Errors and uncertainties
1.3What the syllabus asks of you
- understand and explain the effects of systematic errors (including zero errors) and random errors in measurements
- understand the distinction between precision and accuracy
- assess the uncertainty in a derived quantity by simple addition of absolute or percentage uncertainties
Read the notes first
Chapter 1: Errors and uncertainties
Drill this topic
Every question on Errors and uncertainties, untimed, marked as you go.
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Choose the years and how many questions, then print it with the answers on separate pages.
96 questions
1May / June 2026 · Paper 11 · Q2Show mark scheme →
A± 1.0%
B± 1.5%
C± 3.0%
D± 6.0%
Mark scheme
2May / June 2026 · Paper 12 · Q4Show mark scheme →
Amore precise reading: X; more accurate reading: X
Bmore precise reading: X; more accurate reading: Y
Cmore precise reading: Y; more accurate reading: X
Dmore precise reading: Y; more accurate reading: Y
Mark scheme
3May / June 2026 · Paper 13 · Q2Show mark scheme →
Ashows if the results are accurate; reduces the effects of random errors
Bshows if the results are accurate; reduces the effects of systematic errors
Cshows if the results are precise; reduces the effects of random errors
Dshows if the results are precise; reduces the effects of systematic errors
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4May / June 2026 · Paper 13 · Q3Show mark scheme →
A1
B3
C4
D5
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5May / June 2026 · Paper 14 · Q2Show mark scheme →
A0.004%
B0.04%
C0.4%
D4%
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6Oct / Nov 2025 · Paper 11 · Q2Show mark scheme →
A45.8 ± 0.2 cm s⁻²
B45.8 ± 0.3 cm s⁻²
C46 ± 2 cm s⁻²
D46 ± 4 cm s⁻²
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7Oct / Nov 2025 · Paper 12 · Q2Show mark scheme →
Adata measured using equipment with small scale divisions
Bdata that is close to the accepted value
Cdata with each value having a low uncertainty
Ddata with repeats that are close to each other
Mark scheme
8Oct / Nov 2025 · Paper 12 · Q4Show mark scheme →
A2%
B4%
C8%
D16%
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9Oct / Nov 2025 · Paper 13 · Q2Show mark scheme →
A45.8 ± 0.2 cm s⁻²
B45.8 ± 0.3 cm s⁻²
C46 ± 2 cm s⁻²
D46 ± 4 cm s⁻²
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10Oct / Nov 2025 · Paper 14 · Q2Show mark scheme →
Ano / no
Bno / yes
Cyes / no
Dyes / yes
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11Oct / Nov 2025 · Paper 14 · Q3Show mark scheme →
A0.5%
B0.7%
C1.1%
D1.3%
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12May / June 2025 · Paper 11 · Q2Show mark scheme →
A7.2, 9.4, 8.3
B9.5, 9.8, 10.2
C9.8, 9.8, 9.9
D10.1, 10.2, 10.1
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13May / June 2025 · Paper 11 · Q3Show mark scheme →
A0.29 cm³
B0.87 cm³
C1.1 cm³
D7.0 cm³
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14May / June 2025 · Paper 12 · Q3Show mark scheme →
A7.8 g cm⁻³ ± 3.0%
B7.8 g cm⁻³ ± 7.0%
C7.8 g cm⁻³ ± 11%
D7.8 g cm⁻³ ± 13%
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15May / June 2025 · Paper 13 · Q3Show mark scheme →
AAn accurate set of measurements always has a small random error.
BA precise set of measurements always has a small systematic error.
CA random error can be reduced by taking an average of several measurements.
DA systematic error creates a random set of measurements spread out about the true value.
Mark scheme
16May / June 2025 · Paper 14 · Q3Show mark scheme →
A(1.0 ± 0.1) mm
B(1.0 ± 0.2) mm
C(2.0 ± 0.1) mm
D(2.0 ± 0.2) mm
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17Feb / March 2025 · Paper 12 · Q2Show mark scheme →
AIt limits the precision of the measured value.
BIt limits the range of values obtained in repeated measurements.
CIt results in repeated measurements having different values from each other.
DIt results in the measured value being different from the correct value.
