A Level Physics 1.3 Errors and Uncertainties MCQs – 30 Practice Questions with Answers (Cambridge 9702)
Free practice questions for Cambridge International AS & A Level Physics (9702), Section 1.3 Errors and Uncertainties – random and systematic errors, accuracy and precision, and how to combine uncertainties in calculations. Every question is original, with a worked explanation under the Show Answer button.
Random & Systematic Errors
Q1. What is a random error?
- (A) An error that shifts every reading by the same amount
- (B) An error that causes readings to be scattered randomly about the true value
- (C) A mistake made when recording a reading
- (D) An error caused by a zero error on the instrument
Show Answer
Answer: B – Random errors vary unpredictably in size and sign from one reading to the next, so the readings scatter around the true value. A fixed shift (option A) describes a systematic error.
Q2. What is a systematic error?
- (A) An error whose size changes unpredictably between readings
- (B) An error that is removed by repeating readings and averaging
- (C) An error that displaces every reading from the true value in a consistent way
- (D) An error caused only by the resolution of the scale
Show Answer
Answer: C – A systematic error biases all readings in the same direction (for example every reading too large by a similar amount), because its cause – a zero error or a miscalibrated instrument – acts the same way every time.
Q3. A micrometer screw gauge reads +0.02 mm when its jaws are fully closed. It is then used to measure the diameter of a wire. What is the effect of this zero error on the readings?
- (A) Every reading is 0.02 mm greater than the true diameter
- (B) Every reading is 0.02 mm smaller than the true diameter
- (C) The readings are scattered randomly by up to 0.02 mm
- (D) There is no effect, because the error is very small
Show Answer
Answer: A – The gauge already reads +0.02 mm at zero, so 0.02 mm must be subtracted from every reading. This is a systematic error: it makes every result too large by the same amount.
Q4. Which procedure reduces the effect of random errors on a final result?
- (A) Calibrating the instrument against a standard
- (B) Checking the instrument for a zero error
- (C) Using an instrument with a finer scale
- (D) Repeating the measurement several times and calculating the mean
Show Answer
Answer: D – Random errors are sometimes positive and sometimes negative, so averaging many repeats makes them partially cancel and brings the mean closer to the true value.
Q5. Repeating a measurement many times and taking the average does NOT reduce the error caused by which of the following?
- (A) Unpredictable fluctuations in the quantity being measured
- (B) A constant zero error on the instrument
- (C) Variation in judging the exact moment an event occurs
- (D) Scatter in readings taken from a scale
Show Answer
Answer: B – A zero error shifts every reading by the same amount, so the average is shifted by that amount too. Averaging only helps with random errors (options A, C and D).
Q6. A student times 20 oscillations of a pendulum with a stopwatch. Her reaction time delays both the starting and the stopping of the watch, and the delays are different on each attempt. The error this introduces into the period is best described as
- (A) systematic, making the period always too small
- (B) systematic, making the period always too large
- (C) a zero error
- (D) random, because the delay varies from trial to trial
Show Answer
Answer: D – Because the reaction-time delay is not the same on every trial, the measured times scatter above and below the true time. It is a random error, and its effect is reduced by timing many oscillations and by repeating.
Q7. A stopwatch runs slightly fast, so every time interval it records is shorter than the actual interval. This is an example of
- (A) a random error
- (B) a parallax error
- (C) a systematic error
- (D) a reading with poor precision
Show Answer
Answer: C – The watch is miscalibrated, so it biases every measurement in the same direction (too short). A consistent bias from the instrument is a systematic error.
Q8. A set of measurements is affected only by a systematic error. What happens to the accuracy and the precision of the measurements?
- (A) Accuracy is reduced, precision is unchanged
- (B) Accuracy is unchanged, precision is reduced
- (C) Both accuracy and precision are reduced
- (D) Neither accuracy nor precision is affected
Show Answer
Answer: A – A systematic error moves all the readings away from the true value (worse accuracy) but the readings can still agree closely with each other (precision unchanged).
Q9. A thermometer reads 2 °C in melting ice and 102 °C in the steam above boiling water at atmospheric pressure, when the true values are 0 °C and 100 °C. The fault in this thermometer is
- (A) a random error
- (B) a parallax error
- (C) an error that can be removed by averaging repeated readings
- (D) a systematic error
Show Answer
Answer: D – Every reading is too large by about the same amount, so the thermometer is miscalibrated. This consistent bias is a systematic error; repeating and averaging would not remove it.
Q10. A student reads the level of a liquid in a burette, but her eye is in a slightly different position for each reading, sometimes above and sometimes below the level of the meniscus. The errors in her volume readings are mainly
- (A) systematic errors
- (B) random errors
- (C) zero errors
- (D) calibration errors
Show Answer
Answer: B – Parallax from a varying eye position makes the readings too large on some occasions and too small on others – the hallmark of a random error. (Reading from one fixed wrong position every time would instead be systematic.)
