Mathematical Modelling · Guided Practice

Errors and Tolerance

10 questions with answers. Try each one before revealing the answer.

1
A component is manufactured to a length of 250\displaystyle 250 mm with a tolerance of ±5\displaystyle \pm 5 mm.
(a) State the absolute error.
(b) Calculate the relative error, as a percentage.
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2
A bag of sugar is labelled 1000\displaystyle 1000 g with a tolerance of ±15\displaystyle \pm 15 g.
Calculate the relative error, as a percentage.
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3
A parcel is advertised as weighing 4.5\displaystyle 4.5 kg with a tolerance of ±0.2\displaystyle \pm 0.2 kg.
State the maximum and the minimum acceptable weight.
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4
A rectangular plot is measured as 18\displaystyle 18 m ±0.3\displaystyle \pm 0.3 m by 12\displaystyle 12 m ±0.2\displaystyle \pm 0.2 m.
Calculate the maximum possible area of the plot.
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5
A rectangular plot is measured as 18\displaystyle 18 m ±0.3\displaystyle \pm 0.3 m by 12\displaystyle 12 m ±0.2\displaystyle \pm 0.2 m.
Calculate the minimum possible area of the plot.
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6
A drone flies a distance of 9\displaystyle 9 km ±0.4\displaystyle \pm 0.4 km in a time of 30\displaystyle 30 minutes ±1\displaystyle \pm 1 minute.
Calculate the maximum possible average speed of the drone, in km/minute.
Give your answer to 3 decimal places.
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7
The length, width and height of a tank are measured with relative errors of 2%\displaystyle 2\%, 3%\displaystyle 3\% and 1.5%\displaystyle 1.5\%.
The volume is found by multiplying the three measurements.
Estimate the relative error in the volume.
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8
The true mass of a sample is 47.6\displaystyle 47.6 g.
A balance reports the mass as 47.9\displaystyle 47.9 g.
(a) State the absolute error.
(b) Calculate the relative error, as a percentage to 1 decimal place.
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9
A square tile has a side measured as 30\displaystyle 30 cm ±0.5\displaystyle \pm 0.5 cm.
Calculate the maximum possible area of the tile.
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10
A machine part should measure 60.00\displaystyle 60.00 mm.
Machine A produces parts measuring 60.4\displaystyle 60.4, 60.5\displaystyle 60.5 and 60.4\displaystyle 60.4 mm.
Machine B produces parts measuring 59.7\displaystyle 59.7, 60.3\displaystyle 60.3 and 60.0\displaystyle 60.0 mm.
State which machine is more precise and which is more accurate. Justify your answer.
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