Course: Combined Science + Separate Physics | Tier: Foundation + Higher | These skills are tested throughout both papers, especially in required practical questions.
Notes
Variables
- Independent variable: the one you change.
- Dependent variable: the one you measure.
- Control variables: the ones you keep the same to make it a fair test.
- Continuous variables can have any value (e.g. length, temperature). Categoric variables are named groups (e.g. type of material).
Quality of results
- Accurate: close to the true value.
- Precise: very little spread around the mean.
- Repeatable: the same person, using the same method and equipment, gets similar results.
- Reproducible: someone else, or a different method or equipment, gets similar results.
- Resolution: the smallest change an instrument can show (e.g. 1 mm on a ruler).
- Uncertainty: the range the true value is likely to be in. Estimate it as ± half the range of repeat readings.
Errors
- Random error: readings vary unpredictably (e.g. reaction time). Reduce it by repeating and calculating a mean.
- Systematic error: every reading is wrong by the same amount (e.g. a badly calibrated balance). Repeating does not remove it.
- Zero error: a type of systematic error – the instrument doesn’t read zero when it should.
- Anomalous result: a result that doesn’t fit the pattern. Check it, and leave it out when calculating a mean.
Graphs
Use a line graph when both variables are continuous and a bar chart when the independent variable is categoric. Put the independent variable on the x-axis. Draw a smooth line or curve of best fit. A straight line through the origin means the variables are directly proportional.
Units, prefixes and significant figures
| Prefix | Symbol | Multiply by |
|---|---|---|
| giga | G | 109 |
| mega | M | 106 |
| kilo | k | 103 |
| milli | m | 10−3 |
| micro | μ | 10−6 |
| nano | n | 10−9 |
Give your answer to the same number of significant figures as the least precise data in the question.
Safety
A hazard is something that could cause harm (e.g. hot water). The risk is the chance of harm happening. A control measure reduces the risk (e.g. use a heatproof mat and don’t carry hot beakers).
📊 See it applied: the required practicals slideshow has a working scientifically slide for every practical – variables, hazards, accuracy and precision, and random and systematic errors – plus sample results with repeats and anomalies.
Questions
Q1 (F) A student investigates how the height a ball is dropped from affects how high it bounces. Name the independent, dependent and one control variable.
Show answer
Independent: drop height. Dependent: bounce height. Control: e.g. the same ball, the same surface.
Q2 (F) What is the difference between accurate and precise results?
Show answer
Accurate results are close to the true value. Precise results are close together, with very little spread around the mean – but they could all be wrong by the same amount.
Q3 (F) What is the resolution of a ruler marked in millimetres?
Show answer
1 mm – the smallest change it can show.
Q4 (F) Should you use a line graph or a bar chart to show how the type of material affects how well it insulates? Why?
Show answer
A bar chart, because the independent variable (type of material) is categoric.
Q5 (F) Four repeat timings are 3.42 s, 3.48 s, 3.39 s and 3.51 s. Calculate the mean.
Show answer
Mean = (3.42 + 3.48 + 3.39 + 3.51) ÷ 4 = 13.80 ÷ 4 = 3.45 s
Q6 (F/H) Estimate the uncertainty in the mean from Q5.
Show answer
Range = 3.51 − 3.39 = 0.12 s
Uncertainty = half the range = ± 0.06 s, so the time is 3.45 ± 0.06 s.
Q7 (F/H) Readings of 12.1 cm, 12.3 cm, 15.8 cm and 12.2 cm are taken. Identify the anomaly and calculate the mean.
Show answer
15.8 cm is anomalous – leave it out.
Mean = (12.1 + 12.3 + 12.2) ÷ 3 = 36.6 ÷ 3 = 12.2 cm
Q8 (F/H) A balance reads 0.3 g with nothing on it. What type of error is this, and how do you deal with it?
Show answer
A zero error (a type of systematic error). Zero (tare) the balance before use, or subtract 0.3 g from every reading.
Q9 (F/H) Convert: (a) 4.7 kΩ to Ω, (b) 250 mA to A, (c) 3.2 MJ to J in standard form.
Show answer
(a) 4.7 × 1000 = 4700 Ω
(b) 250 ÷ 1000 = 0.25 A
(c) 3.2 × 106 J
Q10 (F/H) What is the difference between repeatable and reproducible results?
