📚 Year 13 AQA Science: Quick Reference Formula & Theorem Handbook | AQA A2 科学：公式定理速查手册
This handbook collects the most essential formulas and theorems from Year 13 AQA Physics, Chemistry and Biology. It is designed as a rapid revision aid, linking each equation to its meaning and typical application so you can check your recall efficiently before mocks and final exams.
这本速查手册汇集了 AQA 物理、化学和生物 Year 13 阶段最核心的公式与定理，旨在帮助同学们快速梳理考点，将每一个公式与其物理意义、化学原理或生物学解释紧密对应，让考前自查更加高效。
1. Physics: Mechanics and Materials | 物理：力学与材料
The SUVAT equations apply when acceleration is constant. They link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
v = u + at
匀加速直线运动的基本方程，末速度等于初速度加上加速度与时间的乘积。
Newton’s second law defines resultant force as the rate of change of momentum. For constant mass it simplifies to F = ma.
F = ma
牛顿第二定律说明合力等于动量变化率；质量不变时可简化为合力等于质量乘加速度。
Momentum is conserved in all collisions provided no external resultant force acts.
p = mv
动量定义为质量与速度的乘积，在封闭系统中碰撞前后总动量守恒。
Kinetic energy and gravitational potential energy are the two mechanical energy stores most commonly interchanged.
Ek = ½mv² | Ep = mgΔh
动能等于二分之一质量乘速度平方；重力势能等于质量、重力场强与高度变化的乘积。
Hooke’s law relates the extension of a spring to the applied force, up to the limit of proportionality. The Young modulus describes the stiffness of a material.
F = kΔL | E = stress/strain
胡克定律指出弹性限度内弹力与伸长量成正比；杨氏模量定义为应力与应变之比，表征材料抵抗形变的能力。
Work done by a constant force is the product of the force, displacement and the cosine of the angle between them. Power is the rate of doing work.
W = F s cosθ | P = W/t = F v
恒力做功等于力、位移与两者夹角余弦的积；功率是做功的速率，可写为牵引力与速度的乘积。
2. Physics: Waves and Optics | 物理：波与光学
All waves obey the wave speed equation linking frequency, wavelength and speed. For light in a vacuum c = 3.00 × 10⁸ m s⁻¹.
v = f λ
波速等于频率与波长的乘积, 在真空中电磁波的波速为光速。
Snell’s law describes refraction at a boundary. The refractive index n can be expressed as the ratio of speeds or the ratio of sines.
n = c/v | n₁ sin θ₁ = n₂ sin θ₂
折射定律说明入射角与折射角的正弦之比等于两种介质折射率之反比；折射率亦为真空中光速与介质中光速之比。
The critical angle for total internal reflection depends only on the refractive indices of the two media.
sin C = n₂ / n₁ (for n₁ > n₂)
当光从光密介质射向光疏介质时，入射角大于临界角发生全内反射，临界角的正弦值为折射率之比。
Young’s double-slit experiment gives the fringe spacing on a distant screen.
λ = a x / D
杨氏双缝干涉条纹间距 x 与波长 λ、缝间距 a 和屏幕距离 D 的关系式。
For a diffraction grating, constructive interference occurs when the path difference is an integer multiple of the wavelength.
d sin θ = n λ
衍射光栅公式中 d 为光栅常数，θ 为衍射角，n 为光谱级次。
3. Physics: Electricity and Magnetism | 物理：电与磁
Ohm’s law holds for ohmic conductors at constant temperature.
V = I R
欧姆定律：导体两端电压等于通过电流与电阻的乘积。
Electrical power can be expressed in three equivalent forms using the resistance of the component.
P = I V = I²R = V²/R
电功率与电压、电流和电阻之间的关系，适用焦耳热和电路能量转换计算。
The emf of a source is equal to the terminal p.d. plus the lost volts across the internal resistance.
ε = I (R + r)
电源电动势等于外电路电压与内电阻上电压之和。
Capacitance is defined as charge stored per unit potential difference. The energy stored in a capacitor is given by three equivalent expressions.
C = Q/V | E = ½ Q V = ½ C V² = ½ Q² / C
电容定义为单位电压下储存的电荷量；储存能量可依已知量选择三种形式之一进行计算。
The discharge of a capacitor through a resistor follows an exponential decay with time constant τ = RC.
Q = Q₀ e^(–t/RC) | τ = RC
电容放电时电荷随时间指数衰减，时间常数 τ 决定衰减快慢。
The force on a current-carrying conductor in a magnetic field is given by Fleming’s left-hand rule, with magnitude proportional to the sine of the angle between current and field.
F = B I L sin θ
通电导线在磁场中受到安培力，力的大小与磁感应强度、电流、导线长度及夹角正弦成正比。
Faraday’s law and Lenz’s law combine to give the induced emf, which opposes the change in magnetic flux.
ε = – N ΔΦ/Δt
法拉第电磁感应定律说明感应电动势与磁通量变化率的负值乘以线圈匝数。
4. Physics: Thermal and Kinetic Theory | 物理：热物理与气体动理论
The ideal gas equation links pressure, volume, temperature and the amount of gas in moles. The Boltzmann constant version uses the number of particles.
p V = n R T | p V = N k T
理想气体状态方程将宏观量压强、体积、温度与物质的量关联；用分子数表达时引入玻尔兹曼常数。
The average translational kinetic energy of a gas molecule is directly proportional to the absolute temperature.
½ m⟨c²⟩ = (3/2) k T
气体分子平均平动动能公式，说明温度是分子平均动能的量度。
The first law of thermodynamics relates the change in internal energy to the heat added to the system and the work done on the system.
