Limits of accuracy and bounds

There are some sheets of paper in a pile. The height of the pile is 10.4 cm, correct to the nearest mm. The thickness of each sheet of paper is 0.17 mm, correct to 2 significant figures. Calculate the upper bound for the number of sheets of paper in the pile. You must show all your working.

w = 435 correct to the nearest 5 a = 9.8 correct to 2 significant figures. c = 2.5 correct to 2 significant figures. By considering bounds, calculate the value of T to a suitable degree of accuracy. You must show all your working and give a reason for your final answer.

P = 5.8810⁸correct to 3 significant figures. Q = 3.610⁵correct to 2 significant figures. Work out the lower bound for R. Give your answer as an ordinary number correct to the nearest integer. You must show all your working.

Ebony makes some bracelets to sell. The materials to make all the bracelets cost £190, correct to the nearest £5 Ebony sells all the bracelets for a total of £875, correct to the nearest £5 The total time taken to make and sell all these bracelets was 72 hours, correct to the nearest hour. Ebony uses this method to calculate her hourly rate of pay total selling price total cost of materials Hourly rate of pay total time taken

The minimum hourly rate of pay for someone of Ebony’s age is £8.20 By considering bounds, determine if Ebony’s hourly rate of pay was definitely more than £8.20 You must show all your working.

ABC is a right-angled triangle.

AB = 9.3 cm correct to the nearest mm. AC = 12.6 cm correct to the nearest mm. Calculate the lower bound for the size of the angle marked x. You must show all your working.

A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km. Sam runs the race in a time of 31 minutes 48 seconds, correct to the nearest second. Sam’s average speed in this race is Vkm/hour. By considering bounds, calculate the value of V to a suitable degree of accuracy. You must show all your working and give a reason for your answer.

e = 6.8 correct to 1 decimal place. f = 0.05 correct to 1 significant figure. Work out the upper bound for the value of p. Give your answer correct to 3 significant figures. You must show all your working.

21The time period, T seconds, of a simple pendulum of length lcm is given by the formula

Katie uses a simple pendulum in an experiment to find an estimate for the value of g. Here are her results. l = 52.0 correct to 3 significant figures. T = 1.45 correct to 3 significant figures. Work out the upper bound and the lower bound for the value of g. Use π = 3.142 You must show all your working.

The diagram shows a cube.

AH = 11.3 cm correct to the nearest mm. Calculate the lower bound for the length of an edge of the cube. You must show all your working.

c = 10.9 correct to 3 significant figures.

By considering bounds, work out the value of d to a suitable degree of accuracy. Give a reason for your answer.

u 26.2 correct to 3 significant figures a 4.3 correct to 2 significant figures

Calculate the upper bound for the value of D. Give your answer correct to 6 significant figures. You must show all your working.

The lower bound for the value of D is 78.6003 correct to 6 significant figures.

By considering bounds, write down the value of D to a suitable degree of accuracy. You must give a reason for your answer.

A high speed train travels a distance of 487 km in 3 hours.

The distance is measured correct to the nearest kilometre. The time is measured correct to the nearest minute.

By considering bounds, work out the average speed, in km/minute, of the train to a suitable degree of accuracy. You must show all your working and give a reason for your answer.

Jackson is trying to find the density, in g/cm³, of a block of wood. The block of wood is in the shape of a cuboid.

He measures the length as 13.2 cm, correct to the nearest mm the width as 16.0 cm, correct to the nearest mm the height as 21.7 cm, correct to the nearest mm

He measures the mass as 1970 g, correct to the nearest 5 g.

By considering bounds, work out the density of the wood. Give your answer to a suitable degree of accuracy.

You must show all your working and give a reason for your final answer.

A factory makes 450 pies every day. The pies are chicken pies or steak pies.

Each day Milo takes a sample of 15 pies to check.

The proportion of the pies in his sample that are chicken is the same as the proportion of the pies made that day that are chicken.

On Monday Milo calculated that he needed exactly 4 chicken pies in his sample.

Work out the total number of chicken pies that were made on Monday.

On Tuesday, the number of steak pies Milo needs in his sample is 6 correct to the nearest whole number.

Milo takes at random a pie from the 450 pies made on Tuesday.

Work out the lower bound of the probability that the pie is a steak pie.

The petrol consumption of a car, in litres per 100 kilometres, is given by the formula

Nathan’s car travelled 148 kilometres, correct to 3 significant figures. The car used 11.8 litres of petrol, correct to 3 significant figures.

Nathan says,

“My car used less than 8 litres of petrol per 100 kilometres.”

Could Nathan be wrong? You must show how you get your answer.

A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.

Jake finds out that the track is 270 km long. He assumes that the track has been measured correct to the nearest 10 km.

Could the average speed of the train have been greater than 160 km/h? You must show how you get your answer.

Jake’s assumption was wrong. The track was measured correct to the nearest 5 km.

Explain how this could affect your decision in part (a).