📚 IB & Edexcel Science: Formula Summary Handbook | IB & Edexcel 科学：公式汇总手册
Mastering scientific formulae is essential for success in both IB and Edexcel science courses. This handbook gathers the most frequently used equations across physics, chemistry, and biology, presented in a clear bilingual format so you can revise efficiently and avoid mixing up symbols and units.
掌握科学公式是 IB 与 Edexcel 科学课程取得高分的关键。本手册汇集了物理、化学、生物中最常用的方程，采用清晰的中英双语对照，让你高效复习，不再混淆符号与单位。
1. Motion & Kinematics | 运动学
The equations of uniformly accelerated motion allow us to predict an object’s velocity, displacement, and acceleration over time.
匀加速运动方程可用来预测物体在一段时间内的速度、位移和加速度。
v = u + at
v = final velocity, u = initial velocity, a = constant acceleration, t = time.
v = 末速度，u = 初速度，a = 恒定加速度，t = 时间。
s = ut + ½at²
s = displacement; this equation links distance covered with initial speed, acceleration, and time.
s = 位移；该方程将位移与初速度、加速度和时间联系起来。
v² = u² + 2as
Useful when time is not given. All quantities are along the same straight line.
当时间未知时使用。所有量均沿同一直线。
2. Forces & Newton’s Laws | 力与牛顿定律
Newton’s second law is the cornerstone of dynamics. It connects net force, mass, and acceleration.
牛顿第二定律是动力学的基石，它将合力、质量和加速度联系在一起。
Fnet = ma
Fnet is the resultant force in newtons (N), m is mass in kilograms (kg), a is acceleration in m/s².
Fnet 为合力（牛顿），m 为质量（千克），a 为加速度（米/秒²）。
W = mg
Weight (W) is the force due to gravity; g is gravitational field strength (≈ 9.81 N/kg on Earth).
重量（W）是重力引起的力；g 为引力场强度（地球表面约为 9.81 N/kg）。
F = kΔx
Hooke’s law for springs: k is the spring constant, Δx is extension from natural length.
胡克定律：k 为弹簧常数，Δx 为伸长量。
3. Work, Energy & Power | 功、能与功率
Energy is conserved, but we calculate its transfer using these fundamental relations.
能量是守恒的，我们借助这些基本关系计算能量的传递。
W = Fs cosθ
Work done = force × displacement × cosine of angle between them. θ = 0° when force and motion are parallel.
功 = 力 × 位移 × 两者夹角的余弦。当力与运动平行时，θ = 0°。
KE = ½mv²
Kinetic energy of a moving object. m is mass, v is speed.
运动物体的动能。m 为质量，v 为速率。
GPE = mgh
Gravitational potential energy near Earth’s surface. h is the height above a reference level.
地球表面附近的重力势能。h 为相对参考平面的高度。
P = W / t = Fv
Power (P) is the rate of doing work, also equals force × average velocity when force is constant.
功率（P）是做功的速率，当力恒定时也等于力 × 平均速度。
4. Electricity & Circuits | 电学与电路
Electric circuit formulae link current, voltage, resistance, and power.
电路公式将电流、电压、电阻和功率联系起来。
V = IR
Ohm’s law: V is potential difference (volts), I is current (amperes), R is resistance (ohms).
欧姆定律：V 为电势差（伏特），I 为电流（安培），R 为电阻（欧姆）。
P = IV = I²R = V²/R
Electrical power dissipated in a component. Use the appropriate form depending on known quantities.
元件消耗的电功率。根据已知量选用适当形式。
Rseries = R₁ + R₂ + …
Resistors in series add directly.
串联时电阻直接相加。
1/Rparallel = 1/R₁ + 1/R₂ + …
Parallel resistors combine as the reciprocal of the sum of reciprocals.
并联电阻的合成为倒数之和的倒数。
5. Waves & Optics | 波与光学
Wave behaviour is described by speed, frequency, and wavelength, as well as optical laws.
波的行为可用波速、频率、波长以及光学定律来描述。
v = fλ
Wave speed (v) = frequency (f) × wavelength (λ). True for all wave types.
波速 v = 频率 f × 波长 λ。适用于所有波。
n = c / v
Refractive index (n) of a medium: c = speed of light in vacuum, v = speed in medium.
介质折射率 n = 真空光速 c / 介质中光速 v。
n₁ sinθ₁ = n₂ sinθ₂
Snell’s law for refraction. θ is measured from the normal.
斯涅尔折射定律。θ 从法线量起。
1/f = 1/u + 1/v
Thin lens equation: f = focal length, u = object distance, v = image distance. Use sign conventions.
薄透镜公式：f 为焦距，u 为物距，v 为像距。需遵守符号约定。
6. Thermodynamics & Gas Laws | 热力学与气体定律
Thermal physics includes heat transfer, ideal gas behaviour, and changes of state.
热物理涵盖热传递、理想气体行为以及物态变化。
Q = mcΔT
Heat transferred = mass × specific heat capacity × temperature change. No phase change occurs.
传递的热量 = 质量 × 比热容 × 温度变化。用于无相变时。
Q = mL
Latent heat: L is specific latent heat (fusion or vaporisation) in J/kg.
潜热：L 为比潜热（熔化或汽化），单位 J/kg。
pV = nRT
Ideal gas law: p = pressure, V = volume, n = number of moles, R = 8.31 J/mol·K, T = absolute temperature.
理想气体状态方程：p 为压强，V 为体积，n 为摩尔数，R = 8.31 J/mol·K，T 为绝对温度。
p₁V₁ / T₁ = p₂V₂ / T₂
Combined gas law for a fixed mass of gas.
