Bounds - Worksheets, Questions and Revision

19 original exam-style questions - 8 pages of questions with a full mark scheme - free printable PDF.

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7.2 Bounds

EDEXCEL 1MA1 · Calculator allowed · about 65 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
The length of a corridor is 4.8 m, correct to 1 decimal place.
Which of these is the upper bound for the length?
  • A) 4.75
  • B) 4.80
  • C) 4.85
  • D) 4.90
(Total for Question 1 is 1 mark)
2
A pencil has a length of 18 cm, measured to the nearest centimetre.
(a)Write down the lower bound of the length.(1)
(b)Write down the upper bound of the length.(1)
(Total for Question 2 is 2 marks)
3
A parcel has a mass of 230 g, correct to the nearest 10 g.
Write down the error interval for the mass, m grams, using inequality notation.
(Total for Question 3 is 2 marks)
4
A bag of sugar has a mass of 2.3 kg, correct to 1 decimal place.
(a)Write down the lower bound of the mass.(1)
(b)Write down the upper bound of the mass.(1)
(Total for Question 4 is 2 marks)
5
The number of spectators at a rugby match is 34000, correct to 2 significant figures.
(a)Write down the lower bound for the number of spectators.(1)
(b)Write down the upper bound for the number of spectators.(1)
(Total for Question 5 is 2 marks)
6
A number, n, is 60 correct to the nearest 10.
Explain why n cannot equal 66.
(Total for Question 6 is 1 mark)
7
The height of a tree is 35 m, measured to the nearest 5 m.
(a)Write down the lower bound of the height.(1)
(b)Write down the upper bound of the height.(1)
(Total for Question 7 is 2 marks)
8
A number, x, is truncated to 1 decimal place. The result is 6.7.
Write down the error interval for x.
(Total for Question 8 is 2 marks)
9
A rectangular lawn has length 12 m and width 7 m, each measured correct to the nearest metre.
Diagram NOT accurately drawn
12 m 7 m
(a)Calculate the upper bound for the perimeter of the lawn.(3)
(b)Calculate the lower bound for the perimeter of the lawn.(2)
(Total for Question 9 is 5 marks)
10
Three parcels have masses of 4.6 kg, 3.2 kg and 5.1 kg, each measured correct to the nearest 0.1 kg.
Work out the upper bound for the total mass of the three parcels.
(Total for Question 10 is 3 marks)
11
A metal rod has length 45 mm and a shorter rod has length 18 mm, each measured correct to the nearest mm.
(a)Work out the upper bound for the difference between the lengths of the rods.(2)
(b)Work out the lower bound for the difference between the lengths of the rods.(2)
(Total for Question 11 is 4 marks)
12
A rectangular tile has length 8.4 cm and width 5.6 cm, each correct to 1 decimal place.
Diagram NOT accurately drawn
8.4 cm 5.6 cm
(a)Show that the upper bound for the area of the tile, correct to 3 significant figures, is 47.7 cm2.(2)
(b)Calculate the lower bound for the area of the tile. Give your answer correct to 3 significant figures.(2)
(Total for Question 12 is 4 marks)
13
A car travels a distance of 250 miles, measured to the nearest 10 miles, in a time of 4.5 hours, measured to the nearest 0.1 hour.
(a)Calculate the upper bound for the average speed of the car. Give your answer correct to 3 significant figures.(3)
(b)Calculate the lower bound for the average speed of the car. Give your answer correct to 3 significant figures.(3)
(c)Sunita says, 'The speed of the car, correct to the nearest whole number, is 57 mph.' Explain why Sunita might be wrong.(1)
(Total for Question 13 is 7 marks)
14
A rectangular photo has length 15 cm and width 10 cm, each measured correct to the nearest cm. A framer claims the area of the photo could be as large as 160 cm2.
Using bounds, show whether the framer's claim is correct. You must show your working.
Diagram NOT accurately drawn
15 cm 10 cm
(Total for Question 14 is 3 marks)
15
A circular pond has a radius of 3.5 m, measured to the nearest 0.5 m.
Calculate the upper bound for the area of the pond. Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
3.5 m
(Total for Question 15 is 3 marks)
16
The volume of a cuboid is 240 cm3, correct to 2 significant figures. The base of the cuboid is a square with side length 6 cm, correct to the nearest cm.
Calculate the upper bound for the height of the cuboid. Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
6 cm 6 cm h
(Total for Question 16 is 4 marks)
17
A metal ball has a mass of 45 g, measured to the nearest gram, and a volume of 5 cm3, measured to the nearest 0.5 cm3.
Density = mass / volume.
Calculate the lower bound for the density of the metal. Give your answer correct to 3 significant figures.
(Total for Question 17 is 3 marks)
18
The time period, T seconds, of a pendulum of length L metres is given by the formula T = 2 x π x √L / 10, where 10 (m/s2) is an approximation used for gravity in this formula.
The length L = 2.5 m, correct to 1 decimal place.
Calculate the upper bound for T. Give your answer correct to 3 significant figures.
(Total for Question 18 is 3 marks)
19
a = 6.4, correct to 1 decimal place. b = 2.5, correct to 1 decimal place.
Work out the upper bound of (a - b) / b. Give your answer correct to 3 significant figures.
(Total for Question 19 is 4 marks)
Mark scheme · 7.2 Bounds

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