📚 AS CCEA Science: Formula and Theorem Quick Reference Handbook | AS CCEA 科学：公式定理速查手册
This quick reference handbook brings together the essential formulas and theorems you need for the AS CCEA Science specification. It covers core concepts from physics, chemistry and biology and presents each key relationship in a clear, bilingual format to support both understanding and exam revision.
这本速查手册汇集了 AS CCEA 科学课程所需的基本公式与定理。它涵盖物理、化学和生物的核心概念，并以清晰的双语形式呈现每一个关键关系，帮助理解和考试复习。
1. Equations of Motion (Physics) | 运动学方程（物理）
For an object moving with uniform acceleration a, initial velocity u, final velocity v, displacement s and time t, the four SUVAT equations apply. Always choose a consistent sign convention for direction.
对于匀加速直线运动，初速度 u，末速度 v，位移 s，加速度 a 和时间 t，四个 SUVAT 方程适用。必须为方向确定一致的符号约定。
v = u + at
Final velocity equals initial velocity plus acceleration multiplied by time.
末速度等于初速度加上加速度乘以时间。
s = ut + ½at²
Displacement when the object starts with initial velocity u and accelerates uniformly.
物体以初速度 u 匀加速运动时的位移。
s = ½(u + v)t
Displacement using average velocity; valid only when acceleration is constant.
用平均速度求位移；仅在加速度恒定时有效。
v² = u² + 2as
Links final speed, initial speed, acceleration and displacement without requiring time.
将末速度、初速度、加速度和位移联系起来，不涉及时间。
2. Forces and Newton’s Laws (Physics) | 力与牛顿定律（物理）
Newton's second law states that the resultant force on an object is proportional to its rate of change of momentum. For constant mass, the most commonly used form is given below.
牛顿第二定律指出，物体所受的合力与其动量的变化率成正比。当质量恒定时，最常用的形式如下。
F = ma
Resultant force F equals mass m multiplied by acceleration a. The unit of force is the newton (N).
合力 F 等于质量 m 乘以加速度 a。力的单位是牛顿 (N)。
Weight W is the gravitational force on a mass: W = mg, where g is gravitational field strength (9.81 m s⁻² on Earth).
重量 W 是作用在物体上的重力：W = mg，其中 g 为重力场强度（地球表面约为 9.81 m s⁻²）。
Coefficient of friction μ relates frictional force F to normal reaction R: F = μR.
摩擦系数 μ 将摩擦力 F 与法向反力 R 联系起来：F = μR。
3. Work, Energy and Power (Physics) | 功、能与功率（物理）
Work done W by a constant force F moving an object through displacement s when the force and displacement are parallel: W = Fs. When the force acts at angle θ to the displacement: W = Fs cosθ.
恒力 F 使物体沿力的方向发生位移 s 所做的功：W = Fs。当力与位移成 θ 角时：W = Fs cosθ。
Kinetic energy: Eₖ = ½mv². Gravitational potential energy near Earth's surface: Eₚ = mgh.
动能：Eₖ = ½mv²。重力势能（近地表面）：Eₚ = mgh。
Principle of conservation of energy: total energy in a closed system remains constant, though it may be transformed between forms. Power P is the rate of doing work: P = W/t = Fv.
能量守恒定律：封闭系统的总能量保持不变，但可以在不同形式之间转化。功率 P 是做功的快慢：P = W/t = Fv。
4. Wave Properties (Physics) | 波的性质（物理）
The wave speed v, frequency f and wavelength λ are related by the wave equation. This applies to both transverse and longitudinal waves.
波速 v、频率 f 和波长 λ 通过波动方程相互联系，适用于横波和纵波。
v = fλ
Wave speed equals frequency multiplied by wavelength. Units: m s⁻¹ = Hz × m.
波速等于频率乘以波长。单位：米/秒 = 赫兹 × 米。
Refractive index n of a medium: n = c/v, where c is the speed of light in vacuum. Snell's law: n₁ sinθ₁ = n₂ sinθ₂.
介质的折射率 n：n = c/v，其中 c 为真空中光速。斯涅耳定律：n₁ sinθ₁ = n₂ sinθ₂。
5. Electricity and Circuits (Physics) | 电学与电路（物理）
Ohm's law for a metallic conductor at constant temperature: potential difference V is directly proportional to current I, with resistance R as the constant of proportionality.
