AQA A-Level Physics Unit 3 Insert January 2019: Practical Skills Revision Guide | AQA 物理 A-level 第三单元附表 2019年1月：实践技能复习指南

📚 AQA A-Level Physics Unit 3 Insert January 2019: Practical Skills Revision Guide | AQA 物理 A-level 第三单元附表 2019年1月：实践技能复习指南

The AQA A-Level Physics Unit 3 (PHYA3) paper assesses your investigative and practical skills in AS Physics. In the January 2019 sitting, the insert booklet supplied all the experimental data, apparatus diagrams and additional constants you needed to answer the written questions. This guide takes you through every aspect of that insert — how to read raw data tables, plot and interpret graphs, handle uncertainty, and write a convincing evaluation — so that you can tackle insert-based questions with confidence.

AQA A-level 物理第三单元（PHYA3）考查的是 AS 物理阶段的调查研究与实践技能。在2019年1月的考试中，附卷提供了回答书面问题所需的全部实验数据、装置图以及额外物理常量。本指南将带你逐一掌握附卷中的每个要点——如何读取原始数据表、绘制并解读图像、处理不确定度，以及撰写令人信服的评估结论——使你能自信应对所有基于附卷的考题。

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1. What Was Inside the January 2019 Insert | 2019年1月附卷包含什么

The insert was a printed booklet of approximately eight pages designed to replace the physical laboratory session. It reproduced the results a candidate would have obtained had they performed the experiment themselves. A typical insert had four components: a short introductory paragraph describing the experimental set-up; a raw data table with repeated readings and columns for processed values; pre-drawn axes or partially completed graphs; and a set of additional physical data such as the density of water or the Young modulus of copper that was not printed on the standard formula sheet.

附卷是一份约八页的印刷册，旨在替代实际实验室操作环节。它再现了考生亲自完成实验本应获得的结果。典型的附卷包含四个部分：一段简要的实验装置说明文字；一张原始数据表，包含重复读数及待填充的处理值列；预先绘制的坐标轴或部分完成的图像；以及一组标准公式手册中没有印出的额外物理数据，例如水的密度或铜的杨氏模量。

Tip: Before answering any question, spend two minutes scanning the whole insert. Knowing where the data table ends and where the graph starts prevents clumsy page-turning during the exam.

提示：在回答任何问题之前，先用两分钟通览整份附卷。明确数据表在哪里结束、图像从哪里开始，可以避免考试中手忙脚乱地翻页。

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2. Key Experimental Methods Assessed in Unit 3 | 第三单元考察的关键实验方法

Unit 3 draws on the core practicals from AS Physics, and the January 2019 insert focused on experiments you would have studied in class. These include measuring the spring constant using Hooke’s law, determining the acceleration due to gravity with a pendulum, investigating resistivity of a metal wire, and verifying the density of regular and irregular solids. The insert supplied the apparatus diagram plus an example of how readings were recorded, and you were expected to recognise the technique immediately.

第三单元考查 AS 物理的核心实验内容，2019年1月附卷聚焦于你在课堂上学习过的实验。这些包括利用胡克定律测量劲度系数、用单摆测定重力加速度、探究金属导线电阻率，以及验证规则与不规则固体的密度。附卷提供了装置图和读数记录示例，你需要立刻识别出对应的实验技术。

• Hooke’s law: F = kΔL | 胡克定律：F = kΔL（力与伸长量的关系）

• Simple pendulum: T = 2π√(L/g) | 单摆周期公式：T = 2π√(L/g)

• Resistivity: ρ = RA/L | 电阻率公式：ρ = RA/L

• Density: ρ = m/V | 密度公式：ρ = m/V

Notice that in each case the insert gave you raw length, mass or time data, not the final calculated quantity. The examiner wants to see that you can process raw data yourself.

