📚 IGCSE OCR Science: Formula Handbook | IGCSE OCR 科学：公式汇总手册
Mastering the key formulas is essential for success in IGCSE OCR Science. This handbook brings together the most important equations from Physics, Chemistry, and Biology, with clear explanations and correct units. Use it to support your revision and to build confidence in tackling calculation questions across all three sciences.
掌握关键公式是 IGCSE OCR 科学考试成功的关键。本手册汇集了物理、化学和生物学科中最重要的方程式，并配有清晰的解释和正确单位。可用于辅助复习，并在解答三科计算题时建立信心。
1. Physics: Motion and Forces | 物理：运动与力
Speed describes how fast an object moves. It is calculated using v = s ÷ t, where v represents speed (m/s), s stands for distance (m), and t is time (s).
速度描述物体运动的快慢。公式为 v = s ÷ t，其中 v 代表速度（米/秒），s 代表距离（米），t 是时间（秒）。
Acceleration is the rate of change of velocity. The equation is a = (v – u) ÷ t. Here a is acceleration (m/s²), v is final velocity, u is initial velocity, and t is time taken. You may also see the rearranged form v = u + a t.
加速度是速度的变化率。方程为 a = (v – u) ÷ t。其中 a 是加速度（米/秒²），v 是末速度，u 是初速度，t 是所用时间。你可能还会看到变形 v = u + a t。
For uniform acceleration, the motion of an object can be linked using v² – u² = 2 a s, where s is displacement. This equation does not require time.
对于匀加速运动，物体的运动可通过 v² – u² = 2 a s 关联，其中 s 是位移。该方程不需要时间。
Newton’s second law states that force equals mass times acceleration: F = m × a (unit: newton, N). Weight is the force due to gravity: W = m × g, with g ≈ 9.8 m/s² on Earth.
牛顿第二定律指出力等于质量乘加速度：F = m × a（单位：牛顿，N）。重量由重力产生：W = m × g，地球上 g 约为 9.8 米/秒²。
Momentum is given by p = m × v (kg m/s). The force acting on an object can also be expressed as the rate of change of momentum: F = Δp ÷ t or F = (m v – m u) ÷ t.
动量的计算式为 p = m × v（千克·米/秒）。作用在物体上的力也可表示为动量变化率：F = Δp ÷ t 或 F = (m v – m u) ÷ t。
2. Physics: Energy and Power | 物理：能量与功率
Kinetic energy of a moving object is KE = ½ m v², where m is mass (kg) and v is speed (m/s). The unit of energy is the joule (J).
运动物体的动能为 动能 = ½ m v²，其中 m 是质量（千克），v 是速度（米/秒）。能量单位为焦耳 (J)。
Gravitational potential energy gained by rising through a height h is GPE = m × g × h. Again, m is mass, g is gravitational field strength, and h is vertical height (m).
物体升高 h 所获得的重力势能为 GPE = m × g × h。同样，m 是质量，g 是重力场强度，h 是竖直高度（米）。
Work done when a force moves an object is W = F × d, where F is the force (N) and d is distance moved in the direction of the force (m). Work and energy are interchangeable.
力使物体移动时做功为 W = F × d，其中 F 是力（牛顿），d 是沿力方向移动的距离（米）。功与能量可相互转换。
Power is the rate of doing work or transferring energy: P = W ÷ t or P = E ÷ t. Power is measured in watts (W). When an object moves at constant speed v, power can also be P = F × v.
功率是做功或传递能量的速率：P = W ÷ t 或 P = E ÷ t。功率单位为瓦特 (W)。当物体匀速运动时，功率也可表示为 P = F × v。
Efficiency compares useful output with total input: Efficiency = (useful output ÷ total input) × 100%. It has no units.
效率用于比较有用输出与总输入：效率 = (有用输出 ÷ 总输入) × 100%。无单位。
3. Physics: Electricity | 物理：电学
Electric charge transferred depends on current and time: Q = I × t, where Q is charge (coulombs, C), I is current (A), and t is time (s).
