📚 A-Level Physics: June 2018 Mark Scheme 5 – Experimental Investigation | A-Level 物理：2018年6月卷5评分标准实验探究
Paper 5 of the Cambridge International A-Level Physics examination is a one‑hour, 15‑minute practical paper that challenges students to plan an investigation and then analyse and evaluate experimental data provided within the question. The June 2018 mark scheme for this paper offers a clear window into the standard of response examiners expect, particularly regarding the precision of measurements, the handling of uncertainties, and the logical construction of an experimental procedure. This article explores the core skills tested in that paper, using the classic pendulum experiment to illustrate planning, data analysis, and evaluation while referencing the mark scheme criteria throughout.
剑桥国际 A-Level 物理的第五卷是一场 1 小时 15 分钟的实践性考试，要求学生先设计一项实验探究，再对题目提供的实验数据进行分析与评估。2018 年 6 月该卷的评分标准清晰地展示了考官所期待的回答水准，尤其是在测量精度、不确定度处理以及实验步骤的逻辑构建方面。本文将以经典的单摆实验为例，围绕该卷的评分要求，深入讲解实验计划、数据分析和评估三大核心技能。
1. Understanding the Paper 5 Format | 理解卷五考试形式
Paper 5 consists of two compulsory questions. Question 1 carries 15 marks and typically presents a laboratory scenario with a short aim—for instance, “determine the acceleration of free fall using a simple pendulum”—and asks the candidate to design a full investigation. This includes listing additional apparatus, describing a step‑by‑step method, identifying variables to control, and explaining how to analyse results. Question 2 carries 15 marks and provides a set of real or simulated data; candidates must process the raw data, calculate absolute and percentage uncertainties, draw an appropriate table, plot a graph with error bars, and finally evaluate the reliability of the procedure.
卷五包含两道必答题。第一题占 15 分，通常给出一段实验室场景和简短目标——例如”用单摆测定重力加速度”——要求考生设计完整的探究方案，包括列出额外器材、描述分步方法、指明需控制的变量以及解释数据分析方式。第二题同样占 15 分，提供一组真实或模拟数据；考生需要处理原始数据，计算绝对与百分比不确定度，绘制合适的表格，画出带误差棒的图线，并最终评估实验过程的可靠程度。
2. June 2018 Scenario: Pendulum for g | 2018 年 6 月场景：用单摆测 g
In Question 1 of the June 2018 Paper 5, one common variant described a student using a pendulum to measure the acceleration of free fall. Although examiners’ reports cannot be quoted directly, the mark scheme rewards clear identification of the independent variable (pendulum length L), the dependent variable (period T), and the quantity to be kept constant (amplitude of swing, mass of bob). Such clarity tells the examiner that the candidate understands the theoretical relationship T = 2π √(L/g) and can transform it into a straight‑line equation for graphing.
在 2018 年 6 月卷五第一题的一个常见版本中，学生要用单摆测量重力加速度。虽然不能直接引用考官报告，但评分标准特别赞赏清晰指出自变量（摆长 L）、因变量（周期 T）以及需要保持恒定的量（摆动幅度、摆球质量）。这样的清晰表述会让考官明白，考生理解理论关系 T = 2π √(L/g)，并能将其转化为用于绘制图线的直线方程。
3. Planning: Independent, Dependent, and Control Variables | 计划：自变量、因变量与控制变量
A top‑scoring plan begins by naming the independent variable and giving its range and increment. For the pendulum, a candidate might state: “Length L is the independent variable; I will vary L from 0.200 m to 1.000 m in steps of 0.100 m.” The dependent variable T should be described as the time for 10 complete oscillations divided by 10, to reduce human reaction‑time error. Control variables must be listed with practical keeping‑constant methods: “angle of swing kept below 10° using a protractor; same metal bob used throughout.” The June 2018 mark scheme awards at least one mark for each variable properly described.
一份高分的实验计划首先会指明自变量，并给出其变化范围与步长。对单摆实验，可以写道：”摆长 L 为自变量；L 从 0.200 m 变化到 1.000 m，步长 0.100 m。” 因变量 T 应描述为测量 10 次完整摆动的时间再除以 10，从而减小人的反应时间误差。控制变量必须列出并附上实际的保持方法：”用半圆仪控制摆角小于 10°；全程使用同一个金属摆球。” 2018 年 6 月的评分标准为每个合理描述的变量至少赋予 1 分。
4. Additional Apparatus and Method Steps | 额外器材与步骤描述
The mark scheme expects every piece of additional apparatus to be listed with its precision. For example: “metre rule (±1 mm), digital stopwatch (±0.01 s), protractor (±1°), clamp stand, string, mass hanger, and a set square to ensure the ruler is vertical.” The method should be written in clear, logical steps, using the passive voice where possible. Key phrases include: “The length L is measured from the point of suspension to the centre of the bob, using the metre rule and set square.” Examiners also look for a step that records repeated readings of the time for 10 oscillations and then calculates the average period.
