📚 IGCSE Science: Formula Summary Handbook | IGCSE 科学：公式汇总手册
Mastering the essential formulas is the key to success in IGCSE Science, whether you are tackling Physics, Chemistry or Biology questions. This handbook collects the most important equations, explains each symbol clearly and shows you how to use them step by step. Each formula is presented with an English description followed immediately by its Chinese equivalent so you can learn both languages.
掌握核心公式是攻克 IGCSE 科学的关键，无论你面对的是物理、化学还是生物题目。本手册汇集了最重要的方程式，清晰解释每一个符号，并逐步展示使用方法。每个公式都先给出英文说明，紧接着提供对应的中文解释，帮助你实现双语学习。
1. Speed, Velocity and Acceleration | 速度、速度与加速度
Speed is the distance travelled per unit time: v = s / t, where v is speed (m/s), s is distance (m) and t is time (s). For motion in a straight line, the same equation applies to velocity if direction is constant.
速度是单位时间内移动的距离：v = s / t，其中 v 表示速度（米/秒），s 表示距离（米），t 表示时间（秒）。若物体沿直线运动且方向不变，同一公式也适用于速度。
Acceleration is the rate of change of velocity: a = (v − u) / t. Here a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s) and t is the time taken (s).
加速度是速度变化的快慢：a = (v − u) / t。其中 a 为加速度（米/秒²），v 为末速度（米/秒），u 为初速度（米/秒），t 为所用时间（秒）。
When acceleration is constant, the relationship between initial velocity, final velocity, acceleration and displacement is given by v² = u² + 2as, where s stands for the displacement (m) along the line of motion.
当加速度恒定时，初速度、末速度、加速度和位移之间的关系可用 v² = u² + 2as 表示，其中 s 代表沿线位移（米）。
2. Newton’s Second Law and Weight | 牛顿第二定律与重量
Newton’s second law relates force, mass and acceleration: F = m × a. The force F is measured in newtons (N), mass m in kilograms (kg) and acceleration a in m/s². This law explains why a larger force produces a larger acceleration, and why a heavier object accelerates less for the same force.
牛顿第二定律将力、质量和加速度关联起来：F = m × a。力 F 的单位是牛顿 (N)，质量 m 的单位是千克 (kg)，加速度 a 的单位是米/秒²。该定律说明更大的力会产生更大的加速度，也解释了相同外力下质量越大的物体加速度越小。
Weight is the force of gravity acting on an object: W = m × g. Here W is weight (N), m is mass (kg) and g is the gravitational field strength (N/kg). On Earth, g is approximately 9.8 N/kg, so a 1 kg mass weighs about 9.8 N.
重量是作用在物体上的重力：W = m × g。其中 W 为重量 (N)，m 为质量 (kg)，g 为引力场强度 (N/kg)。在地球表面，g 约为 9.8 N/kg，因此 1 kg 的物体约重 9.8 N。
3. Momentum and Impulse | 动量与冲量
Momentum is the product of an object’s mass and velocity: p = m × v, where p is momentum (kg m/s), m is mass (kg) and v is velocity (m/s). Momentum is a vector quantity and its direction is the same as the velocity.
动量是物体质量与速度的乘积：p = m × v，其中 p 为动量 (kg·m/s)，m 为质量 (kg)，v 为速度 (m/s)。动量是矢量，方向与速度方向相同。
Impulse is the change in momentum and equals the average force multiplied by the time for which it acts: F × Δt = Δp = m × v − m × u. This relationship explains how airbags and crumple zones reduce injury by increasing the time over which a force acts, thereby reducing the peak force.
冲量等于动量的变化量，也等于平均力乘以力的作用时间：F × Δt = Δp = m × v − m × u。这个关系解释了安全气囊和褶皱区为何能减少伤害——它们延长了力作用的时间，从而降低了峰值力。
The principle of conservation of momentum states that in a closed system with no external forces, total momentum before a collision equals total momentum after the collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
动量守恒定律指出，在没有外力的封闭系统中，碰撞前的总动量等于碰撞后的总动量：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
4. Work, Energy and Power | 功、能量与功率
Work done is the energy transferred when a force moves an object: W = F × d. Work W is measured in joules (J), force F in newtons (N) and distance d in metres (m) moved in the direction of the force. If the force and motion are perpendicular, no work is done.
