AS AQA Science: Formula & Theorem Quick Reference Handbook | AS AQA 科学：公式定理速查手册

📚 AS AQA Science: Formula & Theorem Quick Reference Handbook | AS AQA 科学：公式定理速查手册

This quick reference handbook compiles the essential formulas and theorems for AQA AS-level science subjects, including physics, chemistry, and biology. It serves as a concise revision tool to reinforce key quantitative concepts and prepare for problem-solving questions across the three disciplines.

本速查手册汇编了 AQA AS 级科学课程（包括物理、化学、生物）的核心公式与定理，可作为强化重点定量概念、备战三门学科解题型考题的简洁复习工具。

1. Mechanics & Forces | 力学与力

Kinematic equations for uniform acceleration in a straight line relate displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). They are vital for solving motion problems without needing calculus.

匀加速直线运动方程联系位移(s)、初速度(u)、末速度(v)、加速度(a)和时间(t)，对于无需微积分求解运动问题至关重要。

v = u + a t, s = u t + ½ a t², s = ½ (u+v) t, v² = u² + 2 a s

Newton’s second law states that the resultant force acting on an object produces an acceleration directly proportional to the force and inversely proportional to the mass. It is often written as the rate of change of momentum.

牛顿第二定律指出，作用在物体上的合力产生的加速度与力成正比、与质量成反比。它常写成动量变化率的形式。

F = m a, F = Δp / Δt

Momentum p is conserved in closed systems during collisions and explosions. Impulse equals the change in momentum and equals the area under a force–time graph.

动量 p 在封闭系统中的碰撞和爆炸过程中守恒。冲量等于动量的变化，也等于力-时间图下的面积。

p = m v, Impulse = F Δt = Δp

Work done by a constant force is the product of the force magnitude and the distance moved in the direction of the force. Energy can be stored as kinetic energy (KE) or gravitational potential energy (GPE).

恒力做功是力的大小与沿力方向移动距离的乘积。能量可以储存为动能(KE)或重力势能(GPE)。

W = F s cos θ, KE = ½ m v², GPE = m g h

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2. Electricity Basics | 电学基础

Electric current is the rate of flow of charge. Ohm’s law holds for many conductors at constant temperature, linking potential difference V, current I and resistance R.

电流是电荷流动的速率。欧姆定律在恒温下对许多导体成立，联系电势差 V、电流 I 和电阻 R。

I = ΔQ / Δt, V = I R

Resistance of a uniform wire depends on its resistivity (ρ), length (L) and cross-sectional area (A). Power dissipated in a circuit component can be expressed in several useful ways.

均匀导线的电阻取决于其电阻率(ρ)、长度(L)和横截面积(A)。电路元件消耗的功率可以用多种实用形式表达。

R = ρ L / A, P = I V = I² R = V² / R

Kirchhoff’s junction rule states the sum of currents entering a point equals the sum leaving it. The loop rule says the total emf in any closed loop equals the sum of the potential differences across components.

基尔霍夫节点规则指出流入某点的电流之和等于流出电流之和。回路规则指出任一闭合回路的总电动势等于各元件电势差之和。

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3. Waves & Optics | 波与光学

The wave speed v is the product of frequency f and wavelength λ. The period T is the reciprocal of the frequency and describes the time for one complete oscillation.

波速 v 是频率 f 和波长 λ 的乘积。周期 T 是频率的倒数，描述一次完整振动所需的时间。

v = f λ, T = 1 / f

Refractive index n of a medium is the ratio of the speed of light in vacuum c to its speed in the medium v. Snell’s law relates the angles of incidence and refraction at a boundary. When light travels from a denser to a less dense medium, total internal reflection occurs at angles greater than the critical angle θc.

介质的折射率 n 是光在真空中的速度 c 与其在介质中速度 v 之比。斯涅耳定律关联边界上的入射角和折射角。当光从光密介质入射到光疏介质，入射角大于临界角 θc 时发生全内反射。

n = c / v, n₁ sin θ₁ = n₂ sin θ₂, sin θc = 1 / n

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4. Materials & Thermal Physics | 材料与热物理

Stress σ is the force applied per unit cross-sectional area, while strain ε is the fractional extension compared to the original length. Young’s modulus E characterises stiffness in the linear elastic region.

应力 σ 是施加在单位横截面积上的力，应变 ε 是相对于原长的延伸分数。杨氏模量 E 表征线弹性区内的刚度。

σ = F / A, ε = ΔL / L₀, E = σ / ε

Specific heat capacity c determines how much energy is needed to raise the temperature of a unit mass by 1 K. Specific latent heat L is the energy for phase change without temperature change.

比热容 c 决定将单位质量的物质温度升高 1 K 所需能量。比潜热 L 是发生相变而温度不变所需的能量。

Q = m c Δθ, Q = m L

The ideal gas equation links the pressure p, volume V, amount of substance n and absolute temperature T through the molar gas constant R.

理想气体方程通过摩尔气体常数 R 将压强 p、体积 V、物质的量 n 和热力学温度 T 联系起来。

p V = n R T

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5. Atomic Structure & Quantum Phenomena | 原子结构与量子现象

Photon energy E is directly proportional to frequency f and inversely proportional to wavelength. Planck’s constant h is the proportionality factor.

光子能量 E 与频率 f 成正比，与波长成反比。普朗克常数 h 是比例因子。

E = h f = h c / λ

The photoelectric effect reveals that electrons are only emitted if the photon energy exceeds the work function Φ of the metal. The maximum kinetic energy of emitted electrons and the stopping potential V₀ are given by Einstein’s photoelectric equation.

光电效应揭示，只有当光子能量超过金属的逸出功 Φ 时电子才会发射。发射电子的最大动能和遏止电势 V₀ 由爱因斯坦光电方程给出。

KE_max = h f − Φ, e V₀ = KE_max

Electron transitions between energy levels in an atom result in photon emission or absorption. The energy difference between levels equals the photon energy.

原子中电子在能级间的跃迁产生光子发射或吸收。能级间的能量差等于光子能量。

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6. Amount of Substance & Moles | 物质的量与摩尔

The mole is the SI unit for amount of substance, containing exactly 6.022×10²³ elementary entities (Avogadro’s constant N_A). Molar mass M links mass to moles.

摩尔是物质的量的 SI 单位，精确包含 6.022×10²³ 个基本单元（阿伏伽德罗常数 N_A）。摩尔质量 M 将质量与摩尔数关联。

n = m / M, n = N / N_A

Concentration c of a solution is defined as the number of moles of solute per cubic decimetre of solution. The ideal gas equation also allows calculation of the amount of gaseous substance.

溶液的浓度 c 定义为单位体积溶液（立方分米）中溶质的摩尔数。理想气体方程也可用于计算气态物质的量。

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