📚 A-Level Physics Unit 3 Mark Scheme Jan20: Experimental Investigation Techniques | A-Level 物理 Unit 3 评分标准 2020年1月：实验探究技巧
Mastering the Unit 3 practical paper in A-Level Physics requires a deep understanding of experimental design, measurement techniques, uncertainty analysis, and graphical skills. The January 2020 mark scheme reveals precisely what examiners look for, from identifying independent and dependent variables to calculating percentage uncertainties and interpreting error bars. This article breaks down the key techniques, linking each concept to the assessment criteria so that you can build confidence in planning, carrying out, and evaluating practical investigations.
掌握 A-Level 物理 Unit 3 实验卷需要对实验设计、测量技术、不确定度分析以及图形处理技能有深刻理解。2020 年 1 月的评分方案准确揭示了考官所关注的内容，从识别自变量和因变量到计算百分误差和解读误差棒。本文将逐一分解关键技巧，将每个概念与评分标准联系起来，帮助你自信地规划、实施和评估实验探究。
1. Identifying Key Variables | 识别关键变量
The mark scheme places strong emphasis on correctly identifying the independent variable (IV), dependent variable (DV), and control variables. The independent variable is the quantity you deliberately change; the dependent variable is what you measure in response. Any variable that could affect the DV but is kept constant is a control variable. In the Jan20 paper, marks were awarded for stating these clearly in the experimental plan.
评分方案非常强调正确识别自变量 (IV)、因变量 (DV) 和控制变量。自变量是刻意改变的量；因变量是测得的结果量。任何可能影响因变量但被保持恒定的量都是控制变量。在 2020 年 1 月的试卷中，清晰地在实验计划中说明这些变量即可得分。
- Independent variable: e.g., length of a wire, applied force, angle of incidence.
- 自变量：例如，导线长度、施加的力、入射角。
- Dependent variable: e.g., current, extension, angle of refraction.
- 因变量：例如，电流、伸长量、折射角。
- Control variables: temperature, cross‑sectional area, light intensity, etc.
- 控制变量：温度、横截面积、光强等。
2. Designing a Logical Procedure | 设计逻辑清晰的步骤
A logical sequence of practical steps is essential. The Jan20 mark scheme rewarded candidates who described the procedure in a clear, repeatable manner, including how apparatus was set up and how measurements were taken. Using diagrams to support the description is always encouraged.
逻辑清晰的实验步骤至关重要。2020 年 1 月的评分方案奖励了那些以清晰、可重复的方式描述步骤的考生，包括如何搭建装置以及如何获取测量值。使用图示辅助说明永远是被鼓励的。
- Begin with a labelled diagram of the experimental setup.
- 先用带标注的示意图展示实验装置。
- Specify the range of the IV and the number of readings (at least six different values).
- 指定自变量的取值范围和读数数量（至少六个不同的值）。
- Mention that each reading should be repeated to calculate a mean.
- 提及每次读数应重复测量以求平均值。
- State that the value of each control variable must be recorded.
- 说明每个控制变量的值都必须记录。
3. Choosing Appropriate Measuring Instruments | 选择合适的测量仪器
The mark scheme expects you to select instruments with appropriate precision for the quantity being measured. A common pitfall is using a metre rule where a vernier calliper or micrometer is needed. The Jan20 paper included marks for justifying the choice of instrument and stating its resolution.
评分方案期望我们能选择对被测量量具有适当精度的仪器。一个常见陷阱是在需要使用游标卡尺或千分尺的地方使用了米尺。2020 年 1 月的试卷中包含了对仪器选择理由的说明并陈述其分辨率的得分点。
| Quantity | Suitable Instrument | Typical Resolution |
|---|---|---|
| Length > 5 cm | Metre rule | 1 mm |
| Small length (e.g., diameter) | Vernier calliper | 0.1 mm |
| Very small length | Micrometer screw gauge | 0.01 mm |
| Time (manual) | Stopwatch | 0.01 s |
| Current | Digital ammeter | 0.01 A |
4. Repeating Readings and Calculating Means | 重复读数和计算平均值
Repeating measurements allows you to identify anomalies and improve reliability. The Jan20 mark scheme expected candidates to take at least two repeat readings for each value of the independent variable and then calculate a mean. If a reading is clearly anomalous, it should be excluded and the mean recalculated from the remaining values.