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18Feb / March 2025 · Paper 12 · Q12Show mark scheme →
A2%
B5%
C15%
D18%
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19Oct / Nov 2024 · Paper 11 · Q3Show mark scheme →
A± 0.01 g cm⁻³
B± 0.02 g cm⁻³
C± 0.05 g cm⁻³
D± 0.13 g cm⁻³
Mark scheme
20Oct / Nov 2024 · Paper 12 · Q3Show mark scheme →
A± 0.21%
B± 0.22%
C± 0.90%
D± 1.4%
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21May / June 2024 · Paper 11 · Q6Show mark scheme →
A0.5%
B0.8%
C1.3%
D1.7%
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22May / June 2024 · Paper 12 · Q2Show mark scheme →
AW = XY
BW = 2XY
CW = \frac{X}{Y^2}
DW = \frac{Y}{X^2}
Mark scheme
23May / June 2024 · Paper 13 · Q2Show mark scheme →
AA systematic error cannot be reduced by adjusting the apparatus.
BA systematic error results in a different reading each time the measurement is taken.
CRandom errors are always caused by the person taking the measurement.
DRandom errors can be reduced by taking the average of several measurements.
Mark scheme
24May / June 2024 · Paper 13 · Q3Show mark scheme →
Alength of wire before force applied, L, 2.043 ± 0.002 m
Bdiameter of wire, d, 0.54 ± 0.02 mm
Cforce applied, F, 19.62 ± 0.01 N
Dextension of wire with force applied, x, 5.2 ± 0.2 mm
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25Oct / Nov 2023 · Paper 11 · Q3Show mark scheme →
AThe random error can be reduced by adding the diameter of the ball to the distance PQ.
BThe random error can be reduced by subtracting the diameter of the ball from the distance PQ.
CThe systematic error can be reduced by adding the diameter of the ball to the distance PQ.
DThe systematic error can be reduced by subtracting the diameter of the ball from the distance PQ.
Mark scheme
26Oct / Nov 2023 · Paper 12 · Q3Show mark scheme →
A(0.11 ± 0.01) m s⁻²
B(0.11 ± 0.02) m s⁻²
C(0.15 ± 0.01) m s⁻²
D(0.15 ± 0.02) m s⁻²
Mark scheme
27Oct / Nov 2023 · Paper 13 · Q3Show mark scheme →
ARandom error and systematic error are both reduced.
BRandom error and systematic error are both unaffected.
CRandom error is reduced but systematic error is unaffected.
DRandom error is unaffected but systematic error is reduced.
Mark scheme
28May / June 2023 · Paper 11 · Q3Show mark scheme →
Aaccurate and precise
Baccurate but not precise
Cnot precise and not accurate
Dprecise but not accurate
Mark scheme
29May / June 2023 · Paper 12 · Q3Show mark scheme →
A2.4%
B4.6%
C6.1%
D6.7%
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30May / June 2023 · Paper 13 · Q3Show mark scheme →
AIt is less accurate and less precise than the measurement of student Y.
BIt is less accurate but more precise than the measurement of student Y.
CIt is more accurate and more precise than the measurement of student Y.
DIt is more accurate but less precise than the measurement of student Y.
Mark scheme
31Feb / March 2023 · Paper 12 · Q3Show mark scheme →
A(280 ± 10) cm^2
B(282.7 ± 0.2) cm^2
C(420 ± 30) cm^2
D(424.1 ± 0.3) cm^2
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32Oct / Nov 2022 · Paper 11 · Q3Show mark scheme →
A1%
B5%
C8%
D11%
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33Oct / Nov 2022 · Paper 12 · Q3Show mark scheme →
A1.6%
B1.8%
C8.0%
D16%
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34Oct / Nov 2022 · Paper 13 · Q3Show mark scheme →
A(3.06 ± 0.02) A
B(3.06 ± 0.04) A
C(3.06 ± 0.05) A
D(3.06 ± 0.07) A
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35May / June 2022 · Paper 11 · Q3Show mark scheme →
AThe value is accurate but not precise.
BThe value is both precise and accurate.
CThe value is neither precise nor accurate.
DThe value is precise but not accurate.
Mark scheme
36May / June 2022 · Paper 12 · Q3Show mark scheme →
AA systematic error can be caused by using an incorrectly calibrated instrument.
BOne particular type of systematic error can affect all the measurements by the same amount.
CThe effect of a systematic error can be reduced by repeating and averaging the measurements.
DZero error is a type of systematic error.
