OxfordAQA International A Level Physics
OxfordAQA International A Level Physics 3.1 Measurements and Their Errors Exam Questions
Free OxfordAQA International A Level Physics revision for 3.1 Measurements and Their Errors: what you need to know, common mistakes and exam-style questions with answers. Covers si base and derived units, prefixes, random and systematic errors, precision, accuracy, uncertainties and order of magnitude estimates.
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About OxfordAQA International A Level Physics 3.1 Measurements and Their Errors
Measurements and their errors is the opening section of the OxfordAQA International AS course and is assessed in Unit 1 (PH01), Mechanics, materials and atoms. It gives you the language of experimental physics: SI units, prefixes, the difference between random and systematic error, and how to quote and combine uncertainties. Although it is a short section, these skills are tested again in every practical-based question, and heavily in Unit 5 (PH05), Physics in practice. Examiners like to ask you to convert units, find the percentage uncertainty in a calculated quantity, judge whether a result is accurate or precise, and produce sensible order of magnitude estimates.
What you need to know
- 3.1.1 SI units The SI base units are kg, m, s, A, K and mol; every other unit is derived from these, for example the newton is kg m s-2. Learn the prefixes from tera (10^12) down to pico (10^-12), and the conversion 1 eV = 1.60 x 10^-19 J.
- Random and systematic errors Random errors scatter readings either side of the true value and are reduced by repeating and averaging. Systematic errors shift every reading in the same direction (for example a zero error or a stretched ruler) and are not removed by repeats; they are corrected by calibration or by fixing the method.
- Precision, repeatability and accuracy Precise measurements have little spread. Repeatable results are the same when the original experimenter repeats them; reproducible results are the same when someone else or a different method is used. An accurate value is close to the true value. Resolution is the smallest change an instrument can show.
- Combining uncertainties Absolute uncertainty has the units of the quantity; percentage uncertainty = (absolute uncertainty / value) x 100. For sums and differences add absolute uncertainties. For products and quotients add percentage uncertainties. For a power, multiply the percentage uncertainty by the power.
- Graphs and error bars Plot error bars to show the uncertainty in each point. Draw a line of best fit and a worst acceptable line through the error bars; the uncertainty in the gradient is the difference between the two gradients, and the same method works for an intercept.
- 3.1.3 Estimation Order of magnitude estimates use sensible values (a person about 70 kg, a car about 1000 kg, a room about 3 m high) and give the answer to the nearest power of ten. Show the assumptions you made.
Common mistakes in 3.1 Measurements and Their Errors
- Saying that repeating readings removes systematic error. Repeats only reduce the effect of random error; a systematic error needs calibration or correction of the method.
- Doubling the uncertainty for a squared quantity by adding absolute values. For A = pi d^2 / 4 you double the percentage uncertainty in d.
- Mixing up accuracy and precision. Precise means closely grouped readings; accurate means close to the true value.
- Quoting a final answer to far more significant figures than the data justify. Match the least precise measurement, usually 2 or 3 significant figures.
- Forgetting to convert prefixes before calculating, for example using mm in an equation that needs m.
Try three 3.1 Measurements and Their Errors exam-style questions
1. State the difference between a random error and a systematic error, giving one example of each. (2 marks)
Show the mark scheme answer
Random error causes readings to vary unpredictably about the true value, e.g. reaction time when using a stopwatch; systematic error shifts all readings by the same amount or proportion in one direction, e.g. a zero error on a micrometer.
2. The diameter of a wire is measured as 0.50 +/- 0.01 mm. Calculate the percentage uncertainty in the cross-sectional area of the wire. (2 marks)
Show the mark scheme answer
Percentage uncertainty in diameter = 0.01 / 0.50 x 100 = 2%; area depends on d^2 so percentage uncertainty = 2 x 2% = 4%.
3. Express the newton and the joule in SI base units. (2 marks)
Show the mark scheme answer
F = ma so N = kg m s-2; W = Fs so J = kg m^2 s-2.
3.1 Measurements and Their Errors FAQs
What does OxfordAQA International A Level Physics 3.1 Measurements and Their Errors cover?
It covers SI units and prefixes, types of error, precision and accuracy, absolute and percentage uncertainties, error bars and uncertainties in gradients, and order of magnitude estimation.
Which unit is 3.1 Measurements and Their Errors examined in?
The content belongs to Unit 1 (PH01), but the skills are used throughout the course and are central to Unit 5 (PH05), Physics in practice.
How do I find the uncertainty in a gradient?
Draw the line of best fit and the steepest or shallowest line that still passes through all the error bars. The uncertainty is the difference between the two gradients, and the percentage uncertainty is that difference divided by the best fit gradient, multiplied by 100.
