OCR GCSE Maths
Also involves Angle facts
The pie chart shows the proportion of games won by a sports team.
The sports team won 9 games.
Work out how many games the sports team played.
The ratio of the number of games drawn by the sports team to the number of games lost by the sports team was 2: 1.
Complete the pie chart above.
Write a number in each box to make each statement true.
Also involves Tables, charts and diagrams
A food stall only sells burgers and hotdogs. Each burger or hotdog is sold either with onions or with no onions.
The frequency tree below shows that one day a total of 270 burgers and hotdogs were sold.
of the food sold on that day were burgers.
Complete the frequency tree.
Show that 40% of the food sold on that day were with onions.
Work out, giving your answers as fractions.
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.
Find the value of d.
Also involves Converting between units
Sasha makes some cupcakes. Each cupcake is topped with red or white or yellow icing. 
of the cupcakes have red icing. 
of the cupcakes have white icing.
Work out the fraction of the cupcakes that have yellow icing.
Sasha makes all of the icing using butter and sugar in the ratio 1: 2. Each cupcake has 60 g of icing.
Sasha uses 0.7 kg of butter to make the yellow icing.
Find the total number of cupcakes Sasha makes. You must show your working.
An examination has two parts. A student scores 10 out of 15 marks on Part 1. They score 4 out of 10 marks on Part 2.
To pass the examination the student needs to score 54% of the total marks.
Show that the student passes the examination.
Find the value of d.
Work out.
÷ 
Give your answer as a mixed number in its simplest form. You must show your working.
Also involves Fractions, decimals and percentages
A bag contains only round tiles and square tiles. Each tile is either black or white.
The ratio of round tiles to square tiles is 3: 1. 45% of all the tiles are round black tiles. 9% of all the tiles are square white tiles.
Show that the proportion of round tiles that are black is less than the proportion of square tiles
that are black.
200 students at a school were asked how they travel to school. The pictogram shows the results for four of the ways they travel to school.
How many students walk to school?
How many more students travel by car to school than travel by tram to school?
The rest of the 200 students cycle to school.
Complete the pictogram to show the number of students who cycle to school.
The total number of students at the school is 800.
What fraction of the students at the school were asked how they travel to school? Give your answer in its simplest form.
The deposit for a holiday is 
of the total cost. A customer pays a deposit of £618.
Calculate the total cost of the holiday.
Work out.
Work out.
Give your answer in its simplest form.
Also involves Fractions, decimals and percentages
In a particular town last year:
• it rained on 17 of the 30 days in November
• it rained on 18 of the 31 days in December.
Which month, November or December, had the highest proportion of rainy days? Show how you decide.
Sam says, I think the probability it will rain on December 25th next year is 
What assumption has Sam made?
Machine A makes enough lollipops to fill 300 packs.
There are 8 lollipops in each pack.
Show that 2400 lollipops are made by machine A.
Machine B makes 3600 lollipops in the same time it took by machine A to make 2400 lollipops.
Machine B makes lollipops one at a time and at a constant rate.
What fraction of the time needed to fill 300 packs is saved if machine B is used rather than machine A? Give your answer in its simplest form.
Work out.
Also involves Forming and solving equations
Work out.
131 
8
2x × 4y = 16
A bag only contains red counters and blue counters. 
of the counters are red. There are 20 blue counters.
Complete the table to show the fraction of the counters that are blue and the number of red counters.
| red | blue | |
| fraction | 3 7 | ................... |
| number | ................... | 20 |
A sports team scored 400 points. The defenders scored 
of the points. The midfielders and the forwards scored the remainder of the points in the ratio 1: 5.
Find the percentage of the 400 points that were scored by the forwards. You must show your working.
Work out the following, giving each answer as a fraction in its simplest form.
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.
Jane and Kofi both have the same number of newspapers to deliver.
By 8 am
• Jane has delivered 64% of her newspapers
• Kofi has delivered 
of his newspapers.
