📚 A-Level Physics: Unit 3 Insert (Jan 2019) Concept Guide | A-Level 物理：Unit 3 插入页（Jan 2019）概念指南
The Edexcel IAL Physics Unit 3 (WPH13) examination focuses on experimental and practical skills. The inserted booklet provided in the exam is a life‑saving resource, containing essential constants, geometrical formulas, logarithmic identities, uncertainty equations and more. Being fluent with this insert can save you time, reduce errors and boost your confidence when tackling data‑analysis questions. This article dissects the January 2019 version of the insert, explaining every key concept and showing you how to use each formula in context.
Edexcel IAL 物理 Unit 3 (WPH13) 主要考察实验与实践技能。考试中提供的插入页是一份“救命”资源，包含基本常数、几何公式、对数性质、不确定度方程等。熟练掌握这份数据页能帮你节省时间、减少错误，并在处理数据分析题时更有底气。本文将拆解2019年1月版的插入页，解释每一个核心概念，并展示如何在具体情境中运用这些公式。
1. Overview of the Insert | 插入页总体结构
The Unit 3 insert is usually a double‑sided sheet. One side lists physical constants and general mathematical formulae, while the other side concentrates on uncertainty relationships and practical‑skill reminders. You should familiarise yourself with the layout before the exam so you can locate any item within seconds.
Unit 3 插入页通常是一张双面印刷页。一面列出物理常数和通用数学公式，另一面则集中给出不确定度关系式和实验技能提示。考前熟悉版面布局，能让你在几秒钟内找到所需条目。
In the Jan 2019 paper, the insert included values such as g, Planck’s constant h, the mass of the electron, as well as formulas for areas, volumes, logarithms and trigonometric identities. On the reverse, you would find definitions of absolute and percentage uncertainties, plus rules for combining them.
2019年1月卷的插入页包含了重力加速度 g、普朗克常量 h、电子质量等数值，还有面积、体积、对数和三角恒等式。另一面则是绝对不确定度与百分不确定度的定义，以及它们合成时的规则。
2. Physical Constants | 物理常数
The insert supplies a compact table of constants adopted for the paper. You do not need to memorise them, but you must know when to apply each one. For example, g = 9.81 m s⁻² is used in pendulum, free‑fall and force‑extension experiments. Planck’s constant h = 6.63 × 10⁻³⁴ J s appears when dealing with the photoelectric effect or LED threshold voltages. The elementary charge e = 1.60 × 10⁻¹⁹ C often appears in electrolysis or capacitor discharge questions.
插入页提供了一个精简的常数表格。你无需背诵它们，但必须知道每个常数何时适用。例如，g = 9.81 m s⁻² 用于单摆、自由落体和力‑伸长实验中；普朗克常量 h = 6.63 × 10⁻³⁴ J s 在光电效应或 LED 截止电压中出现；基本电荷 e = 1.60 × 10⁻¹⁹ C 常用于电解或电容器放电题型。
Other constants like the speed of light c = 3.00 × 10⁸ m s⁻¹ and the Avogadro constant NA = 6.02 × 10²³ mol⁻¹ appear less often in Unit 3, but they may be needed for unit conversions or checking the plausibility of experimental results.
其它常数如光速 c = 3.00 × 10⁸ m s⁻¹ 和阿伏伽德罗常数 NA = 6.02 × 10²³ mol⁻¹ 在 Unit 3 中出现频率较低，但可能用于单位换算或检验实验结果的合理性。
3. Geometric and Algebraic Formulae | 几何与代数公式
The insert lists area and volume expressions for common shapes: area of a circle (A = πr²), surface area and volume of a sphere (4πr² and ⁴⁄₃πr³), and volume of a cylinder (πr²h). These are frequently needed when determining the density of a material or the cross‑sectional area of a wire.
插入页给出了常见图形的面积和体积表达式：圆面积 (A = πr²)、球表面积与体积 (4πr² 和 ⁴⁄₃πr³)、圆柱体积 (πr²h)。在测定材料密度或导线截面积时这些公式经常用到。
Quadratic formula and logarithmic identities are also included. You may need the relationship log(AB) = log A + log B when processing data for a variable that follows an exponential or power law. Similarly, indices rules help you linearise equations: for example, if T = kL½, plotting lg T against lg L yields a straight line of gradient ½.
插入页还包含二次公式和对数恒等式。处理指数或幂律关系的数据时，你可能用到 log(AB) = log A + log B 这个关系。同理，指数法则有助于方程线性化：若 T = kL½，以 lg T 对 lg L 作图，可得到一条斜率为 ½ 的直线。
4. Absolute and Percentage Uncertainty | 绝对不确定度与百分不确定度
The insert defines absolute uncertainty (Δx) as the half‑range or the instrument’s resolution, and percentage uncertainty as (Δx / x) × 100%. Understanding this distinction is the foundation of all error analysis in Unit 3.
