📚 Year 12 OCR Science: Formula & Theorem Quick Reference Handbook | 12年级OCR科学：公式定理速查手册
Welcome to your essential quick reference for Year 12 OCR Science. This handbook brings together the core formulas, theorems and relationships from physics, chemistry and biology that you are expected to recall and apply confidently. Use it alongside your class notes and past paper practice to solidify your understanding.
欢迎使用你的12年级OCR科学必备速查手册。本手册汇集了物理、化学和生物学科中你需要熟练掌握并应用的核心公式、定理与关系式。请配合课堂笔记和历年真题练习使用，以巩固理解。
1. Kinematics | 运动学
The four SUVAT equations describe motion with constant acceleration in a straight line. They link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
四个SUVAT方程描述匀加速直线运动，联系了位移(s)、初速度(u)、末速度(v)、加速度(a)和时间(t)。
v = u + a t
English: The first equation links final velocity to initial velocity, acceleration and time.
中文：第一个方程将末速度与初速度、加速度和时间联系起来。
s = u t + ½ a t²
English: This calculates displacement when the object starts with an initial velocity and accelerates uniformly.
中文：用于计算物体以初速度开始并匀加速运动时的位移。
v² = u² + 2 a s
English: Use this equation when time is not given but velocity, acceleration and displacement are involved.
中文：当未给出时间但涉及速度、加速度和位移时使用此方程。
s = ½ (u + v) t
English: This gives displacement from the average velocity multiplied by time.
中文：该方程通过平均速度乘以时间求得位移。
Acceleration due to gravity near Earth' urface is taken as g = 9.81 m s⁻², and for vertical motion a = −g when upward is positive.
地球表面附近的重力加速度取 g = 9.81 m s⁻²，当以向上为正方向时竖直运动中的 a = −g。
2. Forces and Newton's Laws | 力与牛顿定律
Newton's second law states that the net force acting on an object equals the product of its mass and acceleration.
牛顿第二定律指出，作用于物体上的合力等于物体质量与加速度的乘积。
F = m a
English: Force is measured in newtons (N), mass in kilograms (kg) and acceleration in m s⁻².
中文：力的单位是牛顿(N)，质量单位是千克(kg)，加速度单位是米每二次方秒(m s⁻²)。
gravitational force on an object: W = m g. It always acts towards the centre of the Earth.
重量是物体所受的重力：W = m g，其方向始终指向地心。
Momentum is the product of mass and velocity, a vector quantity conserved in isolated systems.
动量是质量与速度的乘积，是矢量，在孤立系统中守恒。
p = m v
vital for collision and explosion problems: total momentum before = total momentum after.
中文：动量守恒定律是碰撞和爆炸问题的关键：碰撞前总动量等于碰撞后总动量。
Impulse equals change in momentum and is also given by the product of force and collision time.
冲量等于动量的变化，也可表示为力与碰撞时间的乘积。
F Δt = Δp
3. Energy, Work and Power | 能量、功与功率
Work done is the energy transferred when a force moves an object through a distance. When the force is at an angle θ to the displacement, only the component along the displacement does work.
功是力使物体移动一段距离时所传递的能量。当力与位移方向成角度θ时，只有沿位移方向的分力做功。
W = F s cos θ
English: Kinetic energy is the energy an object possesses due to its motion.
中文：动能是物体由于运动而具有的能量。
Eₖ = ½ m v²
English: Gravitational potential energy in a uniform field is proportional to height.
中文：均匀场中的重力势能与高度成正比。
Eₚ = m g h
English: The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed.
中文：能量守恒原理指出，能量不能被创造或消灭，只能被转移或转化。
Power is the rate of doing work or transferring energy. It can also be expressed as the product of force and velocity when the force is parallel to the motion.
功率是做功或传递能量的速率。当力与运动方向平行时，它也可表示为力与速度的乘积。
P = W / t = F v
English: Efficiency is the ratio of useful output energy (or power) to total input energy.
中文：效率是有用输出能量（或功率）与总输入能量之比。
4. Waves and Optics | 波与光学
The wave equation connects wave speed, frequency and wavelength. It applies to all types of progressive waves.
波速方程将波速、频率和波长联系起来，适用于所有行波。
v = f λ
English: Frequency is measured in hertz (Hz) and wavelength in metres (m).
中文：频率的单位是赫兹(Hz)，波长的单位是米(m)。
For refraction at a boundary, Snell's law describes the relationship between angles of incidence and refraction and the refractive indices of the media.
对于边界处的折射，斯涅尔定律描述了入射角、折射角与介质折射率之间的关系。
n₁ sin θ₁ = n₂ sin θ₂
English: The critical angle for total internal reflection occurs when light travels from a denser to a less dense medium.
