📚 AS Cambridge Science: Quick-Reference Handbook of Formulas & Theorems | AS剑桥科学：公式定理速查手册
This compact revision handbook brings together the most important formulas, equations and key theorems from the AS Cambridge Science curriculum spanning Physics, Chemistry and Biology. Use it to quickly recall the relationships you need for problem-solving, to check your understanding before exams, or as a daily drill for numerical confidence. Each section presents the formula in bold, followed by a matched pair of explanations in English and Chinese to reinforce both the concept and the symbolic notation.
这本精炼的速查手册汇集了 AS 剑桥科学课程（涵盖物理、化学和生物）中最重要的公式、方程和核心定理。你可以用它快速回顾解题所需的关系式，在考试前检查自己的理解，或作为每日训练提升数字敏感度。每个部分都以粗体列出公式，并配有中英文配对解释，帮助强化概念和符号记忆。
1. Kinematic Equations | 运动学方程
For objects moving with constant acceleration along a straight line, the following four equations link displacement, velocity, acceleration and time. They are derived from the definitions of velocity and acceleration and are fundamental to analysing motion in AS Physics.
对于沿直线做匀加速运动的物体，以下四个方程将位移、速度、加速度和时间联系起来。它们由速度和加速度的定义导出，是 AS 物理中分析运动的基础。
v = u + a t
This equation gives the final velocity (v) of an object when the initial velocity (u), the constant acceleration (a) and the time (t) are known.
当已知初速度 u、恒定加速度 a 和时间 t 时，此方程用于求末速度 v。
s = u t + ½ a t²
The displacement (s) after a time t is calculated as the product of initial velocity and time plus half the acceleration multiplied by the square of time.
经过时间 t 的位移 s 等于初速度与时间的乘积，加上加速度与时间平方乘积的一半。
v² = u² + 2 a s
When time is not given, this relation connects the final velocity, initial velocity, acceleration and displacement.
当时间未知时，这一关系式连接末速度、初速度、加速度和位移。
s = ½ (u + v) t
Displacement is equal to the average velocity multiplied by time, useful when acceleration is constant but not directly needed.
位移等于平均速度乘以时间，在加速度恒定且不直接需要加速度值的情况下特别有用。
2. Dynamics & Momentum | 动力学与动量
Newton's laws of motion govern the relationship between force, mass and acceleration, while momentum is the product of mass and velocity and is conserved in all collisions and explosions as long as no external force acts.
牛顿运动定律支配着力、质量和加速度之间的关系；动量是质量与速度的乘积，只要没有外力作用，在任何碰撞和爆炸中都守恒。
F = m a
The resultant force (F) acting on an object equals its mass (m) multiplied by the acceleration (a) it experiences. Both force and acceleration are vectors.
作用在物体上的合力 F 等于物体的质量 m 与其加速度 a 的乘积。力和加速度都是矢量。
p = m v
Linear momentum (p) is defined as the product of an object's mass and its velocity. Its SI unit is kg m s⁻¹.
线动量 p 定义为物体的质量与速度的乘积，其 SI 单位是 kg·m·s⁻¹。
Impulse = F Δt = Δp
The impulse of a force equals the change in momentum it produces. Graphically, it is the area under a force–time graph.
力的冲量等于它引起的动量变化量。在图上，冲量是力–时间图线下的面积。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In the absence of external forces, total momentum before an interaction equals total momentum after the interaction.
在没有外力的情况下，相互作用前的总动量等于相互作用后的总动量。
3. Work, Energy & Power | 功、能与功率
Energy can be transferred by doing work or by heating. The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another.
能量可以通过做功或热传递来转移。能量守恒原理指出能量不能被创造或消灭，只能从一种形式转化为另一种形式。
W = F s cos θ
Work done (W) by a constant force is the product of the force (F), the displacement (s) in the direction of the force, and the cosine of the angle θ between them.
