Compound measures

A metal solid has volume 11 cm³

Work out the mass of the solid.

A metal solid has volume 11 cm³

Work out the mass of the solid.

Which packet of rice is better value for money? Tick a box.

You must show your working.

Emma and Chan each drive 154 miles from A to B.

Emma drives the whole way at an average speed of 56 miles per hour.

Chan drives 85 miles at an average speed of 50 miles per hour and then the rest of the way at an average speed of 60 miles per hour.

Who takes less time, Emma or Chan? Show working to support your answer.

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.

A car travels 4 miles in 5 minutes.

Work out the average speed in miles per hour.

Some oil has a mass of 537 g

1 m³ = 1000 litres

Work out the volume of the oil. Give your answer in litres.

Some oil has a mass of 537 g

1 m³ = 1000 litres

Work out the volume of the oil. Give your answer in litres.

Three shops sell shirts.

At which shop is it cheapest to buy 6 shirts ? Show working to support your answer.

An electric car uses 1 unit of electricity to travel 3 miles. 1 unit of electricity costs 50 pence.

Work out the cost of electricity, in pounds, to travel 270 miles.

Concrete from a truck is poured at 10.9 kg per second for 30 minutes.

Is more than 20 tonnes of concrete poured? Tick a box.

You must show your working.

On Monday, Larrs swims 50 metres in 40 seconds at a constant speed. On Tuesday, Larrs swims 1.5 kilometres.

Assume he swims at the same constant speed as on Monday.

How many minutes does he swim for on Tuesday?

In fact, on Tuesday Larrs swims at a slower constant speed than on Monday.

What does this mean about the number of minutes he swims for on Tuesday? Tick the correct box.

Town A has a population of 84 000 an area of 7 square miles.

Town B has a population density of 4695 people per square kilometre.

Which town has the greater population density?

Use 1 square mile = 2.6 square kilometres Tick a box.

Show working to support your answer.

On Monday, Larrs swims 50 metres in 40 seconds at a constant speed. On Tuesday, Larrs swims 1.5 kilometres.

Assume he swims at the same constant speed as on Monday.

How many minutes does he swim for on Tuesday?

In fact, on Tuesday Larrs swims at a slower constant speed than on Monday.

What does this mean about the number of minutes he swims for on Tuesday? Tick the correct box.

Town A has a population of 84 000 an area of 7 square miles.

Town B has a population density of 4695 people per square kilometre.

Which town has the greater population density?

Use 1 square mile = 2.6 square kilometres Tick a box.

Show working to support your answer.

Last week, Erik worked for 10 hours. He paid no tax and received £90

This week, Erik works for 15 hours. He assumes he will be paid at the same rate and pay no tax.

How much does he expect to receive this week?

In fact, this week, Erik is paid an extra 50p per hour pays £8.90 tax.

What does this tell you about the amount he receives? Tick one box.

Show working to support your answer.

The boundaries of a city form a trapezium.

The population density of the city is 9450 people per square kilometre.

Work out the number of people who live in the city.

Tasha drove 198 miles. Her average speed for the first 3 hours was 45 miles per hour. Her average speed for the rest of the journey was 31.5 miles per hour.

Work out her average speed for the whole journey.

miles per hour

Tasha drove 198 miles. Her average speed for the first 3 hours was 45 miles per hour. Her average speed for the rest of the journey was 31.5 miles per hour.

Work out her average speed for the whole journey.

miles per hour

Sanjit buys 1.75 kg of potatoes and 4 kg of leeks. The total cost is £9.03 The potatoes cost 84p per kg

Work out the cost per kg of the leeks.

Answer £ per kg

Des delivers takeaways to houses A, B and C.

Des drives from T to A and back and from T to B, then B to C, then C to T.

Des is paid 40p for each mile he drives and £1.35 for each house he delivers to.

How much is Des paid in total for this work?

An exhibition was open for 240 hours and had 29 760 visitors. For of the time the exhibition was open, there were 172 visitors per hour.

For the remaining time, how many visitors per hour were there?

A solid trophy consists of a stand and a player.

The stand is made by removing a small pyramid from a large pyramid.

Large pyramid Square base, edge 8 cm Perpendicular height 16 cm Small pyramid Square base, edge 5 cm Perpendicular height 10 cm

Show that the volume of the stand is 258 cm³

The trophy is made from a metal of density 7.5 grams per cm³ The total mass of the trophy is 2340 grams.

Work out the volume of the player.

Liz travels 18 miles in 20 minutes. Work out her average speed in miles per hour.

A journey has two stages.

A bowl is a hemisphere with radius 12 cm

Water is poured into the bowl at a rate of 325 cm³ per second for 8 seconds. Does the water fill more than 70% of the bowl? You must show your working.