Who has delivered the greater proportion of their newspapers? Show how you decide.
Work out the smallest possible number of newspapers that Jane must deliver.
A school is deciding on a charity to support. Each student at the school votes for one of four charities, A, B, C or D. The results are to be shown in a pie chart.
This pie chart shows the sector for charity A. Twice as many students voted for charity C than charity B. Twice as many students voted for charity D than charity C.
Show that the sector for charity B will have an angle of 44°.
Complete the pie chart.
39 students voted for charity A.
Calculate the total number of students at the school.
The school asks 80 of the students to choose a new logo from three designs G, H and J. The same results are shown in a pie chart and in a bar chart.
Give one advantage of using the pie chart rather than the bar chart.
Give one disadvantage of using the pie chart rather than the bar chart.
Sasha and Taylor each have a stamp collection.
They organise their stamp collections according to where the stamps come from: United Kingdom (UK), European Union (EU), Other.
The table shows the number of stamps in each collection and the ratio UK: EU: Other.
| Number of stamps | Ratio UK : EU : Other | |
| Sasha’s collection | 1638 | 9 : 3 : 2 |
| Taylor’s collection | 660 | 8 : 1 : 2 |
When they put the two stamp collections together, Sasha and Taylor claim that at least 
of all the stamps come from the UK.
Are they correct? Show how you decide.
They are........ because........
Also involves Standard units and compound measures
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 bottle contains 
litres of cordial.
Work out the maximum number of cups that can be filled from the bottle of cordial. You must show your working.
The diagram shows a number line.
P Q R
Q is the midpoint of PR.
Find the value of R. Give your answer as a mixed number in its simplest form. You must show your working.
Also involves Forming and solving equations
Two bags of fruit contain only apples and bananas. In bag X, the ratio of apples to bananas is 5: 7. In bag Y, 
of the fruit are apples.
Finley says
Bag X and bag Y contain the same number of apples.
Tick the correct statement.
Show how you decided.
Finley adds 4 apples to bag X. The ratio of apples to bananas is now 11: 14.
How many bananas are in bag X?
What fraction of this shape is shaded?
Write down 50% of 80.
Use your answer to part (a)(i) to complete this statement.
50% of 80 is the same as........ % of 160
Write 36 as a fraction of 120. Give your answer in its simplest form.
Work out.
Give your answer as a mixed number.
Work out.
Also involves Forming and solving equations
A bag contains only red, green and blue counters.
• 8 of the counters are red.
• 15 of the counters are green.
• The rest of the counters are blue.
Sam chooses one counter at random from the bag. The probability that this is a green counter is 
Work out the number of blue counters in the bag.
A student has a pencil case containing 60 pencils. 
of the pencils are red. 
of the red pencils need sharpening.
Work out how many of the red pencils need sharpening.
Dev and Emma share some money in the ratio 2: 3.
Dev says
What mistake has Dev made? Give the fraction of the money Dev actually receives.
The fraction of the money Dev receives is........
Dev receives £100.
Work out how much money Dev and Emma shared between them.
Work out.
Give your answer as a fraction in its simplest form.
Finley has 72 sweets. Finley gives
• 25% of the sweets to Alex
Complete this statement by writing the missing value in the box.
Work out.
Work out, giving your answer as a fraction in its simplest form. 2 15 5× 16
Also involves Converting between units
Taylor performs in a show. Taylor spends 
of the show singing, 
of the show dancing and the remaining 55 minutes backstage.
Work out how long the show lasted. Give your answer in hours and minutes. You must show your working.
Work out.
Give your answer as a fraction in its simplest form.
Work out.
where 
is a fraction in its lowest terms. Find the value of p and the value of q.
Write a number in each box to make each statement true.
Box A contains 56 books. Box B contains 75 books.
Ling has read 
of the books in box A. Ling has also read the same number of books in box B.
Work out the fraction of the books in box B that Ling has read. Give your answer as a fraction in its lowest form.
Work out.
A straight line, L, is shown below.
