Limits of accuracy & bounds

The length of a fence panel is 160 cm to the nearest 10 cm

Complete the error interval.

A different fence panel measures 2 metres to the nearest 10 cm Kim says that the total length of three of these fence panels must be less than 6.2 m

Show that Kim is correct.

The length of a fence panel is 160 cm to the nearest 10 cm

Complete the error interval.

A different fence panel measures 2 metres to the nearest 10 cm Kim says that the total length of three of these fence panels must be less than 6.2 m

Show that Kim is correct.

14 For a small plane, (a)

• the mass of the empty plane is 800 kg, to the nearest 100kg

• the mass of fuel is 190 kg, to the nearest 5 kg

• the mass of the passengers is 163 kg, to the nearest kg

The total mass of a plane is calculated by adding these three masses. The maximum mass for the plane to take off safely is 1200 kg

Can this plane definitely take off safely? Tick a box.

Show working to support your answer.

A different plane travels 1250 miles in 2 hours 30 minutes at a constant speed.

On the grid, draw a speed/time graph to represent this information.

The length of a wall is 9 metres to the nearest metre. Complete the error interval for the length of the wall.

The attendance for a rugby match is 8400 people to the nearest 100

Write down the minimum possible attendance.

Write down the maximum possible attendance.

The attendance for a rugby match is 8400 people to the nearest 100

Write down the minimum possible attendance.

Write down the maximum possible attendance.

Jack is loading a van. The van can safely carry 1375 kg of furniture. Jack has already loaded 1200 kg of furniture to the nearest 50 kg A table has mass 140 kg to the nearest 10 kg

Can the table safely be added to the furniture in the van? You must show your working.

a = 65 to the nearest integer b = 30 to 1 significant figure Work out the upper bound for 2a² – b² You must show your working.

k is a whole number between 40 and 50 The cube root of k is 3, to the nearest whole number. Work out the largest possible value of k.

Fay tries to solve x² = 100 She says, ‘‘The only possible value of x is 10’’ Give a reason why she is not correct.

k is a whole number between 40 and 50 The cube root of k is 3, to the nearest whole number. Work out the largest possible value of k.

Fay tries to solve x² = 100 She says, ‘‘The only possible value of x is 10’’ Give a reason why she is not correct.

Two sides of a triangle are measured to 1 decimal place. The angle between the sides is measured to the nearest degree.

Work out the upper bound for the area of the triangle.

You must show your working.

To be rented, a bedroom must have a floor area of at least 6.51 m² A bedroom has a rectangular floor. The floor measures 2.4 m by 2.9 m, each correct to 2 significant figures. Show that the bedroom can be rented.

The number of people living in a town is 47 000 to the nearest 1000 Which one of these is a possible number of people living in the town? Circle your answer.

46 000 46 500 47 500 48 000

a = 4.72 to 3 significant figures. b = 158 to 3 significant figures. Work out the upper bound of You must show your working.

Edith’s van can safely carry a maximum load of 920 kilograms. She wants to use her van to carry 30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram and 20 sacks of carrots, each of mass 7.5 kilograms to 1 decimal place. Can she definitely use her van safely in one journey? You must show your working.

To the nearest 1000, there are 18 000 people at a festival.

Write down the minimum possible number of people at the festival.

Write down the maximum possible number of people at the festival.

To the nearest 1000, there are 18 000 people at a festival.

Write down the minimum possible number of people at the festival.

Write down the maximum possible number of people at the festival.

p = 68.3 correct to 1 decimal place. b = 8.7 correct to 1 decimal place. Work out the lower bound for m.

To the nearest pound, Jon has £9 To the nearest 50p, Ellie has £6.50

Work out the maximum possible total amount of money.

To the nearest pound, Jon has £9 To the nearest 50p, Ellie has £6.50 Work out the maximum possible total amount of money.

An approximation for the value of π is given by

Use your calculator to show that this approximation is within 0.1 of 3.14

The length of a roll of ribbon is 30 metres, correct to the nearest half-metre. A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll. Work out the maximum possible length of ribbon left on the roll.

The length of each side of a regular pentagon is 8.4 cm to 1 decimal place.

Complete the error interval for the length of one side.

Complete the error interval for the perimeter.

The length of each side of a regular pentagon is 8.4 cm to 1 decimal place.

Complete the error interval for the length of one side.

Complete the error interval for the perimeter.

A tank is a cuboid measuring 50 cm by 35 cm by 20 cm All lengths are to the nearest centimetre. A container has a capacity of exactly 34 litres.

Which has the greater capacity? Tick one box.

Show working to support your answer.

Three whole numbers are each rounded to the nearest 10 The sum of the rounded numbers is 70 Work out the maximum possible sum for the original three numbers.

Three whole numbers are each rounded to the nearest 10 The sum of the rounded numbers is 70 Work out the maximum possible sum for the original three numbers.

The dimensions of a rectangular floor are to the nearest 0.1 metres.

A force of 345 Newtons is applied to the floor. The force is to the nearest 5 Newtons.

Work out the upper bound of the pressure. Give your answer to 4 significant figures. You must show your working.

The length of a pipe is 6 metres to the nearest metre. Complete the error interval for the length of the pipe.

The length of a different pipe is 4 metres to the nearest metre. Olly says, “The total length of the two pipes is 11 metres to the nearest metre.” Give an example to show that he could be correct.

The length of a pipe is 6 metres to the nearest metre. Complete the error interval for the length of the pipe.

The length of a different pipe is 4 metres to the nearest metre. Olly says, “The total length of the two pipes is 11 metres to the nearest metre.” Give an example to show that he could be correct.

This sign shows when a lift is safe to use. Total mass of people must be 450 kg or less

Ben and some other people are in the lift. Their total mass is 525 kg to the nearest 5 kg Ben gets out. He has a mass of 78 kg to the nearest kg Is the lift now safe to use? You must show your working.