Year 12 OCR Science: Quick Reference to Formulas and Theorems | 12年级OCR科学：公式定理速查手册

📚 Year 12 OCR Science: Quick Reference to Formulas and Theorems | 12年级OCR科学：公式定理速查手册

This quick reference compiles essential formulas, theorems and key quantitative relationships from the Year 12 OCR science specifications (Physics, Chemistry and Biology). Having these equations at your fingertips will help you tackle numerical problems efficiently and reinforce your understanding of core concepts. Always consult the official OCR data sheets and practical handbooks provided in your assessments for precise notation and allowed use.

这份速查手册汇总了12年级OCR科学课程（物理、化学和生物）中的必备公式、定理和关键定量关系。掌握这些公式有助于你高效解决计算题并巩固核心概念。请始终查阅OCR官方数据表和实践手册，以获取准确的符号和允许使用的公式。

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1. Mechanics and Motion | 力学与运动

v = u + at

The first SUVAT equation links final velocity (v), initial velocity (u), constant acceleration (a) and time (t).

第一个SUVAT方程关联末速度（v）、初速度（u）、恒定加速度（a）和时间（t）。

s = ut + ½at²

Displacement (s) from an initial velocity u over time t under uniform acceleration a.

在匀加速度a下，初速度u经过时间t产生的位移（s）。

v² = u² + 2as

Relates final velocity squared to displacement without requiring time.

无需时间便可关联末速度平方与位移。

s = ½(u + v)t

Displacement equals average velocity multiplied by time; useful when acceleration is not given directly.

位移等于平均速度乘以时间；当未直接给出加速度时很有用。

F = ma

Newton's second law: resultant force (N) equals mass (kg) times acceleration (m s⁻²).

牛顿第二定律：合力（N）等于质量（kg）乘以加速度（m s⁻²）。

W = mg

Weight (N) is mass (kg) times gravitational field strength g (≈9.81 N kg⁻¹).

重力（N）等于质量（kg）乘以重力场强g（≈9.81 N kg⁻¹）。

p = mv

Momentum (kg m s⁻¹) is product of mass and velocity. Momentum is conserved in isolated systems.

动量（kg m s⁻¹）是质量与速度的乘积。孤立系统中动量守恒。

Impulse = Δp = FΔt

Impulse (N s) equals change in momentum and equals average force time contact time.

冲量（N s）等于动量的变化，也等于平均力乘以接触时间。

W = Fs cos θ

Work done (J) is force times displacement times cosine of the angle between them.

做功（J）等于力乘以位移再乘以两者夹角余弦。

Eₖ = ½mv²

Kinetic energy (J) of an object of mass m moving at speed v.

质量为m、速度为v的物体的动能（J）。

Eₚ = mgh

Gravitational potential energy change (J) near Earth's surface for height change h.

近地表处高度变化h所引起的重力势能变化（J）。

P = W / t = Fv

Power (W) is work done per unit time; for constant force parallel to velocity, P = Fv.

功率（W）是单位时间内做功的速率；当力与速度方向恒定时 P = Fv。

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2. Waves and Optics | 波与光学

v = f λ

Wave speed (m s⁻¹) is frequency (Hz) multiplied by wavelength (m).

波速（m s⁻¹）等于频率（Hz）乘以波长（m）。

T = 1 / f

Period T (s) is the reciprocal of frequency.

周期T（s）是频率的倒数。

n = c / v

Absolute refractive index n of a medium is the ratio of the speed of light in vacuum c to its speed in the medium v.

介质的绝对折射率n是真空光速c与该介质中光速v之比。

n₁ sin θ₁ = n₂ sin θ₂

Snell's law of refraction for two media: the product of refractive index and sine of the angle to the normal is constant.

斯涅尔折射定律：两种介质中折射率与入射/折射角正弦的乘积相等。

sin θ_c = n₂ / n₁   (n₁ > n₂)

Critical angle for total internal reflection; occurs when light travels from an optically denser medium to a less dense one.

