AQA A-Level Physics: Errors and Uncertainties in Measurements — mark scheme explained

The question

A student measures the length of a table as 1.50 m with an absolute uncertainty of ±0.02 m. Calculate the percentage uncertainty in the measurement. [Paraphrased for study — not reproduced from any exam paper.]

Mark scheme, decoded

What each mark is really for — in plain English — and the wording trap that loses it.

• S1

  Step 1: Identify the measured value (x) and the absolute uncertainty (Δx).

• S2

  x = 1.50 m, Δx = 0.02 m

• S3

  Step 2: Calculate the fractional uncertainty (Δx/x).

• S4

  Fractional uncertainty = Δx / x = 0.02 / 1.50 = 0.0133

• S5

  Step 3: Convert the fractional uncertainty to a percentage.

• S6

  Percentage uncertainty = 0.0133 × 100% = 1.33%

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Step 1: Identify the measured value (x) and the absolute uncertainty (Δx).

2. S2

   x = 1.50 m, Δx = 0.02 m

3. S3

   Step 2: Calculate the fractional uncertainty (Δx/x).

4. S4

   Fractional uncertainty = Δx / x = 0.02 / 1.50 = 0.0133

5. S5

   Step 3: Convert the fractional uncertainty to a percentage.

6. S6

   Percentage uncertainty = 0.0133 × 100% = 1.33%

7. Final answer: The percentage uncertainty in the measurement is 1.33%. (2 marks)

Common mistakes

• Confusing precision with accuracy. — Remember that precision is about consistency, and accuracy is about correctness. High precision does not guarantee high accuracy.
• Forgetting to combine uncertainties when performing calculations. — Always remember to combine uncertainties using the appropriate rules for addition, subtraction, multiplication, division, and powers. This ensures that your final answer includes a realistic estimate of the uncertainty.
• Using absolute uncertainties instead of fractional or percentage uncertainties when combining measurements through multiplication or division. — Use absolute uncertainties for addition and subtraction, and fractional or percentage uncertainties for multiplication and division. This ensures that your combined uncertainty is calculated correctly.
• Drawing error bars incorrectly on graphs. — Ensure that error bars are drawn correctly by using twice the absolute uncertainty for their length. If you have uncertainties in both x and y values, draw horizontal and vertical error bars accordingly.
• Failing to consider the range of possible gradients when determining the uncertainty in a graph's gradient. — Always draw two additional lines that represent the maximum and minimum possible gradients within the error bars. The uncertainty in the gradient is half the difference between these two values.
• Not understanding the relationship between significant figures and uncertainties. — The number of significant figures in a measurement should reflect the uncertainty. For example, if the uncertainty is ±0.1 cm, the measurement should be reported to one decimal place (e.g., 5.2 cm).
• Confusing resolution with precision. — Understand that resolution and precision are different concepts. A high-resolution instrument can detect small changes, but it does not guarantee high precision unless the measurements are consistent.
• Not considering systematic errors in experimental design. — Always consider potential sources of systematic errors in your experimental setup. Calibrate instruments accurately and use reliable methods to minimize these errors.

Where the marks go

• Full worked solution (all marking points)2 marks

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