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AS · Practice questions · Errors and uncertainties

Carry the doubt through.

Six original Cambridge-style questions on classifying errors, choosing the right combination rule, propagating uncertainty through a power, and quoting a result honestly.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Right rule, right reason.

01
Analysis
[2 marks]

Distinguish between a random error and a systematic error, and state which one is reduced by averaging repeated readings.

  • A random error scatters readings unpredictably about the true value. A systematic error shifts every reading by a fixed amount in the same direction. ✓
  • Averaging repeated readings reduces the random error; it does not affect the systematic error. ✓
02
Analysis
[2 marks]

A micrometer reads 0.04 mm when its jaws are fully closed. The diameter of a ball bearing is then read as 8.36 mm. State the type of error and give the corrected diameter.

  • This is a systematic (zero) error: every reading is 0.04 mm too high. ✓
  • Corrected diameter = 8.36 − 0.04 = 8.32 mm. ✓
03
Analysis
[3 marks]

The resistance of a component is found from a potential difference of (6.0 ± 0.1) V and a current of (0.50 ± 0.02) A, using R = V / I. Find R and its absolute uncertainty.

  • R = 6.0 / 0.50 = 12 Ω. ✓
  • Percentage uncertainties: V gives (0.1/6.0) = 1.7%, I gives (0.02/0.50) = 4.0%. For a quotient they add: 1.7 + 4.0 = 5.7%. ✓
  • Absolute uncertainty = 5.7% of 12 = 0.68, so R = (12.0 ± 0.7) Ω. ✓
04
Analysis
[3 marks]

The period T of a simple pendulum is used to find g from g = 4π²L / T². The length L has a 1% uncertainty and the period T has a 2% uncertainty. Determine the percentage uncertainty in g.

  • g depends on L to the first power and on T to the power 2 (in the denominator). ✓
  • %Δg = %ΔL + 2 × %ΔT = 1% + 2 × 2% = 5%. ✓
  • The 4π² is an exact constant and contributes nothing. ✓
05
Analysis
[2 marks]

Two readings of a temperature are taken from a thermometer as (84.0 ± 0.5) °C and (21.0 ± 0.5) °C. Find the temperature rise and explain why its percentage uncertainty is larger than that of either reading.

  • Rise = 84.0 − 21.0 = 63.0 °C; absolute uncertainties add, so it is (63.0 ± 1.0) °C. ✓
  • The absolute uncertainty has grown to 1.0 while the value (63.0) is smaller than either reading, so the percentage uncertainty (about 1.6%) exceeds that of each original reading. Subtracting close values inflates relative uncertainty. ✓
06
Analysis
[2 marks]

A student suggests that switching from a stopwatch read by hand to a light gate would "make the experiment more accurate". Comment on whether this is the right word, and explain what actually improves.

  • The main gain is the removal of the human reaction-time scatter, which is a random error, so it improves precision (repeatability) of the timing. ✓
  • It improves accuracy only if reaction time was also acting as a consistent bias; in general, calling it simply "more accurate" is loose. The precise statement is that the random timing uncertainty is greatly reduced. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.