ΔU = Q + W
热力学第一定律：系统内能的增加等于吸收的热量与外界对系统做功之和。
5. Physics: Nuclear and Particle Physics | 物理：核与粒子物理
Mass and energy are equivalent. In nuclear reactions the mass defect appears as released energy.
ΔE = Δm c²
质能方程说明能量变化等于质量变化乘以光速的平方，核反应释放能量来源于质量亏损。
Radioactive decay is a random, exponential process. The activity is proportional to the number of undecayed nuclei.
N = N₀ e^(–λ t) | A = λ N
放射性衰变遵循指数规律，衰变常数 λ 与半衰期 T½ = ln 2 / λ 相关。
The half-life is the time taken for the number of nuclei (or activity) to halve.
T½ = ln 2 / λ
半衰期由衰变常数决定，与初始核数目无关，是指数衰变的重要特征参数。
In photoelectric emission, the maximum kinetic energy of photoelectrons depends on the photon energy and the work function of the metal.
Ek(max) = h f – φ
光电效应方程中光子能量必须大于逸出功才能释放电子，剩余能量转化为电子最大动能。
6. Chemistry: Reaction Kinetics and Equilibria | 化学：反应动力学与平衡
The rate equation expresses how the rate depends on the concentrations of reactants raised to their orders. The rate constant k is temperature dependent.
Rate = k [A]ᵐ [B]ⁿ
速率方程中反应级数 m 和 n 由实验测定，速率常数随温度升高而增大。
The Arrhenius equation quantitatively links the rate constant, activation energy and temperature.
k = A e^(–Eₐ/RT) | ln k = –Eₐ/RT + ln A
阿伦尼乌斯方程说明速率常数的对数与 1/T 成线性关系，斜率可用于求活化能 Eₐ。
The equilibrium constant Kc is derived from the balanced chemical equation at equilibrium. Its value is constant at a given temperature.
Kc = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ)
化学平衡常数 Kc 以产物浓度幂之积除以反应物浓度幂之积，纯固体或液体不写入表达式。
For gaseous equilibria, partial pressures replace concentrations, giving Kp.
Kp = (p_Cᶜ p_Dᵈ) / (p_Aᵃ p_Bᵇ)
分压平衡常数 Kp 与浓度平衡常数类似，只适用于气体反应，压强须以标准压强为参考。
7. Chemistry: Acids, Bases and Thermodynamics | 化学：酸碱与热力学
The pH scale is defined as the negative logarithm of the hydrogen ion concentration. The ionic product of water Kw is constant at a given temperature.
pH = –log[H⁺] | Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ (298 K)
pH 定义为氢离子浓度的负对数；水的离子积在 298 K 时为 1.0 × 10⁻¹⁴。
Weak acids partially dissociate, and their strength is quantified by Ka and pKa.
Ka = [H⁺][A⁻]/[HA] | pKa = –log Ka
弱酸的酸解离常数 Ka 表示其提供质子的能力，pKa 越小酸性越强。
The Henderson–Hasselbalch equation predicts the pH of a buffer solution made from a weak acid and its conjugate base.
pH = pKa + log([A⁻]/[HA])
缓冲溶液 pH 取决于酸解离常数及共轭碱与酸浓度的比值，外加少量酸碱时 pH 变化很小。
Enthalpy change of reaction can be calculated from standard enthalpies of formation using Hess’s law.
ΔH° = Σ ΔHf°(products) – Σ ΔHf°(reactants)
反应焓变等于生成物标准生成焓总和减去反应物标准生成焓总和。
Gibbs free energy change determines the feasibility of a reaction. It combines enthalpy, entropy and temperature.
ΔG = ΔH – TΔS | ΔG° = –RT ln K
吉布斯自由能变 ΔG 为负时反应热力学可行；它通过平衡常数与标准自由能变相联系。
8. Chemistry: Electrochemistry | 化学：电化学
The cell potential is the difference between the reduction potentials of the two half-cells, measured under standard conditions.
E°_cell = E°_right – E°_left
标准电池电动势等于右半电池与左半电池的标准电极电势之差，正值表示电池自发反应。
The Nernst equation allows calculation of cell potential under non-standard concentrations, although a simplified version is used at A-level.
E = E° – (0.0592/n) log Q (at 298 K)
能斯特方程表达浓度对电极电势的影响；在 A-level 考试中常用 298 K 下的简化形式。
The relationship between free energy change and cell potential links thermodynamics to electrochemistry.
ΔG° = –n F E°_cell
标准自由能变与电池标准电动势和转移电子数成正比，负号表明自发反应时 ΔG 为负。
9. Biology: Genetics, Evolution and Populations | 生物：遗传、进化与种群
The Hardy–Weinberg principle predicts allele and genotype frequencies in a non-evolving population. Allele frequencies are represented as p and q.
p + q = 1 | p² + 2pq + q² = 1
哈迪–温伯格定律中 p 与 q 分别代表显性和隐性等位基因频率，p², 2pq, q² 为三种基因型的平衡频率。
Chi-squared test determines whether observed frequencies differ significantly from expected values in genetic crosses or ecological surveys.
χ² = Σ (O – E)² / E
卡方检验通过比较观测值 O 与期望值 E 的差异平方和来判断偏差是否由随机因素引起。
In population size estimation using mark–release–recapture, the Lincoln index provides a simple estimate of total number.
N = (M × C) / R
标记重捕法估算种群大小：N = (标记数 × 第二次捕获总数) / 第二次捕获中含标记的个体数。
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