Year 10 Maths • AC9M10M04 • Authored homework
Measurement error and accuracy of results
Analyse how measurement errors affect the accuracy of calculated results, including absolute error, percentage error, rounding, significant figures and error propagation in practical contexts. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Define measurement error in your own words.
What is the difference between accuracy and precision?
A length is measured as 48 cm but the true length is 50 cm. Find the absolute error.
Using the same measurement, calculate the percentage error.
Why can rounding too early affect a final answer?
State the possible error when a measurement is rounded to the nearest centimetre.
Explain why a small error in radius can cause a larger error in circle area.
Give one example of a systematic measurement error.
Give one example of a random measurement error.
Correct this misconception: “More decimal places always means a more accurate measurement.”
Part B
Long-answer questions
A rectangle is measured as 12.4 cm by 8.1 cm. Each measurement is rounded to the nearest 0.1 cm. Explain the possible error in each measurement and how it may affect the calculated area.
A student measures a cylinder radius as 4.0 cm instead of 4.2 cm. Calculate the percentage error in the radius and explain why the volume may be affected more strongly.
Compare two measurements: 2 mm error in 20 mm and 2 mm error in 200 mm. Calculate percentage error and interpret which is more serious.
A tank volume is calculated using rounded dimensions. Explain why the final answer should not be reported with unrealistic precision.
A speed is calculated from distance and time. Discuss how errors in both measurements can affect the final speed.
A builder measures a room as 5.8 m by 4.2 m. Estimate the floor area and discuss how measurement error affects buying flooring.
A student records 3.0 m, 3.00 m and 3 m as equivalent. Explain how the number of significant figures changes the meaning.
Create a practical measurement problem involving area or volume, include possible measurement errors and explain their impact.
Explain why repeated measurements can reduce random error but may not remove systematic error.
Write a full response for a measurement-error problem, including calculation, units, percentage error and interpretation of reliability.
Part C
Research and understanding task
Choose a real object such as a table, room, container or sports field. Measure or estimate two dimensions, state possible measurement errors, calculate a derived result, and explain how reliable the result is.