📚 Year 9 CIE Maths: Vocabulary & Terminology Memorisation Guide | Year 9 CIE 数学：词汇术语速记指南
Mastering mathematical vocabulary is like learning a new language – once you understand the terms, solving problems becomes much easier. This guide presents key Year 9 CIE Maths terms grouped by topic, with clear explanations and simple memory tricks. Each pair of paragraphs gives the English definition followed by the Chinese equivalent, helping you build a bilingual understanding strong enough to tackle any exam question with confidence.
掌握数学词汇就像学习一门新语言——一旦理解了术语，解题就会变得简单得多。本指南按专题整理了 Year 9 CIE 数学的核心术语，配有清晰的解释和简单的记忆窍门。每一对段落都是先给出英文定义，再给出对应的中文释义，帮助你建立起扎实的双语理解，从容应对任何考试题目。
1. Number Types and Classifications | 数字类型与分类
Natural numbers are the counting numbers 1, 2, 3, ... (some definitions include 0), while whole numbers include 0. Integers extend this set to include negative whole numbers, such as −1, −2, −3.
自然数是从 1 开始计数的数字，而整体数（非负整数）包含 0。整数则把范围扩大到包含负整数，例如 −1、−2、−3。
A rational number is any number that can be written as a fraction a/b, where a and b are integers and b ≠ 0. Irrational numbers cannot be written as a simple fraction; their decimal expansions go on forever without repeating, like √2 or π.
有理数是可以表示为分数 a/b 的任何数（a、b 为整数且 b ≠ 0）。无理数无法写成简单的分数；它们的小数部分无限不循环，例如 √2 或 π。
s (e.g., 2, 3, 5, 7). Composite numbers have more than two factors (e.g., 4, 6, 8). Think: 'prime' = 'primary', the basic building blocks.
质数（素数）是大于 1 且只有两个因数（1 和自身）的整数，例如 2、3、5、7。合数则有超过两个因数，例如 4、6、8。可以记作：质数就是“最基本的数”，是搭积木的原始件。
Factors are numbers that divide exactly into another number without leaving a remainder. Multiples are the results of multiplying a number by an integer (e.g., multiples of 3 are 3, 6, 9, ...).
因数是可以整除一个数且没有余数的数。倍数则是一个数与整数相乘的结果（例如 3 的倍数是 3, 6, 9, …）。
he number as a factor three times (e.g., 2³ = 8). The small raised number is the exponent.
平方数是一个数自乘的结果（如 4² = 16）。立方数是将一个数作为因数乘三次的结果（如 2³ = 8）。角标小数字是指数。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
The top of a fraction is the numerator; the bottom is the denominator. A proper fraction has a numerator smaller than the denominator, an improper fraction has a larger or equal numerator, and a mixed number combines a whole number with a proper fraction.
分数的上部是分子，下部是分母。真分数的分子小于分母，假分数的分子大于或等于分母，带分数则包含一个整数和一个真分数。
plify a fraction by dividing the numerator and denominator by their highest common factor.
等价分数表示相同的值（如 ½ = 2/4）。可以通过将分子和分母同除以它们的最大公因数来化简分数。
ignificant figures give a rounded value based on the most meaningful digits. Percent means 'per hundred', so 30% = 30/100 = 0.3.
小数位数计算小数点后的数字个数；有效数字则是根据最有意义的数字进行四舍五入。百分比意为“每一百份”，因此 30% = 30/100 = 0.3。
al and multiply. Percentage increase or decrease uses the formula: change ÷ original × 100%.
求一个数的百分比时，将百分数化为小数再相乘。百分比增减用公式：变化量 ÷ 原数 × 100%。
A decimal that ends is terminating; one that repeats a pattern is recurring, often shown with a dot or bar. All fractions produce either terminating or recurring decimals.
有限小数会终止，循环小数则会重复一个模式，通常用点或横线表示。所有分数都会产生有限小数或循环小数。
3. Ratio and Proportion | 比与比例
A ratio compares two or more quantities, showing how many times one contains the other. It can be written as a : b. To simplify a ratio, divide all parts by their greatest common divisor.