A bowl is a hemisphere with radius 12 cm

Water is poured into the bowl at a rate of 325 cm³ per second for 8 seconds. Does the water fill more than 70% of the bowl? You must show your working.

This week, Liam works 25 hours at £10.20 per hour and extra hours at the weekend at £11.80 per hour. Here are the extra hours he works at the weekend.

In total, how much is he paid this week?

Charlie is driving 293 miles home. He

• leaves at 9.00 am

• travels the first 176 miles at an average speed of 48 mph

• drives the rest of the way at an average speed of 65 mph

Will he be home by 2.30 pm? You must show your working.

A tank contains 40 litres of water.

Water leaks out of the tank at a rate of 1.2 litres per minute. The leak is stopped after 20 minutes. Show that, when the leak is stopped, the tank contains 16 litres of water.

The tank is refilled with water from a tap. The graph shows the amount of water in the tank after the leak is stopped.

Complete this report by writing a number in each answer space.

A tank contains 40 litres of water.

Water leaks out of the tank at a rate of 1.2 litres per minute. The leak is stopped after 20 minutes. Show that, when the leak is stopped, the tank contains 16 litres of water.

The tank is refilled with water from a tap. The graph shows the amount of water in the tank after the leak is stopped.

Complete this report by writing a number in each answer space.

A ship sails from A on a bearing of 247 ° It travels at a constant speed of 23 mph for 1 hours. Is the ship now closer to B than it was when it left A? You must show your working.

A solid statue has volume 512 cm³ The statue has mass 3.6 kilograms.

density of iron = 7.87 grams per cubic centimetre

Is the statue made of iron? You must show your working.

Part of a running track is the arc of a semicircle joined to a straight line. The semicircle has diameter 45 metres. The straight line has length 75 metres.

Abby runs once along this part of the track in 18 seconds. Work out her average speed. Give your answer to 2 significant figures.

Part of a running track is the arc of a semicircle joined to a straight line. The semicircle has diameter 45 metres. The straight line has length 75 metres.

Abby runs once along this part of the track in 18 seconds.

Work out her average speed. Give your answer to 2 significant figures.

Here are two solid cubes, X and Y. The mass of X is 10.976 kg The area of each face of X is 784 cm²

Zayan wants to know the density of Y. He assumes that Y is identical to X.

What density should he get for Y? Give your answer in grams per cubic centimetre.

In fact, the mass of Y is less than the mass of X the area of each face of Y is greater than the area of each face of X.

What does this mean about the actual density of Y? Tick one box.

A solid has volume 300 cm³ and density 2 g/cm³ Circle the mass of the solid.

150 g 298 g 302 g 600 g

A machine to clean carpets can be hired.

Rana wants to

buy 5 litres of cleaning fluid. Work out the smallest total amount she could pay.

Ali revises each day for five days. On each of the first four days he revises from 5 pm to 8 pm On the fifth day he starts revising at 1 pm He finishes when he has revised for a total of 18 hours for the five days. What time does he finish on the fifth day?

Sofia is revising for Maths. She tries to work out 3 × (4 + 2) Here is her working.

What mistake has she made?

Sam types a constant number of words per minute. He takes 8 minutes to type a report of 416 words. How long does it take him to type an essay of 1534 words? Give your answer in minutes and seconds.

Sam types a constant number of words per minute. He takes 8 minutes to type a report of 416 words. How long does it take him to type an essay of 1534 words? Give your answer in minutes and seconds.

Two objects, J and K, are applying pressure to areas of ground.

For J, the force is 18.9 newtons and the area is 0.45 m² pressure for J: pressure for K = 7: 8 area for J: area for K = 9: 5 Work out the force for K.

Tom and Adil are the two runners in a 200-metre race. Tom completes the race in 24 seconds. Adil completes the race at an average speed of 28.8 kilometres per hour. Who wins the race? You must show your working.

Tom and Adil are the two runners in a 200-metre race. Tom completes the race in 24 seconds. Adil completes the race at an average speed of 28.8 kilometres per hour. Who wins the race? You must show your working.

A town has a population density of 278 people per km² and a population of 158 460

The population increases to 168 720 Work out the population density after the increase.

Working alone, it takes Kevin 4 hours to paint an area of 12 m² Kevin and Steve are going to paint an area of 24 m² Kevin says, “Working together at the same rate it will take us 8 hours, because 24 is 2 × 12” Is he correct?

Give a reason for your answer.

A, B, C and D are junctions on a motorway.

distance CD = 3 × distance AB distance BC = 25 miles Salma drives from A to C. She drives for 30 minutes at an average speed of 62 miles per hour. Work out the distance AD.

A, B, C and D are junctions on a motorway.

distance CD = 3 × distance AB distance BC = 25 miles Salma drives from A to C. She drives for 30 minutes at an average speed of 62 miles per hour. Work out the distance AD.