Show answer
Repeatable: the same person repeats the experiment with the same method and equipment and gets similar results. Reproducible: a different person, or a different method or equipment, gets similar results.
Q11 (H) Explain why repeating readings reduces random error but not systematic error.
Show answer
Random errors make readings scatter both above and below the true value, so they tend to cancel out in a mean. A systematic error shifts every reading by the same amount in the same direction, so the mean is shifted too.
Q12 (H) Light has a wavelength of 450 nm. Write this in metres in standard form.
Show answer
1 nm = 1 × 10−9 m, so 450 nm = 450 × 10−9 m = 4.5 × 10−7 m
📏 Uncertainty and errors: extra practice
🧰 Uncertainty toolkit
1. Uncertainty from repeat readings = half the range
Step 1: cross out any anomalies.
Step 2: range = biggest − smallest.
Step 3: uncertainty = range ÷ 2.
Step 4: write the result as mean ± uncertainty, with the unit – e.g. 20.6 ± 0.2 cm.
2. Uncertainty from the instrument (resolution)
The resolution is the smallest change the instrument can show. A single reading from a scale is usually uncertain by about ± half the smallest division (e.g. a thermometer marked every 1 °C → ±0.5 °C).
3. Zero error
The instrument does not read zero when it should (e.g. a balance shows 0.3 g with nothing on it, or a ruler’s end is worn away). It makes every reading wrong by the same amount, so it is a systematic error.
✅ Fix: reset (tare) the instrument to zero, or correct every reading: true value = reading − zero reading.
⚠️ If the zero reading is negative, subtracting it means you add it on.
| Random error | Systematic error | |
|---|---|---|
| What happens | Readings are scattered – sometimes too high, sometimes too low | Every reading is out by the same amount, in the same direction |
| Examples | reaction time with a stopwatch; reading a scale that is changing | zero error; always reading a scale from above (parallax) |
| Reduce it by | repeating and calculating a mean | checking/resetting the zero; correcting readings. Repeating does not help |
| Affects | precision | accuracy |
4. Ways to reduce uncertainty
• Use an instrument with a better resolution (e.g. a digital balance instead of an analogue one).
• Repeat readings and calculate a mean.
• Measure a bigger quantity – time 10 swings instead of 1, then divide by 10.
• Use light gates or data loggers instead of a stopwatch – they remove human reaction time.
⚠️ Where students lose marks: using the whole range instead of half the range · forgetting the unit on the uncertainty · including the anomaly in the range · adding a zero error instead of subtracting it.
Half the range
Q13 (F) A student measures the length of a spring three times: 20.4 cm, 20.8 cm and 20.6 cm.
(a) Calculate the mean. (b) Calculate the uncertainty. (c) Write the result as mean ± uncertainty.
Show answer
(a) Mean = (20.4 + 20.8 + 20.6) ÷ 3 = 61.8 ÷ 3 = 20.6 cm
(b) Range = 20.8 − 20.4 = 0.4 cm, so uncertainty = 0.4 ÷ 2 = 0.2 cm
(c) 20.6 ± 0.2 cm
Q14 (F) A trolley is timed rolling down a ramp four times: 2.35 s, 2.41 s, 2.29 s, 2.39 s. Calculate the mean and the uncertainty.
Show answer
Mean = (2.35 + 2.41 + 2.29 + 2.39) ÷ 4 = 9.44 ÷ 4 = 2.36 s
Range = 2.41 − 2.29 = 0.12 s, so uncertainty = ± 0.06 s
Result: 2.36 ± 0.06 s
Q15 (F/H) In the specific heat capacity practical, four final temperatures are recorded: 24.5 °C, 24.9 °C, 28.1 °C and 24.7 °C.
(a) Identify the anomaly. (b) Calculate the mean without it. (c) Calculate the uncertainty.
Show answer
(a) 28.1 °C – it is much higher than the others.
(b) Mean = (24.5 + 24.9 + 24.7) ÷ 3 = 74.1 ÷ 3 = 24.7 °C
(c) Range = 24.9 − 24.5 = 0.4 °C, so uncertainty = ± 0.2 °C (the anomaly is not included in the range)
Zero errors
Q16 (F) A newtonmeter reads 0.2 N with nothing hanging on it. With a load attached it reads 3.4 N.