中文：当光从光密介质射向光疏介质时，会发生全反射的临界角。
sin c = 1 / n
English: In a double‑slit interference experiment, fringe spacing depends on wavelength, slit‑to‑screen distance and slit separation.
中文：在双缝干涉实验中，条纹间距依赖于波长、缝屏距离及双缝间距。
Δy = λ D / d
English: The diffraction grating equation gives the angles at which maxima occur for a grating with line spacing d.
中文：衍射光栅方程给出了线间距为 d 的光栅产生极大值的角度。
d sin θ = n λ
5. Electricity | 电学
Electric current is the rate of flow of charge. One coulomb per second equals one ampere.
电流是电荷流动的速率。一库仑每秒等于一安培。
I = ΔQ / Δt
English: Ohm's law states that the potential difference across a conductor is proportional to the current, provided temperature remains constant.
中文：欧姆定律指出，在温度恒定的条件下，导体两端的电位差与电流成正比。
V = I R
English: Resistance depends on the material's resistivity, length and cross‑sectional area.
中文：电阻取决于材料的电阻率、长度和横截面积。
R = ρ L / A
English: Power dissipated in a circuit component can be expressed in three useful forms.
中文：电路元件耗散的功率有三种有用的表达式。
P = I V = I² R = V² / R
) and internal resistance are modelled as ε = I (R + r). The terminal p.d. is V = ε − I r.
中文：电动势和内阻可用 ε = I (R + r) 建模，路端电压为 V = ε − I r。
For resistors in series: Rₛ = R₁ + R₂ + …; in parallel: 1/Rₚ = 1/R₁ + 1/R₂ + ….
串联电阻：Rₛ = R₁ + R₂ + …；并联电阻：1/Rₚ = 1/R₁ + 1/R₂ + …。
6. The Mole and Stoichiometry | 摩尔与化学计量
The mole is the chemist's counting unit, containing 6.02 × 10²³ specified entities (Avogadro constant, Nₐ).
摩尔是化学家的计数单位，包含 6.02 × 10²³ 个指定微粒（阿伏伽德罗常数 Nₐ）。
n = m / M
English: Amount of substance (n) in moles equals mass (m) divided by molar mass (M) in g mol⁻¹.
中文：物质的量(n)以摩尔为单位，等于质量(m)除以摩尔质量(M)，单位为 g mol⁻¹。
For gases at room temperature and pressure, one mole occupies approximately 24.0 dm³ (24.0 L).
在室温和常压下，一摩尔气体约占据 24.0 dm³ (24.0 L) 的体积。
n = V (gas) / 24.0 dm³ mol⁻¹
English: Solution concentration links amount of solute to volume of solution.
中文：溶液浓度将溶质的物质的量与溶液体积联系起来。
c = n / V
English: The ideal gas equation combines pressure, volume, temperature and the number of moles.
中文：理想气体状态方程将压力、体积、温度和摩尔数结合在一起。
p V = n R T
ish: R is the gas constant, 8.31 J mol⁻¹ K⁻¹. Temperature must be in kelvin (T = θ + 273).
中文：R 是气体常数，8.31 J mol⁻¹ K⁻¹。温度必须使用开尔文 (T = θ + 273)。
Stoichiometric calculations use balanced equations to relate reacting amounts; the molar ratio comes directly from the coefficients.
化学计量计算使用配平方程式关联反应物的量；摩尔比直接来自化学计量数。
7. Gas Laws and Energetics | 气体定律与能量学
Boyle's law (constant T): p ∝ 1/V; Charles's law (constant p): V ∝ T; Gay‑Lussac's law (constant V): p ∝ T. These are unified in pV = nRT.
玻意耳定律（恒温）：p ∝ 1/V；查理定律（恒压）：V ∝ T；盖‑吕萨克定律（恒容）：p ∝ T。这些定律统一于 pV = nRT。
t constant pressure. Experimentally it is found from temperature changes using q = m c ΔT.
焓变(ΔH)是恒压条件下传递的热量。实验中通过温度变化使用 q = m c ΔT 求得。
q = m c ΔT
English: Here m is mass of the substance (usually water or solution), c its specific heat capacity (4.18 J g⁻¹ K⁻¹ for water), and ΔT the temperature change.
中文：此处 m 为物质的质量（常为水或溶液），c 为其比热容（水为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化。
ΔH = q / n
English: Divide the heat transferred by the moles of limiting reactant to obtain the molar enthalpy change.
中文：用传递的热量除以限制反应物的摩尔数，即可得到摩尔焓变。
Hess's law states that the total enthalpy change for a reaction is independent of the route taken. It allows the use of enthalpy cycles.
