AQA A-Level Physics Insert 4 (January 2022): Mastering the Data and Formula Sheet | AQA 物理 A级 2022年1月 附录4：掌握数据和公式页

📚 AQA A-Level Physics Insert 4 (January 2022): Mastering the Data and Formula Sheet | AQA 物理 A级 2022年1月 附录4：掌握数据和公式页

The January 2022 AQA A-Level Physics paper came with an insert – often referred to as “Insert 4” – containing essential data, constants, and equations. This insert is more than a reference: it is a strategic tool. Knowing exactly what is printed on it can save time, prevent formula misremembering, and boost confidence during the exam.

2022年1月AQA A级物理试卷附带一份附录——通常称为“附录4”——其中包含必要的数据、常量和方程。这份附录不仅是参考资料，更是一个战略工具。准确了解附录上印有什么，可以节省时间、避免公式记错，并在考试中增强信心。

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1. What Is the Insert and How Should You Use It? | 概述：附录是什么以及如何使用？

The insert is provided in every AQA A-Level Physics paper. It is identical across papers 1, 2, and the synoptic paper 3 for the 7408 specification. It lists physical constants, conversion factors, and many standard equations arranged by topic.

附录是每份AQA A级物理试卷都提供的材料，在7408大纲的试卷1、试卷2和综合性试卷3中完全相同。它按主题列出了物理常量、换算因子以及许多标准方程。

You do not need to memorise everything on it – but you do need to know what is there, and what is not. Many students lose marks because they search for a formula that is not printed, or because they misread a symbol under time pressure.

你不必背诵附录上的所有内容——但你需要知道附录上有什么、没有什么。许多学生因为查找附录上没有的公式，或在时间压力下误读符号而丢分。

Effective use means scanning the relevant section before you start a part of a question, confirming the exact form of an equation (e.g. inverse square law vs exponential decay), and substituting values immediately rather than relying on memory.

有效使用意味着在开始答题前先浏览相关部分，确认方程的确切形式（例如平方反比定律 vs 指数衰减），并立即代入数值，而不是依赖记忆。

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2. Fundamental Constants – Key Values You Must Trust | 基本常数——你必须确信的关键数值

The first section of the insert provides constants like the speed of light, Planck constant, elementary charge, and rest masses. In January 2022, many questions referenced these directly.

附录第一部分提供了诸如光速、普朗克常数、基本电荷和静止质量等常数。在2022年1月的考试中，许多问题直接引用了这些值。

Common constants printed on the insert include:

附录上常见的基本常数包括：

• Speed of light in vacuum, c = 3.00 × 10⁸ m s⁻¹
• Planck constant, h = 6.63 × 10⁻³⁴ J s
• Elementary charge, e = 1.60 × 10⁻¹⁹ C
• Electron rest mass, mₑ = 9.11 × 10⁻³¹ kg
• Proton rest mass, mₚ = 1.67 × 10⁻²⁷ kg
• Neutron rest mass, mₙ = 1.67 × 10⁻²⁷ kg
• Permittivity of free space, ε₀ = 8.85 × 10⁻¹² F m⁻¹
• Permeability of free space, μ₀ = 4π × 10⁻⁷ H m⁻¹
• Gravitational constant, G = 6.67 × 10⁻¹¹ N m² kg⁻²
• Acceleration due to gravity, g = 9.81 m s⁻²
• Boltzmann constant, k = 1.38 × 10⁻²³ J K⁻¹
• Avogadro constant, Nₐ = 6.02 × 10²³ mol⁻¹

Do not round these constants earlier than the final step – use the exact form shown on the insert. For example, using c = 3.00 × 10⁸ m s⁻¹ exactly avoids precision errors in photon energy calculations.

