📚 Pre-U OCR Science: Formula & Theorem Quick Reference Handbook | Pre-U OCR 科学：公式定理速查手册
This quick reference handbook consolidates the most essential formulas and theorems from the OCR Pre-U Science curriculum. Whether you are revising for Physics, Chemistry or Biology, this guide presents each key relationship in a clear, accessible format. Memorising and being able to apply these relationships accurately is crucial for success across all three sciences.
本速查手册汇集了 OCR Pre-U 科学课程中最关键的公式和定理。无论你正在复习物理、化学还是生物，本指南都以清晰易读的形式呈现每一个重要关系。准确记忆并善于应用这些关系，是学好三门科学科目的关键。
1. Kinematics and Dynamics | 运动学与动力学
The equations of motion describe uniformly accelerated linear motion. They are fundamental to solving problems involving displacement, velocity, acceleration and time.
运动学方程描述匀加速直线运动，它们是解决位移、速度、加速度和时间问题的基础。
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- s = ½(u + v)t
Newton’s second law relates net force to mass and acceleration.
牛顿第二定律将合外力与质量和加速度联系起来。
F = ma
Momentum is conserved in a closed system. Impulse equals change in momentum.
动量在封闭系统中守恒。冲量等于动量的变化量。
p = mv ; I = Δp = FΔt
2. Work, Energy and Power | 功、能与功率
Work done is the product of force and displacement in the direction of the force. Energy cannot be created or destroyed, only converted between forms.
功是力与沿力方向的位移的乘积。能量既不能创造也不能消灭，只能在不同形式之间转化。
W = Fs cos θ
Kinetic energy and gravitational potential energy are frequently interconverted in mechanics problems.
动能和重力势能在力学问题中经常相互转化。
Eₖ = ½mv² ; Eₚ = mgh
Power is the rate of doing work or transferring energy.
功率是做功或传递能量的速率。
P = W / t = Fv
3. Waves and Optics | 波与光学
Wave speed depends on frequency and wavelength. This relationship applies to all periodic waves.
波速取决于频率和波长。这一关系适用于所有周期波。
v = fλ
Refractive index governs light bending at an interface and leads to Snell’s law.
折射率决定光在界面处的弯曲，并导出斯涅尔定律。
n = c / v ; n₁ sin θ₁ = n₂ sin θ₂
The double-slit interference condition relates fringe spacing to wavelength and geometry.
双缝干涉条件将条纹间距与波长和几何参数联系起来。
λ = ay / D
4. Electricity and Circuits | 电学与电路
Ohm’s law defines resistance for a metallic conductor at constant temperature.
欧姆定律定义了金属导体在恒温条件下的电阻。
V = IR
Electrical power dissipated can be expressed in three useful forms by combining with Ohm’s law.
电功率耗散可结合欧姆定律用三种有用的形式表示。
P = IV = I²R = V² / R
For series and parallel circuits, total resistance follows distinct combination rules.
对于串联和并联电路，总电阻遵循不同的组合规则。
Series: Rₜₒₜ = R₁ + R₂ + … ; Parallel: 1/Rₜₒₜ = 1/R₁ + 1/R₂ + …
5. Thermal Physics | 热物理学
The first law of thermodynamics relates change in internal energy to heat supplied and work done.
热力学第一定律将内能的变化与热量供给和做功联系起来。
ΔU = Q – W
Specific heat capacity and specific latent heat are used to calculate energy transfers during temperature changes and phase changes.
比热容和比潜热用于计算温度变化和相变过程中的能量转移。
Q = mcΔθ ; Q = mL
The ideal gas equation links macroscopic state variables for a gas under many conditions.
理想气体状态方程联系了气体在许多条件下的宏观状态参量。
pV = nRT
6. Materials and Fluid Mechanics | 材料与流体力学
Stress, strain and the Young modulus describe the elastic deformation of solids.
应力、应变和杨氏模量描述固体的弹性形变。
Stress σ = F / A ; Strain ε = ΔL / L ; E = σ / ε
Pressure in a fluid increases linearly with depth and density, and Archimedes’ principle governs buoyancy.
流体中的压强随深度和密度线性增大，阿基米德原理主宰浮力。
p = ρgh ; F_b = ρgV
7. Chemical Amounts and Stoichiometry | 化学计量与反应量
The mole concept bridges the microscopic and laboratory scales. Mass, molar mass and number of particles are interlinked.
