Measurement, graphs & errors — questions and answers
5 high-yield, syllabus-aligned questions on Measurement, graphs & errors, covering 18 individually creditable mark points. Each one shows the answer that scores full marks under our guide, which phrase earns which mark, and a common incomplete answer — so you can see the difference rather than guess at it.
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Every question and solution is reviewed by examiners versed in WAEC and JAMB, each with more than thirty years of experience.
Mark allocations are TopMarks’ own, written against the published syllabus and Chief Examiners’ reports. They are a guide to how these answers are usually credited, not an official marking scheme.
Distinguish4 marks
Distinguish between fundamental and derived quantities, giving two examples of each.
TopMarks model answer
A fundamental quantity is one that is not defined in terms of any other physical quantity; mass and time are examples. A derived quantity is one obtained by combining two or more fundamental quantities by multiplication or division; velocity, which is length divided by time, and force, which is mass multiplied by acceleration, are examples.
Suggested marking guide
1Fundamental quantities are not defined in terms of others
2Two fundamental examples
3Derived quantities are combinations of fundamental ones
4Two derived examples
Why it scores
Four marks split evenly between the two definitions and the four examples. That structure is visible in the question if you read it as “distinguish (2 marks) giving two examples of each (2 marks)”. Candidates who give only examples score half, and candidates who give only definitions also score half.
A common incomplete answer
“Mass and time are fundamental quantities, while force and velocity are derived quantities.”
What it costs: Two marks of four. All four examples are correct and credited, but neither term is actually defined, and the question said “distinguish”.
Key ideas to include: fundamental quantity, derived quantity, mass, length, time, velocity, force.
State3 marks
State three precautions that should be taken when plotting a graph in a physics practical.
TopMarks model answer
Choose scales that let the plotted points occupy at least half of the graph paper in both directions, and use simple scales such as 1, 2, 5 or 10 units per major division. Label both axes with the quantity and its unit, and give the graph a title. Plot the points accurately, mark each clearly with a cross or an encircled dot, and draw the line of best fit as a single thin straight line with as many points above it as below.
Suggested marking guide
1Suitable scale using at least half the paper
2Both axes labelled with quantity and unit
3Line of best fit drawn
Why it scores
These are marks awarded before any physics is even considered, and they are awarded in every practical paper. The scale mark is the one most often lost — a graph crammed into a corner of the paper cannot be read accurately, so the examiner deducts even when every plotted point is correct.
A common incomplete answer
“Label both axes with their units and choose a suitable scale for the graph.”
What it costs: Two marks of three. The axis labels are credited. The scale is mentioned but with no criterion — “suitable” is not enough — and the line of best fit is not mentioned at all.
Key ideas to include: scale, half the graph paper, axis labels with units, title, line of best fit.
Distinguish4 marks
Distinguish between random errors and systematic errors, giving one example of each and stating how each may be reduced.
TopMarks model answer
A random error is one that varies unpredictably in size and in sign from one reading to the next, for example the error in judging exactly when to start a stopwatch. It can be reduced by taking many readings and finding their mean. A systematic error is one that affects every reading by the same amount and in the same direction, for example a zero error in an ammeter. It cannot be reduced by repeating readings; it is removed by checking and correcting the zero of the instrument, or by calibrating it against a standard.
Suggested marking guide
1Random errors vary unpredictably between readings
2Reduced by averaging many readings
3Systematic errors affect every reading in the same way
4Removed by correcting the zero error or calibrating
Why it scores
The most important idea here is the one that costs marks when it is missed: repeating readings does NOT reduce a systematic error. Averaging twenty readings from an ammeter with a zero error gives a beautifully precise wrong answer. That distinction is what the question is really about.
A common incomplete answer
“Random errors vary unpredictably from reading to reading, while a systematic error affects every reading in the same direction.”
What it costs: Two marks of four. Both definitions are credited, but the question also asked how each may be reduced, and neither method is given.
Key ideas to include: random error, systematic error, zero error, mean, calibration, parallax.
State4 marks
State what is meant by the accuracy of a measuring instrument and give the accuracy of (i) a metre rule (ii) a vernier callipers (iii) a micrometer screw gauge.
TopMarks model answer
The accuracy of an instrument is the smallest change in the quantity that the instrument can detect and record, that is the value of one division on its scale. A metre rule graduated in millimetres has an accuracy of 0.1 cm. A vernier callipers has an accuracy of 0.01 cm. A micrometer screw gauge has an accuracy of 0.001 cm.
Suggested marking guide
1Accuracy is the smallest detectable change, or one scale division
2Metre rule: 0.1 cm
3Vernier callipers: 0.01 cm
4Micrometer screw gauge: 0.001 cm
Why it scores
These three figures are worth committing to memory because they decide which instrument to choose in every practical question. They also tell you how many decimal places to record: a reading taken with a vernier callipers must be written to two decimal places in centimetres, and writing 2.5 cm instead of 2.50 cm loses a mark for false precision.
A common incomplete answer
“A metre rule measures to 1 mm and a micrometer screw gauge to 0.01 mm.”
What it costs: Two marks of four. Both figures given are correct, but accuracy itself is never defined and the vernier callipers is omitted.
Key ideas to include: accuracy, least count, one scale division, metre rule, vernier callipers, micrometer screw gauge.
State3 marks
In an experiment, a graph of extension against load for a spiral spring is a straight line through the origin. State what this shows, and state how the force constant of the spring is obtained from the graph, giving its unit.
TopMarks model answer
A straight line through the origin shows that the extension is directly proportional to the load, which is Hooke's law, and that the elastic limit of the spring has not been exceeded. Because extension is plotted against load, the gradient is the extension per unit load, so the force constant is the RECIPROCAL of the gradient — the change in load divided by the corresponding change in extension, with the extension in metres. Its unit is the newton per metre, N m⁻¹.
Suggested marking guide
1Extension directly proportional to load — Hooke’s law
2Force constant from the gradient — the reciprocal, for this graph
3Correct unit
Why it scores
Two things are being tested. First, a straight line through the ORIGIN means directly proportional; a line that misses the origin is linear but not proportional, and the word “origin” in the question is the clue. Second — and this is where marks are most often thrown away — READ THE AXES. “Extension against load” puts extension on the vertical axis, so the gradient is extension per unit load and the force constant is its reciprocal. If the question had said “load against extension”, the force constant would be the gradient itself. Check which quantity is named first before you write anything down.
A common incomplete answer
“It shows that the spring obeys Hooke's law and the force constant is the gradient of the graph.”
What it costs: One mark of three under this guide. “Obeys Hooke’s law” is stated without saying what it means — that extension is directly proportional to load — no unit is given, and “the gradient” is the wrong way round for a graph of extension against load: it is the reciprocal of the gradient.
Key ideas to include: directly proportional, Hooke's law, elastic limit, gradient, N m⁻¹.
Practise Measurement, graphs & errors on real questions
Reading a full-mark answer is the first half. Writing one under time is the other. A free account opens exam-standard practice in Physics with the full solution on every question.