恒力所做的功 W 等于力 F、沿力方向的位移 s 以及力与位移夹角 θ 的余弦三者的乘积。
Eₖ = ½ m v²
Kinetic energy (Eₖ) of a body of mass m moving at speed v. All moving objects possess this form of energy.
质量为 m、速度为 v 的物体的动能 Eₖ。一切运动的物体都具有这种形式的能量。
ΔEₚ = m g Δh
The change in gravitational potential energy near the Earth's surface depends on mass (m), gravitational field strength (g) and the change in height (Δh).
在地球表面附近，重力势能的变化量 ΔEₚ 取决于质量 m、重力场强度 g 和高度变化 Δh。
P = W / t (and P = F v for constant velocity)
Power is the rate of doing work or transferring energy. For an object moving at constant speed against a resistive force, power equals force times velocity.
功率是做功或能量转移的速率。对于恒速抵抗阻力的物体，功率等于力乘以速度。
4. Wave Properties & Optics | 波的性质与光学
All waves carry energy without transferring matter. The wave equation links speed, frequency and wavelength, and is central to both sound and electromagnetic waves. Refraction is described by Snell's law.
所有波都传递能量而不传递物质。波动方程将波速、频率和波长联系起来，是声波和电磁波的核心。折射由斯涅尔定律描述。
v = f λ
The speed (v) of a wave equals the product of its frequency (f) and wavelength (λ). This applies to all wave types.
波速 v 等于频率 f 与波长 λ 的乘积，适用于所有类型的波。
n = sin i / sin r (Snell's law)
The refractive index (n) of a medium is the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) when light passes from a vacuum (or air) into that medium.
介质的折射率 n 是光从真空（或空气）进入该介质时，入射角 i 的正弦与折射角 r 的正弦之比。
n = c / v
The refractive index is also the ratio of the speed of light in a vacuum (c) to its speed in the medium (v).
折射率也等于光在真空中的速度 c 与光在介质中的速度 v 之比。
sin θ꜀ = 1 / n (critical angle)
The critical angle (θ꜀) for total internal reflection occurs when the angle of refraction is 90°. It is determined solely by the refractive index of the denser medium relative to the rarer one.
全反射的临界角 θ꜀ 出现在折射角为 90° 时，它仅由光密介质相对于光疏介质的折射率决定。
5. Electric Current & Circuits | 电流与电路
Electric current is a flow of charge. Ohm's law, resistance, power dissipation and the rules for series and parallel circuits are essential for analysing any electrical network.
电流是电荷的流动。欧姆定律、电阻、功率消耗以及串联和并联电路的规则是分析一切电网络的基础。
I = ΔQ / Δt
Current (I) is the rate of flow of charge. One ampere is one coulomb per second.
电流 I 是电荷的流动速率，1 安培等于每秒 1 库仑。
V = I R (Ohm's law)
For an ohmic conductor at constant temperature, the potential difference (V) across it is directly proportional to the current (I) passing through it, with resistance (R) as the constant of proportionality.
对于恒定温度下的欧姆导体，其两端的电势差 V 与通过的电流 I 成正比，电阻 R 是比例常数。
P = I V = I² R = V² / R
Electrical power converted in a component can be expressed in three equivalent forms, depending on which quantities are known.
元件中转换的电功率可以用三种等价形式表示，取决于已知哪些量。
Rtotal = R₁ + R₂ + ... (series) ; 1/Rtotal = 1/R₁ + 1/R₂ + ... (parallel)
In series circuits, resistances add directly; in parallel circuits, the reciprocals of the resistances add.
在串联电路中，电阻直接相加；在并联电路中，电阻的倒数相加。
6. The Mole & Ideal Gases | 摩尔计算与理想气体
The mole is the chemical counting unit. Stoichiometric calculations rely on the relationships among mass, molar mass, amount of substance and, for gases, volume. The ideal gas equation unites the macroscopic variables of a gas.
