CAIE IGCSE Mathematics Extended E1.10 Limits of Accuracy Questions

Practise finding bounds from rounded measurements and using them in lengths, speeds, areas, density and formula calculations.

Exam points

choose the correct upper or lower bound for each rounded measurement in the calculation
calculate maximum or minimum values by selecting bounds in formulae
apply bounds to perimeter, area, volume or remaining-length calculations from context

Covered syllabus points

E1.10.1 Give upper and lower bounds for data rounded to a specified accuracy.E1.10.2 Find upper and lower bounds of the results of calculations which have

[Maximum number: 2]

Solve the equation.

\frac{1-x}{3}=5

-14
M1 for $1-x=3\times5$ or better, or $\frac{x}{3}=5-\frac{1}{3}$ or better.

[Maximum number: 3]

A bus travels 440 km , correct to the nearest 10 km . The time taken to complete the journey is 6 hours, correct to the nearest half hour.

Calculate the lower bound of the speed of the bus.
km/h [3]

69.6
M2 for $\frac{430\text{ to }440}{6+0.25}$ or $\frac{440-5}{6\text{ to }6.5}$ oe
or M1 for 440+5 oe or 440-5 oe or 6+0.25 oe or 6-0.25 oe seen

[Maximum number: 5]

(a)

At a football match, there are 29800 people, correct to the nearest 100 .

[ 5 ]

(i)

At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people.
Calculate the lower bound for the number of minutes it takes for all the people to leave.
min

[ 3 ]

70 or 70.165... or 70.17 or 70.2
M2 for $\frac{29750\text{ to }29800}{400+25}$ , $\frac{29750\text{ to }29800}{400+24}$ , or $\frac{29800-50}{400\text{ to }425}$
or B1 for 29750, 29850, 29849, 375, 425 or 424 seen

(ii)

At a cricket match there are 27500 people, correct to the nearest 100 .

Calculate the upper bound for the difference between the number of people at the football match and at the cricket match.

[ 2 ]

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Covered syllabus points

Question 1

Question 2

Question 3

Question (a)

Question (i)

Question (ii)