Standard & Compound Units

Sumeet has a pond in the shape of a prism.

The pond is completely full of water.
Sumeet wants to empty the pond so he can clean it.
Sumeet uses a pump to empty the pond.

The volume of water in the pond decreases at a constant rate.
The level of the water in the pond goes down by 20 cm in the first 30 minutes.

Work out how much more time Sumeet has to wait for the pump to empty the pond completely.

The distance from Fulbeck to Ganby is 10 miles.
The distance from Ganby to Horton is 18 miles.

Raksha is going to drive from Fulbeck to Ganby.
Then she will drive from Ganby to Horton.

Raksha leaves Fulbeck at 10 00
She drives from Fulbeck to Ganby at an average speed of 40 mph.

Raksha wants to get to Horton at 10 35
Work out the average speed Raksha must drive at from Ganby to Horton.

Liquid A has a density of 0.7 g/cm³.
Liquid B has a density of 1.6 g/cm³.

140 g of liquid A and 128 g of liquid B are mixed to make liquid C.

Work out the density of liquid C.

Ibrar mixes 74 g of lead and 126 g of tin to make 200 g of an alloy.

Lead has a density of 11.34 g/cm³.
Tin has a density of 7.31 g/cm³.

Work out the density of the alloy.
Give your answer correct to 1 decimal place.

Olly drove 56 km from Liverpool to Manchester.
He then drove 61 km from Manchester to Sheffield.

Olly's average speed from Liverpool to Manchester was 70 km/h.
Olly took 75 minutes to drive from Manchester to Sheffield.

Work out Olly's average speed for his total drive from Liverpool to Sheffield.

Janie drove from Barnsley to York.

Janie's average speed from Barnsley to Leeds was 80 km/h.
Her average speed from Leeds to York was 60 km/h.

Janie says that the average speed from Barnsley to York can be found by working out the mean of 80 km/h and 60 km/h.

If Janie is correct, what does this tell you about the two parts of Janie's journey?

The density of apple juice is 1.05 grams per cm³.

The density of fruit syrup is 1.4 grams per cm³.

The density of carbonated water is 0.99 grams per cm³.

25 cm³ of apple juice are mixed with 15 cm³ of fruit syrup and
280 cm³ of carbonated water to make a drink with a volume of 320 cm³.

Work out the density of the drink.
Give your answer correct to 2 decimal places.

James and Peter cycled along the same km route.

James took  hours to cycle the km.

Peter started to cycle minutes after James started to cycle.
Peter caught up with James when they had both cycled  km.

James and Peter both cycled at constant speeds.
Work out Peter's speed.

Sean drives from Manchester to Gretna Green.

He drives at an average speed of 50 mph for the first 3 hours of his journey.

He then has 150 miles to drive to get to Gretna Green.
Sean drives these 150 miles at an average speed of 30 mph.

Sean says,

      "My average speed from Manchester to Gretna Green was 40 mph."

Is Sean right?
You must show how you get your answer.

Zahra mixes 150g of metal A and 150g of metal B to make 300g of an alloy.

Metal A has a density of 19.3 g/cm³.
Metal B has a density of 8.9g/cm³.

Work out the density of the alloy.

In May 2019, the distance between Earth and Mars was 3.9 x 10⁷ km.

In May 2019, a signal was sent from Earth to Mars.
Assuming that the signal sent from Earth to Mars travelled at a speed of 3 x 10⁵ km per second,

how long did the signal take to get to Mars?

........................................seconds

The speed of the signal sent from Earth to Mars in May 2019 was actually less than 3 x 10⁵ km per second.

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

The density of ethanol is 1.09 g/cm³
The density of propylene is 0.97 g/cm³

60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze.

Work out the density of the antifreeze.
Give your answer correct to 2 decimal places.

.......................................g/cm³

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 a solid triangular prism.

The prism is made from metal.
The density of the metal is 6.6 grams per cm³.

Calculate the mass of the prism.

and  are 3 service stations on a motorway.

 = 25 miles
 = 25 miles

Aysha drives along the motorway from  to 

Aysha drives at an average speed of 50 mph from to .
She drives at an average speed of 60 mph from to .

Work out the difference in the time Aysha takes to drive from to and the time Aysha takes to drive from to .
Give your answer in minutes.

Sue is driving home from her friend's house.

Sue drives

      10 miles from her friend's house to the motorway
      240 miles on the motorway
      5 miles from the motorway to her home

Sue

      takes 20 minutes to drive from her friend's house to the motorway
      drives at an average speed of 60 mph on the motorway
      takes 25 minutes to drive from the motorway to her home

Sue stops for a 30 minute rest on her drive home.

Sue leaves her friend's house at 9.00 am.

What time does Sue get home?
You must show all your working.

The diagram shows a metal bar in the shape of a prism.

The length of the metal bar is 120 cm.
The cross section of the metal bar is shown below.

All corners are right angles.
The metal bar is made from steel with density 8 g/cm³.

Sean has a trolley.
The trolley can carry a maximum mass of 250 kg.

How many metal bars can the trolley carry at the same time?
You must show your working.

A gold bar has a mass of 12.5 kg.
The density of gold is 19.3 g/cm³.

Work out the volume of the gold bar.
Give your answer correct to 3 significant figures.

A force of 70 newtons acts on an area of 20 cm².

The force is increased by 10 newtons.
The area is increased by 10 cm².

Helen says,
      "The pressure decreases by less than 20%"

Is Helen correct?
You must show how you get your answer.

Find the pressure extered by a force of 900 newtons on an area of 60cm².
Give your answer in newtons/m².

Tame Valley is a company that makes yoghurt.

A machine fills trays of 20 pots with yoghurt.
In one hour, the machine fills a total of 15 000 pots.

Work out how many seconds the machine takes to fill each tray of 20 pots.

There are 18500 gallons of fuel in a fuel tank.

The fuel is pumped from the fuel tank into a plane at a rate of 1700 litres per minute.

1 gallon = 4.5 litres.

How many minutes will it take to empty the fuel tank completely?
Give your answer to the nearest minute.

Axel and Lethna are driving along a motorway.

They see a road sign.
The road sign shows the distance to Junction 8
It also shows the average time drivers take to get to Junction 8

To Junction 8 30 miles 26 minutes

The speed limit on the motorway is 70 mph.

Lethna says
      "We will have to drive faster than the speed limit to drive 30 miles in 26 minutes."

Is Lethna right?
You must show how you get your answer.

Change a speed of 50 metres per second to a speed in kilometres per hour.

.......................... kilometres per hour

A block of wood has a mass of .
The wood has density 

Work out the volume of the block of wood.
Give your answer correct to  significant figures.

Change a speed of  kilometres per hour to a speed in metres per second.

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.

.............. minutes ................ seconds

The mass is divided by 2 and the volume is multiplied by 4

What happens to the density?
Circle your answer.

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