SQA Higher Physics Researching Physics: uncertainties, the skills of scientific inquiry and the assignment

What Researching Physics actually demands

Researching Physics is not a fourth content area: it is the skills of scientific inquiry strand woven through Our Dynamic Universe, Particles and Waves and Electricity. The SQA tests the scientific method, not just recall, and the spine of that testing is uncertainty. Wherever data appears in the question paper, you may be asked to read a scale-reading uncertainty, find a mean and random uncertainty, calculate a percentage uncertainty, or combine the uncertainties in several quantities. The same skills underpin the marking of the assignment.

This guide ties together the uncertainty skills with the wider inquiry skills of planning, processing, concluding and evaluating. The matching dot-point page works through the uncertainty calculations with practice questions; this overview sets out where they fit.

Units, prefixes and quoting a result

Higher Physics uses SI units and standard prefixes, from $\text{n}$ ($10^{-9}$) up to $\text{G}$ ($10^{9}$). Every measured result is quoted as $\text{value} \pm \text{absolute uncertainty}$, both in the same unit, with the uncertainty normally to one significant figure and the value rounded to the same decimal place. Quoting more figures than the doubt allows is a common slip the markers penalise.

The three types of uncertainty

The course names three sources of doubt. The scale-reading (reading) uncertainty is fixed by the resolution of the instrument: half the smallest division on an analogue scale, or one in the last digit on a digital display. The random uncertainty is the scatter in repeated readings, reduced by averaging. The systematic uncertainty is a consistent bias such as a zero error, which survives averaging and must be removed by correcting its cause.

Mean and approximate random uncertainty

For repeated readings, the best estimate is the mean, $\bar{x} = \frac{\sum x}{n}$, and the approximate random uncertainty in the mean is the range divided by the number of readings, $\frac{x_\text{max} - x_\text{min}}{n}$. Dividing by $n$ is the SQA convention, and it shows directly why taking more readings reduces the random uncertainty.

Percentage uncertainty and combining in quadrature

A percentage uncertainty is $\frac{\text{absolute uncertainty}}{\text{measured value}} \times 100\%$. Percentage uncertainties are the working currency because they can be compared and combined. When a result is found by multiplying or dividing measured quantities, combine their percentage uncertainties by adding in quadrature, $\sqrt{(\%\,u_1)^2 + (\%\,u_2)^2 + \dots}$, then convert back to an absolute uncertainty. The largest percentage uncertainty dominates, so improving the least precise measurement gives the biggest gain.

The wider inquiry skills

Across both components the SQA tests five inquiry skills:

• Planning. Identifying variables, selecting a valid procedure, and choosing apparatus that keeps percentage uncertainties small.
• Selecting and presenting. Reading and drawing tables and line graphs correctly.
• Processing. Gradients, areas under graphs, and absolute and percentage uncertainties.
• Analysing and concluding. Drawing valid conclusions supported by the evidence, including whether a theoretical value lies within the experimental uncertainty.
• Evaluating. Judging reliability and validity, distinguishing random from systematic uncertainty, and suggesting improvements.

The assignment

The assignment is a mandatory report worth 20 marks (scaled), written under controlled conditions around a candidate-chosen experiment with a physics basis. Uncertainty runs through the marking: raw data recorded with units and sensible precision, repeated readings averaged with a random uncertainty, percentage uncertainties calculated and combined, and an evaluation that separates random from systematic effects and proposes improvements. It assesses the same inquiry skills examined in the question paper.

Check your knowledge

A mix of recall and calculation questions on uncertainty. Attempt them, then check against the solutions.

1. State the scale-reading uncertainty of a digital voltmeter reading $1.24\text{ V}$ with the last digit in hundredths. (1 mark)
2. Four timings have a mean of $2.50\text{ s}$ and a range of $0.12\text{ s}$. State the approximate random uncertainty in the mean. (1 mark)
3. A length is $0.500\text{ m}$ with an absolute uncertainty of $0.005\text{ m}$. Find the percentage uncertainty. (1 mark)
4. A result is found from two quantities with percentage uncertainties of $3\%$ and $4\%$. Find the combined percentage uncertainty. (2 marks)
5. State which type of uncertainty is not reduced by taking more readings. (1 mark)