📚 A-Level CIE Science: Formula Quick Reference Handbook | A-Level CIE 科学：公式汇总手册
This concise handbook brings together the essential formulas from A-Level CIE Physics, Chemistry and Biology in one place. Whether you are solving numerical problems, analysing data or writing explanations, having these equations at your fingertips will save you time and reduce errors. Every formula is stated with its standard notation, and a short description in English and Chinese helps you recall exactly when and how to apply it.
本手册将 A-Level CIE 物理、化学和生物中的核心公式汇聚一处。无论是求解计算题、分析数据还是书写论述，熟记这些方程都能帮你提高效率、减少差错。每个公式均标注了常用符号，并配以中英文简短说明，帮助你准确掌握使用条件和物理意义。
1. Mechanics Formulas | 力学公式
Velocity–time equation for constant acceleration: v = u + at, where v is final velocity, u is initial velocity, a is constant acceleration and t is time.
匀加速运动的速度–时间关系：v = u + at，其中 v 为末速度，u 为初速度，a 为恒定加速度，t 为时间。
Displacement–time equation: s = ut + ½at², where s is displacement.
位移–时间关系：s = ut + ½at²，s 为位移。
Velocity–displacement relation: v² = u² + 2as.
速度–位移关系：v² = u² + 2as。
Newton’s second law: F = ma, where F is net force, m is mass and a is acceleration.
牛顿第二定律：F = ma，F 为净力，m 为质量，a 为加速度。
Weight: W = mg, where g is gravitational field strength (9.81 N kg⁻¹ on Earth’s surface).
重力：W = mg，g 为重力场强度（地表约 9.81 N kg⁻¹）。
Momentum: p = mv. Impulse: FΔt = Δp.
动量：p = mv；冲量：FΔt = Δp。
Work done: W = Fs cosθ, where θ is the angle between force and displacement.
功：W = Fs cosθ，θ 为力与位移的夹角。
Kinetic energy: Eₖ = ½mv². Gravitational potential energy: Eₚ = mgh.
动能：Eₖ = ½mv²；重力势能：Eₚ = mgh。
Power: P = W/t = Fv (when force and velocity are aligned).
功率：P = W/t = Fv（力与速度同向时适用）。
Hooke’s law: F = kx. Elastic potential energy: E = ½kx².
胡克定律：F = kx；弹性势能：E = ½kx²。
2. Waves and Optics Formulas | 波与光学公式
Wave speed: v = fλ, where f is frequency and λ is wavelength.
波速：v = fλ，f 为频率，λ 为波长。
Refractive index: n = c/v, where c is speed of light in vacuum.
折射率：n = c/v，c 为真空中光速。
Snell’s law: n₁ sinθ₁ = n₂ sinθ₂.
斯涅尔定律：n₁ sinθ₁ = n₂ sinθ₂。
Critical angle: sinθc = n₂/n₁ (where n₁ > n₂).
临界角：sinθc = n₂/n₁（n₁ > n₂）。
Diffraction grating: d sinθ = nλ, where d is grating spacing and n is order.
衍射光栅：d sinθ = nλ，d 为光栅间距，n 为级次。
Young’s double-slit fringe spacing: λ = ax/D, where a is slit separation, x is fringe width and D is screen distance.
杨氏双缝条纹间距：λ = ax/D，a 为缝距，x 为条纹宽度，D 为屏幕距离。
Intensity and amplitude: I ∝ A². Intensity and distance: I = P/(4πr²) for a point source.
强度与振幅：I ∝ A²；点光源强度：I = P/(4πr²)。
3. Electricity and Circuits Formulas | 电学与电路公式
Ohm’s law: V = IR, where V is potential difference, I is current and R is resistance.
欧姆定律：V = IR，V 为电势差，I 为电流，R 为电阻。
Power dissipated: P = IV = I²R = V²/R.
功率：P = IV = I²R = V²/R。
Energy transferred: E = IVt.
能量转移：E = IVt。
Resistivity: R = ρL/A, where ρ is resistivity, L is length and A is cross-sectional area.
电阻率：R = ρL/A，ρ 为电阻率，L 为长度，A 为截面积。
Resistors in series: Rₜ = R₁ + R₂ + …. Resistors in parallel: 1/Rₜ = 1/R₁ + 1/R₂ + ….
串联电阻：Rₜ = R₁ + R₂ + …；并联电阻：1/Rₜ = 1/R₁ + 1/R₂ + …。
Electromotive force and internal resistance: ε = I(R+r) or terminal p.d. V = ε – Ir.
电动势与内阻：ε = I(R+r) 或端电压 V = ε – Ir。
Charge: Q = It. Capacitance: C = Q/V. Energy stored in a capacitor: E = ½CV². Parallel-plate capacitance: C = εA/d.
电荷量：Q = It；电容：C = Q/V；电容器储能：E = ½CV²；平行板电容：C = εA/d。
Time constant for RC circuit: τ = RC. Discharge: V = V₀ e^(-t/RC).
RC 电路时间常数：τ = RC；放电：V = V₀ e^(-t/RC)。
4. Thermodynamics and Gases Formulas | 热力学与气体公式
Ideal gas equation: pV = nRT, where p is pressure, V is volume, n is amount in mol, R is molar gas constant (8.31 J mol⁻¹ K⁻¹) and T is thermodynamic temperature. Also pV = NkT where N is number of molecules and k is Boltzmann constant.
理想气体方程：pV = nRT，p 为压强，V 为体积，n 为物质的量，R 为摩尔气体常数（8.31 J mol⁻¹ K⁻¹），T 为热力学温度。也可写作 pV = NkT，N 为分子数，k 为玻尔兹曼常数。
Average translational kinetic energy of a gas molecule: Eₖ = 3/2 kT.
气体分子平均平动动能：Eₖ = 3/2 kT。
Heat capacity and specific heat capacity: Q = mcΔθ, where c is specific heat capacity. For latent heat: Q = mL, where L is specific latent heat.
热容与比热容：Q = mcΔθ，c 为比热容。潜热：Q = mL，L 为比潜热。
First law of thermodynamics: ΔU = Q + W, where ΔU is change in internal energy, Q is heat supplied to the system and W is work done on the system. (Note: in some physics treatments W is work done by the system, giving ΔU = Q – W; always check sign convention.)
热力学第一定律：ΔU = Q + W，ΔU 为内能变化，Q 为系统吸收的热量，W 为外界对系统做的功。（注意：部分物理教材采用系统对外做功，表达式为 ΔU = Q – W；使用时需确认符号约定。）
Work done in a gas expansion at constant pressure: W = pΔV.
恒压气体膨胀做功：W = pΔV。
5. Nuclear and Particle Physics Formulas | 核物理与粒子物理公式
Mass–energy equivalence: E = mc². Energy released in a nuclear reaction: ΔE = Δm c², where Δm is mass defect.
质能方程：E = mc²；核反应释放能量：ΔE = Δm c²，Δm 为质量亏损。
Binding energy per nucleon = total binding energy / A, where A is mass number.
平均结合能 = 总结合能 / A，A 为质量数。
Radioactive decay law: N = N₀ e^(-λt), where λ is decay constant. Activity: A = λN. Half-life: T½
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