Compound measures

Write 0.0037 in standard form.

A country consists of a south island and a north island. The table below shows the population and area of each island in June 2023.

Work out the overall population density of the country in June 2023.

(b)........ people per km²

A shop assistant works for 7 hours each day for 5 days. The shop assistant is paid the same amount for each hour they work. In the 5 days, the shop assistant earns £448.

How much does the shop assistant earn per hour?

The distance of a car race is 420 km. A car completes the first 210 km at an average speed of 150 km/h. The same car completes the final 210 km at an average speed of 100 km/h.

Show that the average speed of the car for the whole race is less than 125 km/h.

Write 0.0037 in standard form.

A country consists of a south island and a north island. The table below shows the population and area of each island in June 2023.

Work out the overall population density of the country in June 2023.

(b)........ people per km²

A solid steel cube has a mass of 1.05 kg. The density of the steel is 7.9 g/cm³.

Orla says,

The length of one side of the cube is approximately 10 cm.

Use estimation to decide if Orla’s statement is reasonable. Show how you decide.

Orla’s statement is........ because........

Zayn drives from home to a shopping centre. The graph shows information about the journey and the time spent at the shopping centre.

07 00 08 00 09 00 10 00 11 00 12 00 13 00 14 00

State an assumption that has been made when the graph was drawn.

Write down the distance from Zayn’s home to the shopping centre.

Calculate Zayn’s average speed, in km/h, from home to the shopping centre.

Zayn leaves the shopping centre at 11 00. Zayn drives home without stopping. The journey home takes 1 hours.

Complete the graph to show this information.

Force is measured in newtons (N). A force of 140 N is applied to a surface of area 8 cm².

Work out the pressure, in N/cm², applied to this surface.

Complete each statement.

35 kilograms =........ grams.

203 millilitres =........ litres.

4 square centimetres =........ square millimetres.

A train travels 90 km at an average speed of 40 km/h.

Work out the time taken for this journey. Give your answer in hours and minutes.

(b)........ hours........ minutes

The table shows charges made by a gas company to its customers.

The owner of a flat receives a gas bill covering a period of 100 days. They have used 7000 units of gas in this period.

Show that their bill is for £587.

The owner of a house is supplied gas by a different gas company.

• The cost per day is 25p.

• They use 10 000 units of gas in 100 days.

• Their bill covering the period of 100 days is £975.

Work out the cost per unit of gas used, giving your answer in pence.

Shop A and shop B have special offers on the same cupcakes.

Show that the special offer cost of 6 cupcakes from Shop A is £6.25.

Gabi wants 25 cupcakes for a party.

Which shop will be cheapest and by how much? Show how you decide.

(b) Shop........ by........ p

A rock has a mass of 36 920 g and a volume of 14 200 cm³.

Work out the density of the rock. Give the units of your answer.

A housing estate is built on a triangular piece of land.

There are 3951 people living on the estate.

Work out an estimate of the population density of the estate in people per km².

The population of an island is 47 000 people. The area of the island is 560 km².

Calculate the population density of the island in people per km².

The same dog food is sold in three different sized packs. The diagram shows the price of each pack.

Which pack is the best value for money? Show how you decide.

The........ pack because........

A bathroom shower uses water at a rate of 15 litres per minute.

How much water is used in a bathroom shower that lasts 12 minutes?

The table shows how much Amaya earns per hour.

One week Amaya works for 40 hours between Monday and Friday and then for hours on Saturday.³⁴

Amaya says

I will earn at least £900 for my work this week.

By rounding each value to the nearest integer, use estimation to show that Amaya may be

correct.

Give one reason why your working in part (a) shows that Amaya can be certain of earning at least £900 for her work in this week.

Ryan makes a journey of 200 miles from his home to the coast. of the journey is on roads with a speed limit of 40 miles per hour. 40% of the journey is on roads with a speed limit of 50 miles per hour. The remainder of the journey takes a time of 1 hour 30 minutes.

Ryan leaves home at 08 50 and does not exceed the speed limits on the journey.

Find the earliest time that Ryan could arrive at the coast. You must show your working.

