📚 AQA A-Level Physics Unit 3 Insert January 2020: A Complete Guide to Data & Formulae | AQA A-level 物理 Unit 3 答题册（2020年1月）：数据与公式完全指南
The January 2020 insert booklet for AQA A-level Physics Unit 3 is a vital examination resource that supplies the data, fundamental constants, and formula relationships you will need to solve problems efficiently. This guide unpacks every component of that insert so you know exactly what is available, how to retrieve it quickly, and how to avoid the most common errors students make when using it.
2020年1月AQA A-level物理Unit 3答题册是一份关键的考试资源，它提供了你在高效解题时所需的物理数据、基本常量与公式关系。本指南将逐一解析该答题册的每个组成部分，让你清楚知道哪些信息可供使用、如何快速检索，以及如何避免学生在使用它时最常见的错误。
1. Understanding the Insert | 理解答题册
The AQA A-level Physics insert is a separate booklet distributed with Papers 1, 2 and 3. For Unit 3, the insert contains the same data and formula sheet issued across all three papers, meaning you can rely on it throughout every section of the exam. It is designed to be a reference tool, not a teaching aid — you are expected to know which formula applies to which situation before you enter the examination room.
AQA A-level物理答题册是随试卷1、试卷2和试卷3一同分发的独立小册子。Unit 3的答题册包含与三份试卷相同的物理数据与公式表，意味着你在考试的每个部分都可以依赖它。它的设计定位是参考工具而非教学材料——你应当在进入考场之前就清楚哪个公式适用于哪种情境。
The insert is printed on green paper to make it visually distinctive from the question paper. Do not waste time reading it cover-to-cover at the start of the exam; instead, familiarise yourself with its layout beforehand so that you can find a specific constant or equation in under ten seconds during the test.
答题册印在浅绿色纸张上，以便与试卷在视觉上区分开来。不要在考试开始时逐页通读答题册；相反，你应该事先熟悉它的版面布局，以便在考试中能在十秒内找到某个特定常量或方程。
2. SI Prefixes and Unit Conversions | SI前缀与单位换算
The insert lists the standard SI prefixes you must be able to convert between instantly: pico (p) = 10⁻¹², nano (n) = 10⁻⁹, micro (μ) = 10⁻⁶, milli (m) = 10⁻³, centi (c) = 10⁻², kilo (k) = 10³, mega (M) = 10⁶, giga (G) = 10⁹ and tera (T) = 10¹². These prefixes appear constantly in questions involving wavelengths, capacitance, and astronomical distances.
答题册列出你必须能即时换算的标准SI前缀：皮（p）= 10⁻¹²、纳（n）= 10⁻⁹、微（μ）= 10⁻⁶、毫（m）= 10⁻³、厘（c）= 10⁻²、千（k）= 10³、兆（M）= 10⁶、吉（G）= 10⁹和太（T）= 10¹²。这些前缀在涉及波长、电容和天文距离的题目中反复出现。
A common trap in Unit 3 involves capacitance values given in nano-farads or micro-farads. For example, when substituting C = 47 nF into a time-constant equation, you must convert to farads: 47 × 10⁻⁹ F. Students who skip this conversion consistently lose marks even when their physics reasoning is perfect.
Unit 3中的一个常见陷阱涉及以纳法拉或微法拉为单位的电容值。例如，将C = 47 nF代入时间常数方程时，你必须换算为法拉：47 × 10⁻⁹ F。跳过这一步换算的学生即使物理推理完全正确，也会因此失分。
C = 47 nF = 47 × 10⁻⁹ F
3. Fundamental Constants You Must Know | 你必须掌握的基本常量
The insert provides all the fundamental constants you are allowed to use, and you should be comfortable reading them from the sheet without confusion. Key values include: speed of light c = 3.00 × 10⁸ m s⁻¹, Planck constant h = 6.63 × 10⁻³⁴ J s, gravitational constant G = 6.67 × 10⁻¹¹ N m² kg⁻², elementary charge e = 1.60 × 10⁻¹⁹ C, and Avogadro constant Nₐ = 6.02 × 10²³ mol⁻¹.
