📚 Pre-U Edexcel Science: Quick Reference Formula and Theorem Handbook | Pre-U Edexcel 科学：公式定理速查手册
This handbook provides a curated collection of essential equations, theorems, and rules for the Edexcel Pre-U Science curriculum. Each entry is paired with a concise explanation to support rapid revision and problem-solving across physics, chemistry, and biology.
本手册精选了 Edexcel Pre-U 科学课程中必备的方程、定理和法则。每一项都配以简明的双语解释，便于快速复习与解题，涵盖物理、化学与生物三个学科。
1. Mechanics Equations | 力学方程
v = u + at – final velocity in uniformly accelerated motion.
v = u + at – 匀加速运动的末速度。
s = ut + ½at² – displacement with constant acceleration.
s = ut + ½at² – 匀加速运动的位移。
F = ma – Newton’s second law; resultant force equals mass times acceleration.
F = ma – 牛顿第二定律：合力等于质量乘以加速度。
p = mv – linear momentum.
p = mv – 线动量。
Δp = FΔt – impulse-momentum theorem.
Δp = FΔt – 冲量-动量定理。
W = Fd cos θ – work done by a constant force.
W = Fd cos θ – 恒力所做的功。
Eₖ = ½mv² – kinetic energy.
Eₖ = ½mv² – 动能。
Eₚ = mgh – gravitational potential energy near Earth’s surface.
Eₚ = mgh – 地球表面附近的重力势能。
2. Wave and Optics Formulae | 波动与光学公式
v = f λ – wave speed equals frequency times wavelength.
v = f λ – 波速等于频率乘以波长。
n₁ sin θ₁ = n₂ sin θ₂ – Snell’s law of refraction.
n₁ sin θ₁ = n₂ sin θ₂ – 斯涅耳折射定律。
n = c / v – absolute refractive index.
n = c / v – 绝对折射率。
θᵢ = θᵣ – law of reflection.
θᵢ = θᵣ – 反射定律。
d sin θ = n λ – diffraction grating maxima.
d sin θ = n λ – 衍射光栅加强条件。
Δx = λD / a – fringe spacing in Young’s double-slit experiment.
Δx = λD / a – 杨氏双缝干涉条纹间距。
3. Electricity and Magnetism | 电磁学
I = ΔQ / Δt – electric current definition.
I = ΔQ / Δt – 电流定义。
V = IR – Ohm’s law for ohmic conductors.
V = IR – 欧姆导体欧姆定律。
P = IV = I²R = V²/R – electrical power.
P = IV = I²R = V²/R – 电功率。
Rₜₒₜ = R₁ + R₂ + … – resistors in series.
Rₜₒₜ = R₁ + R₂ + … – 串联电阻总阻值。
1/Rₜₒₜ = 1/R₁ + 1/R₂ + … – resistors in parallel.
1/Rₜₒₜ = 1/R₁ + 1/R₂ + … – 并联电阻总阻值。
F = BIL sin θ – force on a current-carrying conductor in a magnetic field.
F = BIL sin θ – 磁场对载流导线的作用力。
Φ = BA cos θ – magnetic flux.
Φ = BA cos θ – 磁通量。
ε = –N (ΔΦ/Δt) – Faraday’s law of electromagnetic induction.
ε = –N (ΔΦ/Δt) – 法拉第电磁感应定律。
4. Thermal Physics | 热物理
ΔE = mcΔθ – specific heat capacity equation.
ΔE = mcΔθ – 比热容公式。
ΔE = mL – latent heat during phase change.
ΔE = mL – 相变潜热。
pV = nRT – ideal gas equation.
pV = nRT – 理想气体状态方程。
p₁V₁/T₁ = p₂V₂/T₂ – combined gas law for a fixed mass.
p₁V₁/T₁ = p₂V₂/T₂ – 一定质量气体的综合气态方程。
½ m⟨c²⟩ = (3/2) kT – average kinetic energy of a gas molecule.
½ m⟨c²⟩ = (3/2) kT – 气体分子的平均动能。
5. Nuclear and Particle Physics | 核物理与粒子物理
E = mc² – mass–energy equivalence.
E = mc² – 质能等价。
A = λ N – activity of a radioactive sample; λ is the decay constant.
A = λ N – 放射性样品活度；λ 为衰变常量。
N = N₀ e^(–λt) – exponential decay law.
N = N₀ e^(–λt) – 指数衰变规律。
t½ = ln 2 / λ – half-life formula.
t½ = ln 2 / λ – 半衰期公式。
λ = h / p – de Broglie wavelength.
λ = h / p – 德布罗意波长。
ΔE Δt ≥ h / 4π – Heisenberg uncertainty principle (energy–time form).
ΔE Δt ≥ h / 4π – 海森堡不确定性原理（能量-时间形式）。
6. Chemical Kinetics | 化学动力学
Rate = k [A]ᵐ[B]ⁿ – rate equation; m and n are orders of reaction.