功是力使物体移动时所传递的能量：W = F × d。功 W 的单位是焦耳 (J)，力 F 的单位是牛顿 (N)，距离 d 的单位是米 (m)，且距离必须是沿力的方向移动的距离。如果力与运动方向垂直，则不做功。
Kinetic energy is the energy of a moving object: K.E. = ½ × m × v². Gravitational potential energy stored in an object raised above the ground is P.E. = m × g × h, where h is the height (m) above a reference level. Both energy forms are in joules.
动能是运动物体具有的能量：K.E. = ½ × m × v²。物体被举高后储存的重力势能是 P.E. = m × g × h，其中 h 为相对参考面的高度（米）。两种能量的单位都是焦耳。
Power is the rate of doing work or transferring energy: P = W / t or P = E / t. Power P is in watts (W), where 1 W = 1 J/s. Another useful form when an object moves at constant speed v under a steady force F is P = F × v.
功率是做功或传递能量的快慢：P = W / t 或 P = E / t。功率 P 的单位是瓦特 (W)，1 W = 1 J/s。当物体在恒力 F 作用下以恒定速度 v 运动时，另一个实用形式为 P = F × v。
5. Density and Pressure | 密度与压强
Density is mass per unit volume: ρ = m / V. The symbol ρ (rho) denotes density (kg/m³ or g/cm³), m is mass and V is volume. An object floats if its average density is less than that of the fluid it is placed in.
密度是单位体积的质量：ρ = m / V。符号 ρ 表示密度（kg/m³ 或 g/cm³），m 为质量，V 为体积。若物体的平均密度小于其所处流体的密度，物体就会漂浮。
Pressure is the force acting per unit area: p = F / A. Pressure p is measured in pascals (Pa), where 1 Pa = 1 N/m². A sharp knife exerts high pressure because the contact area A is small, making cutting easier.
压强是单位面积上承受的力：p = F / A。压强 p 的单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。锋利的刀因接触面积 A 很小而产生很大的压强，使切割更容易。
For a liquid at rest, pressure at a depth h is given by p = ρ × g × h. This pressure acts equally in all directions and increases linearly with depth. It explains why dams are thicker at the bottom.
对于静止的液体，深度 h 处的压强由 p = ρ × g × h 给出。该压强在所有方向上同等作用，并随深度线性增加。这解释了为何大坝的底部更厚。
6. Electricity Formulas | 电学公式
Ohm’s law links voltage, current and resistance: V = I × R, where V is potential difference (volts, V), I is current (amperes, A) and R is resistance (ohms, Ω). For a fixed resistor, current is directly proportional to voltage at constant temperature.
欧姆定律将电压、电流和电阻联系起来：V = I × R，其中 V 为电势差（伏特, V），I 为电流（安培, A），R 为电阻（欧姆, Ω）。对于固定电阻器，温度不变时电流与电压成正比。
Electric charge transferred is Q = I × t, where Q is charge in coulombs (C), I is current and t is time in seconds. This is used when calculating the amount of charge flowing in a circuit.
传递的电荷量计算公式为 Q = I × t，其中 Q 为电荷量（库仑, C），I 为电流，t 为时间（秒）。用于计算电路中流动的电荷量。
Electrical power can be expressed in three equivalent forms: P = I × V, P = I² × R and P = V² / R. Power is in watts. Energy transformed is then E = P × t.
电功率有三种等价形式：P = I × V、P = I² × R 和 P = V² / R。功率的单位是瓦特。转换的电能用 E = P × t 计算。
For series circuits, total resistance adds up: Rtotal = R₁ + R₂ + … while for parallel circuits the reciprocals add: 1 / Rtotal = 1 / R₁ + 1 / R₂ + ….
对于串联电路，总电阻为各电阻之和：R总 = R₁ + R₂ + …；而对于并联电路，总电阻的倒数等于各支路电阻倒数之和：1 / R总 = 1 / R₁ + 1 / R₂ + …。
7. Waves | 波动学公式
The wave equation relates speed, frequency and wavelength: v = f × λ, where v is wave speed (m/s), f is frequency (Hz) and λ is wavelength (m). This applies to all waves, including sound, water and electromagnetic waves.