Which one of these is a unit of density? Circle your answer.

Convert 11.2 kilometres into miles. Use 8 km = 5 miles

Lynn works as a bus driver. She is paid £10.80 per hour for the first 38 hours she works each week. She is paid 25% more per hour for each extra hour she works. One week, Lynn was paid £491.40 In total, how many hours did she work that week? You must show your working.

Boxes of chocolates each contain 25 chocolates. One box costs £3.25 A shop has a special offer.

How much cheaper per chocolate is the special offer?

A machine takes 4 seconds to fill a packet of crisps.

In total, how many packets can 35 of these machines fill in 8 hours?

Each packet of crisps contains 32.5 grams of crisps. At what rate does a machine put the crisps into the packets? Give your answer in grams per second.

The heel of a shoe exerts a pressure of 198 pounds per square inch. Convert this pressure into kilograms per square centimetre. Use 1 pound = 0.45 kilograms 1 square inch = 6.25 square centimetres

The heel of a shoe exerts a pressure of 198 pounds per square inch. Convert this pressure into kilograms per square centimetre. Use 1 pound = 0.45 kilograms 1 square inch = 6.25 square centimetres

Jenny works for 30 hours and is paid £318 Calvin works for 28 hours and is paid £287 Jenny is paid more per hour than Calvin. How much more?

A solid piece of silver has mass 2.625 kilograms volume 250 cm 3 Work out the density of the piece of silver. Give your answer in grams per cubic centimetre.

g/cm 3

A solid piece of silver has mass 2.625 kilograms volume 250 cm 3 Work out the density of the piece of silver. Give your answer in grams per cubic centimetre.

g/cm 3

Chris visits a library. He cycles to the library in half an hour at a speed of 12 miles per hour. He stays at the library for one hour. He then cycles home. The sketch graph represents his visit.

Work out the speed, in miles per hour, at which Chris cycles home.

The pressure in a tyre is 30 pounds per square inch. Convert the pressure into kilograms per square centimetre. Use 1 pound = 0.45 kilograms and 1 inch = 2.54 centimetres

A car journey is in two stages. Stage 1 The car travels 110 miles in 2 hours. Stage 2 The car travels 44 miles at the same average speed as Stage 1 Work out the time for Stage 2 Give your answer in minutes.

A car journey is in two stages. Stage 1 The car travels 110 miles in 2 hours. Stage 2 The car travels 44 miles at the same average speed as Stage 1 Work out the time for Stage 2 Give your answer in minutes.

Ralf has an iron.

The iron applies a force of 25 newtons (N)

Work out the pressure using Ralf’s model.

Is the actual pressure greater than, equal to or less than your answer to part (a)? Tick one box.

Give a reason for your answer.

The cost of 5 kg of potatoes is £3.20

Work out the total cost of 12 kg of potatoes and 1 kg of carrots.

26 Density =

The mass is divided by 2 and the volume is multiplied by 4 What happens to the density? Circle your answer.

× 2 ÷ 2 × 8 ÷ 8

The graph shows how much Molly is paid for working for up to 40 hours. She receives a basic rate of pay for the first 35 hours worked a higher rate of pay for the next 5 hours worked.

Work out the difference between the higher rate of pay and the basic rate of pay. Give your answer in £ per hour.

10 Density =

The mass is divided by 2 and the volume is multiplied by 4 What happens to the density? Circle your answer.

× 2 ÷ 2 × 8 ÷ 8

The graph shows how much Molly is paid for working for up to 40 hours. She receives a basic rate of pay for the first 35 hours worked a higher rate of pay for the next 5 hours worked.

Work out the difference between the higher rate of pay and the basic rate of pay. Give your answer in £ per hour.

A force of 180 newtons (N) is applied to the surface of this triangle.

Work out the pressure.

Beth drives 200 miles in 4 hours. She drives the first 18 miles at an average speed of 36 mph Work out her average speed for the rest of the journey.

Beth drives 200 miles in 4 hours. She drives the first 18 miles at an average speed of 36 mph Work out her average speed for the rest of the journey.

Josh downloads album A. A has 11 tracks. Each track on A costs the same. The total cost of downloading A is £8.80

Josh also downloads album B. B has 14 tracks.

Work out the total cost of downloading B. Assume each track costs the same as a track on A.

In fact, compared to the cost of each track on A the cost of 6 tracks on B is more by 5p each the cost of 8 tracks on B is less by 5p each.

What does this tell you about your answer to part (a)? Tick one box.

Give a reason for your decision.

In one hour a machine can make 600 nuts or 720 bolts.

At 3 pm the machine starts working. It makes 900 nuts and then changes to making bolts.

How many bolts will the machine make by 8 pm?

Two solids, J and K, have the same density.

Complete the table. Include units in your answers.

Two solids, J and K, have the same density. Complete the table. Include units in your answers.