插入页将绝对不确定度 (Δx) 定义为量程的一半或仪器的最小分辨率，百分不确定度则为 (Δx / x) × 100%。理解这一区别是 Unit 3 所有误差分析的基础。
For a single reading taken with a digital multimeter, the absolute uncertainty is often the resolution, e.g. ±0.01 V on a 2‑volt scale. For a ruler, the uncertainty is typically ±1 mm because you must judge the alignment at both ends, giving a total uncertainty of ±2 mm, but the insert may simplify it to the scale division.
对于数字万用表的单个读数，绝对不确定度通常就是分辨率，如 2 V 量程下 ±0.01 V。对于直尺，不确定度一般为 ±1 mm，因为需要对两端分别判读，总绝对不确定度为 ±2 mm；不过插入页可能会简化为最小刻度值。
The percentage uncertainty is dimensionless and allows you to compare the precision of different measurements. A short length of 5.0 cm measured with a ruler (±1 mm) has a percentage uncertainty of (0.1/5.0)×100 = 2%.
百分不确定度无量纲，便于比较不同测量的精度。用直尺 (±1 mm) 测量 5.0 cm 的短长度，百分不确定度为 (0.1/5.0)×100 = 2%。
5. Combining Uncertainties: Addition and Subtraction | 不确定度合成：加减运算
When two measured quantities A and B are added or subtracted, the insert states that the absolute uncertainty in the result R is the sum of the individual absolute uncertainties: ΔR = ΔA + ΔB.
插入页指出，当两个测量量 A 和 B 相加或相减时，结果 R 的绝对不确定度等于各自绝对不确定度之和：ΔR = ΔA + ΔB。
This rule makes intuitive sense: the worst‑case deviation occurs when both errors push the value in the same direction. For example, if you measure the external diameter of a tube as (25.0 ± 0.1) mm and the internal diameter as (20.0 ± 0.1) mm, the thickness is 5.0 mm with an absolute uncertainty of 0.2 mm.
这条规则很直观：当两个误差朝着同一方向叠加时，出现最坏情况。譬如，测量管外径为 (25.0 ± 0.1) mm、内径为 (20.0 ± 0.1) mm，则壁厚为 5.0 mm，绝对不确定度为 0.2 mm。
Do not confuse this with percentage uncertainties. For addition and subtraction, always keep the absolute uncertainties and add them linearly.
切勿与百分不确定度混淆。对于加减运算，始终使用绝对不确定度并直接相加。
6. Combining Uncertainties: Multiplication and Division | 不确定度合成：乘除运算
If a result is obtained by multiplying or dividing measured quantities, the insert instructs you to add the percentage uncertainties: %UR = %UA + %UB.
若结果由测量量相乘或相除得到，插入页指示我们将百分不确定度相加：%UR = %UA + %UB。
This is derived from the fact that small fractional changes add up when quantities are multiplied. For instance, when calculating speed from v = d / t, if d has a 2% uncertainty and t has a 1% uncertainty, the speed’s percentage uncertainty is 3%.
这是基于微小相对变化量在乘除时可叠加的事实。例如，用 v = d / t 计算速度，若 d 的不确定度为 2%，t 为 1%，则速度的百分不确定度为 3%。
A common trap is using this rule for addition or subtraction – it does not work. Always decide whether the operation is additive or multiplicative before choosing the appropriate combining rule.
常见陷阱是把这条规则用于加减法——这是不正确的。一定先判断运算是加减还是乘除，再选择对应的合成规则。
7. Uncertainty from Repeated Measurements | 重复测量的不确定度
For a set of repeated readings, the insert suggests using the half‑range (maximum − minimum)/2 or, in some papers, the standard deviation. The Jan 2019 insert likely mentions that the uncertainty in the mean can be taken as ±(maximum − minimum)/2.
对于一组重复读数，插入页建议使用半范围 (最大值 − 最小值)/2，或某些试卷中会用到标准差。2019年1月的插入页很可能指出，平均值的绝对不确定度可取为 ±(最大值 − 最小值)/2。
If you measured the time for 10 oscillations as 12.3, 12.5, 12.4, 12.6 s, the mean is 12.45 s and the uncertainty is (12.6 − 12.3)/2 = 0.15 s. You would then quote the period as (12.45 ± 0.15) s.
若测量 10 次振荡的时间分别为 12.3、12.5、12.4、12.6 s，平均值为 12.45 s，不确定度为 (12.6 − 12.3)/2 = 0.15 s，于是周期可表示为 (12.45 ± 0.15) s。
This approach yields a conservative estimate, which is acceptable at A‑Level. Remember to check whether the insert asks for the uncertainty in a single reading or in the mean.
这种方法给出的是偏保守的估计，在 A‑Level 层面是可以接受的。注意区分插入页要求的是单次读数的不确定度，还是平均值的不确定度。
8. Logarithmic and Exponential Relationships | 对数与指数关系
The insert provides the identities log(AB) = log A + log B and log(An) = n log A. These are essential when you need to linearise a power‑law or exponential equation to extract a physical constant from a graph.
插入页给出了 log(AB) = log A + log B 以及 log(An) = n log A 等恒等式。当需要将幂律或指数关系线性化以从图像中提取物理常数时，这些等式至关重要。
For example, the period of a simple pendulum follows T = 2π√(L/g). Taking logs gives log T = ½ log L + log(2π/√g). A log‑log plot of T against L thus has a gradient of 0.5, which you can use to verify the relationship or find g.