答题册提供所有允许使用的基本常量，你应当能毫无困惑地从表中读取这些数值。关键数值包括：光速c = 3.00 × 10⁸ m s⁻¹、普朗克常量h = 6.63 × 10⁻³⁴ J s、万有引力常量G = 6.67 × 10⁻¹¹ N m² kg⁻²、基本电荷e = 1.60 × 10⁻¹⁹ C和阿伏伽德罗常量Nₐ = 6.02 × 10²³ mol⁻¹。
You should also know the rest masses: electron mₑ = 9.11 × 10⁻³¹ kg, proton mₚ = 1.67 × 10⁻²⁷ kg and neutron mₙ = 1.67 × 10⁻²⁷ kg. A frequent examination approach is to give you a nuclear equation and ask you to calculate the energy released using Einstein’s mass–energy equivalence; you will need the insert’s values to obtain a precise energy in Joules before converting to MeV if required.
你还应掌握静止质量：电子mₑ = 9.11 × 10⁻³¹ kg、质子mₚ = 1.67 × 10⁻²⁷ kg和中子mₙ = 1.67 × 10⁻²⁷ kg。一种常见的出题方式是为你提供核反应方程，要求你使用爱因斯坦质能等价关系计算释放的能量；你需要使用答题册中的数值先得到以焦耳为单位的精确能量，再根据题目要求换算为MeV。
E = mc² → ΔE = Δm × (3.00 × 10⁸)²
4. Mechanics and Materials | 力学与材料
The mechanics section of the insert covers the SUVAT equations for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. Newton’s second law appears as F = ma (resultant force), and weight is written as W = mg with the insert giving standard gravity g = 9.81 N kg⁻¹. Work done, kinetic energy and gravitational potential energy are listed as W = Fs cos θ, KE = ½mv² and ΔPE = mgΔh respectively.
答题册的力学部分涵盖匀加速直线运动的SUVAT方程：v = u + at、s = ut + ½at²、v² = u² + 2as和s = ½(u + v)t。牛顿第二定律以F = ma（合力）形式给出，重力写作W = mg，答题册给出标准重力加速度g = 9.81 N kg⁻¹。功、动能和重力势能分别列为W = Fs cos θ、KE = ½mv²和ΔPE = mgΔh。
For materials, the insert provides Young’s modulus E = σ/ε where σ is tensile stress and ε is tensile strain. Questions often require you to calculate stress (σ = F/A) and strain (ε = ΔL/L) from a force–extension graph, using the gradient to determine the Young modulus of a wire. You must remember that stress has units of Pa or N m⁻², and strain is dimensionless.
在材料部分，答题册提供杨氏模量E = σ/ε，其中σ为拉伸应力，ε为拉伸应变。题目通常要求你从力–伸长量图中计算应力（σ = F/A）和应变（ε = ΔL/L），利用斜率确定金属丝的杨氏模量。你必须记住应力的单位为Pa或N m⁻²，而应变无量纲。
E = (F/A) / (ΔL/L) = FL / AΔL
5. Waves and Optics | 波动与光学
The insert’s wave section includes the universal wave equation c = fλ, where c is the wave speed in m s⁻¹, f is frequency in Hz and λ is wavelength in metres. You are also given the diffraction grating equation d sin θ = nλ, the refractive index definition n = sin i / sin r, and the critical angle relationship for total internal reflection, sin c = 1/n.
答题册的波动部分包括普适波动方程c = fλ，其中c为波速（m s⁻¹），f为频率（Hz），λ为波长（m）。还给出了衍射光栅方程d sin θ = nλ、折射率定义n = sin i / sin r，以及全内反射的临界角关系sin c = 1/n。
A January 2020-style question might present a laser beam incident on a diffraction grating and ask for the number of visible maxima. Using d sin θ = nλ with θ up to 90°, you calculate the maximum order n = d/λ and then count both positive and negative orders plus the central maximum. Make sure your calculator is in degree mode when sin θ appears with θ in degrees.
一道类似2020年1月风格的题目可能给出激光束入射衍射光栅，要求计算可见极大值的数目。使用d sin θ = nλ且θ最大为90°，计算出最大级数n = d/λ，然后计入正负级次和中央极大。当θ以度为单位出现sin θ时，务必确保计算器处于角度模式。
6. Electricity and Circuits | 电学与电路
For electricity, the insert provides Ohm’s law V = IR, electrical power P = VI = I²R = V²/R, and the resistivity equation R = ρL/A. Series and parallel resistance combinations are given as R_total = R₁ + R₂ + … and 1/R_total = 1/R₁ + 1/R₂ + … . The electromotive force (EMF) and internal resistance relationship ε = I(R + r) or ε = V + Ir is also included.