The cost of 3 calendars is £18 Work out the cost of 5 calendars.

Lucy works for 37 hours per week. Her weekly wage is £303.40 She receives a pay increase of 25p per hour. Work out her new weekly wage.

Here is a list of ingredients needed to make 6 pancakes.

Complete the list of ingredients needed to make 9 pancakes.

Convert 210 millilitres to fluid ounces. Use 1 fluid ounce = 28.4 millilitres Give your answer to 1 decimal place.

The diagrams show the position of a tap when off and fully on. The tap is fully on when the angle of turn is 180°

When fully on, water flows out of the tap at 14 litres per minute. The rate at which water flows out is in direct proportion to the angle of turn. The tap is turned 135°

The water flows into a tank with a capacity of 79.8 litres. Will it take less than 7 minutes to fill the tank? You must show your working.

The volume of a medal is 45 cm³ The medal is made from copper and tin.

Work out the mass of the medal.

Amal drives her car for work. She claims 40p per mile from her employer. Amal’s car travels 52 miles for each gallon of petrol. She pays £5.36 per gallon for petrol. On one journey Amal drives 260 miles. For this journey, how much more does she claim than she pays for petrol?

Priya and Joe travel the same 16.8 km route. Priya starts at 9.00 am and walks at a constant speed of 6 km/h Joe starts at 9.30 am and runs at a constant speed. Joe overtakes Priya at 10.20 am At what time does Joe finish the route?

2 people working at the same rate will take 6 hours to paint a room.

Assuming that they all work at this rate, how long will it take 3 people to paint the room?

In fact, the third person works at a faster rate. How does this affect the time to paint the room?

Some concrete has volume 3.8 m³

The density of the concrete is 2400 kg/m³ Work out the mass of the concrete.

The 3.8 m³ of concrete is made into the shape of a cylinder. The base has radius 0.5 metres.

Work out the height of the cylinder.

A car travels 3.5 miles in 5 minutes. Work out the average speed in miles per hour.

A force of 40 Newtons is applied to an area of 3.2 square metres. Work out the pressure. Give the units of your answer.

15 machines work at the same rate. Together, the 15 machines can complete an order in 8 hours. 3 of the machines break down after working for 6 hours. The other machines carry on working until the order is complete. In total, how many hours does each of the other machines work?

In 2015, Han was paid £1350 per month.

In 2016, he had a 2% increase in his monthly pay worked 37.5 hours per week worked for 47 weeks.

Work out Han’s average pay per hour for 2016

The table shows information about the UK and Germany.

Compare the population densities of the UK and Germany.

Which one of these is a unit of density? Circle your answer.

The table shows information about the UK and Germany.

Compare the population densities of the UK and Germany.

5 2.5 kg of carrots cost £1.70 Work out the cost of 3.25 kg of carrots.

The distance by road from Newport to London is 140 miles. Tom travels by coach from Newport to London. The coach leaves Newport at 1.30 pm

He assumes the coach will travel at an average speed of 50 mph Use his assumption to work out the arrival time in London.

In fact, the coach has a lower average speed. How does this affect the arrival time?

Work out the force when the pressure is 24 N/m² and the area is 3 m² Circle your answer.

0.125 N 8 N 27 N 72 N

The distance by road from Newport to London is 140 miles. Tom travels by coach from Newport to London. The coach leaves Newport at 1.30 pm

He assumes the coach will travel at an average speed of 50 mph Use his assumption to work out the arrival time in London.

In fact, the coach has a lower average speed. How does this affect the arrival time?

Use 8 km/h = 5 mph to convert 96 km/h to mph

x km/h = y mph Use 8 km/h = 5 mph to write a formula for y in terms of x.

22

The mass of solid A is 6 times the mass of solid B. The volume of solid A is 3 times the volume of solid B. Complete the sentence.

If the distance is halved and the time is doubled, what happens to the average speed? Circle your answer.

9

The mass of solid A is 6 times the mass of solid B. The volume of solid A is 3 times the volume of solid B.

Complete the sentence.

If the distance is halved and the time is doubled, what happens to the average speed? Circle your answer.

Lily goes on a car journey. For the first 30 minutes her average speed is 40 miles per hour. She then stops for 15 minutes. She then completes the journey at an average speed of 60 miles per hour. The total journey time is 1 hour.

Draw a distance-time graph for her journey.

Write down the average speed for the total journey.

A shop sells two brands of battery.

One brand A battery powers a toy for 5 hours. One brand B battery powers the same toy for 5 hours. Which brand is better value? You must show your working.

Liam drives his car. He drives the first 9 miles in 9 minutes. He then drives at an average speed of 70 miles per hour for 1 hour 36 minutes. He finds this information about his car.

Use the information to show that his car uses less than 3 gallons of petrol for the drive.