Write down an assumption you have made when working out the answer to part (a).

When Layla walks to school she always takes 28 minutes. When Layla cycles to school her speed is double her walking speed.

One day Layla leaves home at 08 20 and cycles to school.

Find the time that Layla arrives at school.

On another day Layla cycles half-way to school. She walks the rest of the way at her normal walking speed.

Find how many minutes Layla takes to get to school on this day.

1 cm on a map represents 150 km in real life.

Below is part of the map showing City A and City B.

Heidi is planning to walk from City A to City B for charity.

Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm. Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours per day.

Use this information to work out how many days Heidi needs to complete the walk from City A to City B.

Explain why the information used in part (i) is likely to give an underestimate for the number of days Heidi needs to complete the walk.

Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1: 150.

Explain Yoshi’s error and write the scale correctly in the form 1: n.

The correct answer is 1:........

The same dog food is sold in three different sized packs. The diagram shows the price of each pack.

Which pack is the best value for money? Show how you decide.

The........ pack because........

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.

The graph shows the speed of an object during the first 20 seconds of its motion.

Calculate the distance travelled by the object during the 20 seconds.

The graph shows the distance travelled by an object during the first 4 seconds of its motion.

Work out the average speed of this object between 2 and 4 seconds.

Use the graph to estimate the speed of this object at 3 seconds. You must show working to support your estimate.

What happens to the speed of this object during these 4 seconds of motion. Explain how you know.

I know this because........

Ryan makes a journey of 200 miles from his home to the coast. of the journey is on roads with a speed limit of 40 miles per hour. 40% of the journey is on roads with a speed limit of 50 miles per hour. The remainder of the journey takes a time of 1 hour 30 minutes.

Ryan leaves home at 08 50 and does not exceed the speed limits on the journey.

Find the earliest time that Ryan could arrive at the coast. You must show your working.

Write down an assumption you have made when working out the answer to part (a).

A bronze ornament has a volume of 198 cm³. The density of bronze is 8.9 g/cm³.

By rounding each value correct to one significant figure, work out an estimate for the mass of the bronze ornament.

1 cm on a map represents 150 km in real life.

Below is part of the map showing City A and City B.

Heidi is planning to walk from City A to City B for charity.

Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm. Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours per day.

Use this information to work out how many days Heidi needs to complete the walk from City A to City B.

Explain why the information used in part (i) is likely to give an underestimate for the number of days Heidi needs to complete the walk.

Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1: 150.

Explain Yoshi’s error and write the scale correctly in the form 1: n.

The correct answer is 1:........

Heidi and Yoshi compete in the same car race. Heidi completes the race in 6 hours. Heidi’s average speed was 50 miles per hour. Yoshi’s average speed was 48 miles per hour.

Calculate how long it took Yoshi to complete the race. Give your answer in hours and minutes.

The graph shows Taylor’s journey from home to an airport. During the journey Taylor stops for petrol.

For how long did Taylor stop for petrol?

Taylor drives the same route back home from the airport at an average speed of 45 km / h. Taylor leaves the airport at 22:00.

Work out the time when Taylor arrives home.

A solid wooden block has a volume of 900 cm³. The density of the wood is 0.7 g/cm³.

Calculate the mass of the wooden block. Give the units of your answer.

The graph shows Taylor’s journey from home to an airport. During the journey Taylor stops for petrol.

For how long did Taylor stop for petrol?

Taylor drives the same route back home from the airport at an average speed of 45 km / h. Taylor leaves the airport at 22:00.

Work out the time when Taylor arrives home.

The density of some concrete is 2.4 g/cm³. A lump of this concrete has a volume of 400 cm³.

Work out the mass of the lump of concrete.

450 g of flour costs £1.44.

Work out the cost of 1 kg of this flour.

A farmer keeps sheep in a rectangular field measuring 120 m by 180 m. The farmer can keep up to 20 sheep per hectare in the field. 1 hectare is 10 000 square metres.

Work out the maximum number of sheep the farmer can keep in the field.

Kareem runs 2460 metres in 8 minutes.

