A-Level · Physics · AQA · Mark scheme decoded

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

Machine-verifiedchecked against the AQA A-Level Physics specificationlast verified 3 July 2026

The short answer

In AQA A-Level Physics, understanding errors and uncertainties is crucial for accurate measurements and data analysis. This section covers random and systematic errors, precision, repeatability, reproducibility, resolution, accuracy, absolute, fractional, and percentage uncertainties, as well as how to represent uncertainty in graphs and combine uncertainties.

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.]

2 marks

Mark scheme, decoded

How the examiner actually awards the marks on this topic.

Gradora's own decode of the marking approach — not the exam board's published mark scheme.

How marks are awarded

For questions involving uncertainties, ensure that you show all steps in your calculations, including the propagation of uncertainties. Clearly state the final value with its uncertainty and the appropriate number of significant figures. For graph-related questions, draw error bars correctly and clearly label them.

What the command words demand

Calculate: Perform a numerical calculation using given data and appropriate formulas.
Determine: Find the value of a quantity or parameter, often involving multiple steps.
Explain: Provide a clear and detailed account of how something works or why something happens.
Identify: Recognize and name specific elements, errors, or concepts.
State: Give a concise answer without detailed explanation.

Model answer

A full-mark response to the question above, worked through step by step.

Timing: Allocate about 2-3 minutes per mark for questions involving errors and uncertainties. This allows time to carefully consider each step in your calculations and ensure that you present a well-organized answer.

Identify the measured value (x) and the absolute uncertainty (Δx).0 marks
x = 1.50 m, Δx = 0.02 m
Calculate the fractional uncertainty (Δx/x).1 mark
Fractional uncertainty = Δx / x = 0.02 / 1.50 = 0.0133
Convert the fractional uncertainty to a percentage.1 mark
Percentage uncertainty = 0.0133 × 100% = 1.33%

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

Work through every step correctly and you earn all 2 marks.

Another worked example

Two lengths are measured as follows: x = 5.0 cm ± 0.2 cm and y = 3.0 cm ± 0.1 cm. Calculate the combined uncertainty in the sum (x + y) and the difference (x - y).

4 marks

Identify the measured values and their absolute uncertainties.0 marks
x = 5.0 cm, Δx = 0.2 cm; y = 3.0 cm, Δy = 0.1 cm
Calculate the combined uncertainty in the sum (x + y).2 marks
Δ(x + y) = Δx + Δy = 0.2 cm + 0.1 cm = 0.3 cm
Calculate the combined uncertainty in the difference (x - y).2 marks
Δ(x - y) = Δx + Δy = 0.2 cm + 0.1 cm = 0.3 cm

Final answer: The combined uncertainty in the sum (x + y) is ±0.3 cm, and the combined uncertainty in the difference (x - y) is ±0.3 cm. (4 marks)

Work through every step correctly and you earn all 4 marks.

Common mistakes

Confusing precision with accuracy.
Why it happens: Students often mix up these two concepts, thinking that high precision means the measurements are correct. However, precision refers to consistency among repeated measurements, while accuracy refers to how close a measurement is to the true value.
Fix: 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.
Why it happens: Students may perform the main calculation but neglect to propagate the uncertainties through the operations, leading to incorrect final uncertainty values.
Fix: 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.
Why it happens: Students may use the wrong type of uncertainty in their calculations, leading to incorrect results. Absolute uncertainties are used for addition and subtraction, while fractional or percentage uncertainties are used for multiplication and division.
Fix: 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.
Why it happens: Students may draw error bars that are too short or too long, or they may not understand how to represent the uncertainty in both x and y directions.
Fix: 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.
Why it happens: Students may only draw the best-fit line and not consider the maximum and minimum possible gradients within the error bars, leading to an underestimation of the uncertainty in the gradient.
Fix: 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.
Why it happens: Students may report measurements with more significant figures than justified by the uncertainty, leading to an overestimation of precision.
Fix: 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.
Why it happens: Students may think that a higher resolution instrument always provides more precise measurements, but this is not necessarily true. Resolution refers to the smallest detectable change, while precision refers to consistency among repeated measurements.
Fix: 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.
Why it happens: Students may focus only on random errors and neglect to identify and correct for systematic errors, leading to biased results.
Fix: 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

The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.

Question type	What you’re asked to do	Marks
Percentage Uncertainty	Convert an absolute uncertainty in a measurement into a percentage uncertainty.	2
Combining Uncertainties	Add absolute uncertainties to find the combined uncertainty in a sum and a difference.	4
Uncertainty Propagation	Calculate density from mass and volume, then combine their percentage uncertainties for the result.	6
Uncertainty Propagation	Calculate the frequency from the time period and propagate the uncertainty to find its combined value.	4
Total across these question types		16

Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.