重复测量可以帮助你识别异常值并提高数据的可靠性。2020 年 1 月的评分方案期望考生对自变量的每个值至少进行两次重复读数，然后计算平均值。如果某个读数明显异常，则应将其排除，并从剩余数值中重新计算平均值。
A simple mean formula:
mean = (x₁ + x₂ + x₃ + …) ÷ n
平均值简单公式：
平均值 = (x₁ + x₂ + x₃ + …) ÷ n
5. Understanding Uncertainty in Measurements | 理解测量中的不确定度
h is usually ± half the resolution of the instrument. For digital instruments, it is ± the smallest scale division; for analogue instruments, it is ± half the smallest scale division.
每一次测量都存在不确定度。2020 年 1 月的评分方案要求考生说明单次测量的绝对不确定度，通常为仪器分辨率的一半。对于数字仪器，为 ± 最小分度值；对于模拟仪器，为 ± 最小分度值的一半。
- Metre rule (1 mm resolution): absolute uncertainty ± 0.5 mm.
- 米尺（分辨率 1 mm）：绝对不确定度 ± 0.5 mm。
- Digital voltmeter (0.01 V resolution): absolute uncertainty ± 0.01 V.
- 数字电压表（分辨率 0.01 V）：绝对不确定度 ± 0.01 V。
6. Calculating Percentage Uncertainty | 计算百分不确定度
Percentage uncertainty allows you to compare the precision of different measurements. It is found by dividing the absolute uncertainty by the measured value and multiplying by 100%. The Jan20 paper frequently awarded marks for correctly applying this to a reading and to a derived quantity.
百分不确定度使你可以比较不同测量值的精确度。计算方法是用绝对不确定度除以测量值再乘以 100%。2020 年 1 月的试卷经常因为将此公式正确应用于读数和导出量而给分。
percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%
百分不确定度 = (绝对不确定度 ÷ 测量值) × 100%
with a metre rule (uncertainty ± 0.1 cm), the percentage uncertainty is (0.1 ÷ 20.0) × 100% = 0.5%.
如果用米尺（不确定度 ± 0.1 cm）测得长度 L = 20.0 cm，则百分不确定度为 (0.1 ÷ 20.0) × 100% = 0.5%。
7. Uncertainty in Derived Quantities | 导出量的不确定度
ties (if the quantities are multiplied or divided). The Jan20 mark scheme expected this rule to be used, for example, when calculating density (ρ = m/V) or resistance (R = V/I).
当一个量由两个或多个测量值计算得出时，它的总百分不确定度是各单独百分不确定度之和（当这些量相乘或相除时）。2020 年 1 月的评分方案期望在计算密度 (ρ = m/V) 或电阻 (R = V/I) 等场合使用这条规则。
%U(total) = %U(meas₁) + %U(meas₂) + …
总百分不确定度 = %U(测量量₁) + %U(测量量₂) + …
the derived quantity: absolute uncertainty = (percentage uncertainty/100) × derived value.
然后用这个和来求导出量的绝对不确定度：绝对不确定度 = (百分不确定度/100) × 导出值。
8. Plotting an Accurate Graph | 绘制精确的图形
nd accurately plotted points (within ± ½ a small square). Points should be small crosses or dots with circles around them; avoid blobs.
作图是 Unit 3 的重要组成部分。2020 年 1 月的评分方案奖励了带有单位的正确轴标签、使用了超过一半格子的合理标尺，以及精确描点（误差在 ± ½ 小方格内）。数据点应画为小十字或带圆圈的圆点；避免画成大块。
- Independent variable on the x‑axis, dependent variable on the y‑axis.
- 自变量放在 x 轴，因变量放在 y 轴。
- Scale must allow easy interpolation (e.g., 1 cm = 2 units, 1 cm = 5 units).
- 标尺必须便于插值（如 1 cm = 2 个单位、1 cm = 5 个单位）。
- Label each axis with both the quantity and unit, e.g., "Length L / cm".