评分标准要求每样额外器材都须列出并标明精度。例如：”米尺（±1 mm）、数字秒表（±0.01 s）、半圆仪（±1°）、铁架台、细绳、挂钩、用于确保米尺竖直的直角板。” 实验步骤要用清晰、合乎逻辑的被动语态书写。关键词句包括：”从悬挂点到摆球中心的长度 L 用米尺和直角板测量。” 考官也希望看到记录 10 次摆动时间重复读数、再计算平均周期的步骤。
5. Data Analysis Framework | 数据分析框架
To obtain a straight‑line graph, candidates must show the algebraic manipulation: T = 2π √(L/g) → T² = (4π²/g) L. Hence a graph of T² against L yields a straight line through the origin, with gradient = 4π²/g and g = 4π² / gradient. The June 2018 mark scheme explicitly rewards this derivation and the link between the graph quantities and g. If either T² or L is on the wrong axis, no mark is awarded. Furthermore, the candidate must explain how uncertainty in the final g is obtained, either by worst‑line gradient analysis or by calculating percentage uncertainty from the largest gradient and smallest gradient drawn.
要得到一条直线，考生必须展示代数变换：T = 2π √(L/g) → T² = (4π²/g) L。因此，画出 T² 对 L 的图线将是一条过原点的直线，斜率 = 4π²/g，进而 g = 4π²/斜率。2018 年 6 月的评分标准明确对此推导以及图线量与 g 的关联给予分数。如果 T² 或 L 画错坐标轴，则该分全失。此外，考生还需解释最终 g 的不确定度如何获得：可通过最差斜率分析法，或通过所画最大斜率和最小斜率计算百分比不确定度。
6. Question 2: Processing Raw Data and Table Design | 第二题：处理原始数据与表格设计
Question 2 in the same paper usually supplies columns of raw readings with uncertainties. A typical table might list L, time for 10 oscillations t₁, t₂, mean t, period T (= mean t/10), T², and corresponding absolute uncertainties. The June 2018 mark scheme rewards a header row with quantity, unit, and an uncertainty indication, e.g. ‘T² / s² (± 0.002)’. Correct significant figures are crucial: if the raw data have three significant figures, T² must be quoted to three significant figures (e.g. 3.85, not 3.8 or 3.850). The calculated absolute uncertainty in T should be derived as (range of times)/20, following the half‑range method for repeated timings.
同一试卷的第二题通常提供几列带不确定度的原始读数。常见的表格会列出 L、10 次摆动的时间 t₁、t₂、平均时间、周期 T（= 平均时间/10）、T² 及对应的绝对不确定度。2018 年 6 月的评分标准要求表头行必须包含物理量、单位和不确定度说明，例如 ‘T² / s² (± 0.002)’。正确的有效数字至关重要：若原始数据为三位有效数字，T² 也必须给出三位有效数字（如 3.85，而非 3.8 或 3.850）。T 的绝对不确定度应按半范围方法计算：(时间范围)/20。
7. Graph Plotting and Error Bars | 绘图与误差棒
The mark scheme expects six or more points plotted accurately on a grid. Axes must be labelled exactly as ‘T² / s²’ and ‘L / m’, with linear scales that use more than half the grid in both directions. Error bars on T² are required, calculated as the uncertainty in T² = 2 T × ΔT, and must be drawn as vertical lines; if any error bar is too small to draw, it should be stated. Candidates often lose marks for failing to draw a best‑fit line that passes through the centroid of all points or for forcing the line through the origin without theoretical justification. The gradient triangle must be shown, and its coordinates read to half a small square.
评分标准要求准确地在坐标纸上标绘六个或更多数据点。坐标轴必须正确标注 ‘T² / s²’ 和 ‘L / m’，并采用在两个方向上都使用超过半页幅面的线性刻度。T² 上的误差棒必须画出，其值用 T² 的不确定度 = 2 T × ΔT 计算，并以竖直线段呈现；若某个误差棒太小而无法画出，则需文字说明。常见失分点是：最佳拟合线未经过所有点的质心，或缺乏理论依据就强制让直线通过原点。梯度三角形必须显示，其坐标读数须精确到半个小格。
8. Calculating g and Its Uncertainty | 计算 g 及其不确定度
After reading the gradient m (in s² m⁻¹), g = 4π² / m. For a gradient of, say, 4.02, g = 4π² / 4.02 = 9.82 m s⁻². The June 2018 scheme then expects candidates to use the worst‑difference method: either draw the steepest and shallowest acceptable lines, giving m_max and m_min, and then calculate g_max and g_min; the absolute uncertainty Δg = (g_max − g_min)/2. Alternatively, percentage uncertainty in g can be found from % uncertainty in gradient following the same worst‑line approach. The final value of g must be quoted to match its uncertainty, e.g. 9.82 ± 0.05 m s⁻².