Accuracy, Precision & Quoting Uncertainty
Q11. The accuracy of a measurement describes how close it is to
- (A) the other repeated measurements
- (B) the smallest scale division of the instrument
- (C) the true value of the quantity
- (D) the value obtained by a different method
Show Answer
Answer: C – Accuracy is closeness to the true value. Closeness of repeated readings to each other (option A) is precision.
Q12. The precision of a set of repeated measurements describes
- (A) how close the readings are to one another
- (B) how close the mean is to the true value
- (C) whether systematic errors are absent
- (D) how many significant figures are quoted
Show Answer
Answer: A – Precise readings agree closely with each other (small scatter), which usually comes from an instrument with a small scale division. They may still be inaccurate if a systematic error is present.
Q13. A metre rule is graduated in millimetres. The absolute uncertainty in a length taken from a single reading of the rule is usually taken as
- (A) ±0.1 mm
- (B) ±0.5 mm
- (C) ±0.01 mm
- (D) ±1 mm
Show Answer
Answer: D – The absolute uncertainty is normally taken as the smallest scale division of the instrument. For a millimetre rule that is ±1 mm; for a micrometer it is much smaller (see Q14).
Q14. A micrometer screw gauge has a scale division of 0.01 mm. The absolute uncertainty in a diameter measured with it is
- (A) ±0.1 mm
- (B) ±0.01 mm
- (C) ±0.001 mm
- (D) ±1 mm
Show Answer
Answer: B – The uncertainty is one smallest scale division, here ±0.01 mm. (Any zero error must be corrected separately – that is a systematic error, not part of this reading uncertainty.)
Q15. A length is measured as 25.0 cm ± 0.1 cm. The percentage uncertainty in the length is
- (A) 0.04%
- (B) 4%
- (C) 0.4%
- (D) 2.5%
Show Answer
Answer: C – Percentage uncertainty = (0.1 ÷ 25.0) × 100% = 0.4%.
Q16. A mass is measured as 0.500 kg ± 0.002 kg. The fractional uncertainty in the mass is
- (A) 0.004
- (B) 0.4
- (C) 0.002
- (D) 0.25
Show Answer
Answer: A – Fractional uncertainty = absolute uncertainty ÷ measured value = 0.002 ÷ 0.500 = 0.004 (equivalent to a percentage uncertainty of 0.4%).
Q17. A student measures a time interval four times, obtaining 12.3 s, 12.5 s, 12.4 s and 12.6 s. Taking the uncertainty in the mean as half the range of the readings, quoted to one significant figure, the result should be stated as
- (A) 12.45 s ± 0.15 s
- (B) 12.4 s ± 0.3 s
- (C) 12.45 s ± 0.3 s
- (D) 12.5 s ± 0.2 s
Show Answer
Answer: D – Mean = (12.3 + 12.5 + 12.4 + 12.6) ÷ 4 = 12.45 s. Range = 12.6 − 12.3 = 0.3 s, so half the range = 0.15 s, which is 0.2 s to one significant figure. The mean is then quoted to the same decimal place as the uncertainty: 12.5 s ± 0.2 s.
Q18. A calculation gives a resistance of 3.47 Ω with an absolute uncertainty of 0.036 Ω. How should the result be quoted?
- (A) 3.5 Ω ± 0.04 Ω
- (B) 3.47 Ω ± 0.04 Ω
- (C) 3.47 Ω ± 0.036 Ω
- (D) 3.470 Ω ± 0.036 Ω
Show Answer
Answer: B – Quote the uncertainty to one significant figure: 0.036 Ω becomes 0.04 Ω. Then quote the value to the same number of decimal places as the uncertainty (two decimal places): 3.47 Ω ± 0.04 Ω.
Q19. The true value of a quantity is 9.81 units. Which set of repeated readings is precise but NOT accurate?
- (A) 10.21, 10.19, 10.20, 10.22
- (B) 9.79, 9.83, 9.80, 9.82
- (C) 9.5, 10.1, 9.7, 10.0
- (D) 9.81, 9.81, 9.80, 9.81
Show Answer
Answer: A – The readings in A agree very closely with each other (precise) but are all about 0.4 units above the true value (not accurate) – the pattern produced by a systematic error. Set D is both precise and accurate; set B is accurate on average; set C is neither precise nor accurate.
Q20. A resistor is labelled with a measured value of 47 Ω ± 2 Ω. The percentage uncertainty in the resistance is approximately
- (A) 0.04%
- (B) 0.4%
- (C) 4%
- (D) 24%
Show Answer
Answer: C – Percentage uncertainty = (2 ÷ 47) × 100% ≈ 4.3%, which is approximately 4%.
