This set mixes the five skills from measurement and quantities: units, scale reading, means, scalar and vector descriptions, and uncertainty. All questions and data are original and invented for practice. They are not from any past paper.
Work each question on paper first, write units in every answer, then open the worked answer. Keep a note of the ones you miss, and the mistake log and retest queue can help you sort them by error type.
Questions, easy to harder
Q1. Choose a sensible unit for each: the mass of a mango, the time of a 100 m sprint, the length of a football pitch, the volume of a teaspoon.
Show answer
Mango: g (about 300 g, or 0.3 kg). Sprint: s. Football pitch: m. Teaspoon: cm³ or mL. The reasoning is to match the quantity and then choose a unit that gives a manageable number. Sizes are everyday estimates.
Q2. Convert: (a) 3.6 km to m, (b) 450 g to kg, (c) 2.5 h to s.
Show answer
(a) 3.6 × 1000 = 3600 m. (b) 450 ÷ 1000 = 0.45 kg. (c) 2.5 × 3600 = 9000 s (2.5 × 60 = 150 min, and 150 × 60 = 9000 s).
Q3. A cyclist travels at 54 km/h. Give the speed in m/s.
Show answer
54 km/h = 54 000 m ÷ 3600 s = 15 m/s. Check: 15 × 3.6 = 54.
Q4. A sheet has an area of 50 cm². Give the area in m².
Show answer
1 cm² = (0.01 m)² = 0.0001 m² = 10⁻⁴ m². Area = 50 × 10⁻⁴ = 5.0 × 10⁻³ m² (0.005 m²). Dividing by 100 would wrongly give 0.5 m², which is far too large for a small sheet.
Q5. An ammeter scale runs 0 to 1.0 A, labelled 0, 0.2, 0.4, 0.6, 0.8, 1.0. There are four equal spaces between labels. The pointer is exactly on the third small mark after the 0.4 A label. What is the current?
Show answer
One small division = 0.2 ÷ 4 = 0.05 A. Three divisions = 0.15 A. Reading = 0.4 + 0.15 = 0.55 A.
Q6. An object is placed on a ruler with its left end at 2.3 cm and its right end at 9.1 cm. What is its length?
Show answer
9.1 − 2.3 = 6.8 cm. The left end is not at zero, so the start reading must be subtracted.
Q7. Four readings of the width of a book are 12.6 cm, 12.9 cm, 12.7 cm and 12.8 cm. Find the mean width.
Show answer
Sum = 12.6 + 12.9 + 12.7 + 12.8 = 51.0. Mean = 51.0 ÷ 4 = 12.75 cm. The mean lies inside the cluster of readings, which is a good check.
Q8. A ball is timed falling a fixed distance five times: 0.52 s, 0.50 s, 0.48 s, 0.71 s, 0.50 s. Identify the anomalous result and find the mean of the rest.
Show answer
0.71 s is far from the cluster at about 0.48 to 0.52 s, so it is anomalous. Remaining sum = 0.52 + 0.50 + 0.48 + 0.50 = 2.00 s. Mean = 2.00 ÷ 4 = 0.50 s. Dividing by 5 would be wrong.
Q9. A cyclist rides 6 m west then 8 m north. Find (a) the distance and (b) the size of the displacement.
Show answer
(a) Distance = 6 + 8 = 14 m. (b) The legs are at right angles, so displacement = √(6² + 8²) = √(36 + 64) = √100 = 10 m. Displacement (10 m) is less than distance (14 m), as expected.
Q10. Twenty swings of a pendulum are timed four times: 31.2 s, 31.6 s, 31.4 s, 31.8 s. Find (a) the mean time for 20 swings with a half-range uncertainty, and (b) the period with its uncertainty.
Show answer
(a) Sum = 31.2 + 31.6 + 31.4 + 31.8 = 126.0. Mean = 126.0 ÷ 4 = 31.5 s. Half range = (31.8 − 31.2) ÷ 2 = 0.3 s. Result: 31.5 ± 0.3 s.
(b) Divide by 20: 31.5 ÷ 20 = 1.575 s and 0.3 ÷ 20 = 0.015 s. Period = 1.575 ± 0.015 s. Percentage uncertainty = 0.3 ÷ 31.5 × 100% = 0.95% for both the total and the period.
Q11. Two measuring cylinder readings each have an uncertainty of 1 mL: 40 mL and 8 mL. Find each percentage uncertainty and say which reading is more precise in relative terms.
Show answer
40 mL: 1 ÷ 40 × 100% = 2.5%. 8 mL: 1 ÷ 8 × 100% = 12.5%. The 40 mL reading has the smaller percentage uncertainty, so it is relatively more precise. Measuring a small volume in a large cylinder is a common reason for a large percentage uncertainty.
If you got these wrong
| Error you made | Questions | Go to |
|---|---|---|
| Wrong unit, or conversion factor not squared or cubed | Q1 to Q4 | choose a unit appropriate to a quantity |
| Counted marks instead of division values, or forgot the start reading | Q5, Q6 | read an analogue scale with interpolation |
| Wrong divisor, or anomalous result kept | Q7, Q8 | calculate a repeated-measurement mean |
| Added vectors as if they were scalars | Q9 | distinguish scalar and vector descriptions |
| Uncertainty method or percentage uncertainty | Q10, Q11 | state a realistic uncertainty |
What to do next
If you scored well across all five groups, move on to the next Physics topics from the Physics learning guide. If one group keeps slipping, repeat its lesson and then retry that question with changed numbers.
Some students can do these in a quiet hour but not mixed into a timed paper. That is worth raising in online one-to-one Physics tuition, where a teacher can see where your working goes wrong as you write.