📚 Year 7 CAIE Advanced Mathematics: Key Terms Rapid Memorisation Guide | Year 7 CAIE 进阶数学：词汇术语速记指南
Mastering mathematical vocabulary is the first step to excelling in Year 7 CAIE Advanced Mathematics. This guide provides clear definitions with memory tips in both English and Chinese to help you internalise key terms quickly and confidently. Every section pairs English explanations with their Chinese equivalents, making it easier to recall both the concept and the language of mathematics.
掌握数学词汇是学好 Year 7 CAIE 进阶数学的第一步。本指南提供清晰的中英文定义与记忆技巧，助你快速且自信地内化核心术语。每个小节都将英文解释与中文释义配对呈现，让你轻松记住概念和数学语言。
1. Number Types | 数字类型
Natural numbers: The counting numbers starting from 1: 1, 2, 3, 4, ... Think of 'nature'—you naturally start counting from 1.
自然数： 从 1 开始的计数数字：1, 2, 3, 4, ... 联想“自然”—我们计数时自然就从 1 开始。
Whole numbers: All natural numbers together with 0: 0, 1, 2, 3, ... 'Whole' suggests you have a complete set including zero.
整数（非负整数）： 所有自然数和零的集合：0, 1, 2, 3, ... “整”表示你不缺零，完整的数。
Integers: All positive and negative whole numbers, including zero: ..., -2, -1, 0, 1, 2, ... The prefix 'in-' means 'no,' but here think of it as including the negatives too.
整数（含负）： 所有正负非小数数以及零：..., -2, -1, 0, 1, 2, ... 虽然“整”常指完整，但这里的核心是把负数也看作完整的计数单位。
Prime number: A natural number greater than 1 that has exactly two distinct factors: 1 and itself. For example, 7 is prime. Remember 'prime' as 'primary'—the most basic building blocks.
质数（素数）： 大于 1 的自然数，且只有两个不同的因数：1 和它本身。例如 7 是质数。把“质”想成“本质”——最基本的构成单元。
Composite number: A natural number greater than 1 that has more than two factors. 12 is composite (1, 2, 3, 4, 6, 12). It is composed of prime factors.
合数： 大于 1 的自然数，且有多于两个因数。12 是合数（因数 1, 2, 3, 4, 6, 12）。它是由质数“合成”的。
Square number: r by : The result of multiplying an integer by itself, e.g. 9 = 3 × 3. Visualise a square made of dots; 9 dots form a 3 by 3 square.
平方数： 一个整数自己乘自己的结果，如 9 = 3 × 3。想象一个点阵组成的正方形；9 个点能排成 3×3 的方形。
Cube number: The result of multiplying an integer twice by itself, e.g. 8 = 2 × 2 × 2. Think of a Rubik's cube with layers.
立方数： 一个整数连乘三次的结果，如 8 = 2 × 2 × 2。联想魔方的层数——长、宽、高各 2 个单位。
Factor: A whole number that divides another number exactly, leaving no remainder. 4 is a factor of 12. Picture a 'factory' that produces the number by multiplying with another factor.
因数（因子）： 可以整除另一个整数的数，不留余数。4 是 12 的因数。想象一个“工厂”，它与另一个因数相乘就生产出该数。
Multiple: The product of a number and any integer. Multiples of 5 are 5, 10, 15, ... It is like multiple copies of the original number added together.
倍数： 一个数与任意整数的乘积。5 的倍数有 5, 10, 15, ... 就像把原来的数重复相加多次。
Highest common factor (HCF): The largest factor shared by two or more numbers. For 12 and 18, the HCF is 6. Use a Venn diagram of prime factors to find it quickly.
最大公因数（HCF）： 两个或多个数共有的最大因数。12 和 18 的最大公因数是 6。用质因数做维恩图可以快速找到。
Lowest common multiple (LCM): The smallest multiple that two or more numbers share. For 4 and 6, the LCM is 12. Think of the first time both 'rhythms' meet.
最小公倍数（LCM）： 两个或多个数共有的最小倍数。4 和 6 的最小公倍数是 12。想象两条节奏线最早重合的时刻。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
Fraction: A part of a whole, written as numerator over denominator. The line means division.
分数： 整体的一部分，写作分子/分母。分数线表示除法。
Numerator: The top number of a fraction, telling how many parts we have. 'Numerate' means to count—it counts the parts.
分子： 分数线上方的数，表示取了多少份。“分子”像“计数的人”，数出我们拥有的份数。
Denominator: The bottom number, indicating how many equal parts the whole is divided into. 'De-' sounds like 'down', the bottom part.
分母： 分数线下方的数，表示整体被分成了多少等份。“分母”好比“地上”的基数，“De-”让你联想到底部。
Equivalent fractions: You get them by multiplying or dividing both numerator and denominator by the same number.