Write down the ratio v: h when the gradient of line L is 4.
Find the gradient of line L as a fraction in its simplest form when v: h = 14: 6.
Layla and Jamal open a box of sweets. Layla and Jamal share all of the sweets in the ratio 2: 3.
Write down the fraction of the sweets that Layla receives.
Layla eats some of her sweets. She is then left with 18% of the sweets that were in the box.
Work out the percentage of her sweets that Layla has eaten.
It takes a librarian 
minutes to put a plastic cover on a book.
Complete this statement by writing a positive whole number in each box to make two different but equivalent fractions.
Complete this statement by writing a possible positive whole number in the box.
Layla and Jamal open a box of sweets. Layla and Jamal share all of the sweets in the ratio 2: 3.
Write down the fraction of the sweets that Layla receives.
Layla eats some of her sweets. She is then left with 18% of the sweets that were in the box.
Work out the percentage of her sweets that Layla has eaten.
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 Forming and solving equations
A pattern is made out of blue tiles and yellow tiles. 
of the tiles are blue. There are 36 yellow tiles.
Work out the total number of tiles.
120 new homes are built in a village. Each home is either a house or a flat. Each home either has a garage or does not have a garage. 64 of the houses have a garage and 26 of the flats have a garage.
This frequency tree shows the above information.
of the homes are houses.
Complete the frequency tree.
Show that 75% of the homes have a garage.
What fraction of this shape is shaded?
What percentage of this shape is shaded?
Write 0.2 as a fraction. Give your answer in its simplest form.
Work out 80% of 30.
Also involves Standard units and compound measures
In a recipe, the ratio of the amount of flour needed to the amount of butter needed is 4: 1. Rowan mixes 4 kg of flour with 1 g of butter.
Explain what Rowan has done wrong.
Azmi gives 
of their earnings to charity and keeps the remainder. For Azmi’s earnings, find the ratio of the amount they give to charity to the amount they keep.
Give your answer in its simplest form.
Each edge of a fair spinner is coloured either red or blue.
The scale shows the probability of the spinner landing on red and of landing on blue.
Write down, as a fraction, the probability of the spinner landing on red.
Show that the spinner could not have 15 edges.
In a fish tank, the fish are either blue or gold or red.
There are 22 red fish. 
of the fish are blue. 
of the fish are gold. Work out the total number of fish in the fish tank. You must show your working.
Work out 
× 
giving your answer as a fraction in its simplest form. You must show your working.
In a quiz, Darcy answered 16 of the 20 questions correctly.
What fraction of the questions did Darcy answer correctly? Give your fraction in its lowest terms.
Write the fraction as a decimal.
Work out.
There are 150 coins in a jar. 20% of the coins are 10p coins. 
of the coins are 20p coins. The rest of the coins are 50p coins.
Work out the total value, in £, of the 150 coins. You must show your working.
Rowan’s bath has a hot tap and a cold tap. When turned on full, each tap on its own will fill the bath in 6 minutes.
Rowan turns both taps on full.
How long will it take to fill the bath?
Work out.
Give your answer as a mixed number in its simplest form.
Write 0.16 as a fraction in its simplest form.
Also involves Rounding
Charlie and Jasmine share cartons of apple juice. Charlie drinks 
of a carton every day. Jasmine drinks 
of a carton every day.
Any apple juice left in a carton at the end of the day is used the following day.
The cost of a carton is 70p. Charlie and Jasmine buy just enough cartons to last them for 10 days.
How much do they spend in total for these cartons? Give your answer in £. Show your working.
Work out 70% of 50.
Beth multiplies a number by 3 and divides the answer by 10.
By what fraction has the number been reduced?
Find a fraction which is bigger than 
and smaller than 
Also involves The four operations
Jo walks every day. This week she walked an average of 2300 steps a day. Next week she plans to increase this by 15%.
Work out how many steps she plans to walk in total next week?
Jo buys a pair of walking boots for £63 in a sale. She saves 
of the original price of the boots.
