OCR GCSE Maths
Topic questions Number Limits of accuracy and bounds
30 questions · 123 marks · about 2 hours
A kitchen has space for a fridge.
The width, w, of the space is 70 cm, correct to the nearest centimetre.
Complete the error interval for the width, w.
A fridge is advertised as having a width of 69.5 cm, correct to 1 decimal place.
Show that this fridge may not fit in the space.
A kitchen has space for a fridge.
The width, w, of the space is 70 cm, correct to the nearest centimetre.
Complete the error interval for the width, w.
A fridge is advertised as having a width of 69.5 cm, correct to 1 decimal place.
Show that this fridge may not fit in the space.
The width, w, of a car parking space is 2.8 metres, correct to 1 decimal place.
Complete the error interval for the width, w.
A water company is laying pipes to cover a distance of 37 metres, correct to the nearest metre. Each pipe has a length of 2.3 metres, correct to 1 decimal place. Assume the pipes are laid end to end with no gaps or overlaps.
Work out the minimum number of pipes the water company needs to be sure of covering that distance. You must show your working.
A garage is 5 metres long, correct to the nearest metre. A car is 4.5 metres long, correct to 1 decimal place.
Show that the car may not fit in the garage.
A number, n, is given as 2.6, truncated to 1 decimal place.
Complete the error interval for n using a number and a symbol.
A lift can travel at a maximum speed of 9.83 m / s, correct to 3 significant figures. The lift travels a distance of 174 m, correct to the nearest metre, between the ground floor and the top floor of a building.
Use the above information to work out the shortest possible time for the lift to travel between the ground floor and the top floor. You must show your working.
Explain why your answer to part (a) may not be possible to achieve.
A number, r, is 6.2 when rounded correct to 2 significant figures. A number, h, is 6.2 when truncated to 1 decimal place.
Write down a possible value of r that will definitely be less than all possible values of h.
Write down a possible value of h that will definitely be greater than all possible values of r
Write down a possible value of r and a possible value of h such that r is greater than h.
(c) r =........ and h =........
Here is a right-angled triangle.
The area of the triangle is 100cm2, correct to the nearest 10cm2. The length of the base of the triangle is 8 cm, correct to the nearest cm.
Calculate the largest possible height of the triangle.
Also involves Volume and surface area
A box contains 200 matches, correct to the nearest ten matches.
Complete the error interval for n, the number of matches in the box.
The box is a cuboid with
• length 7 cm, correct to the nearest cm
• width 5 cm, correct to the nearest cm
• volume 248 cm3, correct to the nearest cm3.
Show that the smallest possible height of the box is 6 cm.
Also involves Converting between units
A plane flies from London to Tokyo. The distance is 9600 km, correct to the nearest 100 km. The plane travels at an average speed of 820 km/h, correct to the nearest 10 km/h.
Calculate the shortest possible flight time of the plane. Give your answer in hours and minutes, correct to the nearest minute. You must show your working.
Four friends are going on holiday together. They each take a suitcase. The weight of each suitcase is 25 kg, correct to nearest kilogram.
Complete the error interval for the weight, w kg, of one suitcase.
The friends must pay extra if the total weight of their four suitcases is more than 102.4 kg.
Can the friends be certain that they will not have to pay extra? Show how you decide.
Also involves The four operations
Jamie buys fence panels that fit tightly together.
Each panel has a length of 1.8 m, correct to 1 decimal place. Jamie measures the length of a garden as 42 m, correct to the nearest metre.
Work out the minimum number of panels Jamie should buy in order to be certain that there are enough panels for the length of the garden. Show how you decide.
Also involves Rounding
A carpenter measures the length, k metres, of a piece of wood.
They write
3.35 ⩽ k < 3.45.
Put rings around all possible values of k in the list below.
3.349 3.39 3.44 3.45 3.55
The carpenter says
3.35 ⩽ k < 3.45 means that the length of the piece of wood is 3.4 metres correct to the nearest centimetre.
Explain how you know that she is incorrect.
Complete the interval for 3.4 m, correct to the nearest centimetre.
The width, w, of a kitchen cupboard is 60 cm, correct to the nearest centimetre.
Complete the error interval for the width, w.
