Edexcel GCSE Maths
Topic questions Ratio, proportion and rates of change Compound measures
114 questions · 425 marks · about 8 hours
Jamie drives his van for 150 minutes. He stops for a rest. Jamie then drives for a further 75 minutes.
Show that Jamie drives for less than 4 hours in total.
A car travels for 2 hours at a steady speed of 65 mph.
Work out the distance the car travels.
A train travels from Derby to Sheffield. The travel graph shows information about the train’s journey.
Work out the speed of the train. Give your answer in miles per hour.
The train stays at Sheffield for 15 minutes.
Show this information on the travel graph.
27Metal rods are made from steel with density 8 g/cm3 Each metal rod has a volume of 1500 cm3 The maximum mass of metal rods that can be put on a trolley is 300 kg. Work out the greatest number of metal rods that can be put on the trolley.
Metal rods are made from steel with density 8 g/cm3 Each metal rod has a volume of 1500 cm3 The maximum mass of metal rods that can be put on a trolley is 300 kg. Work out the greatest number of metal rods that can be put on the trolley.
In London, 2 kg of carrots cost £3.75 In New York, 5 lbs of carrots cost 4.90 US dollars. £1 = 1.20 US dollars 1 kg = 2.2 lbs In which city are carrots better value for money, London or New York? You must show how you get your answer.
A plane takes 2 hours 24 minutes to fly from Luton to Alicante. The plane flies a distance of 1512 kilometres. Work out the average speed of the plane. Give your answer in kilometres per hour.
........ kilometres per hour
In London, 2 kg of carrots cost £3.75 In New York, 5 lbs of carrots cost 4.90 US dollars. £1 = 1.20 US dollars 1 kg = 2.2 lbs In which city are carrots better value for money, London or New York? You must show how you get your answer.
A plane takes 2 hours 24 minutes to fly from Luton to Alicante. The plane flies a distance of 1512 kilometres. Work out the average speed of the plane. Give your answer in kilometres per hour.
........ kilometres per hour
A car travelled 4.96 miles at an average speed of 30.4 miles per hour.
Work out an estimate for the time taken by the car. Give your answer in minutes.
Is your answer to part (a) an underestimate or an overestimate? Give a reason for your answer.
A car travelled 4.96 miles at an average speed of 30.4 miles per hour.
Work out an estimate for the time taken by the car. Give your answer in minutes.
Is your answer to part (a) an underestimate or an overestimate? Give a reason for your answer.
The diagram shows a solid triangular prism on a horizontal floor.
The face in contact with the floor is a rectangle of width 2 m. The pressure on the floor due to the prism is 80 newtons/m2 The force exerted by the prism on the floor is 720 newtons. Work out the length of the prism.
Also involves Converting between units
In London, a 200 g Choci bar costs £3.50 In Zurich, a 360 g Choci bar costs 7.20 Swiss francs. The exchange rate is £1 = 1.25 Swiss francs. In which city is the Choci bar the better value for money, in London or in Zurich? You must show how you get your answer.
The diagram shows a solid cylinder with base radius 3 cm and height 10 cm.
The cylinder is made from steel. It has a mass of 2250 g. Work out the density of the steel. Give your answer correct to 3 significant figures.
In London, a 200 g Choci bar costs £3.50 In Zurich, a 360 g Choci bar costs 7.20 Swiss francs. The exchange rate is £1 = 1.25 Swiss francs. In which city is the Choci bar the better value for money, in London or in Zurich? You must show how you get your answer.
The diagram shows a solid cylinder with base radius 3 cm and height 8 cm. It also shows a solid cube with side length hcm.
The cylinder is made from steel with a density of 7.86 g/cm3 The cube is made from brass with a density of 8.5 g/cm3 The mass of the cylinder is equal to the mass of the cube. Work out the value of h. Give your answer correct to 1 decimal place.
Harry works in a shop. From Monday to Friday his basic rate of pay is £8 per hour. On Saturday and Sunday, Harry’s rate of pay is 1 
times his basic rate of pay. The table shows the number of hours Harry worked each day last week.
| Day | Mon | Tue | Wed | Thu | Fri | Sat | Sun |
| Hours worked | 6 | 6 | 6 | 6 | 6 | 4 | 3 |
Work out Harry’s total pay last week.
