KCSE 2025 Maths P2 Q2 — Maximum Possible Error When Subtracting Measurements

KCSE 2025 Form 4 Approximations & Errors

Published

The Question

“The temperature in a room was measured as 20 degrees Celsius in the morning and 25 degrees Celsius in the afternoon. The difference in the temperature of the room was calculated. Determine the maximum possible error in the calculation.”

1

Find the absolute error in each reading

Each temperature is measured to the nearest whole degree, so the true value could be up to half a degree above or below the reading. That gives every measurement an absolute error of plus or minus 0.5 degrees, which is the limit of accuracy of the instrument.

Morning=20±0.5∘C\text{Morning} = 20 \pm 0.5^\circ C
Afternoon=25±0.5∘C\text{Afternoon} = 25 \pm 0.5^\circ C
2

Calculate the difference of the readings

The calculation asked for is the difference between the afternoon and morning temperatures. Subtract the two nominal readings to get the actual difference before worrying about the error.

25−20=5∘C25 - 20 = 5^\circ C
3

Add the errors on subtraction

When two measured quantities are subtracted, the errors do NOT cancel. The biggest possible difference happens when one reading sits at its highest and the other at its lowest, so the two individual errors add together. This sum is the maximum possible error.

0.5+0.5=1∘C0.5 + 0.5 = 1^\circ C
Difference=5±1∘C\text{Difference} = 5 \pm 1^\circ C

Final Result

The maximum possible error in the calculated difference is 1 degree Celsius (the difference is 5 plus or minus 1 degree Celsius).

Why this method works

A reading given to the nearest whole degree stands for any true value within half a unit of it, so each measurement has an uncertainty of 0.5 degrees. When you subtract, the largest error occurs at the extreme case where one true value is as high as possible while the other is as low as possible. Those two half-degree uncertainties then reinforce rather than cancel, which is why the maximum possible error in a difference is the sum of the individual absolute errors.

✓

Largest possible difference: 25.5 - 19.5 = 6. Smallest possible difference: 24.5 - 20.5 = 4. Both are exactly 1 degree away from the calculated 5, confirming a maximum error of 1 degree Celsius.