在读取斜率 m（单位 s² m⁻¹）后，g = 4π² / m。例如斜率为 4.02，则 g = 4π² / 4.02 = 9.82 m s⁻²。2018 年 6 月的评分标准随后要求考生采用最差差值法：要么画出最陡和最平的两条可接受直线，得到 m_max 和 m_min，再计算 g_max 和 g_min；绝对不确定度 Δg = (g_max − g_min)/2。另一种方式是用最差线方法求出斜率的百分比不确定度，再以此求得 g 的百分比不确定度。最终 g 值的表述须与不确定度匹配，如 9.82 ± 0.05 m s⁻²。
9. Evaluation: Identifying Errors and Improvements | 评估：识别误差与改进
Every evaluation must link a specific source of error to a practical improvement, not just speculate. For the pendulum, timing with a stopwatch introduces reaction‑time error. A valid improvement is “use a light gate connected to a data‑logger to measure the period directly, eliminating human reaction error.” The June 2018 mark scheme rejects vague statements like “do the experiment more carefully” and rewards precision: “clamp the ruler vertically using a spirit level” or “film the swing with a high‑speed camera and analyse frame‑by‑frame.” Three distinct weaknesses with corresponding improvements are typical for full marks.
每项评估都必须将特定的误差来源与实际的改进措施联系起来，而非泛泛而谈。对单摆实验，秒表计时会导致反应时间误差。一个有效的改进是”使用与数据记录器连接的光电门直接测量周期，从而消除人为反应误差”。2018 年 6 月的评分标准拒绝诸如”更认真地做实验”之类的模糊表述，而赞赏精确的建议：”用水平尺确保米尺竖直”或”用高速摄像机拍摄摆动过程并逐帧分析”。为获得满分，通常需要提出三个不同的缺陷及相应改进。
10. Common Errors Highlighted by the Mark Scheme | 评分标准强调的常见错误
Examiners frequently note that candidates confuse ‘precision’ with ‘accuracy’, misapply the half‑range rule, or use graph scales that are too compressed. Another frequent mistake is to treat the period T directly against L rather than T², losing the linearisation mark. In June 2018, many candidates lost a mark for not stating that the bob should be released from a small angle (<10°) to satisfy simple harmonic motion. Additionally, when calculating the uncertainty in T², the mark scheme explicitly requires the use of 2 T ΔT; forgetting the factor of 2 was penalised. Memorising these formula templates and the logical order of a plan secures foundational marks.
考官常发现的错误包括：混淆”精密度”与”准确度”、误用半范围公式、或坐标轴刻度过于压缩。另一个常见错误是直接将周期 T 对 L 作图，而非 T²，从而丢失线性化的分数。在 2018 年 6 月的考试中，许多考生因未说明摆球应从小于 10° 的角度释放以满足简谐运动条件而失分。此外，计算 T² 的不确定度时，评分标准明确要求使用 2 T ΔT；忘记乘 2 会被扣分。熟记这些公式模板和计划的逻辑顺序，便可稳拿基础分。
11. Using the Mark Scheme for Revision | 用评分标准指导复习
Treat the June 2018 mark scheme as a checklist. Go through each bullet point and ask: can I define my variables like this? Have I included a labelled diagram? Does my table have correct column headings and consistent significant figures? Do I know how to draw a worst‑acceptable‑line and calculate uncertainty in gradient? Self‑marking a practice paper against the scheme reveals which specific skill needs reinforcement. Repeating this with several past Paper 5 variants builds the automaticity required to perform well under time pressure.
将 2018 年 6 月的评分标准当作核查清单。逐项检查每一条要求：我能像这样定义变量吗？我是否画了带标注的示意图？我的表格有正确的列标题和一致的有效数字吗？我是否知道如何画出最差可接受线并计算斜率的不确定度？用该评分标准自我批改一份练习卷，可以揭示哪个具体技能需要加强。对多份往年卷五真题重复这一过程，就能培养在时间压力下出色发挥的熟练度。
12. Conclusion: From Planning to Precision | 结语：从计划到精度
Paper 5 is not a test of laboratory dexterity but a test of scientific thinking. The June 2018 mark scheme rewards logical planning, meticulous data handling, and reflective evaluation. Every uncertainty calculation and every control variable mentioned counts toward a final grade that tells universities a student can design and critique an experiment. Mastering the techniques outlined here—from linearising the pendulum equation to annotating a worst‑fit line—equips learners to approach this paper with confidence and to begin thinking like a physicist.
卷五并非考查动手操作的灵巧度，而是考查科学思维能力。2018 年 6 月的评分标准嘉奖的是逻辑清晰的计划、一丝不苟的数据处理以及反思性的评估。每一项不确定度计算和每一个提到的控制变量，最终都映射到大学所看重的实验设计与批判技能上。掌握本文所概述的技巧——从单摆方程线性化到标注最差拟合线——将使学习者满怀信心地面对这份试卷，并开始像物理学家一样思考。
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