📚 GCSE CIE Science Formula Handbook | GCSE CIE 科学公式汇总手册
This handbook gathers all the key formulas required for CIE GCSE Science (Co-ordinated or separate Biology, Chemistry, Physics). Use it for quick revision, to practise calculations, and to check your understanding before exams. Every formula is accompanied by units and a short explanation.
本手册收录了 CIE GCSE 科学（综合科学或单独的物理、化学、生物）所需的所有核心公式。你可用于快速复习、练习计算，并在考前检查理解。每个公式都配有单位和简要说明。
1. Speed, Acceleration and Motion | 速度、加速度与运动
Average speed is the total distance travelled divided by the total time taken. The SI unit of speed is metres per second (m/s).
平均速度是总行驶距离除以总时间。速度的国际单位是米每秒 (m/s)。
v = s ÷ t
Acceleration is the rate of change of velocity. It can be calculated from the change in velocity divided by the time taken for that change. Acceleration may be positive (speeding up) or negative (slowing down).
加速度是速度的变化率。可以用速度变化量除以变化所用时间计算。加速度可以是正的（加速）或负的（减速）。
a = (v − u) ÷ t
For motion with constant acceleration, four useful equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
对于匀加速运动，四个有用的方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系起来。
v = u + a t
s = (u + v) ÷ 2 × t
s = u t + ½ a t²
v² = u² + 2 a s
On a distance–time graph, the gradient gives speed. On a velocity–time graph, the gradient gives acceleration and the area under the graph gives the distance travelled.
在距离–时间图中，斜率给出速度。在速度–时间图中，斜率给出加速度，图下面积给出所行距离。
2. Forces, Mass and Momentum | 力、质量与动量
The resultant force on an object equals its mass multiplied by its acceleration. This is Newton’s second law.
作用在物体上的合力等于物体质量乘以加速度。这是牛顿第二定律。
F = m a
Weight is the force of gravity on a mass. On Earth the gravitational field strength g is approximately 9.8 N/kg.
重量是重力作用在质量上的力。在地球上，重力场强度 g 约为 9.8 N/kg。
W = m g
Momentum is the product of mass and velocity. It is a vector quantity.
动量是质量与速度的乘积。它是一个矢量。
p = m v
A resultant force causes a change in momentum. The product of force and the time for which it acts is called impulse, which equals the change in momentum.
合力引起动量的变化。力与力的作用时间的乘积叫做冲量，冲量等于动量的变化。
F t = Δ(m v) = m v − m u
3. Energy, Work and Power | 能量、功与功率
Kinetic energy is the energy an object has due to its motion. It depends on mass and the square of speed.
动能是物体因运动而具有的能量。它取决于质量和速度的平方。
Ek = ½ m v²
Gravitational potential energy is the energy stored when an object is raised against gravity. The change in GPE depends on mass, gravitational field strength and height.
重力势能是物体克服重力被抬高时储存的能量。重力势能的变化取决于质量、重力场强度和高度。
ΔEp = m g Δh
Work is done when a force moves an object. Energy transferred equals work done.
当力使物体移动时就做了功。传递的能量等于所做的功。
W = F d
Power is the rate at which energy is transferred or work is done. The unit of power is the watt (W).
功率是能量传递或做功的速率。功率的单位是瓦特 (W)。
P = W ÷ t = ΔE ÷ t
Efficiency is the ratio of useful output energy (or power) to total input energy. It can be expressed as a percentage.
效率是有用的输出能量（或功率）与总输入能量之比。它可以用百分数表示。
efficiency = (useful output ÷ total input) × 100%
4. Density and Pressure | 密度与压强
Density is mass per unit volume. It is measured in kg/m³ or g/cm³.
密度是单位体积的质量。它以 kg/m³ 或 g/cm³ 测量。
ρ = m ÷ V
Pressure is the force acting perpendicularly per unit area. The unit of pressure is the pascal (Pa).
压强是垂直作用在单位面积上的力。压强的单位是帕斯卡 (Pa)。
p = F ÷ A
The pressure at a depth in a liquid depends on the density of the liquid, gravitational field strength and the depth.
液体中某一深度的压强取决于液体的密度、重力场强度和深度。
p = ρ g h
5. Thermal Physics: Specific Heat and Latent Heat | 热学：比热容与潜热
The amount of thermal energy required to change the temperature of a substance depends on its mass, specific heat capacity and the temperature change.
改变物质温度所需的热量取决于质量、比热容和温度变化。
Q = m c Δθ
When a substance changes state, energy is transferred without a change in temperature. The energy needed for a given mass is the product of mass and specific latent heat.
当物质改变状态时，能量会在温度不变的情况下传递。一定质量改变状态所需的能量是质量与比潜热的乘积。
Q = m L
Specific latent heat of fusion is used for melting/freezing, and specific latent heat of vaporisation is used for boiling/condensing.
熔化/凝固使用比熔化潜热，沸腾/凝结使用比汽化潜热。
6. Waves and Optics | 波与光学
The speed of a wave is linked to its frequency and wavelength. This applies to all types of wave, including sound and light.
波速与频率和波长相关。这适用于所有类型的波，包括声波和光波。
v = f λ
The period of a wave is the time for one complete cycle. It is the reciprocal of the frequency.
波的周期是完成一个整循环的时间。它是频率的倒数。
T = 1 ÷ f
Refractive index n relates the angles of incidence and refraction when light passes between two media. Snell’s law applies.
折射率 n 将光线在两种介质间传播时的入射角和折射角联系起来。斯涅尔定律适用。
n = sin i ÷ sin r
The critical angle for total internal reflection is given by this formula when light travels from a denser medium to a less dense one.
当光从光密介质射向光疏介质时，全内反射的临界角由以下公式给出。
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