📚 AS CIE Science: Formula & Theorem Quick Reference | AS CIE 科学：公式定理速查手册
This quick reference handbook compiles essential formulas, laws, and theorems from the AS Level CIE Science curriculum, covering Physics, Chemistry, and Biology. It is designed to help you review key quantitative and qualitative relationships efficiently before exams.
本速查手册汇编了 AS Level CIE 科学课程（涵盖物理、化学和生物）中的基本公式、定律和定理，旨在帮助你在考前高效复习关键的定量与定性关系。
1. Kinematics & Dynamics | 运动学与动力学
v = u + at gives final velocity for uniform acceleration, where u is initial velocity, a is acceleration, and t is time.
v = u + at 描述匀加速直线运动的末速度，其中 u 为初速度，a 为加速度，t 为时间。
Displacement with constant acceleration: s = ut + ½at².
匀加速直线运动的位移：s = ut + ½at²。
A velocity–displacement relation: v² = u² + 2as.
速度与位移的关系式：v² = u² + 2as。
Average-velocity form: s = ½(u + v)t.
平均速度形式的位移公式：s = ½(u + v)t。
Newton’s Second Law: F = ma (resultant force = mass × acceleration).
牛顿第二定律：F = ma（合力 = 质量 × 加速度）。
Linear momentum: p = mv; impulse: Δp = FΔt (force × time).
线动量：p = mv；冲量：Δp = FΔt（力 × 时间）。
Principle of conservation of momentum: total momentum before collision = total momentum after, in a closed system.
动量守恒定律：在封闭系统中，碰撞前的总动量等于碰撞后的总动量。
2. Energy, Work & Power | 能量、功与功率
Work done by a force: W = Fd cos θ, where θ is the angle between force and displacement.
力做的功：W = Fd cos θ，θ 为力与位移间的夹角。
Kinetic energy: Eₖ = ½mv².
动能：Eₖ = ½mv²。
Gravitational potential energy near Earth’s surface: Eₚ = mgh.
地表附近的重力势能：Eₚ = mgh。
Power (work rate): P = W / t; also P = Fv for constant force and velocity in same direction.
功率：P = W / t；当力与速度同向时也可写作 P = Fv。
Principle of conservation of energy: energy cannot be created or destroyed, only transferred or transformed.
能量守恒定律：能量不会凭空产生或消失，只能转移或转化。
3. Waves & Optics | 波与光学
Wave speed: v = fλ (frequency × wavelength).
波速：v = fλ（频率 × 波长）。
Refractive index: n = c / v, where c is the speed of light in vacuum.
折射率：n = c / v，c 为真空光速。
Snell’s law: n₁ sin θ₁ = n₂ sin θ₂.
斯涅耳定律：n₁ sin θ₁ = n₂ sin θ₂。
Critical angle for total internal reflection: sin c = 1 / n (when going from optically denser to rarer medium).
全反射的临界角：sin c = 1 / n（从光密介质到光疏介质时）。
Thin lens formula: 1/f = 1/u + 1/v, with real‑is‑positive sign convention. Magnification: m = v / u.
薄透镜公式：1/f = 1/u + 1/v（实正虚负符号规则）。放大率：m = v / u。
4. Electricity & Magnetism | 电学与磁学
Ohm’s law: V = IR for a fixed resistor at constant temperature.
欧姆定律：恒温下固定电阻满足 V = IR。
Resistance of a uniform wire: R = ρL / A (resistivity × length / cross‑sectional area).
均匀导线的电阻：R = ρL / A（电阻率 × 长度 / 横截面积）。
Electrical power: P = IV = I²R = V² / R.
电功率：P = IV = I²R = V² / R。
Resistors in series: Rₜ = R₁ + R₂ + …; in parallel: 1/Rₜ = 1/R₁ + 1/R₂ + ….
电阻串联：Rₜ = R₁ + R₂ + …；并联：1/Rₜ = 1/R₁ + 1/R₂ + …。
Kirchhoff’s current law: sum of currents entering a junction = sum of currents leaving. Voltage law: sum of e.m.f.s = sum of p.d.s around a closed loop.
基尔霍夫电流定律：流入节点的电流和等于流出节点的电流和。电压定律：闭合回路中，电动势的代数和等于各段电压降的代数和。
Potential divider: Vₒᵤₜ = Vₛ × (R₂ / (R₁ + R₂)).
分压电路：Vₒᵤₜ = Vₛ × (R₂ / (R₁ + R₂))。
5. Thermal Physics & States of Matter | 热物理与物质状态
Kelvin temperature: T / K = θ / °C + 273.
开尔文温度：T / K = θ / °C + 273。
Thermal energy without phase change: Q = mcΔθ (mass × specific heat capacity × temperature change).
无相变时的热量：Q = mcΔθ（质量 × 比热容 × 温度变化）。
Latent heat during phase change: Q = mL (mass × specific latent heat).
相变时的潜热：Q = mL（质量 × 比潜热）。
Ideal gas equation: pV = nRT (pressure × volume = moles × molar gas constant × Kelvin temperature).
理想气体状态方程：pV = nRT（压强 × 体积 = 物质的量 × 摩尔气体常数 × 开尔文温度）。
Boyle’s law: pV = constant (at constant T); Charles’s law: V/T = constant (at constant p); Pressure law: p/T = constant (at constant V).
玻意耳定律：pV = 常数（恒温）；查理定律：V/T = 常数（恒压）；压强定律：p/T = 常数（恒容）。
6. Atomic & Nuclear Physics | 原子与核物理
Radioactive decay law: N = N₀ e^(-λt), where N₀ is the initial number of nuclei and λ is the decay constant.
放射性衰变定律：N = N₀ e^(-λt)，N₀ 为初始原子核数，λ 为衰变常数。
Half‑life: t₁/₂ = ln 2 / λ ≈ 0.693 / λ.