Mark scheme
37May / June 2022 · Paper 13 · Q4Show mark scheme →
A0.2%
B0.4%
C0.6%
D1.2%
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38Feb / March 2022 · Paper 12 · Q3Show mark scheme →
Anot precise to ± 0.1 kg and accurate to ± 0.1 kg
Bnot precise to ± 0.1 kg and not accurate to ± 0.1 kg
Cprecise to ± 0.1 kg and accurate to ± 0.1 kg
Dprecise to ± 0.1 kg and not accurate to ± 0.1 kg
Mark scheme
39Oct / Nov 2021 · Paper 11 · Q5Show mark scheme →
Arandom error: 1 and 2; systematic error: 3 and 4
Brandom error: 1 and 3; systematic error: 2 and 4
Crandom error: 2 and 4; systematic error: 1 and 3
Drandom error: 3 and 4; systematic error: 1 and 2
Mark scheme
40Oct / Nov 2021 · Paper 12 · Q5Show mark scheme →
A0.02%
B4%
C8%
D16%
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41Oct / Nov 2021 · Paper 13 · Q5Show mark scheme →
Arandom, 302
Brandom, 308
Csystematic, 302
Dsystematic, 308
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42May / June 2021 · Paper 11 · Q5Show mark scheme →
A(0.98 ± 0.02) mm
B(1.08 ± 0.02) mm
C(0.98 ± 0.04) mm
D(1.08 ± 0.04) mm
Mark scheme
43May / June 2021 · Paper 12 · Q5Show mark scheme →
A1 precise, 1 accurate
B1 precise, 2 accurate
C2 precise, 1 accurate
D2 precise, 2 accurate
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44May / June 2021 · Paper 13 · Q4Show mark scheme →
A10.34 mm
B11.84 mm
C12.34 mm
D12.84 mm
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45May / June 2021 · Paper 13 · Q5Show mark scheme →
A38.5, ±0.5
B38, ±1
C154, ±2
D154, ±4
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46Feb / March 2021 · Paper 12 · Q4Show mark scheme →
A1.95 mm
B2.45 mm
C2.59 mm
D2.73 mm
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47Feb / March 2021 · Paper 12 · Q5Show mark scheme →
A0.0002%
B0.0004%
C0.02%
D0.04%
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48Oct / Nov 2020 · Paper 11 · Q5Show mark scheme →
A(36.35 ± 0.01) cm³
B(36.35 ± 0.03) cm³
C(36.35 ± 0.09) cm³
D(36.4 ± 0.3) cm³
Mark scheme
49Oct / Nov 2020 · Paper 12 · Q4Show mark scheme →
Ametre rule
Bmicrometer
Ctape measure
Dvernier calipers
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50Oct / Nov 2020 · Paper 12 · Q5Show mark scheme →
A2.4%
B4.6%
C5.1%
D9.3%
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51Oct / Nov 2020 · Paper 13 · Q4Show mark scheme →
A0.30 mA
B0.34 mA
C0.40 mA
D0.44 mA
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52Oct / Nov 2020 · Paper 13 · Q5Show mark scheme →
A2.4%
B2.9%
C5.5%
D7.2%
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53May / June 2020 · Paper 11 · Q5Show mark scheme →
AThe measurement will be subject to a random error. The measurement can be made more accurate by taking the average of several repeated measurements.
BThe measurement will be subject to a random error. The measurement can be made more precise by taking the average of several repeated measurements.
CThe measurement will be subject to a systematic error. The measurement can be made more accurate by taking the average of several repeated measurements.
DThe measurement will be subject to a systematic error. The measurement can be made more precise by taking the average of several repeated measurements.
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54May / June 2020 · Paper 12 · Q4Show mark scheme →
Aboth systematic and random
Bneither systematic nor random
Crandom only
Dsystematic only
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55May / June 2020 · Paper 13 · Q5Show mark scheme →
AThe liquid is not all at the same temperature.
BThe readings are not precise.
CThere is a random error affecting the readings.
DThere is a systematic error affecting the readings.
