📚 AQA A-Level Physics Data and Formula Booklet v1.4 Essentials | AQA A-Level 物理数据与公式手册 v1.4 核心要点
The AQA International A-level Physics Data and Formula Booklet v1.4 is more than a reference sheet: it is an exam-room tool that can save you marks if you use it strategically. This article breaks down the key sections, explains the meaning and use of the main equations, and highlights the most common errors students make when applying the booklet under time pressure.
AQA 国际 A-level 物理数据与公式手册 v1.4 不仅仅是一张参考表，更是考场里能帮你拿分的工具。本文拆解手册的主要板块，解释核心公式的含义和用法，并指出学生在时间压力下应用手册时最常犯的错误。
Everything below is written for students sitting AQA International A-level Physics, but the same working habits transfer directly to the UK AQA A-level specification, where a data and formulae booklet is also issued with every written paper.
以下内容面向参加 AQA 国际 A-level 物理考试的学生，但同样的操作习惯同样适用于英国本土 AQA A-level 大纲，因为每份笔试也会随卷提供数据与公式手册。
1. Exam Context and How to Use the Booklet | 考试背景与手册使用方法
The booklet gives you the equations, but it does not define every symbol and it does not tell you when an equation is valid. You must still learn the precise definitions of electromotive force, potential difference, magnetic flux, magnetic flux linkage, internal energy and specific latent heat.
手册给你公式，但不会定义每个符号，也不会告诉你公式的适用条件。电动势、电势差、磁通量、磁通链、内能和比潜热等概念的准确定义仍必须自己记住。
Before the exam, print a clean copy and tab or highlight the groups you use most: mechanics, materials, waves, electricity, fields, thermal physics and nuclear physics. The faster you locate an equation, the more time you have for unit conversions, substitution and checking significant figures.
考前打印一份干净副本，用标签或荧光笔标出你最常用的板块：力学、材料、波、电学、场、热学和核物理。你定位公式越快，留给单位换算、代入和有效数字检查的时间就越多。
A practical three-step routine works well under timed conditions:
在限时条件下，一个实用的三步流程非常有效：
- Step 1 - Read the question and write down the quantities you are given, with symbols. 第一步：读题，用符号写下已知量。
- Step 2 - Decide which physics principle links them, then find that equation in the booklet. 第二步：判断哪些物理原理把它们联系起来，再在手册中定位该公式。
- Step 3 - Rearrange algebraically first, convert units, then substitute numbers. 第三步：先做代数变形，再换算单位，最后代入数值。
All constants and equations assume SI units unless stated otherwise. Convert grams to kilograms, centimetres to metres, minutes to seconds, kilometres per hour to metres per second, and degrees Celsius to kelvin before substituting into any printed formula.
除特别说明外，所有常数和公式都采用国际单位制。代入任何印刷公式前，必须把克换成千克、厘米换成米、分钟换成秒、千米每小时换成米每秒、摄氏度换成开尔文。
2. Fundamental Constants and SI Units | 基本常数与国际单位制
The constants page carries precise values that appear across every topic, from the photoelectric effect to gravitational fields. Even though the booklet is available, knowing the order of magnitude of each constant helps you spot calculator slips instantly.
常数页列出贯穿所有主题的精确数值，从光电效应到引力场都会用到。即使手册就在手边，记住每个常数的数量级也能让你立刻发现计算器输入错误。
| Quantity 物理量 | Symbol 符号 | Value 数值 |
|---|---|---|
| Speed of light in vacuum 真空光速 | c | 3.00 × 10⁸ m s⁻¹ |
| Planck constant 普朗克常数 | h | 6.63 × 10⁻³⁴ J s |
| Elementary charge 元电荷 | e | 1.60 × 10⁻¹⁹ C |
| Electron rest mass 电子静质量 | mₑ | 9.11 × 10⁻³¹ kg |
| Proton rest mass 质子静质量 | mₚ | 1.67 × 10⁻²⁷ kg |
| Avogadro constant 阿伏加德罗常数 | NA | 6.02 × 10²³ mol⁻¹ |
| Molar gas constant 摩尔气体常数 | R | 8.31 J mol⁻¹ K⁻¹ |
| Boltzmann constant 玻尔兹曼常数 | k | 1.38 × 10⁻²³ J K⁻¹ |
| Gravitational constant 引力常数 | G | 6.67 × 10⁻¹¹ N m² kg⁻² |
| Acceleration due to gravity 重力加速度 | g | 9.81 m s⁻² |
| Permittivity of free space 真空介电常数 | ε₀ | 8.85 × 10⁻¹² F m⁻¹ |
| Permeability of free space 真空磁导率 | μ₀ | 4π × 10⁻⁷ H m⁻¹ |
| Electronvolt 电子伏 | 1 eV | 1.60 × 10⁻¹⁹ J |
| Atomic mass unit 原子质量单位 | 1 u | 1.66 × 10⁻²⁷ kg |
SI prefixes are also worth memorising as a block: pico (10⁻¹²), nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), centi (10⁻²), kilo (10³), mega (10⁶), giga (10⁹) and tera (10¹²). Most lost marks in calculation questions come from prefix errors rather than from the physics itself.