半衰期：t₁/₂ = ln 2 / λ ≈ 0.693 / λ。
Activity: A = λN (decays per unit time).
活度：A = λN（单位时间衰变数）。
Alpha decay: mass number decreases by 4, atomic number decreases by 2. Beta⁻ decay: atomic number increases by 1, mass number unchanged.
α 衰变：质量数减少 4，原子序数减少 2。β⁻ 衰变：原子序数增加 1，质量数不变。
7. Chemical Formulae & Mole Concept | 化学式与摩尔概念
Amount of substance: n = m / M (mass ÷ molar mass).
物质的量：n = m / M（质量 ÷ 摩尔质量）。
Concentration: c = n / V (moles ÷ volume in dm³).
浓度：c = n / V（物质的量 ÷ 体积，体积单位为 dm³）。
Molar volume of a gas at RTP (room temperature and pressure): 24 dm³ mol⁻¹.
常温常压下气体的摩尔体积：24 dm³ mol⁻¹。
Percentage yield: (actual yield / theoretical yield) × 100%.
产率：(实际产量 / 理论产量) × 100%。
Empirical formula: simplest whole‑number ratio of atoms in a compound; molecular formula = (empirical formula)ₙ, where n = Mᵣ / empirical formula mass.
实验式：化合物中各原子最简整数比；分子式 = (实验式)ₙ，n = 相对分子质量 / 实验式质量。
8. Chemical Bonding & Structure | 化学键与结构
Ionic bonding: electrostatic attraction between oppositely charged ions, e.g. NaCl. Often forms giant ionic lattices with high melting points.
离子键：阴阳离子间的静电引力，例如 NaCl。常形成具有高熔点的巨型离子晶格。
Covalent bonding: sharing of electron pairs between atoms. Simple molecular substances (e.g. H₂O, CO₂) have low mp/bp; giant covalent structures (e.g. diamond, SiO₂) are very hard.
共价键：原子间共享电子对。简单分子物质（如 H₂O、CO₂）熔沸点低；巨型共价结构（如金刚石、SiO₂）极硬。
Metallic bonding: lattice of positive ions surrounded by delocalised electrons; accounts for electrical and thermal conductivity, malleability.
金属键：阳离子晶格与离域电子海；解释了导电性、导热性和延展性。
VSEPR theory: linear (180°, e.g. CO₂), trigonal planar (120°, e.g. BF₃), tetrahedral (109.5°, e.g. CH₄), pyramidal (107°, e.g. NH₃), bent (104.5°, e.g. H₂O).
价层电子对互斥理论：线形（180°，如 CO₂）、平面三角形（120°，如 BF₃）、正四面体形（109.5°，如 CH₄）、三角锥形（107°，如 NH₃）、角形（104.5°，如 H₂O）。
Electronegativity difference determines bond polarity; polar molecules have an overall dipole moment if bond dipoles do not cancel.
电负性差决定键的极性；若键偶极不抵消，则分子具有整体偶极矩。
9. Energetics & Equilibria | 能量学与平衡
Enthalpy change ΔH: heat change at constant pressure. Exothermic: ΔH < 0; endothermic: ΔH > 0.
焓变 ΔH：恒压下的热量变化。放热：ΔH < 0；吸热：ΔH > 0。
Hess’s law: ΔH for a reaction is independent of the route taken, provided initial and final states are the same.
赫斯定律：只要始态和终态相同，反应的 ΔH 与途径无关。
Bond energy calculations: ΔH ≈ Σ (bond energies of bonds broken) − Σ (bond energies of bonds formed).
键能计算：ΔH ≈ Σ (断裂键的键能) − Σ (形成键的键能)。
Equilibrium constant: for aA + bB ⇌ cC + dD, Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ) (concentrations at equilibrium).
平衡常数：对反应 aA + bB ⇌ cC + dD，Kc = ([C]ᶜ [D]ᵈ) / ([A]ᵃ [B]ᵇ)（平衡浓度）。
Le Chatelier’s principle: if a system at equilibrium is disturbed, the position of equilibrium shifts to counteract the change.
勒夏特列原理：若平衡系统受到扰动，平衡位置将移动以削弱这种改变。
10. Organic Chemistry Basics | 有机化学基础
Alkanes: general formula CₙH₂ₙ₊₂; saturated hydrocarbons. Alkenes: CₙH₂ₙ; contain a C=C double bond.
烷烃：通式 CₙH₂ₙ₊₂，饱和烃。烯烃：通式 CₙH₂ₙ，含 C=C 双键。
Common functional groups: alcohols (–OH), aldehydes (–CHO), ketones (–CO–), carboxylic acids (–COOH), esters (–COOR).
常见官能团：醇 (–OH)、醛 (–CHO)、酮 (–CO–)、羧酸 (–COOH)、酯 (–COOR)。
Structural isomerism: same molecular formula, different structural arrangement. Example: C₄H₁₀ can be butane or methylpropane.
结构异构：分子式相同，结构不同。示例：C₄H₁₀ 可为丁烷或甲基丙烷。
Addition reactions of alkenes: e.g. C₂H₄ + Br₂ → C₂H₄Br₂; conditions: room temperature, no catalyst needed.
烯烃的加成反应：如 C₂H₄ + Br₂ → C₂H₄Br₂；室温条件下无需催化剂。
Addition polymerisation: many alkene monomers join to form a long chain, e.g. poly(ethene) from ethene.
加聚反应：许多烯烃单体连接成长链，如由乙烯制得聚乙烯。
11. Cell Structure & Microscopy | 细胞结构与显微技术
Magnification: M = image size / actual size. Same units must be used.
放大倍数：M = 图像大小 / 实际大小，必须用相同单位。
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