Mark scheme
56Feb / March 2020 · Paper 12 · Q5Show mark scheme →
A0.01 mm
B0.02 mm
C0.03 mm
D0.05 mm
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57Oct / Nov 2019 · Paper 11 · Q4Show mark scheme →
Awire: calipers; pipe: calipers
Bwire: calipers; pipe: micrometer
Cwire: micrometer; pipe: calipers
Dwire: micrometer; pipe: micrometer
Mark scheme
58Oct / Nov 2019 · Paper 11 · Q5Show mark scheme →
A3%
B7%
C8%
D12%
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59Oct / Nov 2019 · Paper 12 · Q4Show mark scheme →
A0.02850 ± 0.01 m
B0.0285 ± 0.001 m
C(2.850 ± 0.001) × 10⁻² m
D(2.850 ± 0.001) × 10⁻³ m
Mark scheme
60Oct / Nov 2019 · Paper 12 · Q5Show mark scheme →
A0.3%
B1.8%
C3.8%
D30%
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61Oct / Nov 2019 · Paper 13 · Q4Show mark scheme →
Aaveraging a large number of measurements
Bcareful calibration of measuring instruments
Creducing the sample size
Drepeating measurements
Mark scheme
62Oct / Nov 2019 · Paper 13 · Q5Show mark scheme →
A4%
B7%
C8%
D11%
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63May / June 2019 · Paper 11 · Q5Show mark scheme →
AThe speed shown is too high by 1%.
BThe speed shown is too high by 2%.
CThe speed shown is too low by 1%.
DThe speed shown is too low by 2%.
Mark scheme
64May / June 2019 · Paper 12 · Q5Show mark scheme →
A1.7%
B1.9%
C2.8%
D3.7%
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65May / June 2019 · Paper 12 · Q6Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
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66May / June 2019 · Paper 12 · Q7Show mark scheme →
Anot precise to ± 0.1 kg and accurate to ± 0.1 kg
Bnot precise to ± 0.1 kg and not accurate to ± 0.1 kg
Cprecise to ± 0.1 kg and accurate to ± 0.1 kg
Dprecise to ± 0.1 kg and not accurate to ± 0.1 kg
Mark scheme
67May / June 2019 · Paper 13 · Q6Show mark scheme →
A0.2%
B0.4%
C0.6%
D1.2%
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68Feb / March 2019 · Paper 12 · Q5Show mark scheme →
A1 s
B1.7 s
C1.83 s
D1.604 s
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69Oct / Nov 2018 · Paper 11 · Q4Show mark scheme →
A1.90 mm
B2.45 mm
C2.59 mm
D2.73 mm
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70Oct / Nov 2018 · Paper 11 · Q5Show mark scheme →
A(3.06 ± 0.02) A
B(3.06 ± 0.04) A
C(3.06 ± 0.05) A
D(3.06 ± 0.07) A
Mark scheme
71Oct / Nov 2018 · Paper 12 · Q5Show mark scheme →
A1 precise, 1 accurate
B1 precise, 2 accurate
C2 precise, 1 accurate
D2 precise, 2 accurate
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72Oct / Nov 2018 · Paper 13 · Q5Show mark scheme →
A(0.7 ± 0.1) m²
B(0.704 ± 0.006) m²
C(0.704 ± 0.011) m²
D(70.4 ± 0.6) m²
Mark scheme
73May / June 2018 · Paper 11 · Q5Show mark scheme →
A0.01%
B0.3%
C1%
D3%
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74May / June 2018 · Paper 12 · Q3Show mark scheme →
A0.25%
B3%
C4%
D5%
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75May / June 2018 · Paper 12 · Q4Show mark scheme →
A1.5 J
B3 J
C6 J
D8 J
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76May / June 2018 · Paper 13 · Q4Show mark scheme →
Aadjusting the needle on a voltmeter so that it reads zero when there is no potential difference across it
Bmeasuring the diameter of a wire at different points and taking the average
Creducing the parallax effects by using a marker and a mirror when measuring the amplitude of oscillation of a pendulum
Dtiming 20 oscillations, rather than a single oscillation, when finding the period of a pendulum
Mark scheme
77May / June 2018 · Paper 13 · Q5Show mark scheme →
A(1.61 ± 0.04) × 10^{10} N m^{-2}
B(1.61 ± 0.05) × 10^{10} N m^{-2}
C(1.61 ± 0.07) × 10^{10} N m^{-2}
D(1.61 ± 0.09) × 10^{10} N m^{-2}
Mark scheme
78Feb / March 2018 · Paper 12 · Q5Show mark scheme →
Acurrent / A
Bdiameter of wire / mm
Clength of wire / m
Dresistivity of metal in wire / Ω m
Mark scheme
79Oct / Nov 2017 · Paper 11 · Q5Show mark scheme →
A0.1%
B1%
C6%
D10%
Mark scheme
80Oct / Nov 2017 · Paper 12 · Q4Show mark scheme →
A0.5%
B0.75%
C12%
D16%
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81Oct / Nov 2017 · Paper 13 · Q4Show mark scheme →
AThe micrometer gives a more accurate measurement.