摩尔是化学计数的单位。化学计量计算依赖质量、摩尔质量、物质的量以及气体体积之间的关系。理想气体方程将气体的宏观变量统一起来。
n = m / M
The amount of substance (n) in moles equals the mass (m) of the sample divided by its molar mass (M).
物质的量 n（单位：摩尔）等于样品的质量 m 除以其摩尔质量 M。
c = n / V (for solutions)
Concentration (c) of a solution is the amount of solute (n) dissolved in a given volume (V) of solution, usually expressed in mol dm⁻³.
溶液的浓度 c 是溶于一定体积 V 的溶液中的溶质的量 n，通常以 mol·dm⁻³ 表示。
p V = n R T
The ideal gas law relates pressure (p), volume (V), amount (n) and absolute temperature (T). R is the universal gas constant, 8.31 J K⁻¹ mol⁻¹.
理想气体状态方程关联压强 p、体积 V、物质的量 n 和热力学温度 T。R 是摩尔气体常数，8.31 J·K⁻¹·mol⁻¹。
Volume of 1 mol of gas at RTP = 24.0 dm³ (or 24 000 cm³)
At room temperature and pressure (RTP, approx. 20 °C and 1 atm), one mole of any ideal gas occupies 24.0 dm³.
在常温常压（RTP，约 20 °C、1 atm）下，任何理想气体的摩尔体积为 24.0 dm³。
7. Enthalpy Changes & Hess's Law | 焓变与热化学
Enthalpy changes describe heat energy transferred during chemical reactions at constant pressure. Hess's Law allows the calculation of an unknown enthalpy change by combining other thermochemical equations.
焓变描述恒压条件下化学反应过程中转移的热能。赫斯定律允许通过组合其他热化学方程来计算未知的焓变。
ΔH = Σ ΔH꜀(products) – Σ ΔH꜀(reactants)
For a reaction, the standard enthalpy change can be found from the sum of the enthalpies of formation (ΔH꜀) of the products minus the sum for the reactants.
对于某一反应，标准焓变可由生成物标准生成焓 ΔH꜀ 的总和减去反应物标准生成焓的总和求得。
q = m c ΔT
In calorimetry, the heat energy (q) transferred to or from a substance is computed from its mass (m), specific heat capacity (c) and temperature change (ΔT).
在量热法中，传递给物质或从物质传出的热量 q 由质量 m、比热容 c 和温度变化 ΔT 计算。
ΔH = – q / n (for exothermic → negative)
The molar enthalpy change is obtained by dividing the heat energy exchanged by the number of moles reacting, with the sign indicating direction (negative for exothermic).
摩尔焓变由交换的热量除以反应的摩尔数得到，符号表示方向（放热为负）。
Hess's Law: ΔHroute 1 = ΔHroute 2
If a reaction can take place by two different pathways, the total enthalpy change is the same regardless of the route, allowing for algebraic addition of known steps.
若一个反应可通过两种不同途径进行，则无论何种途径，总焓变相同，于是可将已知步骤进行代数相加。
8. Chemical Equilibria & Kc | 化学平衡与 Kc
Many reactions are reversible and reach a dynamic equilibrium where the forward and reverse rates are equal. The equilibrium constant, Kc, expresses the position of equilibrium for a given temperature.
许多反应是可逆的，会达到正向与逆向速率相等的动态平衡。平衡常数 Kc 表达了给定温度下反应平衡的位置。
aA + bB ⇌ cC + dD, Kc = [C]c [D]d / [A]a [B]b
The equilibrium constant is the ratio of the product of equilibrium concentrations of products, each raised to its stoichiometric coefficient, to the product of the equilibrium concentrations of reactants, similarly raised. Pure solids and liquids are omitted.
平衡常数等于各生成物平衡浓度以其化学计量系数为指数的乘积，除以各反应物平衡浓度以其系数为指数的乘积。纯固体和纯液体不写入。
Kc > 1: equilibrium favours products; Kc < 1: favours reactants
A large Kc means the equilibrium mixture contains more products;
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