Calculate his average speed in metres per minute.

Kareem says

This means I can run 6150 metres in 20 minutes.

Write down one assumption Kareem has made.

Hiro and Ling work in a restaurant. Hiro is paid £9 per hour and Ling is paid £10 per hour.

One week, Hiro works a total of 30 hours. Ling earns £50 more than Hiro that week.

Work out the number of hours that Ling works.

Write 0.003 86 in standard form.

The speed of sound is 3.43 × 10^-1km/s. An object is travelling at the speed of sound.

Work out how far the object travels in one day.

In a science fiction story, a spacecraft travelling faster than the speed of light is said to be travelling at ‘warp n ’ where n is an integer.

Warp n is defined as n³ × the speed of light.

In the story, a spacecraft needs to travel from Earth to Neptune in less than 2 minutes.

• The speed of light is 3.00 × 10⁵km/s.

• The distance from Earth to Neptune is 4.41 × 10⁹km.

Find the smallest possible warp n at which the spacecraft can travel. You must show your working.

A block made of iron is in the shape of a cuboid. The block is 3.1 cm by 4.9 cm by 2.2 cm. The density of iron is 7.87 g / cm³. Sam thinks that the mass of the block is about 2.4 kg.

Use estimation to decide if Sam’s answer is reasonable. Show how you decide.

Sam’s answer is........ because........

The density of gold is 19.3 g/cm³. Sam has a gold nugget of volume 7.5 cm³.

Calculate the mass of the gold nugget.

A solid block of wood is a cuboid which measures 3 cm by 4 cm by 5 cm. Its density is 0.65 g/cm³.

Work out the mass of the block of wood.

Here are two areas.

State which area is greater. Show how you decide.

Area........ is greater because........

The graph shows the distance travelled by a particle over the first 20 seconds of its motion.

Show that the average speed of the particle over the first 20 seconds of its motion is 1.8 m/s.

Estimate the speed of the particle at 10 seconds. You must show working to support your estimate.

The graph shows the speed of a car during the first 40 seconds of a journey.

Write down the acceleration of the car between 10 seconds and 25 seconds.

Work out the average speed of the car, in m/s, during the 40 seconds. You must show your working.

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.

A machine can dig, on average, 2 cm of tunnel each minute. It operates 24 hours each day.

Work out how many days it should take to dig a tunnel of length 3.5 km. Give your answer to the nearest day.

The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.

How would this affect your answer to part (a) ?

The mass of a stone is 680 g. The density of the stone is 1.6 g / cm³.

Work out the volume of the stone.

Write 1.6 g / cm³ in kg / m³.

A machine can dig, on average, 2 cm of tunnel each minute. It operates 24 hours each day.

Work out how many days it should take to dig a tunnel of length 3.5 km. Give your answer to the nearest day.

The machine actually digs an average of 2.5 cm of tunnel each minute for most of the time and an average of 1.5 cm each minute for the rest of the time.

How would this affect your answer to part (a) ?

An athlete goes for a training run. The graph shows their speed as they run.

Write down the athlete’s acceleration between 400 seconds and 1000 seconds.

Work out the athlete’s average speed, in m/s, during the 1200 seconds. You must show your working.

The mass of a stone is 680 g. The density of the stone is 1.6 g / cm³.

Work out the volume of the stone.

Write 1.6 g / cm³ in kg / m³.

Frankie and Taylor travel the same distance from town A to town B.

Frankie travels at an average speed of 52 kilometres per hour (km/h). Taylor travels at an average speed of 15 metres per second (m/s).

The journey takes Frankie 4 hours.

Calculate how long the journey takes Taylor. Give your answer in hours and minutes, correct to the nearest minute. You must show your working.

Force is measured in newtons (N). A force of 198.5 N is applied to a rectangular surface of length 4.9 cm and width 4.1 cm.

Work out an estimate of the pressure, in N / cm², applied to this rectangular surface.

[The formula for pressure is: Pressure =

A shop sells the same milk in three different sized cartons. The diagram shows the price of each carton.

Which carton is the best value for money? Show how you decide.

