Pre-U CIE Mathematics: Quick Reference Formula and Theorem Handbook | Pre-U CIE 数学：公式定理速查手册

📚 Pre-U CIE Mathematics: Quick Reference Formula and Theorem Handbook | Pre-U CIE 数学：公式定理速查手册

This quick reference handbook covers essential formulas, theorems and standard results from the Cambridge Pre-U Mathematics syllabus (9777/9794). It serves as a concise revision tool to help you recall key algebraic, trigonometric, calculus, vector, complex number, probability and mechanics facts in one place.

本速查手册涵盖剑桥 Pre-U 数学教学大纲中的核心公式、定理与标准结论，是一份精炼的复习工具，帮助你在一个文档中快速回顾代数、三角、微积分、向量、复数、概率与力学的重要知识点。

1. Algebraic Identities and Formulae | 代数恒等式与公式

Square of a sum: (a + b)² = a² + 2ab + b²

和的平方：(a + b)² = a² + 2ab + b²

Square of a difference: (a – b)² = a² – 2ab + b²

差的平方：(a – b)² = a² – 2ab + b²

Difference of two squares: a² – b² = (a – b)(a + b)

平方差公式：a² – b² = (a – b)(a + b)

Binomial theorem for a positive integer n: (a + b)ⁿ = Σ (from r=0 to n) [ⁿCᵣ aⁿ⁻ʳ bʳ], where ⁿCᵣ = n! / [r! (n–r)!]

正整数指数二项式定理：(a + b)ⁿ = Σ(r=0到n) [ⁿCᵣ aⁿ⁻ʳ bʳ]，其中 ⁿCᵣ = n! / [r! (n–r)!]

Quadratic formula for ax² + bx + c = 0:

x = (–b ± √(b² – 4ac)) / (2a)

二次方程 ax² + bx + c = 0 的求根公式：

x = (–b ± √(b² – 4ac)) / (2a)

Discriminant: Δ = b² – 4ac. If Δ > 0, two distinct real roots; if Δ = 0, one repeated real root; if Δ < 0, no real roots.

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