定质量气体的联合气体定律。
7. Chemical Quantities & Moles | 化学计量与摩尔
The mole concept is fundamental for quantifying chemical substances and reactions.
摩尔概念是量化化学物质和反应的基础。
n = m / M
Amount (mol) = mass (g) / molar mass (g/mol).
物质的量 (mol) = 质量 (g) / 摩尔质量 (g/mol)。
n = V / Vm
For gases at rtp: Vm = 24 dm³/mol (or 24.5 L/mol at SATP); at STP: 22.7 dm³/mol.
室温常压下气体：Vm = 24 dm³/mol；标准状况下为 22.7 dm³/mol。
c = n / V
Concentration (mol/dm³) = amount of solute / volume of solution in dm³.
浓度 (mol/dm³) = 溶质的量 / 溶液体积 (dm³)。
N = n × L
Number of particles = amount (mol) × Avogadro constant (L ≈ 6.02×10²³ mol⁻¹).
粒子数 = 物质的量 × 阿伏伽德罗常数 (6.02×10²³ mol⁻¹)。
8. Energetics & Enthalpy | 能量学与焓
Thermochemistry measures heat changes in chemical reactions, usually at constant pressure.
热化学测量化学反应的热量变化，通常在恒压下进行。
q = mcΔT
Heat absorbed/released by a solution: m = mass, c = specific heat capacity, ΔT = temperature change.
溶液吸收或放出的热量：m 为质量，c 为比热容，ΔT 为温度变化。
ΔH = –q / n
Enthalpy change (kJ/mol) = –heat transferred / amount reacted. Negative q if exothermic in the equation context.
焓变 (kJ/mol) = –传递的热量 / 反应物质的量。式中的负号依放热习惯。
ΔH = Σ(bonds broken) – Σ(bonds formed)
Bond enthalpy method; bond breaking is endothermic, bond forming is exothermic.
键焓法；断键吸热，成键放热。
ΔG = ΔH – TΔS
Gibbs free energy change for predicting spontaneity. ΔG < 0 for a feasible process.
吉布斯自由能变，用于判断反应自发性。ΔG < 0 为可行过程。
9. Rates of Reaction | 反应速率
Kinetics studies how fast reactants convert into products and which factors affect the speed.
动力学研究反应物转化为产物的快慢以及影响速度的因素。
Rate = –Δ[R] / t = Δ[P] / t
Average rate measured as change in concentration of a reactant or product over time.
平均速率用反应物或产物浓度随时间的变化表示。
Rate = k [A]m[B]n
Rate law: k = rate constant, m, n are orders of reaction (often 0, 1, or 2).
速率方程：k 为速率常数，m、n 为反应级数（常为 0、1、2）。
t½ = ln 2 / k
Half-life for a first-order reaction, independent of initial concentration.
一级反应的半衰期，与初始浓度无关。
10. Equilibrium & Acids-Bases | 平衡与酸碱
Equilibrium constants quantify the extent of reversible reactions; acid-base theories involve proton transfer.
平衡常数定量描述可逆反应的程度；酸碱理论涉及质子转移。
Kc = [products]/[reactants]
Equilibrium constant in terms of concentration. Each concentration is raised to the power of its stoichiometric coefficient.
浓度平衡常数。各浓度以其化学计量数为指数。
pH = –log[H⁺]
pH is the negative logarithm (base 10) of hydrogen ion concentration.
pH 为氢离子浓度的负对数（以 10 为底）。
Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 298 K)
Ionic product of water. Used to relate pH and pOH.
水的离子积，用于关联 pH 和 pOH。
11. Biology: Magnification & Genetics | 生物学：放大率与遗传
Biology formulae help quantify observations from microscopy and predict genetic outcomes.
生物学公式有助于量化显微镜下的观察结果并预测遗传结果。
M = I / A
Magnification = size of image / actual size of specimen. Ensure units are consistent.
放大率 = 图像大小 / 标本实际大小。务必单位一致。
P = (number of desired outcomes) / (total possible outcomes)
Probability in monohybrid crosses; often presented in Punnett square ratios.
单基因杂交中的概率，常用庞纳特方格比率表示。
X² = Σ [(O – E)² / E]
Chi-squared test for goodness of fit in genetics experiments. O = observed, E = expected frequencies.
遗传学实验中的卡方检验，用于拟合优度。O 为观测值，E 为期望值。
12. Data Handling & Uncertainties | 数据处理与不确定度
Precise scientific measurement requires quantifying uncertainty and combining errors.
精确的科学测量需要量化不确定度并合成误差。
Absolute uncertainty = ± (smallest division / 2) for analogue instruments
For a ruler with 1 mm marks, absolute uncertainty is ±0.5 mm. For digital instruments, it is ± the least significant digit.
对于最小刻度 1 mm 的直尺，绝对不确定度为 ±0.5 mm。数字仪器则为 ± 最后一位有效数字。
% uncertainty = (absolute uncertainty / measured value) × 100%
Percentage uncertainty is used to compare precision across different scales.
百分比不确定度用于跨量程比较精度。
For addition/subtraction: add absolute uncertainties.
When adding or subtracting measurements, sum the absolute uncertainties.
加减运算时，总绝对不确定度为各绝对不确定度之和。
For multiplication/division: add percentage uncertainties.
When multiplying or dividing, sum the percentage uncertainties to get the final percentage uncertainty.
乘除运算时，总百分比不确定度为各百分比不确定度之和。
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