A student only buys milk on a Saturday morning. They use 120 ml of milk each day. Any unused milk has to be thrown away at the end of the following Friday.

Show that it is cheaper for the student to buy the milk they need in 300 ml cartons than in

500 ml cartons.

Force is measured in newtons (N). A force of 198.5 N is applied to a rectangular surface of length 4.9 cm and width 4.1 cm.

Work out an estimate of the pressure, in N / cm², applied to this rectangular surface. [The formula for pressure is: Pressure =

Train A travels 120 km at a constant speed of 80 km/h. Train B travels 120 km at a constant speed of 50 km/h.

How many more minutes does train B take to travel 120 km than train A?

Train C has a speed of x km/h.

Write an algebraic expression for train C’s speed in metres per second.

A solid metal sphere has mass 235 g. The density of the metal is 7.78 g/cm³.

Show that the surface area of this sphere is 46.9 cm², correct to 3 significant figures. You must show your working. [For a sphere with radius r: Volume = r³ Surface area = 4π r².]

The diagram shows Jane’s lawn. It is in the shape of a square of side 36 m and three semi-circles.

She is going to spread fertiliser on the lawn at a rate of 30 g per square metre. The fertiliser is only sold in 10 kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn. You must show all your working.

Clara travels from her home to Stoke.

The distance from her home to Stoke is 100 miles. She travels at an average speed of 50 miles per hour. She stops for 20 minutes on the journey.

Clara arrives in Stoke at 10:10 am.

At what time did she leave home?

A truck is used to transport some wood panels. Each wood panel is a cuboid measuring 2.4 m by 1.2 m by 1.8 cm. The density of each wood panel is 750 kg/m³.

The truck can carry 15 tonnes of these wood panels.

Calculate the maximum number of wood panels that the truck can carry. Show how you decide.

The diagram shows Jane’s lawn. It is in the shape of a square of side 36 m and three semi-circles.

She is going to spread fertiliser on the lawn at a rate of 30 g per square metre. The fertiliser is only sold in 10 kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn. You must show all your working.

The graph shows the speed of a vehicle during the first 40 seconds of motion.

Calculate the distance travelled by the vehicle during the 40 seconds.

The graph shows the distance travelled by a particle over 6 seconds.

Work out the average speed of the particle between 2 and 4 seconds.

Estimate the speed of the particle at 4 seconds.

A truck is used to transport some wood panels. Each wood panel is a cuboid measuring 2.4 m by 1.2 m by 1.8 cm. The density of each wood panel is 750 kg/m³.

The truck can carry 15 tonnes of these wood panels.

Calculate the maximum number of wood panels that the truck can carry. Show how you decide.

Dean drives a distance of 760 km in 9 hours. Robert drives a distance of 559 km in 6 hours 30 minutes.

Who has the highest average speed? Show how you decide.

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

Kim is paid £9.40 per hour for the first 35 hours she works each week. After 35 hours she is paid at one and a quarter times the hourly rate.

One week Kim works 42 hours.

Calculate how much she is paid for that week.

Anna and Paddy take part in the same fun run.

Anna completed the fun run in 2 hours. Her average speed was 6 kilometres per hour. Paddy completed the fun run in 90 minutes.

Work out Paddy’s average speed in kilometres per hour.

Anna says

Because I stopped for drinks, my average running speed was faster than 6 kilometres per hour.

Give one reason to support Anna’s statement.

The volume of a piece of wood is 620 cm³. Its density is 0.85 g/cm³.

Work out its mass.

The graph shows Sarah’s journey from her home to a shopping centre.

State an assumption that has been made when the graph was drawn.

What is the distance from Sarah’s home to the shopping centre?

Between which two times did Sarah stop? Explain how the graph shows this.

From........ to........ shown on the graph by........

Sarah stays at the shopping centre until 13:00. She then travels home without stopping. Her journey home takes 40 minutes.

Complete the graph to show this information.

Work out Sarah’s average speed for her journey home. Give your answer in kilometres per hour.

Delroy drives 240 miles. His car averages 40 miles per gallon of petrol. Petrol costs £1.30 per litre.