Also involves Fractions
16Batteries are sold in packs of 4, in packs of 8 and in packs of 12
A pack of 4 batteries costs £1.80 A pack of 8 batteries costs £3.20 A pack of 12 batteries costs £6.00 Which pack gives the best value for money? You must show how you get your answer.
The diagram shows a plan of a floor.
Petra is going to cover the floor with paint. Petra has 3 tins of paint. There are 2.5 litres of paint in each tin. Petra thinks 1 litre of paint will cover 10 m2 of floor.
Assuming Petra is correct, does she have enough paint to cover the floor? You must show all your working.
Actually, 1 litre of paint will cover 11 m2 of floor.
Does this affect your answer to part (a)? You must give a reason for your answer.
On Monday, Lizzie cycled 36 kilometres in 3 hours.
Work out Lizzie’s average speed.
........ kilometres per hour On Tuesday, Lizzie cycled 36 kilometres at an average speed of 16 kilometres per hour. Lizzie says that the total time she cycled on Monday and Tuesday was less than 5 hours 20 minutes.
Is Lizzie correct? You must show how you get your answer.
Also involves Volume and surface area
Habib has two identical tins. He puts 600 grams of flour into one of the tins. The flour fills the tin completely. The density of the flour is 0.6 g/cm3 Habib puts 600 grams of salt into the other tin. The salt does not fill the tin completely. The volume of the space in the tin that is not filled with salt is 700 cm3 Work out the density of the salt. You must show all your working.
A paddling pool is in the shape of a cylinder.
The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm3 per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.
Habib has two identical tins. He puts 600 grams of flour into one of the tins. The flour fills the tin completely. The density of the flour is 0.6 g/cm3 Habib puts 600 grams of salt into the other tin. The salt does not fill the tin completely. The volume of the space in the tin that is not filled with salt is 700 cm3 Work out the density of the salt. You must show all your working.
A paddling pool is in the shape of a cylinder.
The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm3 per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.
25A piece of glass has a mass of 27 g and a volume of 10 cm3 Work out the density of the piece of glass.
Lydia works for 4 hours. She is paid £50 How much is Lydia paid per hour?
A car travels at an average speed of 37 miles per hour for 3 hours. Work out the distance that the car travels in the 3 hours.
3 kg of flour costs £4.05 5 kg of flour and 6 kg of sugar cost £11.85 Work out the cost of 2 kg of flour and 5 kg of sugar.
The diagram shows an empty tank in the shape of a cylinder.
The cylinder has radius 15 cm and height 43 cm. Water flows into the tank at a rate of 0.47 litres per minute. Calculate the number of minutes it will take to completely fill the tank. Give your answer correct to the nearest minute.
Blake works 32 hours a week in the UK. She is paid £473.28 per week. Blake applies for a job in Australia. The rate of pay is 26.40 Australian dollars per hour. £1 = 1.796 Australian dollars Blake thinks the rate of pay in Australia is greater than the rate of pay in the UK. Is Blake correct? You must show how you get your answer.
Riley travelled by car and by aeroplane. He travelled 143 miles by car at an average speed of 55 miles per hour. Riley then travelled for 5 hours and 20 minutes by aeroplane. Work out, in hours and minutes, Riley’s total travelling time.
Also involves Volume and surface area
27The diagram shows a solid cube placed on a horizontal table.
The pressure on the table due to the cube is 3.5 newtons/cm2 The force exerted by the cube on the table is 504 newtons. Show that the total surface area of the cube is less than 900 cm2
Riley travelled by car and by aeroplane. He travelled 143 miles by car at an average speed of 55 miles per hour. Riley then travelled for 5 hours and 20 minutes by aeroplane. Work out, in hours and minutes, Riley’s total travelling time.
The diagram shows a solid cube placed on a horizontal table.
The pressure on the table due to the cube is 3.5 newtons/cm2 The force exerted by the cube on the table is 504 newtons. Show that the total surface area of the cube is less than 900 cm2
The diagram shows a solid cylinder on a horizontal floor.
The cylinder has a volume of 1200 cm3 height of 40 cm. The cylinder exerts a force of 90 newtons on the floor. Work out the pressure on the floor due to the cylinder.
The diagram shows a solid cylinder on a horizontal floor.
The cylinder has a volume of 1200 cm3 height of 40 cm. The cylinder exerts a force of 90 newtons on the floor. Work out the pressure on the floor due to the cylinder.
Paulo drives at an average speed of 56 km / h for 1 hour 45 minutes. Work out the distance Paulo drives.