不要过早四舍五入这些常数——在最后一步之前使用附录上显示的确切形式。例如，精确使用c = 3.00 × 10⁸ m s⁻¹可以避免光子能量计算中的精度误差。

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3. SI Units and Prefixes – The Hidden Tool | SI单位和词头——隐藏的工具

The insert includes a table of standard prefixes (nano, micro, milli, kilo, mega, giga, etc.). A common mistake in the January 2022 paper was forgetting to convert nm to m or MJ to J.

附录包含标准词头表（纳、微、毫、千、兆、吉等）。2022年1月试卷中的一个常见错误是忘记将nm转换为m，或将MJ转换为J。

The most frequently used prefixes on the AQA insert are:

AQA附录上最常用的词头是：

Prefix | 词头	Symbol | 符号	Multiplication factor | 倍数
giga | 吉	G	10⁹
mega | 兆	M	10⁶
kilo | 千	k	10³
centi | 厘	c	10⁻²
milli | 毫	m	10⁻³
micro | 微	µ	10⁻⁶
nano | 纳	n	10⁻⁹
pico | 皮	p	10⁻¹²

The insert also lists powers of ten and standard form examples. Always write final numerical answers in appropriate significant figures, usually 3 or 4, matching the precision of the data given.

附录还列出了十的幂和标准形式的示例。最终数值答案应使用适当的有效数字，通常为3或4位，与题目给出的数据精度相匹配。

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4. Mechanics Formulas – Motion, Force, and Energy | 力学公式——运动、力和能量

The mechanics section of the insert covers uniformly accelerated motion, Newton’s laws, work, energy, power, and momentum. In the January 2022 paper, a projectile question required the use of both horizontal and vertical equations.

附录的力学部分涵盖匀加速运动、牛顿定律、功、能量、功率和动量。在2022年1月的试卷中，一道抛体运动题需要同时使用水平和垂直方向的方程。

The key equations you will find:

你会在附录中找到的关键方程：

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

Notice that the insert does not give the combined equation for horizontal projectile range; you must derive it. For constant velocity in the horizontal direction, use s = v t, and in the vertical direction, use the kinematic equations above.

注意附录中没有给出抛体水平射程的合成方程；你必须自己推导。水平方向匀速运动使用s = v t，垂直方向使用上述运动学方程。

For Newton’s second law, the insert shows F = Δp / Δt, which is more general than F = m a. This form is useful in questions involving variable mass, such as rocket propulsion or fluid jets.

对于牛顿第二定律，附录显示F = Δp / Δt，这比F = m a更通用。该形式适用于涉及可变质量的问题，如火箭推进或流体射流。

p = m v
Δp = F Δt
Eₖ = ½ m v²
Eᵨ = m g h

Remember that work done is the product of force and displacement in the direction of the force. The insert also includes power as P = W / t and P = F v.

记住，功是力与力的方向上位移的乘积。附录还包括功率P = W / t和P = F v。

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5. Electricity – Circuits and Resistance | 电学——电路和电阻

This section is essential for questions on current, voltage, resistance, and power. The January 2022 paper included a circuit with two resistors in series and one in parallel.

电流、电压、电阻和功率的问题都离不开这一部分。2022年1月试卷包含一个两个电阻串联、一个电阻并联的电路。

V = I R
R = ρ L / A
P = I V = I² R = V² / R

The temperature coefficient of resistance is given, but the insert does not explicitly show the formula for series or parallel combinations. You must know these by heart:

附录给出了电阻温度系数，但没有明确显示串联或并联总电阻的公式。你必须牢记这些：

R_series = R₁ + R₂ + …
1 / R_parallel = 1 / R₁ + 1 / R₂ + …

For electrical energy, the insert lists W = V I t and P = V I. In questions involving electrical heating, use E = V I t directly, and be careful with units – if V is in volts and I in amperes, then W is in joules when t is in seconds.

对于电能，附录列出了W = V I t和P = V I。在涉及电加热的问题中，直接使用E = V I t，并注意单位——当V以伏特、I以安培、t以秒为单位时，功W以焦耳为单位。

The insert also contains the laws for capacitors: C = Q / V, and the energy stored E = ½ Q V = ½ C V². These are crucial for the alternating current and transient analysis questions.

