OCR GCSE Maths
Topic questions Number Standard units & compound measures
72 questions · 361 marks · about 5.5 hours
Also involves The four operations · Rounding
A 1.5 litre carton of orange juice costs £1.30. Gabi has £10 to spend on orange juice and buys the maximum possible number of cartons.
Each day Gabi drinks 350 millilitres of the orange juice she has just bought.
Work out how many days the orange juice will last Gabi. You must show your working.
The ratio 40 grams to 1 kilogram can be written in the form 1: n.
Find the value of n.
Bottle A contains 1.5 litres of water and bottle B contains 100 millilitres of water.
1.5 litres 100 millilitres
Water is poured from bottle A into bottle B until both bottles contain the same amount.
How many millilitres of water are poured from bottle A into bottle B ?
Leo and Eve attempt the same puzzle. Leo takes 1 minute 15 seconds to solve the puzzle. Eve takes 2 minutes 5 seconds to solve the puzzle.
Write Leo’s time as a fraction of Eve’s time. Give your answer in its simplest form.
Also involves Systematic listing and the product rule for counting
Sundip has some £5, £10, £20 and £50 bank notes. She buys 30 litres of fuel for her car. One litre of fuel costs £1.50.
Sundip pays the exact amount of money for the fuel using three bank notes.
Work out the three bank notes that she uses to pay for the fuel.
(a) £........, £........ and £........
On one journey, Sundip’s car uses fuel at a rate of one litre every 16 kilometres. At the start of the journey, her car has 50 litres of fuel. At the end of the journey, her car has used 
of this fuel. Use the conversion 5 miles = 8 kilometres to work out the number of miles Sundip travels on this journey. You must show your working.
Write 1% as a decimal.
Write 35% as a fraction. Give your answer in its simplest form.
Work out 15% of 2 litres. Give your answer in millilitres.
Also involves Converting between units
Sam sees a computer tablet for sale on the internet for 126 euros (€). Sam has £105 to spend.
The exchange rate is £1 = €1.15.
Can Sam buy the tablet? Show how you decide.
Also involves Volume and surface area
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........
Also involves Fractions, decimals and percentages
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
Felix makes craft figures at a constant rate. He can make 5 craft figures in 40 minutes.
Find the number of craft figures Felix can make in 4 hours.
Darcie makes craft figures 10% quicker than Felix.
Work out how long Darcie takes to make 15 craft figures.
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 machine makes 15 boxes in 12 minutes. The machine works continuously.
Work out how many boxes are made by this machine in 7 hours.
Use one of these symbols <, > or = to make each statement true.
60 mm........ 6 cm
320 g........ 3.2 kg
Compost is used to grow plants. Ivan has a sack containing 50 litres of compost. He uses this compost to fill pots for his plants.
Ivan fills six large pots each holding 7.5 litres.
Work out how much compost is left in the sack.
Ivan uses the remaining compost to fill small pots each holding 400 ml.
Work out the maximum number of small pots Ivan can fill with the remaining compost.
Work out how much compost will then be left in the sack.
Also involves The four operations
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).
Give your answer correct to 1 decimal place.
Write 400 metres as a fraction of 2 kilometres. Give your answer in its simplest form.
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:........
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:........
A painter mixes red paint and yellow paint in the ratio 2: 3. They make a total of 1.5 litres of paint.
Work out how much red paint they use. Give your answer in millilitres.
Alex and Emma use this recipe to make scones. The recipe shows the ingredients needed to make 16 scones.
Alex makes 24 scones.
He uses a tablespoon to measure the amount of milk he needs. The size of a tablespoon is 15 ml.
How many tablespoons of milk should Alex use to make 24 scones?
Emma has 1 kg of flour and 240 g of sultanas. She has lots of all of the other ingredients.
Work out the maximum number of scones that Emma can make. You must show your working.
Also involves Converting between units
Write an expression for the weight, in grams, of an object weighing x kilograms.
Write an expression for the area, in m2, of a garden of area ycm2.
A sheet of A4 card weighs 1.19 × 10-2 kg.
Work out the weight of 500 sheets of the A4 card.
Card is classified using W, the weight in grams per square metre (gsm).
A sheet of A4 card is a rectangle that is 21 cm by 29.7 cm.
Calculate W for this A4 card.
Also involves Converting between units
Write an expression for the weight, in grams, of an object weighing x kilograms.
Write an expression for the area, in m2, of a garden of area ycm2.
Also involves Area and perimeter
A sheet of A4 card weighs 1.19 × 10-2 kg.
Work out the weight of 500 sheets of the A4 card.
Card is classified using W, the weight in grams per square metre (gsm).