国际单位制词头也值得整块记住：皮（10⁻¹²）、纳（10⁻⁹）、微（10⁻⁶）、毫（10⁻³）、厘（10⁻²）、千（10³）、兆（10⁶）、吉（10⁹）和太（10¹²）。计算题丢分大多来自词头错误，而不是物理本身。
3. Mechanics: Kinematics, Forces and Momentum | 力学：运动学、力与动量
The mechanics page contains the four constant-acceleration equations, Newton's second law, and the momentum and impulse relations. These are the highest-frequency equations in the whole booklet, so they should be recognised instantly without turning a page.
力学页包含四个匀加速运动方程、牛顿第二定律以及动量和冲量关系式。这些是整本手册出现频率最高的公式，应当一眼认出，而不用翻页查找。
= u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t
ion as zero and vertical acceleration as ±g. Never mix the two directions in one equation.
先规定正方向。抛体问题要分解为水平和竖直两个方向，水平加速度为零，竖直加速度为 ±g。切勿在同一个方程里混用两个方向的分量。
F = ma W = mg p = mv FΔt = Δp
t route through collision and safety questions such as airbags and crumple zones: extending the collision time reduces the average force for the same change in momentum. The principle of conservation of linear momentum applies when no external resultant force acts on the system.
冲量形式 FΔt = Δp 是解决碰撞与安全问题的捷径，例如安全气囊和溃缩区：在动量变化相同的情况下延长碰撞时间可减小平均作用力。当系统不受外力合力作用时，动量守恒定律成立。
emember that the resultant force must point towards the centre; centripetal force is a role, not a new kind of force, so always name the real force providing it.
圆周运动部分手册给出 v = ωr、a = v²/r = ω²r 和 F = mv²/r。切记合力必须指向圆心；向心力是一种角色而非新的力，因此一定要说明是哪一个真实的力在提供它。
4. Work, Energy, Power and Materials | 功、能量、功率与材料
Energy questions are usually multi-step: a force does work, energy is transferred, and a final speed or extension is required. Writing the full energy balance before substituting numbers prevents most algebraic slips.
能量题通常是多步的：力做功、能量发生转移，最后要求出末速度或伸长量。在代入数值前先写出完整的能量平衡式，可避免大多数代数失误。
θ Eₖ = ½mv² ΔEₚ = mgΔh P = W/t P = Fv
Work is only done when the force has a component along the displacement, so a force perpendicular to motion does zero work. Efficiency is useful output power divided by total input power, expressed as a percentage.
只有当力在位移方向上有分量时才做功，因此与运动方向垂直的力做功为零。效率等于有用输出功率除以总输入功率，用百分数表示。
Materials questions rely on the stress, strain and Young modulus trio, plus Hooke's law and elastic potential energy. The elastic limit, limit of proportionality and yield point must be described using the correct technical vocabulary.
材料学题目依赖应力、应变和杨氏模量三件套，外加胡克定律和弹性势能。弹性极限、比例极限和屈服点必须使用准确的术语来描述。
p; ε = x/L E = σ/ε = FL/(Ax) F = kx Eₚ = ½kx² = ½Fx
Note the difference between the gradient of a force-extension graph (which gives the stiffness k) and the area under it (which gives the stored elastic energy). Label both axes with quantities and units before reading any value from a graph.
注意力—伸长量图像的斜率（给出劲度系数 k）与图像下方面积（给出储存的弹性势能）的区别。读取图像数值前，务必为两个坐标轴标注物理量和单位。
5. Waves, Oscillations and Superposition | 波、振动与叠加
The waves section links wave speed, frequency, period and wavelength, and then extends to refraction, diffraction and interference. Most candidates lose marks by forgetting that frequency is fixed when a wave crosses a boundary, while speed and wavelength change.
波的部分把波速、频率、周期和波长联系起来，并延伸到折射、衍射和干涉。多数考生失分的原因是忘记波跨越界面时频率不变，而波速和波长会改变。
v = fλ T = 1/f n = c/v = sin i / sin r sin C = 1/n
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