赫斯定律指出，反应的总焓变与途径无关，这允许使用焓循环进行计算。
ΔH = Σ (bonds broken) − Σ (bonds formed). You must use average bond enthalpies for gases.
键能计算：ΔH = Σ (断裂键的键能) − Σ (形成键的键能)。必须使用气态粒子的平均键焓。
8. Equilibrium and Acids | 平衡与酸
The equilibrium constant Kc expresses the ratio of product concentrations to reactant concentrations, each raised to the power of its stoichiometric coefficient in the balanced equation.
平衡常数 Kc 表示产物浓度与反应物浓度的比值，每种物质的浓度以其在配平方程式中的化学计量数为指数。
Kc = [products]ᵖ / [reactants]ʳ
English: For the reaction aA + bB ⇌ cC + dD, Kc = [C]ᶜ / ([A]ᵃ[B]ᵇ). Only gases and aqueous species appear; solids and pure liquids are omitted.
中文：对于反应 aA + bB ⇌ cC + dD，Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ)。只有气体和溶液中的物种出现，固体和纯液体不列入。
Le Chatelier's principle predicts the direction in which an equilibrium shifts when conditions (concentration, pressure, temperature) are changed.
勒夏特列原理预测当条件（浓度、压力、温度）变化时平衡移动的方向。
ward: for a monoprotic strong acid, [H⁺] equals the acid concentration, and pH = −log[H⁺].
强酸的 pH 计算直接：对于一元强酸，[H⁺] 等于酸浓度，pH = −log[H⁺]。
pH = −log₁₀[H⁺]
English: The ionic product of water at 298 K is Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶.
中文：298 K 时水的离子积 Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶。
9. Microscopy and Magnification | 显微镜与放大倍数
In optical microscopy, the total magnification is the product of the eyepiece lens magnification and the objective lens magnification. However, the most commonly used formula relates image size and actual size.
在光学显微镜中，总放大倍数是目镜放大倍数与物镜放大倍数的乘积。但最常用的公式将图像大小与实际大小联系起来。
Magnification = I / A
English: I is the image size (measured in mm or µm), A is the actual object size. Both must be in the same units.
中文：I 为图像大小（以 mm 或 µm 测量），A 为物体的实际大小。两者单位必须一致。
to find actual size: A = I / magnification. This is crucial when interpreting micrographs.
该公式可变形以求得实际大小：A = I / 放大倍数。这在解读显微照片时至关重要。
The graticule and stage micrometer are used to calibrate the eyepiece graticule. After calibration, each eyepiece unit corresponds to a known length.
目镜测微尺和镜台测微尺用于校准目镜尺。校准后，每个目镜单位对应已知的长度。
When calculating surface area to volume ratio, remember it decreases as cell size increases, affecting diffusion efficiency.
计算表面积与体积比时，要记住随着细胞增大该比值减小，这会影响扩散效率。
10. Genetics and Hardy–Weinberg | 遗传学与哈代‑温伯格定律
The Hardy–Weinberg principle predicts allele and genotype frequencies in a non‑evolving population. For two alleles (dominant A, recessive a) with frequencies p and q:
哈代‑温伯格定律预测一个不进化群体中的等位基因和基因型频率。对于两种等位基因（显性 A，隐性 a），其频率分别为 p 和 q：
p + q = 1
English: The expected genotype frequencies are given by the expansion of (p + q)².
中文：预期的基因型频率由 (p + q)² 展开式给出。
p² + 2 p q + q² = 1
English: p² is the frequency of homozygous dominant (AA), 2pq of heterozygous (Aa), and q² of homozygous recessive (aa).
中文：p² 为显性纯合子(AA)频率，2pq 为杂合子(Aa)频率，q² 为隐性纯合子(aa)频率。
These equations help estimate carrier frequencies and test whether allele frequencies are changing over generations.
这些方程有助于估计携带者频率并检验等位基因频率是否在代际间发生变化。
For dihybrid crosses, the expected phenotypic ratio in the F₂ generation (assuming independent assortment) is 9 : 3 : 3 : 1. The chi‑squared (χ²) test can determine whether observed ratios deviate significantly from expected.
对于双因子杂交，F₂ 代的预期表型比（假设自由组合）为 9 : 3 : 3 : 1。卡方(χ²)检验可判断观察比例是否显著偏离预期。
χ² = Σ (O − E)² / E
English: O is the observed frequency, E the expected frequency. Compare the calculated χ² to critical values at (n − 1) degrees of freedom.
中文：O 为观察频数，E 为预期频数。将计算出的 χ² 值与自由度为 (n − 1) 时的临界值比较。
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