Asha buys 180 cans of cola. The cans are sold in packs. There are 12 cans in each pack. Each pack costs £3
Work out the total cost of the cola Asha buys.
Ethan buys a box of 24 cans of lemonade for £7 There are 330 ml of lemonade in each can.
Work out the cost of 100 ml of lemonade. Give your answer correct to the nearest penny.
Rowena drove from her home to a beach. Here is a travel graph for her journey.
Rowena stopped at a cafe on her way to the beach.
How many minutes did Rowena take to drive to the cafe?
Write down the distance from Rowena’s home to the cafe.
Rowena stayed at the beach for 1 
hours. She then drove home without stopping. Rowena arrived home at 16 00
On the grid, complete the travel graph.
Work out the average speed for the journey from the beach to Rowena’s home.
120 boxes cost £6 270 bags cost £10 A bag is cheaper than a box. How much cheaper? Give your answer in pence correct to 1 decimal place.
25Lava flows from a volcano at a constant rate of 11.9 m3/s How many days does it take for 67 205 600 m3 of lava to flow from the volcano? Give your answer correct to the nearest day.
A solid cuboid is made of metal. The metal has a density of 9 g/cm3 The volume of the cuboid is 72 cm3 Work out the mass of the cuboid.
Lava flows from a volcano at a constant rate of 11.9 m3/s How many days does it take for 67 205 600 m3 of lava to flow from the volcano? Give your answer correct to the nearest day.
A solid cuboid is made of metal. The metal has a density of 9 g/cm3 The volume of the cuboid is 72 cm3 Work out the mass of the cuboid.
14Jenny drives from London to Swindon at an average speed of 54 miles per hour. She drives for 1 
hours.
Work out the distance from London to Swindon.
Aleksy is using a map. The map has a scale of 1: 25 000 On the map a road has a length of 6 cm.
Work out the length, in kilometres, of the real road.
A storage tank exerts a force of 10 000 newtons on the ground. The base of the tank in contact with the ground is a 4 m by 2 m rectangle. Work out the pressure on the ground due to the tank.
........ newtons / m2
A storage tank exerts a force of 10 000 newtons on the ground. The base of the tank in contact with the ground is a 4 m by 2 m rectangle. Work out the pressure on the ground due to the tank.
........ newtons / m2
A shop has two different special offers on milk.
Pay for 2 bottles Pay for 1 bottle get 1 bottle free get 1 bottle half price Which offer gives the better value for money? You must show how you get your answer.
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.
2.5 kg of onions and 2 kg of carrots cost a total of £2.36 3 kg of carrots cost £1.74 Stuart has £2 He wants to buy 4 kg of onions. Does Stuart have enough money to buy 4 kg of onions? You must show how you get your answer.
Carly cycles to her friend’s house. She stays at her friend’s house for a number of minutes. Then she cycles home. Here is the travel graph for her journey.
For how many minutes did Carly stay at her friend’s house?
How far is Carly from her home at 08 50?
Work out Carly’s speed, in km/h, for the first 20 minutes of her journey.
The pyramid P is formed from two parts made of different materials.
The top part of P has a mass of 92.8 g and is made from material with a density of 2.9 g/cm3 The bottom part of P has a mass of 972.8 g The average density of P is 4.7 g/cm3 Calculate the volume of the top part of P as a percentage of the total volume of P. Give your answer correct to 1 decimal place. You must show all your working.
Savio leaves his home at 07 30 to drive to work. He drives a distance of 50 miles. Savio thinks he drives at an average speed of 40 miles per hour.
If Savio is correct, at what time will he arrive at work?
In fact, Savio’s average speed was greater than 40 miles per hour.
How does this affect your answer to part (a)?
Here are two cubes, A and B.
Cube A has a mass of 81 g. Cube B has a mass of 128 g. Work out the density of cube A: the density of cube B Give your answer in the form a: b, where a and b are integers.
Also involves Volume and surface area
Here are two cubes, A and B.
Cube A has a mass of 81 g. Cube B has a mass of 128 g. Work out the density of cube A: the density of cube B Give your answer in the form a: b, where a and b are integers.
Also involves Area and perimeter
24Festival A will be in a rectangular field with an area of 80 000 m2 The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700 m by 2000 m. The greatest number of people allowed to attend Festival B is 6750 The area per person allowed for Festival B is greater than the area per person allowed for Festival A.
