A Level Physics Practical Guide

Systematic and random errors

Systematic errors always deviate from the true value by the same magnitude and sign when measurements are repeated.

Examples: instrumental (zero error, calibration error, end error), poor technique (measuring a pendulum's length to the surface of the bob instead of its centre), and external factors (background radiation, heat loss).

Reduce them by taring and calibrating instruments, applying end corrections and using correct technique. Averaging does not reduce systematic errors.

Random errors deviate from the true value with varying magnitude and sign when measurements are repeated.

Examples: the observer (reaction time, judgement), the environment (fluctuating temperature or pressure) and intrinsic variation (non-uniform wire diameter, varying contact resistance).

Random errors can only be reduced, not eliminated, by taking repeated readings and averaging, or by plotting a line of best fit.

Trap: Repeating readings and averaging only helps with random error. If a question asks how to reduce a systematic error such as a zero error, averaging is the wrong answer.

Accuracy and precision

Accuracy: how close the average experimental value is to the true value. High accuracy means a small systematic error.

Precision: how close all the readings are to one another. High precision means a small random error.

A set of readings can be precise but inaccurate (tightly grouped, but offset by a zero error), or accurate but imprecise (scattered around the true value).

Trick: Link each word to its error: accuracy goes with systematic, precision goes with random. Most accuracy vs precision questions are just asking which error is present.

Expressing and combining uncertainties

Uncertainty in a reading comes from random errors or the precision of the instrument used.

Write a result as A ± ΔA. Give ΔA to 1 significant figure, then give A to the same decimal place as ΔA.

Uncertainties always add up. For addition or subtraction, add the absolute uncertainties. For multiplication, division and powers, add the fractional (or percentage) uncertainties, multiplying each by its power.

First principle method: when a relationship is too complex, or a quantity is measured directly several times, find the maximum and minimum values. The mean of the two is the value, and half their difference is the uncertainty.

Trap: Subtracting two close readings, like two lengths, adds their absolute uncertainties, so the percentage uncertainty in the difference can be very large. Students often subtract the uncertainties instead.

What Paper 4 (9478) tests

Paper 4 is a 2 h 30 min, 50-mark practical worth 20% of H2 Physics, split into two sections with 1 h 15 min of apparatus access each.

Planning (P), 4%: define the problem, describe a clear, logical procedure, explain how the data will be used to reach a conclusion, and assess risks and precautions.

Manipulation, measurement and observation (MMO): handle apparatus well, record readings to an appropriate precision, make sensible decisions about measurements, and spot anomalous results with reasons.

Presentation of data and observations (PDO): present information clearly, process measurements to find trends, and give data to a suitable number of decimal places or significant figures.

Analysis, conclusions and evaluation (ACE): interpret data, draw conclusions, make predictions, identify significant sources of error and limitations, and suggest how to reduce them. MMO, PDO and ACE together are worth 16%.

Spreadsheets (new in 9478): you must process and analyse data in spreadsheet software: import or enter data, use and copy formulae (including trig in radians, logs and exponentials), plot labelled line graphs, add a linear trendline and display its equation, and find areas under curves and gradients at a point.

Trick: When asked how to improve an experiment, name the specific error first, then give a fix that targets it. 'Repeat and average' only earns marks when the error you named is random.

Worked Example

A student finds g from a simple pendulum using g = 4π²L/T². She measures L = 0.800 ± 0.002 m, and times 20 oscillations as 35.9 ± 0.2 s.

Why this question is a good test of the topic: T is squared, so its fractional uncertainty counts twice and dominates. Students who forget the factor of 2, or who don't round Δg to 1 s.f. and match g's decimal place, lose easy marks.

Frequently Asked Questions