欧姆定律（恒温下金属导体）：电势差 V 与电流 I 成正比，比例常数为电阻 R。
V = IR
Resistance leads to the equation R = V/I. Electrical power: P = IV = I²R = V²/R.
电阻公式 R = V/I。电功率：P = IV = I²R = V²/R。
In series circuits, total resistance Rₜ = R₁ + R₂ + R₃ + …. In parallel circuits, 1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + …. Charge Q = It.
串联电路总电阻：Rₜ = R₁ + R₂ + R₃ + …。并联电路：1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + …。电荷量：Q = It。
6. The Mole and Stoichiometry (Chemistry) | 摩尔与化学计量（化学）
amount of substance; one mole contains 6.022 × 10²³ specified particles (Avogadro constant Nₐ). The mass of one mole of a substance is its molar mass M in g mol⁻¹.
摩尔是物质的量的 SI 单位；1 摩尔包含 6.022 × 10²³ 个指定粒子（阿伏伽德罗常数 Nₐ）。1 摩尔物质的质量即其摩尔质量 M，单位为 g mol⁻¹。
n = m/M
Amount of substance n (mol) equals mass m (g) divided by molar mass M (g mol⁻¹).
物质的量 n (mol) 等于质量 m (g) 除以摩尔质量 M (g mol⁻¹)。
For solutions, concentration c (mol dm⁻³): n = cV, where V is volume in dm³. At room temperature and pressure (RTP), one mole of any gas occupies 24.0 dm³.
对于溶液，浓度 c (mol dm⁻³)：n = cV，其中 V 为体积 (dm³)。在常温常压下，1 摩尔任何气体体积为 24.0 dm³。
7. Enthalpy Changes (Chemistry) | 焓变（化学）
The enthalpy change ΔH for a reaction is calculated using the equation that relates heat transferred to mass, specific heat capacity and temperature change. In solution, the experiment typically uses a calorimeter.
反应的焓变 ΔH 可通过热量传递与质量、比热容及温度变化的关系式计算。溶液反应常用量热计测量。
q = mcΔT
Heat change q (J) = mass m (g) × specific heat capacity c (J g⁻¹ K⁻¹) × temperature change ΔT (K or °C).
热量变化 q (J) = 质量 m (g) × 比热容 c (J g⁻¹ K⁻¹) × 温度变化 ΔT (K 或 °C)。
Then ΔH = –q/n, where n is the amount of limiting reactant. For combustion, enthalpy of combustion ΔH꜀ is always negative. Hess's law states that the total enthalpy change for a reaction is independent of the route taken.
然后 ΔH = –q/n，其中 n 为限量反应物的物质的量。燃烧焓 ΔH꜀ 总为负值。盖斯定律指出，反应的总焓变与途径无关。
8. Bond Enthalpies and Reaction (Chemistry) | 键焓与反应（化学）
Mean bond enthalpy is the energy required to break one mole of a specific covalent bond in the gaseous state, averaged over a range of compounds. Enthalpy change can be estimated using bond energies.
平均键焓是在气态下断裂 1 摩尔特定共价键所需的能量，并在一系列化合物中取平均值。焓变可用键能估算。
ΔH ≈ Σ(bonds broken) – Σ(bonds formed)
Energy is absorbed to break bonds (endothermic, positive); energy is released when bonds form (exothermic, negative). The net enthalpy change indicates whether the reaction is overall exothermic or endothermic.
断裂化学键吸收能量（吸热，正值）；形成化学键释放能量（放热，负值）。净焓变表明反应总体上放热还是吸热。
9. Biological Molecules (Biology) | 生物分子（生物）
Carbohydrates have the general formula (CH₂O)ₙ. Monosaccharides like glucose (C₆H₁₂O₆) are the monomers; two monosaccharides join by a glycosidic bond in a condensation reaction releasing water.
碳水化合物的通式为 (CH₂O)ₙ。单糖如葡萄糖 (C₆H₁₂O₆) 是单体；两个单糖通过糖苷键在缩合反应中连接，释放出水。
Proteins are polymers of amino acids joined by peptide bonds. Each amino acid has an amino group (–NH₂), a carboxyl group (–COOH) and a variable R group. The primary structure is the sequence of amino acids.