How much greater? Give your answer correct to the nearest whole number.
Callum says, “300 cm2 is the same as 3 m2 because there are 100 cm in 1 m so you divide by 100” Callum’s method is wrong.
Explain why.
In Spain, Sam pays 27 euros for 18 litres of petrol. In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol. 1 euro = £0.85 4.5 litres = 1 gallon Sam thinks that petrol is cheaper in Spain than in Wales. Is Sam correct? You must show how you get your answer.
Also involves Area and perimeter
Festival A will be in a rectangular field with an area of 80 000 m2 The greatest number of people allowed to attend Festival A is 425 Festival B will be in a rectangular field 700 m by 2000 m. The greatest number of people allowed to attend Festival B is 6750 The area per person allowed for Festival B is greater than the area per person allowed for Festival A.
How much greater? Give your answer correct to the nearest whole number.
Callum says, “300 cm2 is the same as 3 m2 because there are 100 cm in 1 m so you divide by 100” Callum’s method is wrong.
Explain why.
In Spain, Sam pays 27 euros for 18 litres of petrol. In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol. 1 euro = £0.85 4.5 litres = 1 gallon Sam thinks that petrol is cheaper in Spain than in Wales. Is Sam correct? You must show how you get your answer.
The face in contact with the floor is a rectangle of length 1.2 metres and width x metres. Work out the value of x.
Jo is going to buy 15 rolls of wallpaper. Here is some information about the cost of rolls of wallpaper from each of two shops.
Jo wants to buy the 15 rolls of wallpaper as cheaply as possible. Should Jo buy the wallpaper from Chic Decor or from Style Papers? You must show how you get your answer.
Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour.
Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs. Work out Amy’s average speed. Give your answer in miles per hour.
3 kg of carrots cost £1.80 2 kg of carrots and 5 kg of potatoes cost a total of £3.45 Work out the total cost of 4 kg of carrots and 2 kg of potatoes. You must show all your working.
Nazima uses this graph to find out how much money she is paid for the number of hours she has worked.
How much money is Nazima paid for each hour she works?
Last week Nazima worked for 36 hours.
How much money was Nazima paid?
Sam drives his car on a journey. Here is the travel graph for the first 15 minutes of his journey.
Work out Sam’s speed, in km/h, for the first 15 minutes of his journey.
At 10 15 Sam stops for 10 minutes and then drives for 20 minutes at a speed of 75 km/h.
On the grid, complete the travel graph for Sam’s journey.
Sam drives his car on a journey. Here is the travel graph for the first 15 minutes of his journey.
Work out Sam’s speed, in km/h, for the first 15 minutes of his journey.
At 10 15 Sam stops for 10 minutes and then drives for 20 minutes at a speed of 75 km/h.
On the grid, complete the travel graph for Sam’s journey.
Liquid A has a density of 1.8 g/cm3 Liquid B has a density of 1.2 g/cm3 80 cm3 of liquid A is mixed with 40 cm3 of liquid B to make 120 cm3 of liquid C. Work out the density of liquid C.
Write 196 minutes in hours and minutes.
A train travels x miles in 2 hours.
Write down an expression, in terms of x, for the average speed of the train.
Natalie makes potato cakes in a restaurant. She mixes potato, cheese and onion so that weight of potato: weight of cheese: weight of onion = 9: 2: 1 Natalie needs to make 6000 g of potato cakes. Cheese costs £2.25 for 175 g. Work out the cost of the cheese needed to make 6000 g of potato cakes.
A water tank is empty. Anil needs to fill the tank with 2400 litres of water. Company A supplies water at a rate of 8 litres in 1 minute 40 seconds. Company B supplies water at a rate of 2.2 gallons per minute. 1 gallon = 4.54 litres Company A would take more time to fill the tank than Company B would take to fill the tank. How much more time? Give your answer in minutes correct to the nearest minute.
Natalie makes potato cakes in a restaurant. She mixes potato, cheese and onion so that weight of potato: weight of cheese: weight of onion = 9: 2: 1 Natalie needs to make 6000 g of potato cakes. Cheese costs £2.25 for 175 g. Work out the cost of the cheese needed to make 6000 g of potato cakes.