1 gallon is 4.5 litres.

How much does Delroy spend on petrol for this journey?

Simplify.

h³ × h^-3

The length of each side of a plastic cube is 2 a millimetres. The cube has mass 32a² grams.

Find an expression for the density of the cube in its simplest form. Give the units of your answer.

T is a radar tower. A and B are two aircraft.

At 3pm

• aircraft A is 3250 km from T on a bearing of 015°

• aircraft B is 4960 km from T on a bearing of 057°.

Aircraft A flies directly towards radar tower T at a speed of 890 km/h.

At what time will the aircraft pass over radar tower T? Give your answer to the nearest minute.

Calculate the distance that was between aircraft A and aircraft B at 3pm.

Tea bags of similar quality are sold in three different sized packs:

Which pack is the best value for money? Show how you decide.

Explain why someone may buy a pack which is not the best value for money.

Hector can run 400 metres in 66 seconds.

Use this information to show that he could run 5 kilometres in less than 14 minutes.

Hector tries to run 5 kilometres in less than 14 minutes.

Give one reason why he might not achieve this.

A water company charged the following in 2017.

£2.00 for each m³ of water used plus a fixed charge of £45

In 2017 Jenny used 110 m³ of water. For the 12 months of 2017 she paid £20 per month to the water company.

How much more money does Jenny need to pay to the water company?

A bee flies from its hive to a flower at a constant speed of 7.5 metres per second for 10 seconds. The bee then takes 15 seconds to fly back to the hive. Assume the bee always flies in a straight line.

Ignoring the time spent at the flower, work out the overall average speed of the bee in its flight from the hive to the flower and back.

(a)........ metres per second

If the bee is not assumed to fly in a straight line, how might your answer be affected?

Hector can run 400 metres in 66 seconds.

Use this information to show that he could run 5 kilometres in less than 14 minutes.

Hector tries to run 5 kilometres in less than 14 minutes.

Give one reason why he might not achieve this.

A solid metal block has mass 500 g and volume 125 cm³.

Work out the density of the block. Give the units of your answer.

Reuben hires a car. It costs £150, plus 85p for each mile he travels.

When Reuben hires the car, its mileage is 27 612 miles. When Reuben returns the car, its mileage is 28 361 miles.

How much did Reuben pay to hire the car?

The scale diagram below shows two cities, P and Q.

A plane departs from P at 09 47 and arrives at Q at 12 07.

Work out the average speed, in kilometres per hour, of the plane.

Give one reason why your answer may be inaccurate.

Viraj cycled from his home to visit his aunt. He drew this graph to show his journey. He stopped at a shop 7 km from his home.

State one assumption that Viraj made when he drew his graph.

For how long did Viraj stop at the shop?

Work out Viraj’s average speed between his home and the shop. Give your answer in metres per minute.

(c)........ metres per minute

How can you tell, without doing any calculations, that Viraj’s average speed between his home and the shop is greater than his average speed between the shop and his aunt?

Tea Biscuits can be bought in packets of 20 or packets of 24. All biscuits are identical in size and quality.

Nada says

The packet of 24 biscuits is better value.

Is Nada correct? Show how you decide.

Nada is........ because........

The scale diagram below shows two cities, P and Q.

A plane departs from P at 09 47 and arrives at Q at 12 07.

Work out the average speed, in kilometres per hour, of the plane.

Give one reason why your answer may be inaccurate.

Here is the floor plan of a rectangular room.

Tim buys carpet tiles for this room.

Each tile is a square measuring 50 cm by 50 cm. The tiles are only sold in packs of ten. Each pack costs £20. Tim pays for fitting at a rate of £7.50 per square metre, with any fraction of a square metre rounded up.

Work out the total cost of the tiles and fitting.

The graph shows the speed of a tram as it travels from the library to the town hall.

Calculate the deceleration of the tram as it approaches the town hall.

Calculate the distance travelled by the tram between the library and the town hall.

What was the maximum speed of the tram as it travelled between the library and the town hall? Give your answer in kilometres per hour.