蛋白质是由氨基酸通过肽键连接而成的多聚体。每个氨基酸含有一个氨基 (–NH₂)、一个羧基 (–COOH) 和一个可变的 R 基团。一级结构是氨基酸的序列。
Lipids are triglycerides formed from glycerol and three fatty acids by ester bonds. Phospholipids have a phosphate group, making one end hydrophilic and the other hydrophobic – critical for cell membranes.
脂类是由甘油和三个脂肪酸通过酯键形成的甘油三酯。磷脂含有磷酸基团，使一端亲水、另一端疏水，这对细胞膜至关重要。
10. Cell Structure and Membranes (Biology) | 细胞结构与膜（生物）
The fluid mosaic model describes the cell membrane as a phospholipid bilayer with embedded proteins, cholesterol and glycoproteins. Transport across membranes may be passive (diffusion, facilitated diffusion, osmosis) or active (requiring ATP).
流动镶嵌模型将细胞膜描述为磷脂双分子层，其中嵌有蛋白质、胆固醇和糖蛋白。跨膜运输可分为被动运输（扩散、易化扩散、渗透）或主动运输（需 ATP）。
= Ψₛ + Ψₚ; in animal cells, water potential is determined mainly by solute potential Ψₛ = –iCRT, where i is the ionisation constant, C is molar concentration, R is the pressure constant and T is temperature in kelvin.
水势 Ψ = Ψₛ + Ψₚ；在动物细胞中，水势主要由溶质势决定，Ψₛ = –iCRT，其中 i 为电离常数，C 为摩尔浓度，R 为压力常数，T 为开尔文温度。
Magnification formula: Magnification = Image size ÷ Actual size. For enzyme–substrate complexes, the lock-and-key and induced-fit models explain specificity.
放大倍数公式：放大倍数 = 图像大小 ÷ 实际大小。对于酶–底物复合物，锁钥模型和诱导契合模型解释了特异性。
11. Genetics and Inheritance (Biology) | 遗传与继承（生物）
Monohybrid inheritance follows Mendel' es (Aa × Aa) is 1 AA : 2 Aa : 1 aa, giving a phenotypic ratio of 3:1 for a dominant trait.
单性状遗传遵循孟德尔分离定律。使用旁氏表，杂合子杂交 (Aa × Aa) 的基因型比为 1 AA : 2 Aa : 1 aa，显性性状的表型比为 3:1。
Codominance – both alleles express equally (e.g. blood groups A and B producing AB). Hardy–Weinberg principle for a population in equilibrium: p² + 2pq + q² = 1 and p + q = 1, where p and q are allele frequencies.
共显性——两个等位基因均等表达（例如血型 A 和 B 产生 AB 型）。平衡种群的哈迪–温伯格定律：p² + 2pq + q² = 1 且 p + q = 1，其中 p 和 q 为等位基因频率。
The chi-squared (χ²) test for goodness of fit: χ² = Σ[(O – E)² / E], where O is the observed frequency and E is the expected frequency. Compare with critical value at appropriate degrees of freedom.
拟合优度卡方 (χ²) 检验：χ² = Σ[(O – E)² / E]，其中 O 为观察值，E 为预期值。与相应自由度下的临界值比较。
12. Gas Laws and Kinetic Theory (Physics) | 气体定律与分子运动论（物理）
The ideal gas law combines Boyle's, Charles's and the pressure law into a single relationship linking pressure p, volume V, amount n and temperature T (in kelvin).
理想气体定律将玻意耳定律、查理定律和压力定律结合为一个关系式，将压强 p、体积 V、物质的量 n 和热力学温度 T 联系起来。
pV = nRT
R is the molar gas constant (8.31 J mol⁻¹ K⁻¹). For a fixed mass of gas, pV/T = constant. The kinetic theory equation links macroscopic pressure to microscopic molecular speed: p = ⅓ρ⟨c²⟩, where ρ is density and ⟨c²⟩ is mean square speed.
R 为摩尔气体常数 (8.31 J mol⁻¹ K⁻¹)。对于一定质量气体，pV/T = 常数。分子运动论方程将宏观压强与微观分子速率联系起来：p = ⅓ρ⟨c²⟩，其中 ρ 为密度，⟨c²⟩ 为均方速率。
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