在电学部分，答题册提供欧姆定律V = IR、电功率P = VI = I²R = V²/R以及电阻率方程R = ρL/A。串联和并联电阻组合分别给出为R_total = R₁ + R₂ + …和1/R_total = 1/R₁ + 1/R₂ + …。同时还包含电动势（EMF）与内阻关系ε = I(R + r)或ε = V + Ir。
When solving internal resistance problems, students often neglect the terminal potential difference V = ε − Ir. For example, a battery with ε = 6.0 V and r = 0.50 Ω supplying a current of 2.0 A has a lost voltage of 1.0 V, so the terminal voltage across the external load is only 5.0 V. The insert gives you the equation, but you need to understand the underlying circuit physics to apply it correctly.
解答内阻问题时，学生常常忽略路端电压V = ε − Ir。例如，一个ε = 6.0 V、r = 0.50 Ω的电池输出2.0 A电流时，内阻损耗电压为1.0 V，因此外部负载上的路端电压仅为5.0 V。答题册给了你方程，但你需要理解背后的电路物理才能正确运用。
7. Fields: Gravitational, Electric and Magnetic | 场：引力场、电场与磁场
The fields section is the most information-dense part of the insert. Gravitational field strength g = GM/r², gravitational potential V = −GM/r and Newton’s law of gravitation F = GMm/r² appear together. Electric field strength E = F/Q, Coulomb’s law F = kQ₁Q₂/r² with k = 1/(4πε₀), and electric potential V = Q/(4πε₀r) are also listed.
场论部分是答题册中信息密度最高的区域。引力场强度g = GM/r²、引力势V = −GM/r以及万有引力定律F = GMm/r²一同出现。电场强度E = F/Q、库仑定律F = kQ₁Q₂/r²（其中k = 1/(4πε₀)）以及电势V = Q/(4πε₀r)也一并列出。
Magnetic fields appear with the force on a current-carrying conductor F = BIl sin θ and the force on a moving charge F = Bqv sin θ. The insert also provides the motor effect formula and Faraday’s law ε = −NΔΦ/Δt, which is central to electromagnetic induction questions in Unit 3’s practical section.
磁场部分给出载流导体在磁场中的受力F = BIl sin θ和运动电荷的受力F = Bqv sin θ。答题册还提供电动机效应公式和法拉第定律ε = −NΔΦ/Δt，后者是Unit 3实验部分电磁感应题目的核心。
ε = −N ΔΦ/Δt
8. Thermal Physics and Nuclear | 热学与核物理
Thermal energy transfers are captured by Q = mcΔθ for specific heat capacity and Q = ml for latent heat. The insert also includes the ideal gas equation pV = nRT and the kinetic theory relationship ½mc̄² = ³⁄₂kT, where k is the Boltzmann constant given as 1.38 × 10⁻²³ J K⁻¹.
热传递由比热容公式Q = mcΔθ和潜热公式Q = ml描述。答题册还包含理想气体方程pV = nRT和分子动理论关系½mc̄² = ³⁄₂kT，其中玻尔兹曼常量k = 1.38 × 10⁻²³ J K⁻¹。
The nuclear section provides the decay law N = N₀e^(−λt) and activity A = λN, with the decay constant λ related to half-life by λ = ln2 / T½. For mass–energy calculations, 1 u (atomic mass unit) is given as 1.66 × 10⁻²⁷ kg, and the conversion factor 1 MeV = 1.60 × 10⁻¹³ J is also printed. Check whether the question asks for energy in MeV or Joules before you begin your calculation.
核物理部分提供衰变定律N = N₀e^(−λt)和活度A = λN，衰变常量λ与半衰期的关系为λ = ln2 / T½。对于质能计算，1原子质量单位u = 1.66 × 10⁻²⁷ kg，同时印有换算因子1 MeV = 1.60 × 10⁻¹³ J。开始计算之前务必确认题目要求的能量单位是MeV还是J。
9. Capacitors and SHM | 电容器与简谐运动
Capacitance relationships on the insert include C = Q/V, the exponential discharge equations Q = Q₀e^(−t/RC), V = V₀e^(−t/RC) and I = I₀e^(−t/RC), along with the time constant τ = RC. The energy stored in a capacitor is given as E = ½QV = ½CV². These formulas often appear in Unit 3 data-analysis questions where you must read half-life values from a capacitor discharge graph.
答题册中的电容关系包括C = Q/V、指数放电方程Q = Q₀e^(−t/RC)、V = V₀e^(−t/RC)和I = I₀e^(−t/RC)，以及时间常数τ = RC。电容器储存的能量为E = ½QV = ½CV²。这些公式经常出现在Unit 3数据分析题中，你需要从电容器放电图上读取”半衰期”数值。
Simple harmonic motion equations are provided in both acceleration form a = −ω²x and displacement form x = A cos(2πft). The period of a mass-spring system is T = 2π√(m/k) and the period of a simple pendulum is T = 2π√(l/g). For SHM questions involving resonance, identify whether the system is forced or free and apply the correct period formula.