- 每个轴都要标注物理量和单位，例如 "长度 L / cm"。
9. Drawing the Best‑Fit Line | 绘制最佳拟合线
The best‑fit line is a single straight line or smooth curve that passes through as many points as possible, with roughly equal numbers of points lying above and below it. The Jan20 mark scheme expected the line to be drawn with a sharp pencil and a clear ruler, not forcing it through the origin unless the relationship is known to be proportional.
最佳拟合线是一条尽可能通过更多数据点的单一直线或光滑曲线，并且线上方和线下方的点数大致相等。2020 年 1 月的评分方案期望用尖锐铅笔和透明直尺画线，除非已知关系为正比，否则不要强行让线通过原点。
Anomalous points should be identified with a ring and ignored when drawing the best fit. The mark scheme often has a specific tolerance (e.g., within 1 mm vertically of the accepted line).
异常点应该用圈标出，并在绘制最佳拟合线时忽略。评分方案通常有特定的容差（例如，在公认线的垂直方向上允许 ± 1 mm）。
10. Determining Gradient and Intercept | 确定斜率和截距
Once the best‑fit line is drawn, large triangle coordinates should be used to calculate the gradient. The Jan20 mark scheme insisted that the triangle should cover at least half of the drawn line and that coordinates must be read from the line, not from data points. The intercept is read directly from the y‑axis.
画出最佳拟合线后，应使用大三角形的坐标来计算斜率。2020 年 1 月的评分方案坚持三角形应至少覆盖所画直线的一半，且坐标必须从直线上读取，而非从数据点读取。截距则直接从 y 轴上读取。
gradient = (y₂ − y₁) ÷ (x₂ − x₁)
斜率 = (y₂ − y₁) ÷ (x₂ − x₁)
Both the gradient and intercept should be given to an appropriate number of significant figures and accompanied by their correct units.
斜率和截距都应保留合适数量的有效数字，并附带正确的单位。
11. Using Error Bars and Worst‑Fit Lines | 使用误差棒和最差拟合线
When absolute uncertainties are known, vertical (and sometimes horizontal) error bars should be added to each point. The Jan20 mark scheme often asked for a worst‑fit line: a straight line that passes through the extremes of the error bars, giving the steepest or shallowest plausible slope. The uncertainty in the gradient is then estimated as half the difference between the best and worst gradients.
当已知绝对不确定度时，应为每个点添加竖直（有时还有水平）误差棒。2020 年 1 月的评分方案常要求绘制最差拟合线：一条穿过误差棒极端的直线，给出可能的最陡或最平缓斜率。然后，斜率的不确定度估计为最佳斜率与最差斜率差值的一半。
Δgradient = (best gradient − worst gradient) ÷ 2
斜率不确定度 = (最佳斜率 − 最差斜率) ÷ 2
This method is explicitly rewarded in the mark scheme and demonstrates a thorough understanding of uncertainty.
这种方法在评分方案中得到明确奖励，体现了对不确定度的透彻理解。
12. Evaluating the Experiment and Proposing Improvements | 实验评价与提出改进方案
The final part of a Unit 3 question often asks you to discuss the reliability of the results and suggest realistic improvements. The Jan20 mark scheme looked for comments on the size of error bars, the match between the best‑fit line and the data, and any sources of systematic or random error. Suggestions for improvement must be specific and linked to the experimental procedure, e.g., using digital instruments to reduce reading uncertainty or taking more repeat measurements at each value.
Unit 3 题目的最后部分常要求你讨论结果的可靠性并提出切实可行的改进方案。2020 年 1 月的评分方案会寻找关于误差棒的大小、最佳拟合线与数据的匹配程度，以及任何系统或随机误差来源的评论。改进建议必须具体且与实验步骤相关联，例如使用数字仪表来减小读数不确定度，或在每个数值处进行更多重复测量。
Always relate the evaluation back to the calculated percentage uncertainty and the graphical analysis. A well‑argued evaluation that identifies the most significant source of uncertainty can make the difference between a good and an excellent answer.
始终将评价与计算出的百分不确定度以及图形分析联系起来。一份论证充分、能明确最主要不确定度来源的评价，能让你的答案从良好变为优秀。
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