比用于比较两个或更多的数量，显示一个数量包含另一个数量的倍数。可以写成 a : b 的形式。化简比时，将所有项都除以它们的最大公约数。
/d. In direct proportion, as one quantity increases, the other increases at the same rate. In inverse proportion, one increases while the other decreases.
比例是一个等式，表明两个比相等，例如 a/b = c/d。正比例中，一个量增加时，另一个量以相同速率增加。反比例中，一个量增加而另一个减少。
The unitary method finds the value of a single unit first, then multiplies to find the total. It is extremely useful for solving proportion problems step by step.
单位法先求出一个单位的值，再乘以所需数量得到总数。这种方法对于一步步解决比例问题非常有用。
Dividing a quantity in a given ratio involves finding the total number of parts first, then allocating shares accordingly. Ratios often appear in recipes, maps, and scale drawings.
按给定比分配量时，先求总份数，再相应分配份额。比经常出现在食谱、地图和比例图中。
4. Algebraic Expressions | 代数表达式
A variable is a letter that stands for an unknown number (e.g., x, y). A constant is a fixed number (e.g., 5, −3). A coefficient is the number multiplied by a variable (e.g., in 4x, 4 is the coefficient).
变量是表示未知数的字母（如 x、y）。常量是一个固定的数（如 5、−3）。系数是乘在变量前的数（例如 4x 中，4 是系数）。
A term is a single number, variable, or product of both, separated by + or − signs in an expression. Like terms have identical variable parts and can be combined by adding or subtracting their coefficients.
项是由加号或减号分隔的单个数字、变量或两者的乘积。同类项具有相同的变量部分，可以通过系数的加减来合并。
collect all like terms. Expanding means multiplying out brackets, e.g., 3(m + 2) = 3m + 6.
表达式是不含等号的一系列项的组合。化简表达式就是合并所有同类项。展开括号指将乘积乘出来，例如 3(m + 2) = 3m + 6。
highest common factor and put the rest inside brackets. For instance, 5x + 10 = 5(x + 2).
因式分解是展开的逆过程：提取最大公因数并把剩余部分放进括号里。例如 5x + 10 = 5(x + 2)。
5. Equations and Inequalities | 方程与不等式
ion true. Inequalities use symbols <, >, ≤, ≥ to show that one side is less than or greater than the other.
方程是用等号（=）连接两个表达式的语句，表示它们相等。方程的解就是使等式成立的变量的值。不等式使用 <、>、≤、≥ 符号表示一边小于或大于另一边。
The balance method means performing the same operation on both sides of an equation, keeping the two sides equal. This can involve adding, subtracting, multiplying, or dividing.
天平法指的是在方程两边进行相同的运算，保持两边相等。可以涉及加、减、乘、除。
When solving an inequality, the same rules apply as for equations, except when multiplying or dividing by a negative number, the inequality sign reverses direction.
解不等式时适用与方程相同的规则，唯一需要注意的是：当两边同乘或同除以一个负数时，不等号方向要改变。
Solutions can be shown on a number line: an open circle means the value is not included, a closed circle means it is included. The arrow indicates the direction of all values that satisfy the inequality.
解集可以在数轴上表示：空心圆圈表示该值不包含在内，实心圆圈表示包含在内。箭头指示满足不等式的所有值的范围方向。
6. Sequences and Patterns | 数列与规律
A sequence is an ordered list of numbers following a rule. Each number in the sequence is called a term. The rule that lets you find any term, often written as the nth term, uses n to represent the position in the sequence (1st, 2nd, 3rd, ...).
数列是按照某种规则排列的一串数字。数列中的每个数字称为一项。通项公式（通常写成第 n 项）让你可以求出任意项，其中 n 代表位置（第1项、第2项、第3项…）。
., 3, 7, 11, 15, ... where d = 4. The nth term is a + (n − 1)d, where a is the first term.
等差数列的相邻项之差（d）为常数，例如 3, 7, 11, 15, … 中 d = 4。通项公式为 a + (n − 1)d，其中 a 是首项。
., 2, 6, 18, 54, ... where r = 3. The nth term is arⁿ⁻¹. Notice the exponent uses (n − 1).
等比数列的相邻项之比（r）为常数，例如 2, 6, 18, 54, … 中 r = 3。通项公式为 arⁿ⁻¹。注意指数用到了 (n −
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