📚 Year 12 Cambridge Science: Formula & Theorem Quick Reference Handbook | 剑桥12年级科学：公式定理速查手册
This quick reference handbook summarises the essential formulas, equations and theorems across Physics, Chemistry and Biology for Year 12 Cambridge Science students. It is designed for rapid revision and handy reference during both learning and exam preparation.
本速查手册汇总了剑桥12年级科学课程中物理、化学和生物的核心公式、方程和定理，旨在帮助您快速复习和便捷查阅，无论是日常学习还是备考冲刺都用得上。
1. Kinematics Equations | 运动学公式
For uniformly accelerated motion in a straight line, the four kinematic equations connect initial velocity u, final velocity v, acceleration a, time t and displacement s. They are the first tools you should reach for in any AS Level mechanics question.
在匀加速直线运动中，四个运动学方程把初速度 u、末速度 v、加速度 a、时间 t 和位移 s 联系起来。它们是 AS Level 力学题目中首先应该想到的工具。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u + v)t / 2
In these equations, u is initial velocity, v is final velocity, a is uniform acceleration, t is time and s is displacement. All quantities are vectors in principle, so you must choose a positive direction before substituting values.
在这些方程中，u 为初速度，v 为末速度，a 为匀加速度，t 为时间，s 为位移。原则上所有量都是矢量，因此代入数值前必须先规定正方向。
For free fall near the Earth' .81 m s⁻², directed downwards. If you take upwards as positive, then a = −g = −9.81 m s⁻².
在地球表面附近的自由落体中，加速度由重力产生，大小为 g = 9.81 m s⁻²，方向向下。若取向上为正，则 a = −g = −9.81 m s⁻²。
- Exam tip: the equations apply only when acceleration is constant and motion is along a straight line.
考试提示：这些方程只适用于加速度恒定且沿直线运动的情况。 - Common trap: confusing displacement s with distance travelled; when motion reverses direction, they are not the same.
常见陷阱：把位移 s 与路程混淆；当运动反向时，两者并不相同。
2. Newton's Laws & Momentum | 牛顿定律与动量
Newton's first law states that a body remains at rest or moves with constant velocity unless acted on by a resultant force. In formula terms, if Fnet = 0, then acceleration a = 0.
牛顿第一定律指出，物体在不受合力作用时保持静止或匀速直线运动。用公式表示，若 Fnet = 0，则加速度 a = 0。
Newton's second law defines the relationship between resultant force, mass and acceleration. It is the central equation for dynamics problems:
牛顿第二定律给出了合力、质量与加速度之间的关系，是动力学问题的核心方程：
F = ma
Here F is the resultant force in newtons, m is mass in kilograms, and a is acceleration in metres per second squared. The force and acceleration are always in the same direction.
其中 F 为合力，单位为牛顿；m 为质量，单位为千克；a 为加速度，单位为米每二次方秒。合力与加速度方向始终相同。
Newton's third law states that if body A exerts a force on body B, then B exerts an equal and opposite force on A. These two forces act on different bodies, so they never cancel each other out.
牛顿第三定律指出，若物体 A 对物体 B 施加一个力，则 B 对 A 施加大小相等、方向相反的力。这两个力作用在不同物体上，因此永远不会相互抵消。
Linear momentum is defined as the product of mass and velocity. Impulse is the change in momentum and equals force multiplied by the time for which it acts:
线动量定义为质量与速度的乘积。冲量是动量的变化量，等于力与作用时间的乘积：
p = mv
Δp = FΔt
In a closed system with no external forces, total momentum before a collision equals total momentum after the collision. This is the principle of conservation of momentum:
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。这就是动量守恒原理：
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
For elastic collisions, kinetic energy is also conserved; for inelastic collisions, kinetic energy is not conserved, although momentum still is. In exam questions, always state clearly which conservation law you are using.
弹性碰撞中动能也守恒；非弹性碰撞中动能不守恒，但动量仍然守恒。考试作答时，务必明确写出你使用的是哪一条守恒定律。
3. Work, Energy & Power | 功、能与功率
Work done by a constant force at an angle θ to the displacement is given by the product of force, displacement and the cosine of the angle between them.
恒力与位移夹角为 θ 时所做的功，等于力、位移以及两者夹角余弦的乘积。
W = Fs cosθ
W = 0 and the force does no work on the object. When θ = 180°, the work done is negative.
当 θ = 0° 时，W = Fs，力做最大正功。当 θ = 90° 时，W = 0，力对物体不做功。当 θ = 180° 时，做功为负。
Kinetic energy is the energy possessed by a moving object. Gravitational potential energy near the Earth's surface depends on mass, gravitational field strength and height:
动能是运动物体具有的能量。地球表面附近的重力势能取决于质量、重力场强度和高度：
KE = ½mv²
GPE = mgh
Elastic potential energy stored in a stretched or compressed spring is EPE = ½kx², where k is the spring constant and x is the extension or compression from natural length.
