Error Intervals - Worksheets, Questions and Revision

20 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Number

3.1 Error Intervals

EDEXCEL 1MA1 · Calculator allowed · about 55 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Round each of these numbers to the accuracy shown.
(a)Round 3872 to the nearest 100.(1)
(b)Round 6.482 to 1 decimal place.(1)
(c)Round 0.00567 to 2 significant figures.(1)
(Total for Question 1 is 3 marks)
2
A plank of wood is measured as 8 cm, correct to the nearest centimetre.
(a)Write down the minimum possible length of the plank (the lower bound).(1)
(b)Write down the maximum possible length of the plank (the upper bound).(1)
(Total for Question 2 is 2 marks)
3
A number, n, is rounded to the nearest whole number. The result is 15.
Write down the error interval for n.
(Total for Question 3 is 2 marks)
4
The mass of a bag of sugar is 750 g, correct to the nearest 10 g.
Write down the error interval for the mass, m grams.
(Total for Question 4 is 2 marks)
5
A number x is given as 6.4, correct to 1 decimal place.
Write down the error interval for x.
(Total for Question 5 is 2 marks)
6
The population of a town is 24 000, correct to 2 significant figures.
Write down the error interval for the population, P.
(Total for Question 6 is 2 marks)
7
A steel rod has length L = 12 cm, correct to the nearest centimetre.
Circle the correct error interval for L.
  • A) 11 ≤ L < 12
  • B) 11.5 ≤ L < 12.5
  • C) 11.5 < L ≤ 12.5
  • D) 11 < L ≤ 12
(Total for Question 7 is 1 mark)
8
A value v = 3.80, correct to 3 significant figures.
Write down the error interval for v.
(Total for Question 8 is 2 marks)
9
The error interval for a number w is 15.5 ≤ w < 16.5.
Write down the value that w was rounded to.
(Total for Question 9 is 2 marks)
10
A plank of wood has length 2.4 m, measured to the nearest 10 cm.
Write down the error interval for the length, l metres.
(Total for Question 10 is 2 marks)
11
Two numbers are each given correct to the nearest 10: a = 60 and b = 30.
Work out the upper bound for a + b.
(Total for Question 11 is 2 marks)
12
The number n = 25, correct to the nearest 5.
For each statement below, write True or False.
(i)The error interval for n is 22.5 ≤ n < 27.5.(1)
(ii)n could equal 27.4.(1)
(iii)n could equal 27.5.(1)
(iv)n could equal 22.(1)
(Total for Question 12 is 4 marks)
13
a = 8.2, correct to 1 decimal place. b = 3.7, correct to 1 decimal place.
Work out the lower bound for a - b.
(Total for Question 13 is 2 marks)
14
A rectangular field has length 40 m and width 25 m, each measured correct to the nearest metre.
Work out the upper bound for the perimeter of the field.
Diagram NOT accurately drawn
40 m 25 m
(Total for Question 14 is 3 marks)
15
A rectangle has length 12 cm and width 5 cm, each correct to the nearest centimetre.
Work out the lower bound for the area of the rectangle.
Diagram NOT accurately drawn
12 cm 5 cm
(Total for Question 15 is 3 marks)
16
A car travels 150 miles, correct to the nearest 10 miles, in a time of 3 hours, correct to the nearest 0.5 hours.
Work out the upper bound for the average speed of the car. Give your answer correct to 3 significant figures.
(Total for Question 16 is 3 marks)
17
The mass of a metal cube is 540 g, correct to the nearest 10 g. The volume of the cube is 65 cm3, correct to the nearest 5 cm3.
Density = mass / volume.
Work out the minimum possible density of the metal. Give your answer correct to 3 significant figures.
(Total for Question 17 is 3 marks)
18
x = 7.2, correct to 1 decimal place. y = 3, correct to the nearest whole number.
Work out the error interval for x + y.
(Total for Question 18 is 3 marks)
19
The length of a side of a square is given as 9 cm, correct to the nearest whole number.
Diagram NOT accurately drawn
9 cm 9 cm 9 cm 9 cm
(a)Sam calculates the upper bound for the area of the square by working out 9 x 9.5 = 85.5 cm2. Explain why Sam's method is incorrect.(1)
(b)Work out the correct upper bound for the area of the square.(2)
(Total for Question 19 is 3 marks)
20
A rectangular garden has length 15 m and width 8 m, each measured correct to the nearest metre. A fence is to be built around the perimeter of the garden. Fencing costs 12.50 pounds per metre. James has a budget of 575 pounds.
By considering the upper bound of the perimeter, determine whether James definitely has enough money to pay for the fencing. You must show your working.
Diagram NOT accurately drawn
15 m 8 m
(Total for Question 20 is 4 marks)
Mark scheme · 3.1 Error Intervals

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20