波动方程将波速、频率和波长联系起来：v = f × λ，其中 v 为波速（米/秒），f 为频率（赫兹），λ 为波长（米）。该方程适用于所有波，包括声波、水波和电磁波。
The period T of a wave is the time for one complete oscillation and is the inverse of frequency: T = 1 / f. If a wave has a frequency of 50 Hz, its period is 0.02 s.
波的周期 T 是完成一次完整振动所需的时间，是频率的倒数：T = 1 / f。若某波频率为 50 Hz，其周期即为 0.02 秒。
8. Moles and Stoichiometry | 摩尔与化学计量
The mole is the unit for amount of substance. The number of moles n can be calculated from mass: n = m / M, where m is the mass in grams and M is the molar mass in g/mol (numerically equal to the relative formula mass Mr).
摩尔是物质的量的单位。摩尔数 n 可通过质量求得：n = m / M，其中 m 为质量（克），M 为摩尔质量（g/mol），其数值与相对分子质量 Mr 相同。
For gases at room temperature and pressure (rtp), one mole occupies 24 dm³. Thus the volume V (in dm³) of a gas is V = n × 24. This allows chemists to convert between moles and gas volume in reactions.
在常温常压 (rtp) 下，1 摩尔任何气体的体积为 24 dm³。因此气体体积 V（dm³）可用 V = n × 24 计算。这使得化学家可以在反应中相互转换摩尔数和气体体积。
Concentration of a solution is the amount of solute per unit volume: c = n / V, where c is concentration in mol/dm³, n is the number of moles and V is the volume of solution in dm³. A 1 mol/dm³ solution contains 1 mole of solute per 1 dm³ of solution.
溶液的浓度是单位体积中所含溶质的量：c = n / V，其中 c 为浓度（mol/dm³），n 为摩尔数，V 为溶液体积（dm³）。1 mol/dm³ 的溶液表示 1 dm³ 溶液中含有 1 摩尔溶质。
Percentage yield compares the actual amount of product obtained to the theoretical maximum: % yield = (actual yield / theoretical yield) × 100. Atom economy measures how much of the reactant atoms end up in the desired product: % atom economy = (Mr of desired product / sum of Mr of all reactants) × 100.
产率百分比将实际得到的产物的量与理论最大量进行比较：产率 % = (实际产量 / 理论产量) × 100。原子经济性衡量有多少反应物原子最终进入了目标产物：原子经济性 % = (目标产物的 Mr / 所有反应物 Mr 之和) × 100。
9. Titration Calculations | 滴定计算
Titrations use the relationship cA × VA / a = cB × VB / b when a balanced equation aA + bB → products. Simply put, moles of A and B are in the ratio a:b. The most common shortcut for 1:1 reactions is c1 V1 = c2 V2. Remember to convert volumes to dm³ when using mol/dm³.
滴定利用方程式 cA × VA / a = cB × VB / b 进行计算，该式源于化学计量比 aA + bB → 产物。最简单的情形是 1:1 反应，常用 c1 V1 = c2 V2。注意使用 mol/dm³ 时需将体积换算为 dm³。
10. Biological Calculations | 生物计算
Magnification is the ratio of the size of an image to the real size of the object: magnification = image size / actual size. Both measurements must be in the same unit. A magnification of ×400 means the image is 400 times larger than the real specimen.
放大率是图像大小与物体实际大小的比值：放大率 = 图像大小 / 实际大小。测量时必须使用相同单位。例如放大率为 ×400 表示图像比实际标本大 400 倍。
Percentage change is widely used to compare initial and final values: % change = ((final value − initial value) / initial value) × 100. This helps biologists analyse growth, population changes or experimental results.
百分比变化广泛用于比较初始值和最终值：变化率 % = ((终值 − 初值) / 初值) × 100。这能帮助生物学家分析生长、种群变化或实验结果。
Efficiency of energy transfer between trophic levels is calculated by efficiency = (energy available to the next level / energy that was available to the current level) × 100, or similarly for biomass. It is normally around 10% in food chains.
营养级之间的能量传递效率可通过 效率 = (可用于下一级的能量 / 当前级可用的能量) × 100 计算，生物量传递效率类似。在食物链中，该效率通常约为 10%。
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