等值分数： 表示相同数值的不同分数，如 1/2 = 2/4。通过对分子分母同乘或同除一个数得到。
Proper fraction: A fraction where the numerator is smaller than the denominator, so the value is less than 1. 3/5 is proper.
真分数： 分子小于分母的分数，值小于 1。3/5 是真分数。
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, like 7/4. 'Improper' only means it is not in the usual less-than-one form.
假分数： 分子大于或等于分母的分数，如 7/4。“假”不是错误，仅表示它不是小于 1 的常规形式。
Mixed number: A whole number combined with a proper fraction, e.g. 2 1/4. It is a mix of whole and fractional parts.
带分数： 整数与真分数结合的形式，如 2 1/4。是整数与分数部分的混合体。
Decimal: A number expressed in the base-10 system using a decimal point. The digits after the point show tenths, hundredths, etc.
小数： 用十进制和小数点表示的数。点后的数字依次表示十分位、百分位……
Decimal place: The position of a digit after the decimal point. The first decimal place is tenths, the second is hundredths.
小数位： 小数点后数字的位置。第一位是十分位，第二位是百分位。
Percentage: A fraction with denominator 100, denoted by %. 45% means 45 out of 100. Think 'per cent' = per hundred.
百分比： 分母为 100 的分数，用 % 表示。45% 即每 100 份里的 45 份。“百分”望文生义——每一百。
Convert: To change a number from one form to another, e.g. fraction to decimal: divide numerator by denominator.
转换： 将数从一种形式变成另一种，如分数转小数：用分子除以分母。
3. Algebraic Expressions | 代数表达式
Variable: A letter or symbol that stands for an unknown number. In 3x + 2, x is the variable. It can vary—take different values.
变量： 代表未知数的字母或符号。在 3x + 2 中，x 是变量。它可变——取不同的值。
Constant: A fixed numerical value that does not change. In 5x + 7, 7 is a constant.
常量： 固定不变的数值。在 5x + 7 中，7 是常量。
Coefficient: The number multiplying a variable. In 4y, the coefficient of y is 4. Think 'co-' together with the variable.
系数： 乘在变量前面的数。在 4y 中，y 的系数是 4。它与变量“协同”出现。
Term: A single number, variable, or product of numbers and variables. 3x is a term; 3x + 5 has two terms.
项： 单个的数字、变量或数与变量的乘积。3x 是一项；3x + 5 有两项。
Expression: A mathematical phrase combining terms with operations, with no equals sign. 2a + b is an expression.
表达式： 由项和运算符号组成的数学短语，没有等号。2a + b 是一个表达式。
Like terms: Terms that have exactly the same variable parts and powers. 2x and -5x are like terms; 3x² and 4x are unlike.
同类项： 变量部分和指数完全相同的项。2x 和 -5x 是同类项；3x² 与 4x 不是。
Simplify: To combine like terms and reduce an expression to its simplest form. 3x + 2x simplifies to 5x.
化简： 合并同类项，将表达式化为最简形式。3x + 2x 化简为 5x。
Expand: To multiply out brackets using the distributive law. 3(a + 2) expands to 3a + 6.
展开： 利用分配律去掉括号。3(a + 2) 展开得 3a + 6。
Factorise: The reverse of expanding: write an expression as a product of its factors. 3a + 6 factorises to 3(a + 2).
因式分解： 展开的逆运算：把一个表达式写成它的因式的乘积。3a + 6 可分解为 3(a + 2)。
Substitution: Replacing a variable with a given number. If x = 4, then 2x + 1 becomes 9.
代入： 用给定数字替换变量。若 x = 4，则 2x + 1 变为 9。
4. Equations and Inequalities | 方程与不等式
Equation: tement that two expressions are equal, shown by an equals sign. 2x + 1 = 7 is an equation.
方程： 表明两个表达式相等的陈述，用等号连接。2x + 1 = 7 是一个方程。
Solve: To find the value of the unknown that makes the equation true.
解（求解）： 找出使方程成立的未知数的值。
Solution (or root): e value of the variable that satisfies the equation. For x + 3 = 5, the solution is x = 2.
解（根）： 满足方程的变量的值。对于 x + 3 = 5，解是 x = 2。
Unknown: The variable we are trying to find in an equation.
未知数： 方程中我们试图找出的变量。
Inequality: quantities using <, >, ≤, or ≥. It shows one side is greater or less than the other.
不等式： 用 <、>、≤、≥ 比较两个量的数学语句。说明一边大于或小于另一边。
Strict inequality: Uses < or > and does not include the boundary value. x > 3 means x is strictly greater than 3, not equal to 3.
严格不等式： 使用 < 或 >，不包括边界值。x > 3 表示 x 严格大于 3，不能等于 3。
Balance method: A way to solve equations by performing the same operation on both sides to keep the equation balanced. Think of a set of scales.
