📚 Pre-U CCEA Science: Formula & Theorem Quick Reference Handbook | Pre-U CCEA 科学：公式定理速查手册
This handbook provides a concise, at-a-glance compilation of the essential formulas and theorems encountered in the Pre-U CCEA Science curriculum. Designed for rapid revision and last-minute checks, it covers core concepts in physics, chemistry, and the quantitative aspects of biology, helping you bridge theory with numerical problem-solving effectively.
本手册简明扼要地汇编了 Pre-U CCEA 科学课程中涉及的核心公式与定理，旨在帮助快速复习和考前速查。手册覆盖物理、化学的核心概念以及生物学中的定量内容，力求帮助你在理论与数值解题之间建立高效的联系。
1. Kinematics Equations | 运动学方程
The motion of an object under uniform acceleration is described by four SUVAT equations. These relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = ½ (u + v)t
物体在匀加速直线运动中的运动由四个 SUVAT 方程描述，这些方程关联了位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）。选择方程时需确认三个已知量，再求解第四个未知量。
2. Forces & Dynamics | 力与动力学
Newton’s second law establishes the direct proportionality between net force and acceleration. Momentum and impulse provide a complementary view on motion, especially during collisions.
F = ma
p = mv
FΔt = Δp
F = mv²/r = mω²r
牛顿第二定律表明了合外力与加速度的正比关系。动量与冲量为运动的分析提供了互补视角，尤其在碰撞类问题中。向心力公式用于匀速圆周运动，需明确向心力是合力而非单一性质的力。
3. Energy, Work & Power | 能量、功与功率
Energy can be stored as kinetic or potential energy and transferred via work done or heat. The principle of conservation of energy is fundamental to all scientific disciplines.
W = Fd cos θ
Eₖ = ½ mv²
Eₚ = mgh
P = W/t = Fv
能量可以动能或势能形式储存，并通过做功或热传递进行转移。能量守恒定律是所有科学分支的基石。计算功时必须注意力与位移的夹角，功率则表征做功的快慢。
4. Electricity & Circuits | 电学与电路
Ohm’s law and the rules for combining resistors in series and parallel are essential for circuit analysis. Power dissipation in a resistor can be expressed in three equivalent forms.
V = IR
R = ρL/A
Rₛₑᵣᵢₑₛ = R₁ + R₂ + …
1/Rₚₐᵣₐ = 1/R₁ + 1/R₂ + …
P = IV = I²R = V²/R
欧姆定律以及电阻串并联的法则是电路分析的基础。电阻消耗的功率有三种等价表达式，可根据已知量灵活选用。电动势与内阻的关系 V = ε – Ir 对于分析实际电源至关重要。
5. Waves & Optics | 波动与光学
The wave equation links speed, frequency and wavelength. Snell’s law and the critical angle condition govern refraction and total internal reflection.
v = f λ
n₁ sin θ₁ = n₂ sin θ₂
sin C = 1/n
Δx = λD/d
波动方程将波速、频率与波长联系起来。斯涅尔定律和临界角条件决定了折射与全反射行为。杨氏双缝干涉的条纹间距公式 Δx = λD/d 需明确各量的几何意义。
6. Gas Laws & Thermal Physics | 气体定律与热物理学
The ideal gas equation unifies Boyle’s, Charles’s and the pressure law. The first law of thermodynamics expresses conservation of energy in thermal processes.
pV = nRT
pV = NkT
ΔU = Q – W
理想气体状态方程统一了玻意耳定律、查理定律与压强定律。热力学第一定律 ΔU = Q – W 表达了热过程中能量的守恒，符号约定（系统对外做功取正）必须保持一致。
7. Moles & Stoichiometry | 摩尔与化学计量
The mole is the central unit for quantifying chemical amounts. Relating mass, volume of gas, and concentration to moles enables stoichiometric calculations.
n = m/M
n = V/Vₘ (Vₘ = 24.0 dm³ mol⁻¹ at RTP)
c = n/V
% yield = (actual yield/theoretical yield) × 100%
摩尔是量化化学物质的中心单位。将质量、气体体积和溶液浓度与物质的量关联，就能进行反应物与产物的定量计算。原子经济性与产率共同反映合成路径的效率。
8. Equilibrium & Kinetics | 化学平衡与速率
The equilibrium constant Kc summarises the position of equilibrium at a given temperature. Rate laws and the Arrhenius equation illuminate the factors controlling reaction speed.
Kc = [C]c[D]d / [A]a[B]b
rate = k[A]m[B]n
k = A e-Ea/(RT)
平衡常数 Kc 定量描述某一温度下的平衡位置，只随温度改变。速率方程和阿伦尼乌斯方程揭示了浓度、温度及活化能对反应速率的影响，催化剂通过降低 Ea 提高速率常数 k。
9. Acids, Bases & pH | 酸碱与 pH
The pH scale quantifies the acidity of aqueous solutions. The ionic product of water Kw and acid dissociation constant Ka describe the extent of proton transfer.
pH = -log₁₀[H⁺]
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (at 298 K)
Ka = [H⁺][A⁻]/[HA]
pH = pKa + log₁₀([A⁻]/[HA])
pH 标度量化了水溶液的酸度。水的离子积 Kw 和酸解离常数 Ka 描述了质子转移的程度。亨德森-哈塞尔巴尔赫方程用于缓冲溶液 pH 的计算，当 [A⁻] = [HA] 时 pH = pKa。
10. Genetics & Population Biology | 遗传学与群体生物学
The Hardy–Weinberg principle predicts allele and genotype frequencies in a non-evolving population, providing a null model for studying microevolution.
p + q = 1
p² + 2pq + q² = 1
哈代–温伯格原理预测了非进化群体中的等位基因频率和基因型频率，为微观进化的研究提供了零假设模型。应用时需确认群体满足无限大、随机交配、无选择 / 突变 / 迁移等条件。
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