📚 A-Level Science: Formula Handbook | A-Level 科学：公式汇总手册
This handbook brings together the most important equations from A-Level Physics, Chemistry, and Biology. Whether you are solving mechanics problems, analysing reaction kinetics, or calculating magnification in a microscope, these formulas are your essential tools for exam success.
本手册汇集了 A-Level 物理、化学和生物中最关键的公式。无论你是在解决力学问题、分析反应动力学还是计算显微镜放大倍数，这些方程式都是你考试成功的必备工具。
1. Kinematics | 运动学
For an object moving in a straight line with constant acceleration, the following four equations link initial velocity u, final velocity v, displacement s, acceleration a, and time t.
对于沿直线做匀加速运动的物体，以下四个方程联系了初速度 u、末速度 v、位移 s、加速度 a 和时间 t。
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
In the absence of air resistance, vertical motion under gravity can be treated with the same equations by replacing a with g (9.81 m s&supminus;²).
在没有空气阻力的情况下，重力下的垂直运动可以用同样的方程处理，只需将 a 替换为 g（9.81 m s&supminus;²）。
v = u + g t
2. Dynamics & Momentum | 动力学与动量
Newton’s second law states that the net force acting on an object equals its mass multiplied by its acceleration. This is the foundation of classical mechanics.
牛顿第二定律指出，作用在物体上的净力等于物体的质量乘以其加速度。这是经典力学的基础。
F = m a
Momentum p is the product of mass and velocity. In a closed system, total momentum is always conserved during collisions or explosions.
动量 p 是质量与速度的乘积。在封闭系统中，碰撞或爆炸过程中总动量始终守恒。
p = m v
The impulse of a force is equal to the change in momentum. This relationship is particularly useful for analysing impacts and safety features.
力的冲量等于动量的变化。这个关系对于分析碰撞和安全装置特别有用。
F Δt = Δp
3. Work, Energy & Power | 功、能量与功率
Work done by a constant force is the product of the force, the displacement in the direction of the force, and the cosine of the angle between them. When the force and displacement are parallel, the formula simplifies.
恒力做的功是力、沿力方向位移以及力与位移夹角余弦的乘积。当力与位移平行时，公式可简化。
W = F d cos θ
Kinetic energy is the energy of motion, while gravitational potential energy depends on height above a reference point. Elastic potential energy stored in a stretched spring follows Hooke’s law.
动能是运动的能量，而重力势能取决于相对于参考点的高度。储存在拉伸弹簧中的弹性势能遵循胡克定律。
Ek = ½ m v²
Ep = m g h
Ee = ½ k x²
Power is the rate of doing work or transferring energy. For a constant force moving an object at constant velocity, power can also be expressed using force and velocity.
功率是做功或能量转移的速率。对于恒力推动物体匀速运动的情况，功率也可用力与速度表示。
P = W / t = F v
4. Circular Motion & Gravitation | 圆周运动与引力
An object moving in a circle of radius r with constant speed v and angular speed ω experiences a centripetal acceleration directed towards the centre. The centripetal force required is provided by tension, friction, or gravity.
物体以恒定速率 v 和角速度 ω 在半径为 r 的圆周上运动时，会受到指向圆心的向心加速度。所需的向心力由拉力、摩擦力或引力提供。
v = ω r
a = v² / r = ω² r
F = m v² / r = m ω² r
Newton’s law of universal gravitation explains the attraction between any two point masses. The gravitational field strength g at the surface of a planet is derived from this law.
牛顿万有引力定律解释了任意两个质点间的吸引力。行星表面的引力场强度 g 就是由这一定律推导而来。
F = G m1 m2 / r²
g = G M / r²
For a satellite in a stable circular orbit, the gravitational force provides the centripetal force, leading to the orbital velocity formula.
对于沿稳定圆形轨道运行的卫星，万有引力提供向心力，从而得出轨道速度公式。
v = √(G M / r)
5. Simple Harmonic Motion | 简谐运动
In SHM, acceleration is directly proportional to displacement from equilibrium and always directed towards it. The constant of proportionality involves the angular frequency ω.
在简谐运动中，加速度与离开平衡位置的位移成正比，且总是指向平衡位置。比例常数中含有角频率 ω。
a = -ω² x
The displacement, velocity, and maximum speed can be expressed in terms of amplitude A. The period T is the reciprocal of frequency.