例如，单摆周期遵循 T = 2π√(L/g)。取对数得 log T = ½ log L + log(2π/√g)。因此 T 对 L 的双对数图斜率为 0.5，可用于验证关系或求 g。
The insert may also remind you that lg is log₁₀ and ln is logₑ. Either can be used, but you must be consistent throughout one calculation.
插入页可能还会提示 lg 表示 log₁₀，ln 表示 logₑ。任选一种都可以，但整个计算过程中必须保持一致。
9. Graphical Analysis: Gradient and Intercept | 图表分析：斜率与截距
Unit 3 frequently asks you to determine a gradient from a linear graph and then use it to calculate a constant such as the acceleration due to gravity, Young modulus or resistivity. The insert includes the standard formula for a straight line: y = mx + c.
Unit 3 经常要求从线性图中求斜率，进而计算某个常数，如重力加速度、杨氏模量或电阻率。插入页会给出直线标准形式 y = mx + c。
To find the uncertainty in the gradient, you can draw the steepest and shallowest acceptable lines that pass through the error bars, compute their gradients, and then state the uncertainty as (max gradient − min gradient)/2.
要确定斜率的不确定度，可画出通过误差棒的最陡和最平缓的两条可接受直线，计算它们的斜率，然后以 (最大斜率 − 最小斜率)/2 作为斜率的不确定度。
If the graph is curved, the insert’s log identities help transform the variables to make it linear. Always label your axes with the transformed quantities, e.g. ln V against t for a capacitor discharge, and give the relevant units.
若图像是曲线，插入页中的对数恒等式可帮助你变换变量以得到直线。务必在坐标轴上标注变换后的量，如电容器放电时以 ln V 对 t 作图，并标注相应单位。
10. Percentage Difference and Significance of Results | 百分差异与结果的显著性
The insert may remind you how to compare an experimental value with a known reference: percentage difference = |experimental value − reference| / reference × 100%. This helps you discuss the reliability of your data.
插入页可能提醒如何将实验值与已知参考值进行比较：百分差异 = |实验值 − 参考值| / 参考值 × 100%。这有助于你讨论数据的可靠性。
If the percentage difference is smaller than or comparable to the calculated percentage uncertainty, your result is consistent with the accepted value. If it is much larger, systematic errors are probably present.
若百分差异小于或相当于计算出的百分不确定度，说明你的结果与公认值相符；若大得多，则可能存在系统误差。
Use this idea in your evaluation: state the percentage uncertainty, the percentage difference and then conclude whether the experiment successfully verified the theory.
在评估题中运用这一思路：先给出百分不确定度和百分差异，然后判断实验是否成功验证了理论。
11. Common Mistakes and How to Avoid Them | 常见错误及避免方法
One frequent error is mixing absolute and percentage uncertainties. Always check whether the quantity you are calculating is obtained by addition/subtraction or multiplication/division.
一个常见错误是混淆绝对不确定度与百分不确定度。务必先判断所计算的量是通过加减得到还是乘除得到。
Another mistake is forgetting to convert units. The insert constants are given in SI units, so your raw data must be in metres, kilograms, seconds and amperes before substituting them into a formula.
另一个错误是忘记单位转换。插入页常数均为国际单位制，因此代入公式前原始数据必须转换为米、千克、秒和安培。
Students also sometimes quote the final uncertainty with too many significant figures. The uncertainty should normally be given to 1 significant figure, or occasionally 2 if it begins with a 1 or 2, and the main value should be rounded to the same decimal place.
学生有时还把最终不确定度写成过多有效数字。不确定度通常只保留1位有效数字，若首位是 1 或 2 可保留 2 位，而主值应保留到相同的小数位。
12. Summary and Revision Checklist | 总结与复习清单
Mastering the Unit 3 insert means you can quickly recall: the value of g, the form of area and volume formulas, the difference between absolute and percentage uncertainty, the adding rules for uncertainties, and how to linearise equations with logs. You must also be able to determine gradient uncertainty from a graph and calculate percentage differences.
掌握 Unit 3 插入页，意味着你能快速想起：g 的数值、面积体积公式的形式、绝对与百分不确定度的区别、不确定度合成规则，以及如何用对数线性化方程。同时还要能依据图像求斜率的不确定度，并计算百分差异。
An effective revision strategy is to take a blank copy of the insert and, without looking, reconstruct each section from memory. Then practise applying every formula to a concrete set of measurements, such as those from a pendulum or resistivity experiment, until the process becomes automatic.
一种高效复习策略是，拿一张空白插入页，不看原版，凭记忆重构每一部分。然后用一套具体测量数据，如单摆或电阻率实验数据，练习运用每一条公式，直到运用自如。
By the day of the exam, the insert should feel like a familiar toolkit rather than an unfamiliar sheet of numbers. With that confidence, you will be ready to tackle any practical‑based question that appears in Unit 3.
到考试那天，插入页应成为一个熟悉的工具箱，而不是一张充满陌生数字的纸。带着这份信心，你就能从容应对 Unit 3 中出现的任何实践类题目。
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