This graph shows part of Lucy’s car journey from London to Sheffield. The car made one stop at a service station.

Use the graph to answer these questions.

For how long did the car stop at the service station?

Work out the average speed of the car, in miles per hour, between London and the service station.

Sheffield is 180 miles from London. Lucy arrived in Sheffield at 14 20.

Complete the graph.

A 100 g packet of tea costs £4.16. A 25 g packet of the same tea costs £1.05.

Which packet is better value for money? Show how you decide.

Halina cycled from A to B at an average speed of 26 km per hour. She then cycled from B to C at an average speed of 20 km per hour.

She left A at 10.00 am, did not stop at B and arrived at C at 3.00 pm.

It took Halina x hours to cycle from A to B.

Explain why the distance from A to B, in kilometres, is 26 x.

Write down an expression, in terms of x, for the time taken to cycle from B to C.

Hence show that the distance from B to C, in kilometres, is 100 – 20 x.

The total distance cycled by Halina from A to C is 118 km.

Find the distance from A to B.

Lucy and Ben share £42. Lucy’s share is £30.

Write the ratio Lucy’s share: Ben’s share in its simplest form.

The ratio 2.5 metres to 70 centimetres can be written in the form 1: n.

Find the value of n.

Water flows at a steady rate from a tap. It takes 50 seconds to fill a 5 litre watering can from this tap.

The rate at which water flows from the tap is halved.

Complete.

Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimetres per second (cm³/s).

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.

Work out the average speed of the vehicle during the 50 seconds. Give your answer in metres per second.

Work out the value of k.

Calculate the gradient of the graph in the final 10 seconds of the journey.

Describe what this gradient represents.

Trish and Marc both cycled the same distance. Trish completed the distance in 2 hours. Her average speed was 16 miles per hour. Marc completed the distance in 4 hours.

Find Marc’s average speed for the journey.

Lillian works 7 hours each day for 5 days a week. She earns £420 each week.

How much does she earn per hour?

Lillian decides that she is going to work 7 hours each day for only 4 days a week. Her earnings are to be reduced by 20%. Lillian thinks that this reduction is reasonable.

Explain why a reduction of 20% is reasonable.

How much will Lillian earn working 4 days a week?

The graph shows Mia’s journey from her home to university.

Calculate Mia’s average speed for the whole journey.

Grapes cost £2 per kilogram.

Calculate the cost of 380 g of grapes.

Ruth buys 19 identical tickets for £280.25.

Estimate the cost of one ticket. Show your working.

A village has a population of 4200 and a population density of 700 people per km². An estate is built next to the village. The estate has an area of 2 km² and a population density of 800 people per km².

Work out the population density for the village and the estate together.

........ people per km²

A sculpture is formed from a cylinder resting on top of a cuboid. The cylinder has radius 45 cm and height 80 cm. The cuboid measures 90 cm by 90 cm by 150 cm.

The sculpture is made of granite. The granite has a density of 2.7 g/cm³.

Calculate the total mass of the sculpture in tonnes.

The graph shows the speed, v metres per second (m/s), of a car at time t seconds.

Find the speed of the car at t = 7.

It is claimed that the car has accelerated from 0 to 60 miles per hour in the first 10 seconds.

Does the graph support this claim? Show your reasoning.

Use 1 mile = 1.6 kilometres.

Use the graph to estimate the acceleration at t = 7.

The speed of this car is directly proportional to the square of the time.

Find a formula linking v and t.

Georgina says that the graph shows that the speed of the car will continue to increase after 10 seconds.

Make one comment to show that this statement is incorrect.

The graph shows Mia’s journey from her home to university.

Calculate Mia’s average speed for the whole journey.

The object below is made from a square-based pyramid joined to a cuboid.

The base of the cuboid and the base of the pyramid are both squares of side 4 cm. The height of the cuboid is 8 cm and the total height of the object is 13 cm. The total mass of the object is 158 g.

The cuboid is made from wood with density 0.67 g/cm³. The pyramid is made from granite.

Calculate the density of the granite. [The volume of a pyramid is _× area of base_× perpendicular height.]