📚 Year 9 Edexcel Mathematics: Formula & Theorem Quick Reference Handbook | Year 9 Edexcel 数学：公式定理速查手册
This handbook is your go-to revision guide, covering all the essential formulas and theorems you'll need for Year 9 Edexcel Mathematics. From basic algebra to geometry and statistics, master these key concepts to boost your confidence and exam performance.
本手册是你的终极复习指南，涵盖 Year 9 Edexcel 数学所有必备公式和定理。从基础代数到几何和统计，掌握这些核心概念，提升你的信心与考试成绩。
1. Order of Operations | 运算顺序
BIDMAS (or BODMAS) is the rule for the order of calculations: Brackets first, then Indices (powers and roots), then Division and Multiplication (working left to right), and finally Addition and Subtraction (working left to right).
BIDMAS（或 BODMAS）是运算顺序规则：先算括号，再算指数（乘方和开方），接着从左到右计算除法和乘法，最后从左到右计算加法和减法。
Division and multiplication have equal priority; addition and subtraction also have equal priority. If unsure, use brackets to make the order clear.
除法和乘法优先级相同；加法和减法也是如此。如果不确定，可使用括号使顺序清晰。
first: 3² = 9, 9 − 4 = 5, then multiplication: 2 × 5 = 10, finally addition: 8 + 10 = 18.
例如：8 + 2 × (3² − 4) → 先算括号：3² = 9，9 − 4 = 5，然后乘法：2 × 5 = 10，最后加法：8 + 10 = 18。
2. Algebraic Expressions | 代数表达式与化简
ised to the same power. You can add or subtract like terms: 3a + 5a = 8a, 7x² − 2x² = 5x².
同类项是指含有相同字母且指数相同的项。可以对同类项进行加减：3a + 5a = 8a，7x² − 2x² = 5x²。
g terms, multiply the coefficients and apply index laws to the variables: 4a × 3a² = 12a³.
项相乘时，系数相乘，字母部分应用指数法则：4a × 3a² = 12a³。
Always present algebraic expressions in simplified form, with terms usually ordered by descending powers.
代数表达式总是化为最简形式，项通常按降幂排列。
Simplifying: 2x + 5y − x + 3y = (2x − x) + (5y + 3y) = x + 8y
化简：2x + 5y − x + 3y = (2x − x) + (5y + 3y) = x + 8y
3. Solving Linear Equations | 解一元一次方程
To solve an equation, keep it balanced by performing the same operation on both sides. The goal is to isolate the unknown variable.
解方程时，在等式两边同时进行相同运算以保持平衡。目标是求出未知数。
Step 1: Eliminate added/subtracted terms by doing the inverse; Step 2: Eliminate multiplied/divided coefficients by doing the inverse; Step 3: Check your solution by substitution.
步骤1：通过逆运算消除加减项；步骤2：通过逆运算消除乘除系数；步骤3：将解代入原方程进行检验。
Solve 5x + 3 = 2x + 12. Subtract 2x: 3x + 3 = 12. Subtract 3: 3x = 9. Divide by 3: x = 3.
例如：解 5x + 3 = 2x + 12。两边减 2x：3x + 3 = 12。两边减 3：3x = 9。两边除以 3：x = 3。
General solution: ax + b = c ⇒ x = (c − b)/a (if a ≠ 0)
一般解法：ax + b = c ⇒ x = (c − b)/a (a ≠ 0)
4. Expanding and Factorising | 展开与因式分解
Expanding : Multiply each term inside brackets by the factor outside. a(b + c) = ab + ac. For two brackets, (a + b)(c + d) = ac + ad + bc + bd.
展开：将括号外的因数乘以括号内的每一项。a(b + c) = ab + ac。两个括号相乘：(a + b)(c + d
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