附录还包含电容器的定律：C = Q / V，以及储存的能量E = ½ Q V = ½ C V²。这些对于交流电和瞬态分析问题至关重要。

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6. Thermal Physics and Ideal Gases | 热力学和理想气体

Thermal physics questions often appear in the multiple-choice and long-answer sections. The insert provides both the specific heat capacity equation and the internal energy of an ideal gas.

热物理学问题经常出现在选择题和简答题部分。附录提供了比热容方程和理想气体内能的公式。

ΔE = m c Δθ
E = ½ m v²_rms (for one molecule)
C_v = 3/2 R (for monatomic ideal gas)

The ideal gas equation is given in two forms:

理想气体方程给出两种形式：

p V = n R T
p V = ¹⁄₃ N m v²_rms

From these, you can derive the mean kinetic energy of a gas molecule as ³⁄₂ k T, but you must show your line of reasoning. The insert does include the Boltzmann constant, so use it directly in calculations.

由此，你可以推导气体分子的平均动能是³⁄₂ k T，但必须写出推理过程。附录确实包含玻尔兹曼常数，因此在计算中可直接使用。

For heating without a phase change, the equation ΔE = m c Δθ is sufficient. However, for phase transitions (melting or boiling), you must use the specific latent heat equation Q = m L, which is not printed on the insert – you need to remember it and state it clearly.

对于没有相变的加热，使用ΔE = m c Δθ即可。但对于相变（熔化或沸腾），必须使用比潜热方程Q = m L，该方程未印在附录上——你需要记住并清楚地写出它。

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7. Waves and Oscillations – SHM and Wave Speed | 波动和振动——简谐运动和波速

The waves section includes the universal wave equation, phase difference, and the simple harmonic motion (SHM) definition. On the January 2022 paper, a star’s spectrum required Doppler shift interpretation, and the SHM equation was used to find maximum speed.

波动部分包括通用波动方程、相差和简谐运动（SHM）定义。在2022年1月的试卷上，恒星光谱需要多普勒频移解释，并使用SHM方程求最大速度。

v = f λ
a = – ω² x
x = A cos(ω t)
v = – A ω sin(ω t)

For intensity and amplitude, the insert lists I ∝ A², and for stationary waves on a string, the frequency is given by f = (n/2L)√(T/μ). Ensure you know what each symbol stands for: T is tension, μ is mass per unit length.

对于强度和振幅，附录列出了I ∝ A²；对于弦上驻波，频率由f = (n/2L)√(T/μ)给出。确保你知道每个符号的含义：T为张力，μ为单位长度质量。

The insert also includes the diffraction grating equation d sin θ = n λ. This appeared in the January 2022 paper as a question about the maximum order of spectrum visible.

附录还包括衍射光栅方程d sin θ = n λ。2022年1月试卷中有一道关于可见光谱最大级数的问题就使用了该方程。

Do not confuse interference and diffraction. The insert gives the path difference condition for constructive interference, but you must apply it correctly to double-slit and thin-film problems.

不要混淆干涉和衍射。附录给出了相长干涉的光程差条件，但你必须正确应用于双缝和薄膜问题。

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8. Fields – Gravitational, Electric, and Magnetic | 场——引力场、电场和磁场

This is often the highest-scoring section in Paper 2. The insert contains separate formulas for gravitational and electrostatic forces, both following inverse-square laws.

这通常是试卷2中分值最高的部分。附录分别给出了引力和静电力公式，两者都遵循平方反比定律。

F_g = G m₁ m₂ / r²
g = G M / r²
F_e = Q₁ Q₂ / (4 π ε₀ r²)

For uniform fields, the insert also provides E = V / d (electric field strength) and E = – ΔV / Δr (as gradient). Magnetic fields include the force on a current-carrying wire:

对于均匀场，附录还提供了E = V / d（电场强度）和E = – ΔV / Δr（作为梯度）。磁场包括载流导线所受的力：

F = B I l sin θ
F = B Q v sin θ

In January 2022, a cyclotron question required the use of the radius of curvature formula r = m v / (B Q). This formula is not printed on the insert, but can be derived by equating the magnetic force to centripetal force. Write the derivation explicitly.

