

Percentage increase – the amount added to an original value, expressed as a percentage of the original. New = Original × (1 + increase%).

百分比增加 – 原值增加的百分比例。新值 = 原值 × (1 + 增幅)。

Percentage decrease – the amount removed from an original value, as a percentage. New = Original × (1 − decrease%).

百分比减少 – 原值减少的百分比例。乘子小于1。

Multiplier – a decimal used to calculate percentage change directly. For a 15% increase, multiplier = 1.15.

乘数 – 直接计算百分比变化的小数。增加用大于1，减少用小于1。

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3. Algebraic Expressions & Identities | 代数表达式与恒等式

Variable – a symbol, usually a letter, that represents an unknown number or a quantity that can change. e.g., x, y.

变量 – 用字母表示可变的或未知的数。想想“变化”的量。

Coefficient – the numerical factor multiplying a variable in a term. In 5x, 5 is the coefficient.

系数 – 项中乘在变量前的数字因数。 “co-” 共同，和效率无关；但记住它“系”住变量。

Term – a single number, variable, or product of numbers and variables separated by + or − signs. e.g., 3x², -7.

项 – 由加减号分隔的单个数学单元。多项式的每一块。

Expression – a combination of terms using operations (+, −, ×, ÷) but without an equals sign. e.g., 2x + 5.

表达式 – 用运算符号连接的式子，无等号。不代表等式，只是一个量。

Equation – a mathematical statement showing that two expressions are equal, using an equals sign (=). e.g., 3x + 2 = 11.

方程 – 含有等号表明两表达式相等的式子。强调“等于”。

Identity (≡) – an equality that holds for all values of the variable. Sometimes shown with an extra bar ≡. e.g., x + x = 2x.

恒等式 – 对所有变量值都成立的等式。恒久相等。常用三条横线表示。

Like terms – terms that have exactly the same variable(s) raised to the same power(s). e.g., 3x and -5x.

同类项 – 变量及其指数完全相同的项。可以合并加减。

Expand – to remove brackets by multiplying each term inside by the factor outside. e.g., 3(x+2) = 3x + 6.

展开 – 乘法分配律去掉括号，把乘积写开。

Factorise – to rewrite an expression as a product of its factors. Opposite of expansion. e.g., 6x + 9 = 3(2x + 3).

因式分解 – 把表达式写成乘积形式，提取公因数。

Linear expression – an algebraic expression where the highest power of the variable is 1. e.g., 4x − 7.

线性式 – 变量最高次数为1的代数式。图像为直线。

Quadratic expression – an expression where the highest power of the variable is 2. e.g., x² + 5x + 6.

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