请注意，在每种情况下附卷给出的都是原始的长度、质量或时间数据，而非最终计算量。考官希望看到你能自行处理原始数据。

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3. Reading Data Tables Accurately | 准确读取数据表

The most common errors in Unit 3 arise from misreading the data table. In January 2019 the table had three columns: the independent variable (for example, load in newtons), the dependent variable (extension in millimetres) and a third column for the calculated quantity (such as 1/T² or cross-sectional area). You must check the heading of every column before copying any number, and note the units carefully. A value ‘14.2’ in a column labelled ‘extension / mm’ means 14.2 millimetres, not centimetres.

第三单元最常见的错误源于误读数据表。在2019年1月的试卷中，数据表包含三列：自变量（例如载荷，单位牛顿）、因变量（伸长量，单位毫米），以及第三列用于计算量（如 1/T² 或横截面积）。在抄写任何数字之前，你必须检查每一列的表头，并仔细注意单位。标注为”伸长量/mm”的一列中的数值”14.2″意味着14.2毫米，而非厘米。

Load / N	Extension / mm	Mean extension / mm
2.0	18, 20, 22	20
4.0	39, 41, 40	40
6.0	58, 61, 60	60

When repeated readings are provided, you should calculate the mean before doing any further processing. In the table above, the three extension values at 4.0 N give a mean of (39 + 41 + 40)/3 = 40 mm. Round only at the final stage of a calculation to avoid accumulated rounding error.

当提供重复读数时，你应先计算平均值，再进行后续处理。在上表中，4.0 N 时的三个伸长量为 (39 + 41 + 40)/3 = 40 mm。只在计算的最后一步进行四舍五入，以避免累积舍入误差。

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4. Graph Skills: Lines of Best Fit and Gradients | 图表技能：最佳拟合线与斜率

The January 2019 insert contained one pre-printed grid for plotting your own graph. You were expected to plot the processed data points, draw a line of best fit, and calculate its gradient. A line of best fit should be a single straight line (or smooth curve) that has roughly the same number of points above and below it. Do not force the line through the origin unless the question tells you to; the y-intercept itself carries physical meaning, such as the unstretched length of a spring or the zero-error of an instrument.

2019年1月附卷包含一个预先印好的坐标网格，用于你自己绘图。你应该在网格上标出处理后的数据点，绘制最佳拟合线，并计算其斜率。最佳拟合线应为一条直线（或平滑曲线），使落在线上的数据点数目大致等于线下方的数据点数目。除非题目明确要求，否则不要强行让直线穿过原点；y 轴截距本身具有物理意义，例如弹簧的原长或仪器的零误差。

gradient m = Δy / Δx = (y₂ − y₁) / (x₂ − x₁)

To calculate the gradient, choose two points on the line that are far apart — never use two data points unless they lie exactly on the drawn line. Show your working clearly by drawing a triangle on the graph and writing the coordinates of the two chosen points next to it.

计算斜率时，应选择直线上相距较远的两个点——除非数据点恰好落在所画直线上，否则绝不能使用两个原始数据点。通过在图上画出辅助三角形并标出所选两点的坐标，可以清晰展示你的计算过程。

If the relationship is non-linear, such as T² = (4π²/g)L for a pendulum, you should plot the linearised form. In this case, plotting T² against L gives a straight line through the origin with gradient 4π²/g; the insert often gave you a column already computed for T² to guide you.

如果关系是非线性的，例如单摆的 T² = (4π²/g)L，你应该绘制线性化形式。在这种情况下，以 T² 对 L 作图可得一条过原点的直线，其斜率为 4π²/g；附卷通常会预先提供一列 T² 的计算值来引导你。

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5. Uncertainty and Error Analysis | 不确定度与误差分析

Uncertainty is a core requirement of Unit 3, and the January 2019 insert included questions on calculating both absolute and percentage uncertainty. The absolute uncertainty Δx of a single reading with a ruler marked in millimetres is ±0.5 mm, half the smallest division. For a digital stopwatch reading to 0.01 s, the uncertainty is ±0.01 s from the instrument, although human reaction time (typically ±0.2 s) usually dominates timing measurements.