BThe micrometer gives a more precise measurement.
CThe vernier calipers give a more accurate measurement.
DThe vernier calipers give a more precise measurement.
Mark scheme
82Oct / Nov 2017 · Paper 13 · Q5Show mark scheme →
Arandom error: 1 and 2; systematic error: 3 and 4
Brandom error: 1 and 3; systematic error: 2 and 4
Crandom error: 2 and 4; systematic error: 1 and 3
Drandom error: 3 and 4; systematic error: 1 and 2
Mark scheme
83May / June 2017 · Paper 11 · Q9Show mark scheme →
A0.26 ± 0.01 g cm⁻³
B0.26 ± 0.02 g cm⁻³
C2.6 ± 0.1 g cm⁻³
D2.6 ± 0.2 g cm⁻³
Mark scheme
84May / June 2017 · Paper 12 · Q4Show mark scheme →
A10.0 ± 0.2 Ω m
B10.0 ± 0.3 Ω m
C10.0 ± 0.5 Ω m
D10.0 ± 0.8 Ω m
Mark scheme
85May / June 2017 · Paper 12 · Q5Show mark scheme →
A3.81 mm²
B11.4 mm²
C22.8 mm²
D45.6 mm²
Mark scheme
86May / June 2017 · Paper 13 · Q4Show mark scheme →
A2.33 V is less accurate and less precise than 2.344 V.
B2.33 V is less accurate and more precise than 2.344 V.
C2.33 V is more accurate and less precise than 2.344 V.
D2.33 V is more accurate and more precise than 2.344 V.
Mark scheme
87Feb / March 2017 · Paper 12 · Q5Show mark scheme →
Ametre rule
Bmicrometer
Ctape measure
Dvernier calipers
Mark scheme
88Oct / Nov 2016 · Paper 11 · Q4Show mark scheme →
AGraph A: true value/V against meter reading/V, straight line from origin with gradient less than 1
BGraph B: true value/V against meter reading/V, straight line from origin with gradient greater than 1
CGraph C: true value/V against meter reading/V, curve with decreasing gradient
DGraph D: true value/V against meter reading/V, curve with decreasing gradient
Mark scheme
89Oct / Nov 2016 · Paper 12 · Q5Show mark scheme →
AThe value is accurate but not precise.
BThe value is both precise and accurate.
CThe value is neither precise nor accurate.
DThe value is precise but not accurate.
Mark scheme
90Oct / Nov 2016 · Paper 12 · Q6Show mark scheme →
A(1.0166 ± 0.0162) × 10^5 Pa
B(1.017 ± 0.016) × 10^5 Pa
C(1.017 ± 1.6%) × 10^5 Pa
D(1.02 ± 0.02) × 10^5 Pa
Mark scheme
91Oct / Nov 2016 · Paper 13 · Q4Show mark scheme →
AGraph A: true value/V against meter reading/V, straight line from origin with gradient less than 1
BGraph B: true value/V against meter reading/V, straight line from origin with gradient greater than 1
CGraph C: true value/V against meter reading/V, curve with decreasing gradient
DGraph D: true value/V against meter reading/V, curve with decreasing gradient
Mark scheme
92May / June 2016 · Paper 11 · Q4Show mark scheme →
Aadjusting a voltmeter needle pointer to the zero position before using it to measure a potential difference
Bmeasuring the diameter of a wire at several points and orientations
Cmeasuring the mass of 100 paperclips to determine the mass of one paperclip
Dtiming 20 oscillations of a mass on a spring to determine the period of one oscillation
Mark scheme
93May / June 2016 · Paper 11 · Q5Show mark scheme →
A0.2 A
B0.4 A
C0.6 A
D0.8 A
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94May / June 2016 · Paper 12 · Q5Show mark scheme →
A1.1%
B1.8%
C2.5%
D3.0%
Mark scheme
95May / June 2016 · Paper 13 · Q4Show mark scheme →
AL
BM
Ct
Dw
Mark scheme
96Feb / March 2016 · Paper 12 · Q4Show mark scheme →
Ax + y
Bx – y
Cx + 2y
Dx – 2y
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