Combining Uncertainties
Q21. Two lengths, 25.0 cm ± 0.1 cm and 15.0 cm ± 0.2 cm, are added together. The total length and its absolute uncertainty are
- (A) 40.0 cm ± 0.1 cm
- (B) 40.0 cm ± 0.3 cm
- (C) 40.0 cm ± 0.2 cm
- (D) 40.0 cm ± 0.15 cm
Show Answer
Answer: B – When quantities are added (or subtracted), the absolute uncertainties are added: 0.1 + 0.2 = 0.3 cm. Total = 25.0 + 15.0 = 40.0 cm ± 0.3 cm.
Q22. A temperature rises from 10.2 °C ± 0.1 °C to 12.4 °C ± 0.1 °C. The temperature rise and its absolute uncertainty are
- (A) 2.2 °C ± 0 °C
- (B) 2.2 °C ± 0.1 °C
- (C) 2.2 °C ± 0.05 °C
- (D) 2.2 °C ± 0.2 °C
Show Answer
Answer: D – Even for a subtraction, absolute uncertainties are still added, never subtracted: rise = 12.4 − 10.2 = 2.2 °C, uncertainty = 0.1 + 0.1 = 0.2 °C.
Q23. A rectangle has length 10.0 cm ± 0.1 cm and width 5.0 cm ± 0.1 cm. The absolute uncertainty in its area is
- (A) 1.5 cm2
- (B) 0.5 cm2
- (C) 3.0 cm2
- (D) 0.15 cm2
Show Answer
Answer: A – Area = 10.0 × 5.0 = 50.0 cm2. Percentage uncertainty in length = 0.1/10.0 = 1%; in width = 0.1/5.0 = 2%. For a product, add percentage uncertainties: 1% + 2% = 3%. Absolute uncertainty = 3% of 50.0 = 1.5 cm2.
Q24. The density of a block is found from a mass of 54.0 g ± 0.5 g and a volume of 20.0 cm3 ± 0.5 cm3. The percentage uncertainty in the density is approximately
- (A) 1.6%
- (B) 2.5%
- (C) 3.4%
- (D) 0.93%
Show Answer
Answer: C – Density = mass ÷ volume, so add the percentage uncertainties: mass: 0.5/54.0 ≈ 0.93%; volume: 0.5/20.0 = 2.5%. Total ≈ 0.93% + 2.5% ≈ 3.4%.
Q25. The radius of a circle is measured with a percentage uncertainty of 2%. The percentage uncertainty in the area of the circle (area = πr2) is
- (A) 2%
- (B) 3%
- (C) 6%
- (D) 4%
Show Answer
Answer: D – Because the radius is raised to the power 2, its percentage uncertainty is multiplied by 2: 2 × 2% = 4%. (π is an exact constant and contributes no uncertainty.)
Q26. The side of a cube is measured with a percentage uncertainty of 1%. The percentage uncertainty in the volume of the cube is
- (A) 1%
- (B) 3%
- (C) 0.33%
- (D) 9%
Show Answer
Answer: B – Volume = side3, so the percentage uncertainty is multiplied by the power 3: 3 × 1% = 3%.
Q27. A resistance is calculated from R = V/I using V = 6.0 V ± 0.1 V and I = 0.30 A ± 0.01 A. The percentage uncertainty in R is
- (A) 5%
- (B) 1.7%
- (C) 3.3%
- (D) 2.5%
Show Answer
Answer: A – For a quotient, add percentage uncertainties: V: 0.1/6.0 ≈ 1.7%; I: 0.01/0.30 ≈ 3.3%. Total ≈ 1.7% + 3.3% = 5.0%, i.e. about 5% (so R = 20 Ω ± 1 Ω).
Q28. In a pendulum experiment, g is calculated from g = 4π2l/T2. The length l has a percentage uncertainty of 1% and the period T has a percentage uncertainty of 1%. The percentage uncertainty in g is
- (A) 1%
- (B) 2%
- (C) 3%
- (D) 4%
Show Answer
Answer: C – g is proportional to l/T2. Add the percentage uncertainty in l (1%) and twice the percentage uncertainty in T, because T is squared: 1% + 2 × 1% = 3%.
Q29. A speed is calculated from a distance of 100.0 m ± 0.5 m travelled in a time of 20.0 s ± 0.4 s. The percentage uncertainty in the speed is
- (A) 0.5%
- (B) 2.5%
- (C) 2.0%
- (D) 1.5%
Show Answer
Answer: B – Speed = distance ÷ time, so add percentage uncertainties: distance: 0.5/100.0 = 0.5%; time: 0.4/20.0 = 2.0%. Total = 0.5% + 2.0% = 2.5%.
Q30. The kinetic energy of an object is calculated from E = ½mv2. The mass m has a percentage uncertainty of 2% and the speed v has a percentage uncertainty of 3%. The percentage uncertainty in E is
- (A) 5%
- (B) 11%
- (C) 6%
- (D) 8%
Show Answer
Answer: D – Add the percentage uncertainty in m (2%) and twice the percentage uncertainty in v, because v is squared: 2% + 2 × 3% = 8%. (The factor ½ is exact and contributes nothing.)
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