全反射临界角；光从光密介质射向光疏介质时满足此式。

λ = a x / D

Young' : a = slit separation, D = distance to screen, λ = wavelength. Often written as Δx = λD/d.

杨氏双缝干涉条纹间距x：a为缝距，D为屏距，λ为波长。常用形式Δx = λD/d。

I ∝ A²

Intensity is proportional to the square of the amplitude of the wave.

波的强度与振幅的平方成正比。

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3. Electricity and Circuits | 电学与电路

I = Q / t

Electric current (A) is the rate of flow of charge (C).

电流（A）是电荷（C）流动的速率。

V = W / Q

Potential difference (V) is defined as work done per unit charge.

电势差（V）定义为单位电荷所做的功。

R = V / I

Ohm's law: resistance R (Ω) is the ratio of potential difference to current under constant temperature.

欧姆定律：电阻R（Ω）在温度恒定时为电压与电流的比值。

ρ = R A / L

Resistivity ρ (Ω m) links resistance to the geometry of a uniform wire: R = ρL/A.

电阻率ρ（Ω m）将电阻与均匀导线的几何尺寸联系起来：R = ρL/A。

P = I V = I² R = V² / R

Power (W) dissipated in a component: all three forms are equivalent for ohmic conductors.

元件消耗的功率（W）：对欧姆导体这三种形式等价。

E = Q V

Energy transferred (J) when charge Q moves through a p.d. V.

电荷Q通过电势差V时传递的能量（J）。

Series: R_total = R₁ + R₂ + ... ;    Parallel: 1/R_total = 1/R₁ + 1/R₂ + ...

串联：总电阻等于各电阻之和；并联：总电阻的倒数等于各电阻倒数之和。

Kirchhoff's first law: sum of currents entering a junction = sum leaving. Kirchhoff's second law: sum of e.m.f. round a loop = sum of p.d.s.

基尔霍夫第一定律：流入节点的电流之和等于流出电流之和；第二定律：回路中电动势代数和等于各段电压代数和。

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4. Materials and Thermal Physics | 材料与热物理

F = k ΔL

Hooke's law for springs: extension ΔL is proportional to applied force F; k is spring constant (N m⁻¹).

胡克定律：弹簧伸长量ΔL与施加力F成正比，k为劲度系数（N m⁻¹）。

σ = F / A     ε = ΔL / L

Stress σ (Pa) = force per unit area; strain ε = fractional change in length.

应力σ（Pa）=力/面积；应变ε=长度变化分数。

E = σ / ε

Young modulus E (Pa) = tensile stress divided by tensile strain within the elastic limit.

杨氏模量E（Pa）=弹性限度内拉应力除以拉应变。

Elastic potential energy = ½ F ΔL

Area under force-extension graph for a material obeying Hooke's law.

遵循胡克定律的材料在力-伸长量图下方面积。

ρ = m / V

Density ρ (kg m⁻³) = mass divided by volume.

密度ρ（kg m⁻³）=质量除以体积。

p = F / A     p = ρ g h

Pressure p (Pa) = force per area; for a fluid column, pressure due to depth h is ρgh.

压强p（Pa）=力/面积；液柱深度h产生的压强为ρgh。

Q = m c Δθ     Q = m L

Thermal energy Q: m c Δθ for temperature change; L is specific latent heat for change of state.

热量Q：温度变化用m c Δθ；相变用比潜热L。

p V = n R T     (p V = N k T)

(8.31 J mol⁻¹ K⁻¹), T absolute temperature. N = number of molecules, k Boltzmann constant.

理想气体方程：p压强，V体积，n摩尔数，R摩尔气体常数（8.31 J mol⁻¹ K⁻¹），T绝对温度。N为分子数，k玻尔兹曼常数。

½ m ⟨c²⟩ = ³⁄₂ k T

Average translational kinetic energy of a particle in an ideal gas is directly proportional to absolute temperature.

理想气体中粒子的平均平动动能与绝对温度成正比。

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5. Quantities, Units and Measurements | 量、单位与测量

All physical quantities are expressed in SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (

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