不确定度是第三单元的核心要求，2019年1月附卷包含了计算绝对不确定度和百分比不确定度的问题。使用毫米刻度尺进行单次读数时，绝对不确定度 Δx 为 ±0.5 mm，即最小分度的一半。对于读数精度为0.01 s的数字秒表，仪器带来的不确定度为 ±0.01 s，但人体的反应时间（通常为 ±0.2 s）通常主导计时测量的不确定度。

When quantities are multiplied or divided, you add the percentage uncertainties:

当物理量相乘或相除时，百分比不确定度相加减：

ΔQ / Q = ΔA / A + ΔB / B

For example, if the resistance R = V/I with V = 6.0 ± 0.1 V and I = 2.0 ± 0.05 A, then the fractional uncertainty in R is 0.1/6.0 + 0.05/2.0 = 0.0167 + 0.025 = 0.0417, giving a percentage uncertainty of 4.2%. The resistance is 3.0 Ω ± 4% = 3.0 ± 0.1 Ω.

例如，若 R = V/I，其中 V = 6.0 ± 0.1 V，I = 2.0 ± 0.05 A，则 R 的相对不确定度为 0.1/6.0 + 0.05/2.0 = 0.0167 + 0.025 = 0.0417，即百分比不确定度为 4.2%。因此电阻为 3.0 Ω ± 4%，即 3.0 ± 0.1 Ω。

When a quantity is raised to a power, multiply the percentage uncertainty by the power. For the volume of a sphere V = (4/3)πr³, a 2% uncertainty in r gives a 6% uncertainty in V.

当物理量带有幂次时，将百分比不确定度乘以该幂次。例如球体体积 V = (4/3)πr³，若 r 有 2% 的不确定度，则 V 有 6% 的不确定度。

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6. Significant Figures and Units | 有效数字与单位

Unit 3 markers are strict about significant figures and units. A calculation answer should generally be quoted to the same number of significant figures as the least precise piece of data used. If the insert gives extension values to two significant figures, your final spring constant should also be given to two significant figures unless the mark scheme states otherwise.

第三单元的评分对有效数字和单位要求严格。计算答案通常应保留与所用数据中精度最低者相同的有效数字位数。如果附卷给出的伸长量保留两位有效数字，那么你最终得到的劲度系数也应保留两位有效数字，除非评分标准另有说明。

Common unit errors to avoid: converting millimetres to metres incorrectly (divide by 1000, not 100), using grams instead of kilograms, and writing ‘N’ for newtons but ‘Nm⁻¹’ for spring constant. The insert sometimes included unit conversion hints in a box; always read that box carefully.

需要避免的常见单位错误：毫米到米的换算错误（除以1000，而非100）、误用克代替千克，以及将牛顿写成”N”、劲度系数写成”Nm⁻¹”。附卷有时在方框中提供单位换算提示；务必仔细阅读该方框内容。

For the spring constant experiment, the formula k = F/ΔL requires ΔL in metres. A mean extension of 60 mm corresponds to 0.060 m. If you forget to convert, your spring constant will be out by a factor of 1000.

对于弹簧劲度系数实验，公式 k = F/ΔL 要求 ΔL 以米为单位。平均伸长量 60 mm 对应 0.060 m。如果你忘记换算，弹簧劲度系数就会相差1000倍。

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7. Drawing Conclusions from the Data | 从数据中得出结论

After processing the data, the insert asked you to draw a conclusion that links the graph to the physics theory. A direct proportionality between load and extension supports Hooke’s law with the spring constant equal to the gradient of the graph. You must state the physical meaning of the gradient explicitly — for example, ‘the gradient equals the spring constant k = 50 N m⁻¹’ — rather than merely quoting the numerical value.

