Pre-U Edexcel Science: Quick Reference Formula and Theorem Handbook | Pre-U Edexcel 科学：公式定理速查手册

📚 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。

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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。

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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。

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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。

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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）。

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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。

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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。

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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）。

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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。

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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。

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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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