A sheet of A4 card is a rectangle that is 21 cm by 29.7 cm.
Calculate W for this A4 card.
Also involves Area and perimeter
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.
Alex is 1.34 metres tall. Gabi is 95 centimetres tall.
Find, in centimetres, how much taller Alex is than Gabi.
A volunteer packs boxes for a charity. They can pack 5 boxes in 45 seconds.
Use this information to show that they can pack 55 boxes in less than 9 minutes.
What assumption did you make in part (a) ?
A volunteer packs boxes for a charity. They can pack 5 boxes in 45 seconds.
Use this information to show that they can pack 55 boxes in less than 9 minutes.
What assumption did you make in part (a) ?
Morgan makes 15 cakes. Each cake needs a piece of ribbon 18 cm long for decoration.
Ribbon is only sold in rolls of 1.2 metres, which can then be cut into 18 cm pieces. One roll of ribbon costs 92p.
Calculate the cost of the ribbon that Morgan must buy to decorate the 15 cakes. You must show your working.
Also involves Converting between units
Blake changes £450 into dollars. £1 is worth 1.34 dollars.
Blake says
450 ÷ 1.34 = 335.82 Therefore, £450 is worth 335.82 dollars.
Is Blake correct or incorrect? Give a reason for your decision.
Blake is........ because........
It takes a librarian 
minutes to put a plastic cover on a book.
Ashley goes on a journey. She travels by taxi for 
of the journey. She travels by train for 
of the journey. She walks for the remaining 900 m of the journey.
Find the length of this journey in kilometres. You must show your working.
Also involves Converting between units
In space, distances can be measured in Astronomical Units. In this question, use the conversion 1 Astronomical Unit = 1.5 × 108km.
On a particular day the distance from Earth to Neptune is 29.09 Astronomical Units.
Calculate the distance from Earth to Neptune in kilometres on that day. Give your answer in standard form.
On a particular day the distance from Earth to Mars is 78 340 000 km.
Calculate the distance from Earth to Mars in Astronomical Units on that day.
(b)........ Astronomical Units
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) ?
Also involves The four operations
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) ?
Charlie is making some wooden frames. Charlie has a strip of wood 1.6 m long and 2 cm wide.
Not to scale
Each frame will be made from four pieces of wood cut from the strip to form a rectangle, as shown below.
The width of each frame is x cm. The length of each frame is 2 x cm. The area enclosed by each frame must be 96 cm2.
Work out the maximum number of frames Charlie can make from the 1.6 m length of wood. You must show your working.
Also involves Using a calculator
Light from the Sun travels 1 kilometre in 3.3 × 10-6 seconds. The distance from the Sun to the Earth is 1.5 × 108kilometres.
How long does it take light to travel from the Sun to the Earth? Give your answer in minutes and seconds.
........ minutes........ seconds
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.
Also involves The four operations
A conversion graph between pounds (£) and dollars ($) is shown below.
Explain fully how the graph shows that the number of dollars is directly proportional to the number of pounds.
Use the conversion graph to change £20 into dollars.
Some trainers cost £170 in the UK. The same trainers cost $195 in the USA.
Show that the trainers cost less in the USA.
If the trainers are brought from the USA there is an extra charge for tax and delivery.
Alex wants to pay the lowest total amount for the trainers.
Write down the maximum extra charge for tax and delivery that Alex should be willing to pay. Give your answer in dollars.
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.
A car mechanic has a tin containing 5 litres of engine oil. Each week they use 450 millilitres of this oil for their vehicles.
The car mechanic says
After 9 weeks I will have used over 80% of the oil in this tin.
Are they correct? Show how you decide.
Ellis has 28 m of ribbon. They cut the ribbon into lengths of 60 cm.
What is the least length of ribbon, in cm, that can be left over? You must show your working.
A car mechanic has a tin containing 5 litres of engine oil. Each week they use 450 millilitres of this oil for their vehicles.
The car mechanic says
After 9 weeks I will have used over 80% of the oil in this tin.
Are they correct? Show how you decide.
Also involves Rounding · Using a calculator
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.
Write 350 centimetres in metres.
Write 1.52 litres in millilitres.
Work out.
5.7 cm + 30 mm.
Give your answer in centimetres.
Write each of the following ratios in their simplest form.
12: 15
600 g: 1.8 kg
Also involves Rounding
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.
Also involves Rounding
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.
Also involves Rounding
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.
Work out.
1.52 kg + 80 g
Give your answer in kilograms.
Carol makes birthday cards. Each card takes the same amount of time to make.
She makes 3 cards in 48 minutes. She has an order for 80 cards.
Can she complete this order in 3 days if she works 8 hours each day? Show how you decide.