转移的电荷量取决于电流和时间：Q = I × t，其中 Q 是电荷量（库仑，C），I 是电流（安培，A），t 是时间（秒）。
Ohm’s law links potential difference, current, and resistance: V = I × R. V is in volts (V), I in (A), R in ohms (Ω).
欧姆定律将电位差、电流和电阻联系起来：V = I × R。V 单位为伏特 (V)，I 为安培 (A)，R 为欧姆 (Ω)。
Electrical power can be calculated in several forms: P = I × V, P = I² R, P = V² ÷ R. Use the form that matches the known quantities.
电功率有多种计算形式：P = I × V，P = I² R，P = V² ÷ R。应选用与已知量匹配的形式。
Energy transferred by an electrical component is E = P × t or E = I × V × t. Energy units are joules (J).
电器件传递的能量为 E = P × t 或 E = I × V × t。能量单位为焦耳 (J)。
For resistors in series, total resistance is R = R1 + R2 + …. For resistors in parallel, the reciprocal formula applies: 1/R = 1/R1 + 1/R2 + …. Remember to find the common denominator and invert the final sum.
串联电阻的总电阻为 R = R1 + R2 + …。并联电阻则用倒数公式：1/R = 1/R1 + 1/R2 + …。注意通分后取倒数。
4. Physics: Waves | 物理：波
Wave speed is found using frequency and wavelength: v = f × λ. v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m).
波速可利用频率和波长计算：v = f × λ。v 是波速（米/秒），f 是频率（赫兹），λ 是波长（米）。
The period T of a wave is the time for one complete cycle: T = 1 ÷ f. Period is measured in seconds (s).
波的周期 T 是完成一次全振动所需的时间：T = 1 ÷ f。周期单位为秒 (s)。
5. Physics: Density, Pressure and Hooke’s Law | 物理：密度、压强与胡克定律
Density links mass and volume: ρ = m ÷ V, where ρ is density (kg/m³), m is mass (kg), V is volume (m³). For liquids, use g/cm³ and grams.
密度连接质量与体积：ρ = m ÷ V，其中 ρ 是密度（千克/米³），m 是质量（千克），V 是体积（米³）。液体常用克/厘米³。
Pressure is force per unit area: p = F ÷ A. Pressure p is in pascals (Pa) when F is in newtons and A in m².
压强是单位面积上所受的力：p = F ÷ A。当 F 为牛顿、A 为米² 时，压强 p 单位为帕斯卡 (Pa)。
Hooke’s law for a spring: F = k × x, where k is the spring constant (N/m) and x is extension (m), provided the elastic limit is not exceeded.
弹簧的胡克定律：F = k × x，其中 k 是弹簧常数（牛/米），x 是伸长量（米），前提是未超过弹性限度。
6. Chemistry: The Mole and Mass Calculations | 化学：摩尔与质量计算
The amount of substance is measured in moles. Number of moles, mass, and molar mass are linked by n = m ÷ M, where n is amount (mol), m is mass (g), and M is molar mass (g/mol).
物质的量用摩尔衡量。摩尔数、质量和摩尔质量的关系为 n = m ÷ M，其中 n 为物质的量（摩尔），m 为质量（克），M 为摩尔质量（克/摩尔）。
Number of particles, atoms, or molecules is N = n × Nₐ, where Nₐ is Avogadro’s constant (6.02 × 10²³ mol⁻¹).
粒子、原子或分子数可通过 N = n × Nₐ 计算，Nₐ 为阿伏伽德罗常数 (6.02 × 10²³ mol⁻¹)。
At room temperature and pressure (rtp), one mole of any gas occupies 24 dm³: V = n × 24 (dm³). Use this only when conditions are rtp.
在常温常压下，1 摩尔任何气体占据 24 dm³：V = n × 24 (dm³)。仅当条件为常温常压时适用。
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