Rate = k [A]ᵐ[B]ⁿ – 速率方程；m 和 n 为反应级数。
ln([A]₀/[A]) = kt – integrated rate law for a first-order reaction.
ln([A]₀/[A]) = kt – 一级反应积分速率方程。
t½ = ln 2 / k – half-life of a first-order reaction.
t½ = ln 2 / k – 一级反应半衰期。
k = A e^(–Ea/RT) – Arrhenius equation; Ea is activation energy.
k = A e^(–Ea/RT) – 阿伦尼乌斯方程；Ea 为活化能。
ln k = ln A – Ea/(RT) – logarithmic form of the Arrhenius equation.
ln k = ln A – Ea/(RT) – 阿伦尼乌斯方程的对数形式。
7. Chemical Equilibrium | 化学平衡
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ – equilibrium constant in terms of concentration.
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ – 浓度平衡常数。
Kp = (pC)ᶜ(pD)ᵈ / (pA)ᵃ(pB)ᵇ – equilibrium constant in terms of partial pressure.
Kp = (pC)ᶜ(pD)ᵈ / (pA)ᵃ(pB)ᵇ – 分压平衡常数。
Δn = (c+d) – (a+b) – change in moles of gas; used for Kp and Kc relation.
Δn = (c+d) – (a+b) – 气体摩尔数变化；用于关联 Kp 与 Kc。
Kp = Kc (RT)^(Δn) – relationship between Kp and Kc.
Kp = Kc (RT)^(Δn) – Kp 与 Kc 的关系式。
Le Chatelier’s principle – a system at equilibrium, when disturbed, shifts to counteract the change.
勒夏特列原理 – 处于平衡的系统受到干扰时，会朝着减弱干扰的方向移动。
8. Thermodynamics in Chemistry | 化学热力学
ΔH = ΣΔHf°(products) – ΣΔHf°(reactants) – standard enthalpy change of reaction.
ΔH = ΣΔHf°(产物) – ΣΔHf°(反应物) – 反应标准焓变。
q = mcΔT – heat energy transferred in a calorimetry experiment.
q = mcΔT – 量热实验中传递的热量。
ΔG = ΔH – TΔS – Gibbs free energy change; determines spontaneity.
ΔG = ΔH – TΔS – 吉布斯自由能变；判断反应自发性。
ΔG° = –RT ln K – link between standard free energy and equilibrium constant.
ΔG° = –RT ln K – 标准自由能与平衡常数的关系。
ΔSₜₒₜ = ΔSₛᵧₛ + ΔSₛᵤᵣᵣ ≥ 0 – second law of thermodynamics (total entropy change).
ΔSₜₒₜ = ΔSₛᵧₛ + ΔSₛᵤᵣᵣ ≥ 0 – 热力学第二定律（总熵变判据）。
9. Cell Processes (Respiration and Photosynthesis) | 细胞过程（呼吸与光合作用）
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP – overall aerobic respiration equation.
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP – 有氧呼吸总方程式。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ – overall photosynthesis equation.
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ – 光合作用总方程式。
Rf = distance moved by substance / distance moved by solvent front – retention factor in chromatography.
Rf = 物质移动距离 / 溶剂前沿移动距离 – 色谱保留因子。
Magnification = image size / actual size – calculation for micrographs and scales.
放大率 = 图像尺寸 / 实际尺寸 – 显微图及比例尺计算。
10. Genetics and Hardy-Weinberg | 遗传学与哈迪-温伯格平衡
p + q = 1 – allele frequency sum for a gene with two alleles.
p + q = 1 – 两等位基因的基因频率之和。
p² + 2pq + q² = 1 – Hardy-Weinberg equilibrium genotype frequencies.
p² + 2pq + q² = 1 – 哈迪-温伯格平衡基因型频率。
Expected heterozygotes = 2pq × total population – used to test for equilibrium.
预期杂合子数 = 2pq × 总个体数 – 用于检验遗传平衡。
Chi-squared test: χ² = Σ (O–E)² / E – statistical test for genetic data.
卡方检验: χ² = Σ (O–E)² / E – 遗传数据的统计检验。
11. Practical Skills and Error Analysis | 实验技能与误差分析
Mean = Σx / n – arithmetic mean.
平均值 = Σx / n – 算术平均数。
Uncertainty = ± (half the range) or ± (instrument precision) – common estimate of absolute uncertainty.
不确定度 = ±（极差的一半）或 ±（仪器精度） – 绝对不确定度的常用估计方法。
% uncertainty = (absolute uncertainty / measured value) × 100% – percentage uncertainty.
% 不确定度 = （绝对不确定度 / 测量值）× 100% – 百分不确定度。
If Q = aᵇ, then %U(Q) = |b| × %U(a) – propagation for power functions.
若 Q = aᵇ，则 %U(Q) = |b| × %U(a) – 幂函数的不确定度传递。
If Q = a × b, then %U(Q) = %U(a) + %U(b) – propagation for multiplication/division.
若 Q = a × b，则 %U(Q) = %U(a) + %U(b) – 乘除法的不确定度传递。
Random errors reduce by repeating measurements; systematic errors affect accuracy.
随机误差可通过重复测量减小；系统误差影响准确度。
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