📚 Year 7 AQA Chinese: Quick Reference Handbook of Formulas and Theorems | Year 7 AQA 中文：公式定理速查手册
Welcome to your bilingual quick-reference guide for Year 7 AQA Chinese. This handbook brings together the essential formulas, rules and theorems you encounter in mathematics and science, presented in both English and Chinese. Use it to build confidence in expressing mathematical ideas clearly in Mandarin, and to strengthen your understanding of key concepts across the curriculum.
欢迎使用这本双语速查手册，专为 Year 7 AQA 中文课程设计。本手册汇集了你在数学和科学中会遇到的必背公式、定理和法则，以中英对照的形式呈现。它可以帮你自信地用中文表达数学思想，同时加深对核心概念的理解。
1. Basic Arithmetic Laws | 基本运算法则
Addition and multiplication follow several universal laws. Knowing their Chinese names helps you discuss problems clearly in Mandarin.
加法和乘法遵循几条通用法则。记住它们的中文名称，有助于你用中文清晰地讨论问题。
Commutative law of addition: swapping the order of addends does not change the sum.
加法交换律：交换加数的位置，和不变。
a + b = b + a
Commutative law of multiplication: swapping factors does not change the product.
乘法交换律：交换因数的位置，积不变。
a × b = b × a
Associative law of addition: grouping addends differently does not affect the sum.
加法结合律：加数分组方式改变，和不变。
(a + b) + c = a + (b + c)
Associative law of multiplication: regrouping factors does not change the product.
乘法结合律：因数重新分组，积不变。
(a × b) × c = a × (b × c)
Distributive law: multiplying a number by a sum is the same as multiplying each addend separately and then adding the products.
分配律：一个数乘以两个数的和，等于把这个数分别乘以这两个加数，再把积相加。
a × (b + c) = a × b + a × c
2. Odd, Even, Prime and Composite Numbers | 奇数、偶数、质数与合数
Understanding number properties in Chinese builds a solid foundation for working with integers and factors.
掌握数字性质的中文表达，能为处理整数和因数打下坚实基础。
Even numbers (偶数) can be divided by 2 with no remainder: 2, 4, 6, 8 … Odd numbers (奇数) leave a remainder of 1 when divided by 2: 1, 3, 5, 7 …
偶数能被 2 整除，没有余数：2, 4, 6, 8 … 奇数除以 2 余 1：1, 3, 5, 7 …
Prime numbers (质数 or 素数) have exactly two factors: 1 and the number itself. The first few are 2, 3, 5, 7, 11. Composite numbers (合数) have more than two factors. The number 1 is neither prime nor composite.
质数（也叫素数）只有两个因数：1 和它本身。最小的几个质数是 2, 3, 5, 7, 11。合数有两个以上的因数。数字 1 既不是质数也不是合数。
Factors (因数) are numbers you multiply together to get another number. Multiples (倍数) are the results of multiplying a number by an integer.
因数是相乘得到某个数的数。倍数是一个数乘以整数得到的结果。
3. Fractions, Decimals and Percentages | 分数、小数和百分数
Being able to convert between fractions (分数), decimals (小数) and percentages (百分数) is an everyday skill. The Chinese terms make these relationships easy to remember.
能够在分数、小数和百分数之间灵活转换是一项日常技能。中文术语让这些关系更容易记忆。
To change a fraction to a decimal, divide the numerator by the denominator. Compare ½ = 1 ÷ 2 = 0.5.
把分数化成小数：用分子除以分母。例如 ½ = 1 ÷ 2 = 0.5。
分数 → 小数: a/b = a ÷ b
To change a decimal to a percentage, multiply by 100 and add the % sign. To change a percentage to a decimal, divide by 100.
把小数化成百分数：乘以 100 再加 % 号。百分数化小数：除以 100。
小数 × 100 = 百分数 ; 百分数 ÷ 100 = 小数
Common equivalents you should memorize:
你需要熟记下列常用等值：
| Fraction (分数) | Decimal (小数) | Percentage (百分数) |
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ¾ | 0.75 | 75% |
| ⅓ | 0.333… | 约 33.3% |
| 1/10 | 0.1 | 10% |
In Chinese, 百分之 (bǎi fēn zhī) means ‘percent’, so 25% is read as 百分之二十五 (literally ’25 out of 100′).
中文里，“百分之”表示百分数，所以 25% 读作“百分之二十五”。
4. Ratio and Proportion | 比率与比例
A ratio compares two quantities, while a proportion states that two ratios are equal. The Chinese word for ratio is 比 (bǐ), and proportion is 比例 (bǐlì).
比表示两个量之间的对比关系，比例则表明两个比相等。中文的“比”即 ratio，“比例”即 proportion。
If the ratio of boys to girls is 3 : 2, we say 男生与女生的比是 3 比 2. To simplify a ratio, divide both terms by their greatest common factor.
如果男生与女生的比是 3 : 2，我们就说“三比二”。要化简比，用各项的最大公因数同时去除。
a : b can be simplified to (a ÷ k) : (b ÷ k)
When two quantities are in direct proportion (正比例), their ratio stays constant. If y is proportional to x, then y = kx (k is a constant). In Chinese: 正比例关系，y 与 x 成正比，y = kx。
当两个量成正比例时，它们的比值保持不变。如果 y 与 x 成正比，那么 y = kx（k 为常数）。
5. Algebraic Foundations | 代数基础
Algebra uses letters to represent numbers. In Mandarin, we call these letters 字母 (zìmǔ) or 未知数 (wèizhīshù) when they stand for unknown values.
