📚 Year 13 CIE Science: Quick-Reference Formulas & Theorems | Year 13 CIE 科学：公式定理速查手册
This quick-reference guide compiles the most important formulas, theorems, and principles from the Year 13 CIE Science syllabus, spanning Physics, Chemistry, and Biology. Each entry is presented with a concise English explanation immediately followed by its Chinese equivalent, making it an ideal tool for bilingual revision and last-minute exam preparation.
本速查手册汇集了 Year 13 CIE 科学课程（涵盖物理、化学和生物）中最重要的公式、定理和原理。每个条目都配有简洁的英文解释，并紧跟相应的中文翻译，是双语复习和考前冲刺的理想工具。
1. Kinematics and Dynamics (Physics) | 运动学与动力学（物理）
v = u + at – Final velocity equals initial velocity plus acceleration multiplied by time, valid only when acceleration is uniform.
v = u + at – 末速度等于初速度加加速度乘以时间，仅适用于匀加速运动。
s = ut + ½at² – Displacement under constant acceleration; the term ½at² accounts for the changing velocity during the motion.
s = ut + ½at² – 匀加速运动中的位移；½at² 项反映了运动过程中速度的变化。
v² = u² + 2as – Links final velocity squared directly to distance travelled, eliminating time from the other SUVAT equations.
v² = u² + 2as – 将末速度的平方与位移直接关联，从而在 SUVAT 方程中消去了时间。
2. Circular Motion and Gravitation | 圆周运动与引力
a = v²/r = rω² – Centripetal acceleration needed to keep an object moving in a circle; v is linear speed, r is radius, ω is angular velocity.
a = v²/r = rω² – 使物体维持圆周运动所需的向心加速度；v 为线速度，r 为半径，ω 为角速度。
F = mv²/r = mrω² – Centripetal force is the resultant force directed towards the centre of the circle.
F = mv²/r = mrω² – 向心力是指向圆心的合力。
v = √2GM/r – Escape velocity from a planet or star of mass M; G is the gravitational constant.
v = √2GM/r – 从质量为 M 的行星或恒星上逃逸所需的速度；G 为引力常量。
3. Simple Harmonic Motion and Waves | 简谐运动与波
a = –ω²x – The defining equation of SHM: acceleration is proportional to displacement from equilibrium and always directed towards it.
a = –ω²x – 简谐运动的定义式：加速度与离开平衡位置的位移成正比，且总指向平衡位置。
T = 2π√m/k – Period of a mass-spring system; m is mass and k is the spring constant.
T = 2π√m/k – 弹簧–质量系统的周期；m 为质量，k 为劲度系数。
v = fλ – Wave speed equals frequency multiplied by wavelength; applies to all progressive waves.
v = fλ – 波速等于频率乘以波长；适用于所有行波。
4. Electric Fields and Capacitance | 电场与电容
E = F/q – Electric field strength is defined as the force per unit positive charge.
E = F/q – 电场强度定义为单位正电荷所受的力。
E = V/d – For a uniform field between parallel plates, field strength equals potential difference divided by plate separation.
E = V/d – 平行板间的匀强电场中，场强等于电势差除以板间距。
C = Q/V – tance is the charge stored per unit potential difference; energy stored is E = ½QV = ½CV².
C = Q/V – 电容为单位电势差下储存的电荷量；储存能量 E = ½QV = ½CV²。
5. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
F = BIL sinθ – Force on a current-carrying conductor in a magnetic field; θ is the angle between current and field.
F = BIL sinθ – 载流导体在磁场中所受的力；θ 为电流与磁场方向之间的夹角。
F = Bqv sinθ – Force on a moving charge; when θ = 90°, the path becomes circular with radius r = mv/(Bq).
F = Bqv sinθ – 运动电荷在磁场中所受的力；θ=90° 时路径为圆周，半径 r = mv/(Bq)。
ε = –dΦ/dt – Faraday's law: induced emf equals the negative rate of change of magnetic flux linkage.
ε = –dΦ/dt – 法拉第定律：感应电动势等于磁通量链变化率的负值。
6. Thermal Physics and Ideal Gases | 热物理与理想气体
pV = nRT – Ideal gas equation; p is pressure, V volume, n number of moles, R molar gas constant, T absolute temperature.
pV = nRT – 理想气体状态方程；p 为压强，V 为体积，n 为物质的量，R 为摩尔气体常数，T 为热力学温度。
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ΔU = q + w – First law of thermodynamics: change in internal energy equals heat added plus work done on the system.
ΔU = q + w – 热力学第一定律：内能的变化等于系统吸收的热量与外界对系统做功之和。
7. Quantum and Nuclear Physics | 量子与核物理
E = hf – Energy of a photon; h is Planck's constant. The photoelectric effect requires hf ≥ Φ.
E = hf – 光子能量；h 为普朗克常量。光电效应要求 hf ≥ Φ（逸出功）。
λ = h/p – De Broglie wavelength of a particle with momentum p, demonstrating wave-particle duality.
λ = h/p – 动量为 p 的粒子的德布罗意波长，体现了波粒二象性。
ΔE = Δmc² – Mass-energy equivalence; the energy released in a nuclear reaction equals the mass defect multiplied by c².
ΔE = Δmc² – 质能方程；核反应释放的能量等于质量亏损乘以光速的平方。
A = λN; T½ = ln2/λ – Activity equals decay constant times number of undecayed nuclei; half-life is inversely proportional to decay constant.
A = λN; T½ = ln2/λ – 放射性活度等于衰变常量乘以未衰变核的数目；半衰期与衰变常量成反比。
8. Chemical Equilibrium and Free Energy | 化学平衡与自由能
Kc = [C]c[D]d / [A]a[B]b – Equilibrium constant in terms of concentration for the reaction aA + bB ⇌ cC + dD.
Kc = [C]c[D]d / [A]a[B]b – 对反应 aA + bB ⇌ cC + dD，用浓度表示的平衡常数。
ΔG° = –RT ln K – Standard Gibbs free energy change is related to the equilibrium constant; a negative ΔG° indicates a spontaneous forward reaction.
ΔG° = –RT ln K – 标准吉布斯自由能变与平衡常数相关；ΔG° 为负表明正向反应自发进行。
ΔG = ΔH – TΔS – Gibbs free energy combines enthalpy and entropy to predict reaction feasibility at constant temperature.
ΔG = ΔH – TΔS – 吉布斯自由能结合焓变和熵变，用于判断恒温下反应的可能性。
9. Chemical Kinetics and Arrhenius Equation | 化学动力学与阿伦尼乌斯方程
rate = k[A]m[B]n – Rate law where k is the rate constant, and m and n are reaction orders determined experimentally.
rate = k[A]m[B]n – 速率方程，k 为速率常数，m 和 n 是实验测定的反应级数。
k = A e–Eₐ/RT – Arrhenius equation: rate constant depends exponentially on temperature and activation energy Eₐ.
k = A e–Eₐ/RT – 阿伦尼乌斯方程：速率常数随温度和活化能 Eₐ 呈指数变化。
ln k = –Eₐ/(RT) + ln A – Linear form used to determine Eₐ from a graph of ln k against 1/T.
ln k = –Eₐ/(RT) + ln A – 线性形式，通过 ln k 对 1/T 作图可求出活化能。
10. Electrochemistry and Nernst Equation | 电化学与能斯特方程
Ecell = E°(cathode) – E°(anode) – Standard cell potential is the difference between the standard reduction potentials of the two half-cells.
Ecell = E°(cathode) – E°(anode) – 标准电池电动势等于两个半电池标准还原电势之差。
E = E° – (RT
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