📚 GCSE Edexcel Maths: Formula Summary Handbook | GCSE Edexcel 数学：公式汇总手册
This handbook is a comprehensive revision aid for GCSE Edexcel Mathematics, covering all the essential formulas required for the Foundation and Higher tiers. Each formula is clearly stated with a brief explanation of how it is used, followed by its Chinese translation. Use this resource for quick reference alongside past papers and revision guides.
本手册是GCSE Edexcel数学的综合复习参考资料，涵盖基础和高级考试中所有必备公式。每条公式都配有简要使用说明，并提供中文翻译。请将此资源与历年真题和复习指南配合使用，以便快速查阅。
1. Arithmetic and Number | 算术与数
Addition/Subtraction of Fractions: a/b ± c/d = (ad ± bc) / bd
To add or subtract fractions, first rewrite them with a common denominator (usually the product of the two denominators). Then simply add or subtract the numerators and keep the shared denominator.
分数的加减法需要先将分数化为同分母（通常取两个分母的乘积），然后分子相加减，分母保持不变。
Multiplication of Fractions: a/b × c/d = (a × c) / (b × d)
Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. Simplify the result if possible.
分数相乘直接将分子相乘、分母相乘即可，最后约简为最简分数。
Division of Fractions: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
To divide by a fraction, multiply by its reciprocal. Invert the second fraction and then carry out the multiplication.
除以一个分数等于乘以它的倒数。将被除数的分母和分子颠倒后，按乘法进行运算。
Order of Operations: BIDMAS
Remember BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction) to determine the correct order when evaluating an expression. Division and multiplication have equal priority, as do addition and subtraction.
进行四则混合运算时要遵守BIDMAS顺序：括号、指数、乘除（同级从左到右）、加减（同级从左到右）。
2. Percentages, Ratios and Proportion | 百分比、比例与比率
Percentage of an Amount: P% of X = (P / 100) × X
a quantity, convert the percentage to a decimal or fraction and multiply. For example, 15% of 200 is (15/100) × 200 = 30.
求某数的百分之几，先将百分数化为小数或分数，再乘以该数。例如，200的15%为 (15/100)×200 = 30。
Percentage Change: % Change = (New − Original) / Original × 100%
The formula gives a positive result for an increase and a negative result for a decrease. It is commonly used in comparing profits, discounts, and population changes.
百分比变化 = (新值 − 原值) / 原值 × 100%。结果为正表示增长，为负表示减少，常用于利润、折扣和人口变化。
Direct Proportion: y = kx
When two quantities are directly proportional, their ratio is constant. The graph is a straight line through the origin. k is the constant of proportionality.
两个量成正比关系时，y = kx，其中k是比例常数，图像是一条过原点的直线。
Inverse Proportion: y = k / x
ant (xy = k). The graph is a rectangular hyperbola. This appears in Higher tier questions.
反比例关系满足 y = k/x，即 xy = k，图像为双曲线。此知识点常见于高级卷。
3. Algebraic Manipulation | 代数运算
Index Law 1: am × an = am + n
When multiplying powers with the same base, add the exponents. For example, x³ × x² = x⁵.
同底数幂相乘，底数不变、指数相加。例如 x³ × x² = x⁵。
Index Law 2: (am)n = am × n
Raising a power to another power means multiplying the exponents. For example, (y²)⁴ = y⁸.
幂的乘方，指数相乘。例如 (y²)⁴ = y⁸。
Index Law 3: a⁰ = 1 (a ≠ 0) and a⁻ⁿ = 1 / aⁿ
Any non-zero number to the power zero equals 1. A negative exponent indicates the reciprocal of the positive power.
任何非零数的零次方等于1。负指数表示取该数正指数幂的倒数。
Expanding Double Brackets: (a + b)(c + d) = ac + ad + bc + bd
Use the FOIL method (First, Outer, Inner, Last) to expand products of two binomials. This is the foundation for quadratic expansions.
展开两个一次二项式的乘积时，使用首外内尾（FOIL）法则：(a+b)(c+d) = ac+ad+bc+bd，这是二次展开的基础。
Difference of Two Squares: a² − b² = (a + b)(a − b)
This special factorisation is very useful for simplifying expressions and solving quadratic equations. Always check for a difference of squares pattern.
平方差公式 a² − b² = (a+b)(a−b) 在因式分解和解方程中非常有用，看到两项平方相减应立即想到这一公式。
4. Equations and Inequalities | 方程与不等式
Quadratic Formula: x = [−b ± √b² − 4ac] /
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