平衡法： 通过对方程两边同时进行同样运算来求解的方法。想象天平的两端始终平衡。
5. Sequences and Functions | 数列与函数
Sequence: An ordered list of numbers following a rule. 2, 4, 6, 8, ... is a sequence.
数列： 按照某一规则排列的一列数。2, 4, 6, 8, ... 是数列。
Term (of a sequence): Each number in a sequence. The 1st term is the first number, denoted T₁.
项（数列项）： 数列中的每一个数。第 1 项是第一个数，记为 T₁。
nth term: An algebraic rule that gives the term in the nᵗʰ position. For 3, 5, 7, 9, ... the nᵗʰ term is 2n + 1.
第 n 项（通项公式）： 给出第 n 个位置数值的代数规则。数列 3, 5, 7, 9, ... 的通项公式是 2n + 1。
Arithmetic sequence: A sequence where each term is found by adding a constant difference, e.g. 5, 9, 13, 17, ... (difference 4).
等差数列： 每一项都通过加上一个固定差值得到的数列，如 5, 9, 13, 17, ...（公差 4）。
Linear sequence: Another name for arithmetic sequence, because its graph forms a straight line.
线性数列： 等差数列的别称，因为它的图像是一条直线。
Function: ut and produces exactly one output. Often written as f(x) = 2x. Think of a number machine.
函数： 一种将输入转换成唯一输出的规则。常写作 f(x) = 2x。可想象成一台数字加工器。
Input (x) and output (y): ou put in is the input; the result is the output. If f(x) = x + 3, input 2 gives output 5.
输入与输出： 函数中放进的值是输入，得到的结果是输出。若 f(x) = x + 3，输入 2 得到输出 5。
Mapping: A diagram showing the relationship between inputs and outputs. It pairs each input with its output.
映射： 展示输入与输出关系的图表。把每一个输入与其输出配对。
6. Geometry: Angles and Lines | 几何：角与线
Angle: The space between two intersecting lines measured in degrees. The vertex is the corner point.
角： 两条相交线间的空间，以度计量。交点称为顶点。
Acute angle: An angle less than 90°. Think of a 'cute' small angle.
锐角： 小于 90° 的角。联想“尖锐”——小小的角。
Right angle: Exactly 90°, often marked with a small square. It represents a quarter turn.
直角： 恰好 90° 的角，常标以小方框。表示四分之一圈。
Obtuse angle: Greater than 90° but less than 180°. 'Obtuse' sounds like 'obese'—a 'fat' angle.
钝角： 大于 90° 且小于 180° 的角。联想“钝”表示不锋利，一种“胖胖的”角。
Reflex angle: Greater than 180° but less than 360°. It 'reflects' the other way around the full circle.
优角： 大于 180° 且小于 360° 的角。它“反射”了圆的其他部分。
Straight angle: Exactly 180°, forming a straight line.
平角： 恰好 180° 的角，形成一直线。
Complementary angles: Two angles that add up to 90°. 'Complement' with 'complete' a right angle.
互余角： 和为 90° 的两个角。它们“互补”成一个直角。
Supplementary angles: Two angles that sum to 180°. They 'supply' what's needed to make a straight line.
互补角： 和为 180° 的两个角。它们“补充”成一条直线。
Parallel lines: Lines that never meet and stay the same distance apart. Think of railway tracks.
平行线： 永不相交、距离保持不变的线。联想铁轨。
Perpendicular lines: Lines that intersect at a right angle (90°). The symbol is ⊥.
垂直线： 相交成直角（90°）的两条线。符号是 ⊥。
Transversal: A line that cuts across two or more lines, creating various angle relationships.
截线： 横穿两条或多条线的直线，产生不同的角关系。
7. Perimeter, Area and Volume | 周长、面积与体积
Perimeter: The total distance around a 2D shape. Add all side lengths. 'Peri' means around, 'meter' measures.
周长： 二维图形一周的总长度。将所有边长相加。“周”就是一圈的意思。
Area: : The amount of surface a shape covers, measured in square units. For a rectangle, area = length × width.
面积： 图形覆盖的平面大小，用平方单位计量。矩形面积 = 长 × 宽。
Volume: object occupies, measured in cubic units. For a cuboid, volume = length × width × height.
体积： 三维物体所占空间，用立方单位计量。长方体体积 = 长 × 宽 × 高。
Capacity: The amount a container can hold, often linked to volume but used for liquids.
容量： 容器能容纳的量，常与体积关联，用于液体。
Square unit: A unit of area such as cm² (square centimetre). It is a square 1 cm by 1 cm.
平方单位： 面积单位，如 cm²（平方厘米）。即边长为 1 cm 的正方形。
Cubic unit: A unit of volume such as cm³ (cubic centimetre). Imagine a 1 cm × 1 cm × 1 cm cube.
立方单位： 体积单位，如 cm³（立方厘米）。想象边长为 1 cm 的小立方体。
Formula for area of triangle
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