A water tank is empty. Anil needs to fill the tank with 2400 litres of water. Company A supplies water at a rate of 8 litres in 1 minute 40 seconds. Company B supplies water at a rate of 2.2 gallons per minute. 1 gallon = 4.54 litres Company A would take more time to fill the tank than Company B would take to fill the tank. How much more time? Give your answer in minutes correct to the nearest minute.
27The diagram shows a prism placed on a horizontal floor.
The prism has height 3 m The volume of the prism is 18 m3 The pressure on the floor due to the prism is 75 newtons/m2 Work out the force exerted by the prism on the floor.
The diagram shows a prism placed on a horizontal floor.
The prism has height 3 m The volume of the prism is 18 m3 The pressure on the floor due to the prism is 75 newtons/m2 Work out the force exerted by the prism on the floor.
Liquid A and liquid B are mixed to make liquid C. Liquid A has a density of 70 kg/m3 Liquid A has a mass of 1400 kg Liquid B has a density of 280 kg/m3 Liquid B has a volume of 30 m3 Work out the density of liquid C.
Pens and pencils are sold in a shop. 12 pencils cost £1.80 The ratio of the cost of a pen to the cost of a pencil is 7: 3 Work out the cost of 5 pens.
Also involves The four operations
Here are the costs of the same type of batteries in two shops.
Harry needs to buy at least 30 batteries. He assumes that he has to buy batteries in whole packs. Harry wants to buy the batteries as cheaply as possible from the same shop.
Which shop should he buy the batteries from, shop A or shop B? You must show all your working.
Harry’s assumption is wrong. He can buy single batteries for 40p each in shop A and for 45p each in shop B.
Does this affect which of these two shops Harry should buy the batteries from? Give a reason for your answer.
Andy cycles a distance of 30 km at an average speed of 24 km/h. He then runs a distance of 12 km at an average speed of 8 km/h. Work out the total time Andy takes. Give your answer in hours and minutes.
29The diagram shows a solid triangular prism.
The prism is made from wood with a density of 0.8 g/cm³ Work out the mass of this prism.
Andy cycles a distance of 30 km at an average speed of 24 km/h. He then runs a distance of 12 km at an average speed of 8 km/h. Work out the total time Andy takes. Give your answer in hours and minutes.
Also involves Real-life graphs
Steve drove from his home to his friend’s house. He stayed at his friend’s house and then drove home.
Here is Steve’s travel graph.
For how many minutes did Steve stay at his friend’s house?
What was Steve’s average speed on his journey home?
Also involves Limits of accuracy and bounds · Scale factors, scale diagrams and maps
The accurate scale drawing shows the positions of port P and a lighthouse L.
Aleena sails her boat from port P on a bearing of 070°
the distance, in km, of port Q from lighthouse L,
the bearing of port Q from lighthouse L.
Also involves Converting between units
A car travels for 18 minutes at an average speed of 72 km/h.
How far will the car travel in these 18 minutes?
David says,
“72 kilometres per hour is faster than 20 metres per second.”
Is David correct? You must show how you get your answer.
Nimer was driving to a hotel. He looked at his Sat Nav at 13 30
| Time | 13 30 |
| Distance to destination | 65 miles |
Nimer arrived at the hotel at 14 48
Work out the average speed of the car from 13 30 to 14 48 You must show all your working.
Nimer was driving to a hotel. He looked at his Sat Nav at 13 30
| Time | 13 30 |
| Distance to destination | 65 miles |
Nimer arrived at the hotel at 14 48
Work out the average speed of the car from 13 30 to 14 48 You must show all your working.
Liquid A and liquid B are mixed together in the ratio 2: 13 by volume to make liquid C.
Liquid A has density 1.21 g/cm3 Liquid B has density 1.02 g/cm3
A cylindrical container is filled completely with liquid C. The cylinder has radius 3 cm and height 25 cm.
Work out the mass of the liquid in the container. Give your answer correct to 3 significant figures. You must show all your working.
Ruth left her home at 9 am and walked to the library. She got to the library at 10 30 am. Ruth walked at a speed of 4 mph.
Work out the distance Ruth walked.
Ruth got to the library at 10 30 am. She stayed at the library for 50 minutes. Then she walked home.
hours to walk home.
At what time did Ruth get home?
Machine A and machine B both make car parts. Machine A makes 6 parts every 10 minutes. Machine B makes 13 parts every 15 minutes. On Monday machine A makes parts for 12 hours machine B makes parts for 10 hours Work out the total number of parts made by the two machines on Monday.