代数用字母表示数。这些字母在中文里叫“字母”或表示未知量时称“未知数”。
When multiplying a number and a letter, the multiplication sign is usually omitted: 3 × x is written as 3x. In Chinese we say 三 x (sān x).
数字与字母相乘时，乘号通常省略：3 × x 写作 3x，读作“三 x”。
a × b = ab ; a ÷ b = a/b
Like terms (同类项) can be combined. For example, 3x + 2x = 5x. The Chinese phrase is 合并同类项 (hébìng tónglèixiàng).
同类项可以合并。例如 3x + 2x = 5x，这个过程叫“合并同类项”。
To solve a simple equation, isolate the variable by performing inverse operations. For x + 5 = 12, subtract 5 from both sides: x = 12 − 5 = 7. The Chinese term for equation is 方程 (fāngchéng).
解简单方程时，通过逆运算把未知数分离出来。如 x + 5 = 12，两边同时减去 5，得 x = 12 − 5 = 7。“方程”就是 equation。
6. Perimeter and Area | 周长与面积
Perimeter (周长) is the distance around a shape. Area (面积) measures the space inside a flat shape. Both use units such as 厘米 (cm) and 平方米 (m²).
周长是指绕图形一周的长度，面积是平面图形内部的大小。常用单位有厘米和平方米。
Square: perimeter P = 4a, area A = a² (a = side length).
正方形：周长 = 边长 × 4，面积 = 边长 × 边长。
正方形周长: C = 4a ; 面积: S = a²
Rectangle: perimeter P = 2×(l + w), area A = l × w (l = length, w = width).
长方形：周长 = (长＋宽) × 2，面积 = 长 × 宽。
长方形周长: C = 2(l + w) ; 面积: S = lw
Triangle: area A = ½ × base × height.
三角形：面积 = 底 × 高 ÷ 2。
三角形面积: S = ½ × b × h
Parallelogram: area A = base × vertical height.
平行四边形：面积 = 底 × 垂直高。
For circles, the circumference is C = 2πr or C = πd, and the area is A = πr², where r is the radius and d is the diameter. Pi (π) is approximately 3.14 or 22/7. The Chinese name for pi is 圆周率 (yuánzhōulǜ).
圆的周长公式为 C = 2πr 或 C = πd，面积公式为 S = πr²，其中 r 是半径，d 是直径。圆周率 π 约等于 3.14 或 22/7，中文称为圆周率。
C = 2πr ; S = πr²
7. Volume and Surface Area | 体积与表面积
Volume (体积) measures how much space a 3D object occupies; surface area (表面积) is the total area of all its faces. In Year 7, we focus on cuboids and cubes.
体积衡量三维物体所占空间的大小，表面积是所有面的面积之和。Year 7 主要学习长方体和立方体。
Cuboid volume: V = length × width × height. In Chinese: 长方体体积 = 长 × 宽 × 高.
长方体体积 = 长 × 宽 × 高。
V = l × w × h
Cube: since all edges are equal (a), the volume V = a³. Surface area of a cube = 6a².
立方体：棱长为 a，体积 V = a³，表面积 = 6a²。
V = a³ ; S = 6a²
Cuboid surface area: SA = 2(lw + lh + wh). The Chinese phrase 表面积 is normally shortened to 表面积.
长方体表面积 = 2(长×宽 + 长×高 + 宽×高)。
8. Angles and Angle Rules | 角与角定理
Angles are measured in degrees (°). A right angle is exactly 90°, an acute angle is less than 90°, an obtuse angle is between 90° and 180°, and a reflex angle is greater than 180° but less than 360°. A straight line equals 180°.
角以度 (°) 为单位。直角恰好 90°，锐角小于 90°，钝角大于 90° 且小于 180°，优角大于 180° 小于 360°。平角为 180°。
Vertically opposite angles are equal. In Chinese: 对顶角相等.
对顶角相等。
对顶角: ∠AOB = ∠COD
Angles on a straight line add up to 180°. Angles around a point sum to 360°.
平角上的角之和为 180°。围绕一个点的所有角之和为 360°。
When a pair of parallel lines is cut by a transversal, corresponding angles (同位角) are equal, alternate interior angles (内错角) are equal, and co‑interior angles (同旁内角) sum to 180°. The Chinese keywords are 同位角相等, 内错角相等, 同旁内角互补.
一组平行线被截线所截时，同位角相等，内错角相等，同旁内角互补（和为 180°）。这些术语的中文是：同位角、内错角、同旁内角。
9. Angle Sum in Triangles and Quadrilaterals | 三角形和四边形的内角和
The sum of the interior angles of any triangle is 180°. In Mandarin, 三角形内角和为 180°.
任何三角形的三个内角之和为 180°。
∠A + ∠B + ∠C = 180°
The exterior angle of a triangle equals the sum of the two opposite interior angles. In Chinese: 三角形的一个外角等于与它不相邻的两个内角之和.
三角形的一个外角等于与它不相邻的两个内角之和。
For any quadrilateral, the sum of interior angles is 360°. You can prove it by dividing the quadrilateral into two triangles.
任意四边形的内角和为 360°。你可以把四边形分成两个三角形来证明。
四边形内角和 = 360°
10. Statistics: Mean, Median, Mode and Range | 统计：平均数、中位数、众数和极差
The mean (平均数) is calculated by adding all values and dividing by the number of
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