简谐运动方程以加速度形式a = −ω²x和位移形式x = A cos(2πft)给出。弹簧振子周期为T = 2π√(m/k)，单摆周期为T = 2π√(l/g)。对于涉及共振的SHM题目，先判断系统是受迫振动还是自由振动，再套用正确的周期公式。
10. Practical Skills: Uncertainties and Graphs | 实验技能：不确定度与作图
Unit 3 is heavily focused on practical skills, and the insert supports this by reminding you of key data-analysis relationships. When calculating uncertainty, absolute uncertainty is half the smallest scale division, and percentage uncertainty is (absolute uncertainty / measured value) × 100%. For repeated readings, use the range: uncertainty = (max − min) / 2.
Unit 3高度聚焦实验技能，答题册通过提醒关键数据分析关系来支持这一部分。计算不确定度时，绝对不确定度为最小刻度的一半，百分比不确定度 =（绝对不确定度 / 测量值）× 100%。对于重复读数，使用极差法：不确定度 =（最大值 − 最小值）/ 2。
When plotting graphs, the insert’s data tables should help you identify which variable goes on which axis. Typically, the independent variable goes on the x-axis and the dependent variable on the y-axis. For a variable that is proportional to 1/r², plotting against 1/r² will produce a straight line through the origin; the gradient then gives the constant of proportionality directly.
作图时，答题册的数据表应帮助你判断哪个变量放在哪个坐标轴上。通常，自变量放在x轴，因变量放在y轴。对于与1/r²成正比的变量，以1/r²为横坐标作图会得到一条过原点的直线；斜率直接给出比例常数。
11. Common Errors and How to Avoid Them | 常见错误与避免方法
The most frequent error in using the insert is misreading the powers of ten — confusing 10⁻¹³ with 10⁻¹⁵, for example, when converting mass defect from atomic mass units to kilograms. Always write the full value before calculation, and check that the final unit makes physical sense. A result of 10⁵⁰ watts in a nuclear question clearly signals a conversion mistake.
使用答题册最常见的错误是读错十的幂次——例如在将质量亏损从原子质量单位换算为千克时，混淆10⁻¹³和10⁻¹⁵。计算前务必写出完整数值，并检查最终单位是否符合物理意义。核物理题中得到10⁵⁰瓦特的结果明显说明换算有误。
A second common error involves mixing up the gravitational potential formula V = −GM/r with electric potential V = Q/(4πε₀r). The minus sign in gravitational potential is crucial: it indicates that potential is zero at infinity and becomes more negative as you approach the mass. The insert shows the negative sign explicitly, so keep it in your equation even if you do not fully understand its derivation.
第二个常见错误是混淆引力势公式V = −GM/r与电势公式V = Q/(4πε₀r)。引力势中的负号至关重要：它表示势能在无穷远处为零，越靠近质量体负值越大。答题册明确标出负号，即使你不完全理解其推导过程，也要在方程中保留它。
12. Exam Strategy: Using the Insert Efficiently | 考试策略：高效使用答题册
Begin by reading the formula panel at the top of the insert once, then place the booklet next to your answer booklet for quick reference. When you encounter a calculation, first identify which section of the specification it tests — mechanics, electricity, fields, nuclear, or thermal — then locate the relevant formula block on the insert. Practise this retrieval process during revision so it becomes automatic by exam day.
首先快速浏览答题册顶部公式栏一次，然后将小册子放在答题本旁边以便快速查阅。遇到计算题时，先判断它考查大纲的哪个部分——力学、电学、场论、核物理还是热学——然后在答题册上定位对应的公式区块。在复习期间反复练习这种检索流程，使它在考试当天成为自动反应。
Finally, remember that the insert is identical for all three AQA Physics papers, so there is no hidden information specific to Unit 3 that you are missing. Master the data sheet thoroughly, practise converting units under exam conditions, and you will enter the January 2020-style exam with complete confidence in your ability to access every resource at your disposal.
最后，请记住答题册在AQA物理三份试卷中完全一致，不存在Unit 3专属的隐藏信息。彻底掌握数据表，在模拟考试条件下练习单位换算，你就能以充分的自信迎接2020年1月风格的考试，并能在考场上充分运用所有可用资源。
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