In October Sally drove 560 miles in her car. The car travelled 34.5 miles for each gallon of petrol used. Petrol cost £1.08 per litre. 1 gallon 4.55 litres. Work out the cost of the petrol the car used in October.
In May 2019, the distance between Earth and Mars was 3.9 
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 
105 km per second,
how long did the signal take to get to Mars?
The speed of the signal sent from Earth to Mars in May 2019 was actually less than 3 
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.
Food Mart and Jan’s Store sell boxes of the same type of breakfast cereal.
Each shop has a special offer.
Which box of cereal is the better value for money? You must show your working.
A plane travels at a speed of 213 miles per hour.
Work out an estimate for the number of seconds the plane takes to travel 1 mile.
Is your answer to part (a) an underestimate or an overestimate? Give a reason for your answer.
A plane travels at a speed of 213 miles per hour.
Work out an estimate for the number of seconds the plane takes to travel 1 mile.
Is your answer to part (a) an underestimate or an overestimate? Give a reason for your answer.
Also involves Volume and surface area
Here is a frustum of a cone.
The diagram shows that the frustum is made by removing a cone with height 3.2 cm from a solid cone with height 6.4 cm and base diameter 7.2 cm.
The frustum is joined to a solid hemisphere of diameter 7.2 cm to form the solid S shown
The density of the frustum is 2.4 g/cm3 The density of the hemisphere is 4.8 g/cm3
Calculate the average density of solid S.
Lara is a skier.
She completed a ski race in 1 minute 54 seconds. The race was 475 m in length.
Lara assumes that her average speed is the same for each race.
Using this assumption, work out how long Lara should take to complete a 700 m race. Give your answer in minutes and seconds.
Lara’s average speed actually increases the further she goes.
How does this affect your answer to part (a)?
Lara is a skier.
She completed a ski race in 1 minute 54 seconds. The race was 475 m in length.
Lara assumes that her average speed is the same for each race.
Using this assumption, work out how long Lara should take to complete a 700 m race. Give your answer in minutes and seconds.
Lara’s average speed actually increases the further she goes.
How does this affect your answer to part (a)?
A cycle race across America is 3069.25 miles in length.
Juan knows his average speed for his previous races is 15.12 miles per hour. For the next race across America he will cycle for 8 hours per day.
Estimate how many days Juan will take to complete the race.
Juan trains for the race. The average speed he can cycle at increases. It is now 16.27 miles per hour.
How does this affect your answer to part (a)?
Emily drives 186 miles in 3 hours.
What is her average speed?
Sarah drives at an average speed of 58 mph for 4 hours.
How many miles does Sarah drive?
Helen says, “The pressure decreases by less than 20%”
Is Helen correct? You must show how you get your answer.
Helen says, “The pressure decreases by less than 20%”
Is Helen correct? You must show how you get 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.
Bronwin works in a restaurant.
The table gives her rates of pay.
Bronwin worked for a total of 20 hours last week. She worked 8 of these 20 hours at the weekend.
Show that Bronwin was paid less than £200 last week.
James and Peter cycled along the same 50 km route.
Peter started to cycle 5 minutes after James started to cycle. Peter caught up with James when they had both cycled 15 km.
James and Peter both cycled at constant speeds.
Work out Peter’s speed.
Ellie makes hats. She makes at least 17 hats per hour. She is paid 46p for each hat she makes.
Reaze is a waiter. He works 35 hours and is paid a total of £266
Show that Ellie’s hourly rate of pay is more than Reaze’s hourly rate of pay.
Mr Page uses oil to heat his home.
At the beginning of November there were 1000 litres of oil in his oil tank.
Mr Page bought enough oil to fill the tank completely. He paid 50p per litre for this oil. He paid a total amount of £750
At the end of February Mr Page had 600 litres of oil in the tank. He bought enough oil to fill the tank completely. The cost of oil had increased by 4%.
Work out the total amount Mr Page paid for the oil he bought in February.
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.
Also involves Converting between units
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.
Sean works for a company. His normal rate of pay is £12 per hour.
When Sean works more than 8 hours a day, he is paid overtime for each hour he works more than 8 hours. Sean’s rate of overtime pay per hour is 1 
times his normal rate of pay per hour. On Monday Sean worked for 10 hours.
Work out the total amount of money Sean earned on Monday.
This rectangular frame is made from 5 straight pieces of metal.
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
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.
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.
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).
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