Also involves The four operations · Converting between units
Kate is 5 feet 2 inches tall. Alice is 1.57 metres tall. Alice says that she is taller than Kate.
Use the conversions below to decide if Alice is correct.
A sunflower grows at a rate of 4 cm each day.
How many days does it take to grow from a height of 80 cm to more than 1.06 m?
If the sunflower grows at a faster rate, how would this affect your answer to part (a) ?
Joan makes cups of tea and coffee at a lunch club. Each cup requires 250 ml of boiling water. She has a kettle that boils up to 1.7 litres of water each time.
She boils 10 litres of water in an urn. She then uses the kettle to boil the rest of the water she needs.
Find the least number of times that Joan needs to boil the kettle to make 56 cups. Show how you decide.
Also involves Using a calculator
Tom researches the weights of plant seeds.
• One poppy seed weighs 3 × 10-4grams.
• 250 pumpkin seeds weigh 21 grams.
• One sesame seed weighs 3.64 × 10-6 kilograms.
Write the three types of seed in order according to the weight of one seed. Write the lightest type of seed first. You must show how you decide.
lightest
Also involves Using a calculator
Tom researches the weights of plant seeds.
• One poppy seed weighs 3 × 10-4grams.
• 250 pumpkin seeds weigh 21 grams.
• One sesame seed weighs 3.64 × 10-6 kilograms.
Write the three types of seed in order according to the weight of one seed. Write the lightest type of seed first. You must show how you decide.
lightest
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 newborn baby has an approximate mass of 3.5 kilograms.
A human cell has an approximate mass of 2.7 × 10-11 grams.
Use these values to estimate the number of human cells in a newborn baby. Give your answer in standard form, correct to 2 significant figures.
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.
Also involves Rounding
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.
Standard bricks have dimensions 21.5 cm by 10.3 cm by 6.5 cm, correct to 1 decimal place.
A house is built using 4663 standard bricks.
Joslin says
Placed end to end, the bricks from the house would definitely reach over 1 km.
Show that Joslin’s statement is correct.
A standard brick should weigh 2.8 kg, correct to 1 decimal place. A truck can carry a maximum load of 20 tonnes.
Calculate the maximum number of standard bricks that the truck should be able to carry.
Explain why your answer to (b)(i) may not be possible to achieve.
Also involves Using a calculator
Donald swims 3 lengths of a swimming pool in 93 seconds.
Use this information to show that he could swim 100 lengths in under 55 minutes.
What assumption did you make in part (a) ?
Donald tries to swim the 100 lengths in under 55 minutes.
Suggest one reason why he might not achieve this.
Also involves Converting between units
Georgia is 4 feet 2 inches tall. There are 12 inches in a foot.
Use the conversion, 1 inch = 2.5 centimetres, to convert Georgia’s height into metres.
Owen weighs 6 stones 4 pounds. There are 14 pounds in a stone.
Use the conversion, 2.2 pounds = 1 kilogram, to convert Owen’s weight into kilograms.
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).
Elsie changes to a decimal.
This is her working.
Where a line of working is wrong, write the correct working beside it.
Ali has 1 litre of squash. He always mixes 0.05 litres of squash with 200 ml of water to make a glass of drink.
Find the total volume of the drink that Ali can make. Give your answer in litres.
Donald swims 3 lengths of a swimming pool in 93 seconds.
Use this information to show that he could swim 100 lengths in under 55 minutes.
What assumption did you make in part (a) ?
Donald tries to swim the 100 lengths in under 55 minutes.
Suggest one reason why he might not achieve this.
Also involves Motion graphs
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.
A farmer has a field that is in the shape of a trapezium. He measures the field so that he can work out the area. He puts his measurements on this diagram of the field.
The farmer has rounded his measurements to two significant figures.
Give a reason why he may have done this.
The field produces 6400 kilograms of wheat per hectare. One hectare is 10 000 m2.
Work out how many kilograms of wheat the field produces.
Also involves The four operations · Using a calculator
Harry needs dollars to go on holiday. He can buy $50 for £40.
How much will $720 cost at the same rate?
Tony returns from holiday with these notes.
| Note | Number of notes |
| €50 | 2 |
| €20 | 4 |
| €10 | 9 |
| €5 | 12 |
The exchange rate is £1 = €1.17.
Work out how much he will get in total when he changes these notes.
Also involves Rounding
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.
Also involves Converting between units
Sunil makes 7.5 litres of soup, correct to the nearest 0.5 litre. He serves the soup in 300 ml portions, correct to the nearest 10 ml. 24 people order this soup.
Does Sunil definitely have enough soup to serve the 24 people? Show how you decide.
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