拉伸或压缩弹簧中储存的弹性势能为 EPE = ½kx²，其中 k 为弹簧劲度系数，x 为相对自然长度的伸长量或压缩量。
Power is the rate of doing work or the rate of energy transfer. For a constant force acting in the same direction as the velocity, power can also be written as force times velocity.
功率是做功的速率或能量传递的速率。当恒力与速度方向相同时，功率也可写成力与速度的乘积。
P = W / t
P = Fv
Energy is conserved in all processes. Efficiency compares useful output energy or power with total input energy or power, and is often expressed as a percentage:
在所有过程中能量都守恒。效率比较有用输出能量或功率与总输入能量或功率，通常用百分数表示：
Efficiency = useful output / total input × 100%
4. Waves, Optics & Sound | 波、光学与声
The wave equation links wave speed, frequency and wavelength. It applies to all waves, including sound, light and waves on a string.
波动方程把波速、频率和波长联系起来，适用于所有波，包括声波、光波和弦上的波。
v = fλ
Here v is wave speed in m s⁻¹, f is frequency in hertz, and λ (lambda) is wavelength in metres. Frequency is determined by the source and does not change when a wave enters a new medium; speed and wavelength do change.
其中 v 为波速，单位 m s⁻¹；f 为频率，单位赫兹；λ 为波长，单位米。频率由波源决定，波进入新介质时频率不变，但波速和波长会改变。
For refraction at a boundary, Snell's law relates the angles of incidence and refraction to the refractive indices of the two media. The critical angle for total internal reflection is found when the angle of refraction is 90°.
在界面折射中，斯涅耳定律把入射角、折射角与两种介质的折射率联系起来。当折射角为 90° 时，对应的入射角即为临界角。
n₁ sinθ₁ = n₂ sinθ₂
sin C = 1 / n
Sound is a longitudinal wave that requires a medium. The Doppler effect describes the change in observed frequency when a source or observer moves relative to the medium.
声波是需要介质的纵波。多普勒效应描述当波源或观察者相对介质运动时，观察到的频率发生变化的现象。
For superposition, constructive interference occurs when path difference is a whole number of wavelengths, and destructive interference occurs when path difference is an odd number of half-wavelengths.
在波的叠加中，当路程差为波长的整数倍时发生相长干涉，当路程差为半波长的奇数倍时发生相消干涉。
Constructive: path difference = nλ
Destructive: path difference = (n + ½)λ
5. Thermal Physics & Gas Laws | 热学与气体定律
The ideal gas equation combines pressure, volume, amount of substance and temperature into a single relationship. It is one of the most frequently examined equations in thermal physics.
理想气体方程把压强、体积、物质的量和温度统一在一个关系式中，是热学中考得最频繁的方程之一。
pV = nRT
In this equation, p is pressure in pascals, V is volume in cubic metres, n is amount of substance in moles, R is the molar gas constant 8.31 J mol⁻¹ K⁻¹, and T is thermodynamic temperature in kelvin.
其中 p 为压强，单位帕斯卡；V 为体积，单位立方米；n 为物质的量，单位摩尔；R 为摩尔气体常数 8.31 J mol⁻¹ K⁻¹；T 为热力学温度，单位开尔文。
For a fixed mass of gas, the combined gas law relates two sets of conditions. Temperatures must always be converted to kelvin before substitution.
对于一定质量的气体，联合气体定律把两组状态联系起来。代入前必须把温度换算为开尔文。
p₁V₁ / T₁ = p₂V₂ / T₂
Specific heat capacity describes the energy needed to raise the temperature of unit mass by one kelvin. Specific latent heat describes the energy needed to change the state of unit mass without a temperature change.
比热容描述使单位质量物质温度升高 1 K 所需的能量。比潜热描述使单位质量物质发生状态变化而温度不变所需的能量。
Q = mcΔT
Q = mL
The first law of thermodynamics relates the change in internal energy to heat supplied and work done on the gas. In the Cambridge convention, W is the work done on the system.
热力学第一定律把内能变化与提供的热量和对气体做的功联系起来。在剑桥约定中，W 表示外界对系统做的功。
ΔU = Q + W
6. Electric Circuits & Fields | 电路与场
Electric current is the rate of flow of charge. Ohm's law relates potential difference, current and resistance for an ohmic conductor at constant temperature.
电流是电荷流动的速率。欧姆定律描述在恒定温度下，欧姆导体的电势差、电流与电阻之间的关系。
Q = It
V = IR
Electrical power can be expressed in three equivalent forms. Choose the form that matches the quantities given in the question.
电功率可以写成三种等价形式。根据题目给出的量选择最方便的形式。
P = VI = I²R = V² / R
For resistors in series, the total resistance is the sum of individual resistances. For resistors in parallel, the reciprocal of the total resistance is the sum of the reciprocals.
串联电阻的总电阻等于各电阻之和。并联电阻的总电阻的倒数等于各电阻倒数之和。
Rseries = R₁ + R₂ + R₃
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