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 mm with a tolerance of mm.
(a) State the absolute error.
(b) Calculate the relative error, as a percentage.
(a) State the absolute error.
(b) Calculate the relative error, as a percentage.
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Answer
(a) mm
(b)
(b)
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2
A bag of sugar is labelled g with a tolerance of g.
Calculate the relative error, as a percentage.
Calculate the relative error, as a percentage.
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Answer
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3
A parcel is advertised as weighing kg with a tolerance of kg.
State the maximum and the minimum acceptable weight.
State the maximum and the minimum acceptable weight.
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Answer
Maximum kg
Minimum kg
Minimum kg
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4
A rectangular plot is measured as m m by m m.
Calculate the maximum possible area of the plot.
Calculate the maximum possible area of the plot.
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Answer
m
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5
A rectangular plot is measured as m m by m m.
Calculate the minimum possible area of the plot.
Calculate the minimum possible area of the plot.
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Answer
m
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6
A drone flies a distance of km km in a time of minutes minute.
Calculate the maximum possible average speed of the drone, in km/minute.
Give your answer to 3 decimal places.
Calculate the maximum possible average speed of the drone, in km/minute.
Give your answer to 3 decimal places.
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Answer
Maximum speed uses the maximum distance and the minimum time.
km/minute
km/minute
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7
The length, width and height of a tank are measured with relative errors of , and .
The volume is found by multiplying the three measurements.
Estimate the relative error in the volume.
The volume is found by multiplying the three measurements.
Estimate the relative error in the volume.
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Answer
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8
The true mass of a sample is g.
A balance reports the mass as g.
(a) State the absolute error.
(b) Calculate the relative error, as a percentage to 1 decimal place.
A balance reports the mass as g.
(a) State the absolute error.
(b) Calculate the relative error, as a percentage to 1 decimal place.
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Answer
(a) g
(b)
(b)
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9
A square tile has a side measured as cm cm.
Calculate the maximum possible area of the tile.
Calculate the maximum possible area of the tile.
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Answer
cm
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10
A machine part should measure mm.
Machine A produces parts measuring , and mm.
Machine B produces parts measuring , and mm.
State which machine is more precise and which is more accurate. Justify your answer.
Machine A produces parts measuring , and mm.
Machine B produces parts measuring , and mm.
State which machine is more precise and which is more accurate. Justify your answer.
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Answer
The parts from Machine A are more precise: their measurements are tightly grouped, with a range of only mm.
The parts from Machine B are more accurate: their measurements average mm, which is the target, while the measurements from Machine A average mm, which is always too large.
The parts from Machine B are more accurate: their measurements average mm, which is the target, while the measurements from Machine A average mm, which is always too large.
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