Six of these kitchen cupboards are to be placed side by side along a kitchen wall. The wall is 363 cm long, correct to the nearest centimetre.
Show that the six cupboards may not fit along the wall.
Find the upper bound of the space remaining if six cupboards do fit along the wall.
The height, h, of a lorry is 4.3 metres, correct to 1 decimal place.
Complete the error interval for the height, h.
Also involves Compound measures
The length, d, of Jamal’s car is 4.72 m, correct to 2 decimal places.
Complete the error interval for the length, d.
Jamal travels 430 km, correct to the nearest 10 km. His average speed is 57.3 km / h, correct to 1 decimal place.
Calculate the shortest possible time for Jamal’s journey. Give your answer correct to the nearest minute.
(b)........ hours........ minutes
Andrea is 165 cm tall, correct to the nearest cm. Joel is 170 cm tall, correct to the nearest 10 cm.
Show that Andrea could be taller than Joel.
Also involves Converting between units
Arron ran a distance of 5 km at an average speed of 2.2 m / s.
How long did Arron run for? Give your answer in minutes and seconds, to the nearest second.
(a)........ minutes........ seconds
Claudine cycled a distance of 53 km in 2.7 hours. The distance is measured correct to the nearest km. The time is given correct to 1 decimal place.
Calculate the lower and upper bounds of her average speed.
Give your answers correct to 2 decimal places.
(b) lower bound =........ km / h
upper bound =........ km / h
A number, g, is given as 4.05, correct to 2 decimal places.
Complete the error interval for g.
A number, h, is given as 3, truncated to 1 significant figure.
Complete the error interval for h.
Also involves Area and perimeter
The area of a rectangle is 56 m2, correct to the nearest m2. The length of the rectangle is 9.2 m, correct to the nearest 0.1 m.
Calculate the smallest possible width of the rectangle.
Also involves Inequalities
Use the symbols <, ⩽, =, >, or ⩾ to complete this statement.
If x = 4.7, truncated to 1 decimal place, then 4.7........ x........ 4.8
Also involves Converting between units · Using a calculator
A £1 coin weighs 8.75 g, correct to the nearest 0.01 g. Mitul weighs the contents of a large bag of £1 coins. The coins weigh 2.63 kg, correct to the nearest 10 g.
Mitul says
I am sure that the bag contains exactly £300 because, using bounds, 2625 ÷ 8.755 = 299.8 to 1 decimal place.
Show that Mitul may not be correct.
The length, a, of a pencil is 15.3 cm, correct to 1 decimal place.
Complete the error interval for the length of the pencil.
Standard bricks have dimensions 21.5 cm by 10.3 cm by 6.5 cm, correct to 1 decimal place.
A house is built using 4663 standard bricks.
Joslin says
Placed end to end, the bricks from the house would definitely reach over 1 km.
Show that Joslin’s statement is correct.
A standard brick should weigh 2.8 kg, correct to 1 decimal place. A truck can carry a maximum load of 20 tonnes.
Calculate the maximum number of standard bricks that the truck should be able to carry.
Explain why your answer to (b)(i) may not be possible to achieve.
Fill in each missing number.
24 –........ = 36
The length of a line is 10.4 cm, correct to 1 decimal place.
Write down the shortest possible length of the line.
Also involves The four operations · Converting between units
A log is 18 m long, correct to the nearest metre. It is to be cut into fence posts which must be 80 cm long, correct to the nearest 10 centimetres.
What is the largest number of fence posts that can possibly be cut from this log?
The mass, m tonnes, of a girder is 12.7, correct to 1 decimal place.
Complete the error interval for the mass, m.
The length of a piece of wood is given as 8 metres, correct to the nearest metre. The length of a metal rod is given as 8.5 metres, correct to 1 decimal place.
Show that the piece of wood could be longer than the metal rod.
The length, L, of a steel rod is 8.3 m, correct to 1 decimal place.
Complete the error interval for length L.
Also involves Converting between units
Sunil makes 7.5 litres of soup, correct to the nearest 0.5 litre. He serves the soup in 300 ml portions, correct to the nearest 10 ml. 24 people order this soup.
Does Sunil definitely have enough soup to serve the 24 people? Show how you decide.
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