📚 IGCSE CIE Science: Formula Handbook | IGCSE CIE 科学：公式汇总手册
This comprehensive handbook brings together all the essential formulas you need for IGCSE CIE Science, covering Physics, Chemistry, and Biology. Mastering these equations is crucial for tackling numerical problems, explaining scientific phenomena, and building confidence for your examinations. Each formula is presented clearly with a brief explanation so you can memorise and apply it effectively.
这本综合手册汇总了 IGCSE CIE 科学考试中所有必备公式，涵盖物理、化学和生物。掌握这些公式是攻克计算题、解释科学现象、建立考试信心的关键。每个公式都配有简明解说，帮助你高效记忆和运用。
1. Kinematics | 运动学
Relationship between final velocity, initial velocity, acceleration and time:
v = u + at
末速度、初速度、加速度与时间的关系：
v = u + at
Displacement travelled under constant acceleration (one form):
s = ut + ½at²
匀加速直线运动的位移（一种形式）：
s = ut + ½at²
Another displacement relation linking velocities:
v² = u² + 2as
连接速度与位移的另一关系式：
v² = u² + 2as
Average velocity and displacement:
s = (u + v)t / 2
平均速度与位移：
s = (u + v)t / 2
Speed from distance and time:
v = s / t
由距离和时间求速率：
v = s / t
Acceleration as the gradient of a velocity-time graph:
a = (v – u) / t
加速度作为速度-时间图线的斜率：
a = (v – u) / t
2. Forces and Momentum | 力与动量
Newton’s second law of motion:
F = m a
牛顿第二定律：
F = m a
Weight and mass:
W = m g
重量与质量：
W = m g
Momentum of a moving object:
p = m v
运动物体的动量：
p = m v
Impulse and change in momentum:
Ft = m v – m u
冲量与动量变化：
Ft = m v – m u
Force exerted by a spring (Hooke’s law up to limit of proportionality):
F = k x
弹簧的弹力（在弹性限度内）：
F = k x
Moment of a force about a pivot:
Moment = F × d
力关于支点的力矩：
力矩 = F × d
3. Energy, Work and Power | 能量、功和功率
Kinetic energy of a moving object:
Ek = ½ m v²
运动物体的动能：
Ek = ½ m v²
Gravitational potential energy near Earth’s surface:
GPE = m g h
地球表面附近的重力势能：
GPE = m g h
Work done by a constant force:
W = F d
恒力做的功：
W = F d
Power as the rate of doing work:
P = W / t
功率表示做功的快慢：
P = W / t
Power related to force and velocity:
P = F v
功率与力和速度的关系：
P = F v
Efficiency as a percentage:
Efficiency = (useful output / total input) × 100%
效率的百分比公式：
效率 = (有用输出 / 总输入) × 100%
4. Pressure and Density | 压强与密度
Pressure from a force acting on an area:
P = F / A
力作用于面积产生的压强：
P = F / A
Hydrostatic pressure in a liquid column:
p = h ρ g
液柱产生的静压强：
p = h ρ g
Density of a material:
ρ = m / V
物质的密度：
ρ = m / V
5. Thermal Physics | 热物理学
Heat transferred with temperature change (specific heat capacity):
Q = m c Δθ
温度变化时传递的热量（比热容）：
Q = m c Δθ
Heat transferred during a change of state (latent heat):
Q = m L
物态变化时传递的热量（潜热）：
Q = m L
Boyle’s law for a fixed mass of gas at constant temperature:
p₁ V₁ = p₂ V₂
一定质量气体在恒温下的玻意耳定律：
p₁ V₁ = p₂ V₂
Charles’s law for a fixed mass of gas at constant pressure:
V₁ / T₁ = V₂ / T₂
一定质量气体在恒压下的查理定律：
V₁ / T₁ = V₂ / T₂
Pressure law for a fixed mass of gas at constant volume:
p₁ / T₁ = p₂ / T₂
一定质量气体在恒容下的压力定律：
p₁ / T₁ = p₂ / T₂
6. Waves | 波
Wave speed, frequency and wavelength:
v = f λ
波速、频率和波长：
v = f λ
Refractive index from angles of incidence and refraction:
n = sin i / sin r
由入射角和折射角求折射率：
n = sin i / sin r
Refractive index and critical angle:
n = 1 / sin c
折射率与临界角：
n = 1 / sin c
Refractive index related to speed of light in different media:
n = c / v
折射率与光在介质中速度的关系：
n = c / v
7. Electricity | 电学
Electric charge transferred over time:
Q = I t
电荷量与电流和时间的关系：
Q = I t
Ohm’s law for a metallic conductor at constant temperature:
V = I R
恒定温度下金属导体的欧姆定律：
V = I R
Electric power dissipated in a component:
P = I V
元件消耗的电功率：
P = I V
Power expressed using resistance:
P = I² R = V² / R
用电阻表示的电功率：
P = I² R = V² / R
Electrical energy transferred:
E = I V t
转移的电能：
E = I V t
Resistors in series:
Rtotal = R₁ + R₂ + R₃ + …
电阻的串联：
R总 = R₁ + R₂ + R₃ + …
Resistors in parallel:
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R
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