(a) What is the true weight of the load? (b) What type of error is this?
Show answer
(a) True weight = 3.4 − 0.2 = 3.2 N
(b) A zero error, which is a systematic error – every reading is 0.2 N too high.
Q17 (F/H) The end of a metre ruler is damaged, so a student starts measuring from the 1.0 cm mark instead of 0. She records the length of a spring as 15.6 cm.
(a) What is the true length? (b) Would repeating the measurement help? Explain.
Show answer
(a) True length = 15.6 − 1.0 = 14.6 cm
(b) No. It is a systematic error – every repeat would be 1.0 cm too long by the same amount. She must correct each reading (or measure from a proper zero).
Q18 (F/H) A digital balance reads −0.05 g when it is empty. A beaker on the balance reads 52.30 g. What is the true mass of the beaker?
Show answer
True mass = reading − zero reading = 52.30 − (−0.05) = 52.30 + 0.05 = 52.35 g
The balance reads too low, so the true mass is bigger. (Better still: press tare to reset it to zero before weighing.)
Resolution and reducing uncertainty
Q19 (F/H) A student times 10 swings of a pendulum with a stopwatch and gets 16.2 s.
(a) Calculate the time for one swing. (b) Explain why timing 10 swings is better than timing 1.
Show answer
(a) 16.2 ÷ 10 = 1.62 s
(b) The error from reaction time (starting and stopping the stopwatch) is about the same whether you time 1 swing or 10. Timing 10 swings makes that error much smaller compared with the total time, and dividing by 10 shares it across all the swings – so the uncertainty in one swing is reduced.
Q20 (H) A thermometer is marked every 1 °C. The water starts at 20 °C and ends at 35 °C.
(a) What is the uncertainty in each reading? (b) What is the temperature rise, and what is the largest uncertainty it could have?
Show answer
(a) Half the smallest division: ± 0.5 °C
(b) Rise = 35 − 20 = 15 °C. Each of the two readings could be out by 0.5 °C, so the rise could be out by up to ± 1 °C. A thermometer with a better resolution (e.g. a digital one reading to 0.1 °C) would reduce this.
Q21 (H) Two students measure the same time. Student A: 5.2 s, 5.4 s, 5.3 s. Student B: 5.0 s, 5.6 s, 5.3 s.
(a) Calculate the mean and uncertainty for each. (b) Whose results are more precise?
Show answer
(a) A: mean 5.3 s, range 0.2 s → 5.3 ± 0.1 s. B: mean 5.3 s, range 0.6 s → 5.3 ± 0.3 s
(b) Student A – the readings are closer together (smaller spread), so the uncertainty is smaller. Both have the same mean, so we can’t tell whose are more accurate without the true value.
Accuracy, systematic errors and graphs
Q22 (H) A student measures the gravitational field strength as 9.5 ± 0.2 N/kg. The accepted value is 9.8 N/kg.
(a) Does the student’s range include the accepted value? (b) What does this suggest about the experiment?
Show answer
(a) The range is 9.3 to 9.7 N/kg, so no – 9.8 N/kg is outside it.
(b) The result is not accurate. As the true value is outside the uncertainty, there is probably a systematic error (e.g. a zero error, or air resistance always slowing the object) – repeating more times would not fix it.
Q23 (H) In the force and extension practical, the graph of force against extension should go through the origin. The student’s line of best fit is straight but crosses the extension axis at 0.3 cm. Suggest a cause and how to correct the results.
Show answer
Cause: a zero error – e.g. the original length was measured incorrectly, or the ruler’s zero wasn’t lined up with the bottom of the spring. Every extension is out by 0.3 cm (a systematic error).
Correct it: subtract 0.3 cm from every extension (or re-measure the original length carefully), then re-plot the graph. The gradient – and so the spring constant – is not affected.
Q24 (H) A student uses a stopwatch to time a trolley rolling 50 cm down a ramp. Suggest two ways to reduce the uncertainty in the time, and explain each.
Show answer
Any two from:
• Use light gates connected to a data logger – this removes human reaction time.
• Repeat the timing several times and calculate a mean – this reduces the effect of random errors.
• Use a longer ramp (bigger distance) – the time is longer, so the reaction-time error is smaller compared with the total time.