位移、速度和最大速率可以用振幅 A 表示。周期 T 是频率的倒数。
x = A cos(ω t)
v = ± ω √(A² – x²)
vmax = ω A
T = 1 / f
For a mass-spring system, the period depends on mass and spring constant. For a simple pendulum, it depends on length and gravitational field strength.
对于弹簧振子系统，周期取决于质量和劲度系数。对于单摆，周期取决于摆长和重力场强度。
T = 2π √(m / k)
T = 2π √(l / g)
6. Waves & Optics | 波与光学
The wave speed v is the product of frequency f and wavelength λ. This applies to all types of wave, including sound and electromagnetic waves.
波速 v 是频率 f 与波长 λ 的乘积。这适用于所有类型的波，包括声波和电磁波。
v = f λ
The refractive index n relates the speed of light in vacuum to its speed in a medium. Snell’s law governs refraction at a boundary, and the critical angle C for total internal reflection is derived from it.
折射率 n 将光在真空中的速度与在介质中的速度联系起来。斯涅尔定律描述了界面处的折射，全内反射的临界角 C 由此推导。
n = c / v
n1 sin θ1 = n2 sin θ2
sin C = 1 / n
For Young’s double-slit experiment, the fringe spacing Δx can be calculated from wavelength, slit separation a, and distance to screen D. The diffraction grating equation gives the angles of the bright maxima.
在杨氏双缝实验中，条纹间距 Δx 可由波长、双缝间距 a 和屏幕距离 D 计算得出。衍射光栅方程给出了亮纹的角度。
λ = a x / D
d sin θ = n λ
7. Electricity & Circuits | 电学与电路
Ohm’s law links potential difference V, current I, and resistance R. Power dissipated in a component can be written in three equivalent forms using these quantities.
欧姆定律将电势差 V、电流 I 和电阻 R 联系在一起。元器件消耗的功率可以用这三个量的三种等价形式表示。
V = I R
P = I V = I² R = V² / R
The EMF ε of a cell drives current through the internal resistance r and external load R. Electric charge Q and energy transferred are fundamental to circuit analysis.
电池的电动势 ε 驱动电流流经内阻 r 和外接负载 R。电荷量 Q 和能量转移是电路分析的基础。
ε = I (R + r)
Q = I t
W = V Q
Capacitors store charge and energy. The time constant τ characterises the rate of charge or discharge.
电容器储存电荷和能量。时间常数 τ 表征了充电或放电的速率。
C = Q / V
E = ½ Q V = ½ C V²
τ = R C
8. Thermal Physics & Ideal Gases | 热力学与理想气体
Temperature in kelvin is an absolute scale where 0 K corresponds to -273.15 °C. The ideal gas equation connects pressure, volume, amount, and temperature.
开尔文温标是绝对温标，0 K 对应 -273.15 °C。理想气体方程将压强、体积、物质的量和温度联系起来。
T (K) = θ (°C) + 273.15
p V = n R T
The kinetic theory explains macroscopic pressure in terms of the mean square speed of molecules. The average translational kinetic energy of a molecule is directly proportional to the absolute temperature.
分子动理论用均方速率解释宏观压强。分子的平均平动动能与绝对温度成正比。
p V = 1/3 N m <c²>
½ m <c²> = 3/2 k T
When materials change temperature or state, specific heat capacity and specific latent heat are used to calculate energy transfers.
当材料温度变化或状态改变时，使用比热容和比潜热来计算能量转移。
Q = m c Δθ
Q = m L
9. Physical Chemistry: Kinetics & Equilibrium | 物理化学：动力学与平衡
The rate of a chemical reaction can be expressed as a rate law, where the order with respect to each reactant is determined experimentally. The Arrhenius equation quantifies the temperature dependence of the rate constant.
化学反应速率可用速率定律表示，其中对各反应物的级数由实验确定。阿伦尼乌斯方程量化了速率常数对温度的依赖。
rate = k [A]m [B]n
k = A e-Ea / R T
The equilibrium constant Kc is a ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients.
平衡常数 Kc 是生成物浓度与反应物浓度之比，各项指数为其化学计量系数。
Kc = [C]c[D]d / [A]a[B]b
Gibbs free energy change determines reaction feasibility. The relationship with the equilibrium constant is crucial for predicting the direction of change.
吉布斯自由能变化决定反应的可行性。它与平衡常数之间的关系对于预测变化方向至关重要。
ΔG = ΔH – T ΔS
ΔG° = -R T ln K
The pH scale and acid dissociation constant Ka quantify
Published by TutorHao | A-Level Science Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导