摩尔概念连接微观尺度和实验尺度。质量、摩尔质量和粒子数目相互关联。
n = m / M ; N = n × Nₐ
Gas volumes at room temperature and pressure (RTP) can be directly calculated from amount.
室温常压（RTP）下的气体体积可由物质的量直接计算。
V(gas) = n × 24 dm³ (at RTP)
Solution concentration links amount, volume and molarity, essential for titration analysis.
溶液浓度联系物质的量、体积和摩尔浓度，对滴定分析至关重要。
n = cV
8. Energetics and Kinetics in Chemistry | 化学能量学与动力学
Enthalpy change for a reaction is calculated from bond enthalpies or from Hess’s law cycles.
反应焓变可通过键焓或盖斯定律循环来计算。
ΔH ≈ Σ(bond enthalpies broken) – Σ(bond enthalpies formed)
The Maxwell-Boltzmann distribution and the Arrhenius equation explain temperature dependence of rate.
麦克斯韦-玻尔兹曼分布和阿伦尼乌斯方程解释了速率对温度的依赖性。
k = A e^(-Ea / RT)
The rate expression and order of reaction are determined experimentally, not from stoichiometry.
速率方程和反应级数由实验确定，而不能从化学计量数推导。
Rate = k [A]ᵐ [B]ⁿ
9. Equilibrium and Acid-Base Chemistry | 化学平衡与酸碱
The equilibrium constant in terms of concentration is written from the balanced equation. Its value indicates the position of equilibrium.
浓度平衡常数由配平的反应方程式写出。它的数值表明平衡的位置。
Kc = [products] / [reactants] (with stoichiometric exponents)
Le Chatelier’s principle predicts how a change in conditions affects equilibrium yield.
勒夏特列原理可预测条件改变如何影响平衡产率。
pH and the dissociation constant for weak acids provide a measure of acidity.
pH 和弱酸的电离常数提供了酸性程度的量度。
pH = -log₁₀[H⁺] ; Kₐ = [H⁺][A⁻] / [HA]
The ionic product of water sets the neutral pH at a given temperature.
水的离子积决定了给定温度下的中性 pH。
K_w = [H⁺][OH⁻] = 1 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K
10. Organic Chemistry Basics | 有机化学基础
Functional groups determine the characteristic reactions of organic families. Naming follows IUPAC rules based on carbon chain length and substituents.
官能团决定了有机化合物家族的特征反应。命名遵循 IUPAC 规则，基于碳链长度和取代基。
Key reaction mechanisms include free-radical substitution, electrophilic addition, nucleophilic substitution and elimination.
关键的反应机理包括自由基取代、亲电加成、亲核取代和消除。
A mark scheme favourite is the test for unsaturation using bromine water, and for carbonyls using 2,4-DNPH.
评分标准中常考的是用溴水检验不饱和键，以及用 2,4-二硝基苯肼检验羰基。
11. Cell Biology and Biochemistry | 细胞生物学与生物化学
Magnification and resolution are distinct concepts used in microscopy.
放大率和分辨率是显微镜学中两个不同的概念。
Magnification = Image size / Actual size
The fluid mosaic model of membrane structure permits selective permeability and cell signalling.
膜的流动镶嵌模型允许选择透过性和细胞信号传导。
The induced-fit model of enzyme action explains specificity and the lowering of activation energy.
酶的诱导契合模型解释了专一性和降低活化能的作用。
ATP provides the energy currency for cellular processes; its hydrolysis is exergonic.
ATP 为细胞过程提供能量货币；其水解释放自由能。
ATP → ADP + Pᵢ + energy
12. Genetics and Evolution | 遗传学与进化
The Hardy–Weinberg principle predicts allele frequencies in a non-evolving population.
哈代-温伯格原理预测了非进化种群中的等位基因频率。
p² + 2pq + q² = 1 ; p + q = 1
Chi-squared test compares observed and expected frequencies to determine if differences are statistically significant.
卡方检验比较观测频率和预期频率，以确定差异是否具有统计学意义。
χ² = Σ (O – E)² / E
Natural selection, genetic drift and gene flow are mechanisms that drive changes in allele frequency over time.
自然选择、遗传漂变和基因流是推动等位基因频率随时间变化的机制。
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