数据处理之后，附卷会要求你得出将图像与物理理论联系起来的结论。载荷与伸长量的正比关系支持胡克定律，弹簧劲度系数等于图像斜率。你必须明确说明斜率的物理意义——例如”斜率等于弹簧劲度系数 k = 50 N m⁻¹”——而不仅是给出数值。

For a pendulum experiment, the graph of T² against L should pass through the origin. If the line has a non-zero intercept, it suggests a systematic error such as incorrect timing of release or an incorrect measurement of the pendulum length. The conclusion should comment on whether the intercept is consistent with zero within the uncertainty of the measurements.

对于单摆实验，T² 对 L 的图像应经过原点。如果直线截距不为零，则提示存在系统误差，例如释放时刻计时错误或摆长测量不正确。结论应说明在测量不确定度范围内截距是否与零一致。

Always quote your final value with a unit and an uncertainty, for example g = 9.8 ± 0.3 m s⁻². This demonstrates that you understand both the result and its reliability.

始终在最终数值后附上单位和不确定度，例如 g = 9.8 ± 0.3 m s⁻²。这表明你既理解结果本身，也理解其可靠性。

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8. Evaluation: Identifying Weaknesses and Improvements | 评估：识别不足与改进方法

The final section of the January 2019 paper asked you to evaluate the experiment described in the insert. You were expected to identify the largest source of uncertainty, explain whether it is random or systematic, and suggest a concrete improvement. A common answer: ‘The measurement of the oscillation period using a hand-held stopwatch has a large random uncertainty due to reaction time; using a light gate with a data logger would reduce this uncertainty by removing human reaction time.’

2019年1月试卷的最后部分要求你评估附卷所述实验。你需要指出最大的不确定度来源，判断其属于随机误差还是系统误差，并提出具体改进方案。常见答案：”使用手持秒表测量振荡周期因反应时间引入了较大的随机不确定度；改用光电门配合数据记录器可以消除人体反应时间，从而减小该不确定度。”

Systematic errors include zero errors on instruments, parallax error when reading a ruler, and heat loss in thermal experiments. Random errors include vibration of the apparatus, difficulty judging the exact oscillation point, and small fluctuations in room temperature. Improvements must be tied to the specific error identified; a vague statement like ‘be more careful’ is not credited.

系统误差包括仪器的零误差、读取直尺时的视差误差以及热实验中的热量散失。随机误差包括装置振动、难以判断精确振荡位置以及室温的微小波动。改进措施必须与所识别的具体误差相对应；像”更加小心”这类笼统表述无法得分。

• Use digital sensors instead of analogue instruments | 使用数字传感器替代模拟仪器

• Repeat measurements a minimum of three times | 每次测量至少重复三次

• Use a fiducial marker to define the measurement point | 使用参考标记界定测量位置

• Reduce friction or air resistance where relevant | 在相关情况下减小摩擦或空气阻力

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9. January 2019-Style Worked Example | 2019年1月风格例题精解

Consider a typical insert question: a metal wire of length 1.500 m and diameter 0.38 mm is stretched by a load of 12.0 N, producing an extension of 1.7 mm. Calculate the cross-sectional area and the stress, then determine the Young modulus.

考虑一道典型附卷题目：一根金属丝长 1.500 m，直径 0.38 mm，受到 12.0 N 的载荷拉伸，伸长量为 1.7 mm。计算横截面积和应力，然后求杨氏模量。

Step 1 — Cross-sectional area: radius r = d/2 = 0.19 mm = 1.9 × 10⁻⁴ m, so A = πr² = π × (1.9 × 10⁻⁴)² = 1.13 × 10⁻⁷ m². Using two significant figures, A = 1.1 × 10⁻⁷ m².

第一步——横截面积：半径 r = d/2 = 0.19 mm = 1.9 × 10⁻⁴ m，因此 A = πr² = π × (1.9 ×

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