在2022年1月，一道回旋加速器问题需要用到曲率半径公式r = m v / (B Q)。该公式未印在附录上，但可通过让磁力等于向心力来推导。务必写出推导过程。

For gravitational potential and electric potential, the insert gives V = – G M / r and V = Q / (4 π ε₀ r). Remember that gravitational potential is always negative, taking zero at infinity, whereas electric potential can be positive or negative depending on the sign of the charge.

对于引力势和电势，附录给出V = – G M / r和V = Q / (4 π ε₀ r)。记住引力势始终为负，无穷远处为零；而电势的正负取决于电荷的符号。

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9. Nuclear and Quantum Physics – Equations from the Insert | 核物理和量子物理——附录中的方程

The quantum section of the insert includes photon energy, work function, and the photoelectric effect. In January 2022, a question on the de Broglie wavelength tested your ability to combine two equations.

附录的量子部分包括光子能量、逸出功和光电效应。在2022年1月，一道关于德布罗意波长的问题考查了你结合两个方程的能力。

E = h f
Eₘₐₓ = h f – φ
λ = h / p

For nuclear decay, the insert provides the radioactive decay law in both exponential and constant forms:

对于核衰变，附录提供了指数形式和常数形式的放射性衰变定律：

A = λ N
N = N₀ e^(– λ t)
T½ = ln 2 / λ

Be careful with units: activity A is in becquerels (Bq), which is s⁻¹. The decay constant λ must be in s⁻¹ if time t is in seconds. Use the insert’s value for ln 2 (0.693) to compute half-life quickly.

注意单位：活度A的单位是贝可勒尔（Bq），即s⁻¹。如果时间t以秒为单位，则衰变常数λ的单位必须是s⁻¹。使用附录中ln 2的值（0.693）可快速计算半衰期。

The insert also gives the energy–mass equivalence E = m c², which is essential for nuclear binding energy calculations. When calculating mass defect, convert atomic mass units (u) to kg using the insert’s value of 1 u = 1.66 × 10⁻²⁷ kg, then multiply by c².

附录还给出了质能等价关系E = m c²，这对核结合能计算至关重要。计算质量亏损时，使用附录中的1 u = 1.66 × 10⁻²⁷ kg，将原子质量单位转换为千克，然后乘以c²。

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10. Exam Tips – How to Avoid Insert Traps | 考试技巧——如何避免附录陷阱

Many students believe the insert contains everything they need, but it is not exhaustive. The AQA specification expects you to remember a small set of equations, such as the lens/ magnification formula, the ideal gas mean kinetic energy relation, and the parallax and luminosity equations. Do not rely on the insert for these.

许多学生认为附录包含所有需要的内容，但实际上它并不详尽。AQA大纲要求你记住一小部分方程，如透镜/放大率公式、理想气体平均动能关系，以及视差和光度方程。不要在这些方面依赖附录。

Top tips for using the insert on exam day:

考试当天使用附录的顶级技巧：

• Before Paper 1, read the constants section silently – this primes your memory for the numerical values.
• When you see a question about a topic, turn to that section of the insert first, even if you think you know the formula. This reduces silly sign errors.
• For multi-step calculations, circle or highlight the relevant equation on the insert with your pen – this helps you focus.
• Never leave a formula derivation step unshown. Even if the final equation is on the insert, start from a printed equation and clearly show the substitution.

最后，练习用附录做题。在模拟考试中，只使用附录，并计时。这样你在真实考试中就不会忘记哪些信息在哪个位置。

Practise with the insert under timed conditions. During mock exams, use only the insert and a timer. This way you will not be lost in the real exam, and you will know exactly where to find every printed formula.

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