Work out how much money Jo saves.
Also involves Converting between units
The ratio 45 minutes to 3 hours 45 minutes can be written in the form 1: n.
Find the value of n.
Reece and Sarah share some money in the ratio 9: 16.
Reece says that Sarah gets more than 60% of this money.
Show that Reece is correct.
Also involves Rounding
Charlie and Jasmine share cartons of apple juice. Charlie drinks 
of a carton every day. Jasmine drinks 
of a carton every day.
Any apple juice left in a carton at the end of the day is used the following day.
The cost of a carton is 70p. Charlie and Jasmine buy just enough cartons to last them for 10 days.
How much do they spend in total for these cartons? Give your answer in £. Show your working.
A bag of sweets contains only mints, sherberts and toffees.
The ratio of the number of mints to sherberts is 2: 3. The ratio of the number of sherberts to toffees is 7: 5.
What fraction of the sweets are sherberts?
Work out.
Give your answer in its simplest form.
By writing each number correct to 1 significant figure, use estimation to show that
On a plane, 
of the passengers were British. 30% of the British passengers were men. There were 36 British men on the plane.
Find the total number of passengers on the plane.
Dani has a pack of 45 cards. Each card is either red or black.
One-third of the cards in the pack are red.
She picks two cards from the pack, without replacement.
Calculate the probability that Dani picks two black cards.
Complete each statement.
Work out.
One day, a group of people had a driving test. 40 of this group were men and the rest were women. 
of the men and 
of the women passed the driving test. The number of men and women that passed the driving test was the same.
Work out the number of women that took the driving test that day.
The pie chart shows how Jack spent his time one evening.
On which activity did Jack spend most time?
Jack says
Show that he is not correct.
The pie chart represents 5 hours.
Find the time, in hours and minutes, that Jack spent reading.
Also involves Probability
A bag contains some counters.
• There are 300 counters in the bag.
• There are only red, white and blue counters in the bag.
• The probability of picking a blue counter is 
• The ratio of red counters to white counters is 2: 1.
Calculate the number of red counters in the bag.
Also involves Fractions, decimals and percentages
120 students in Year 10 and Year 11 sit a test.
• 61 of the students are in Year 10.
• 83 of the students are right-handed.
• 20 of the students in Year 11 are left-handed.
One of the students in Year 10 and one of the students in Year 11 are chosen at random.
Which one is more likely to be left-handed? Show your working. You may use the table if you wish.
Mrs Mills buys 4 packs of treats for her cats, Fluff and Tigger. She gives Fluff 
of a pack each day. She gives Tigger 
of a pack each day. For how many complete days will the 4 packs of treats last?
Elsa divides a two-digit number by another two-digit number. She gets the answer 
.
She says that there is only one possible pair of numbers that will give this answer. Is she correct? Show how you decide.
A bag contains some counters.
• There are 300 counters in the bag.
• There are only red, white and blue counters in the bag.
• The probability of picking a blue counter is
• The ratio of red counters to white counters is 2: 1.
Calculate the number of red counters in the bag.
Work out.
Give your answer as a mixed number.
Isaac and Maya eat part of a pizza. Isaac eats 
of the pizza. Maya then eats 
of the remaining pizza. What fraction of the original pizza is left?
Write 42% as a fraction. Give your answer in its simplest form.
Also involves Angle facts
30 people choose their favourite sport. Matt wants to show their choices in a pie chart. 4 of the people chose ‘tennis’.
Work out the angle of the sector for ‘tennis’.
Sally has 30 feet of ribbon. She cuts strips each of length 
feet from the ribbon. Sally says
I can cut 13 of these strips from this ribbon.
Is she correct? Show how you decide.
Elise wants to divide a sum of money between Hannah and Adil in the ratio 2: 3.
Elise says: Hannah will get 
of the money.
Explain why Elise is not correct.
George has a different sum of money. He divides the money between Siobhan and Iwan. Iwan receives 
of the money. Write the ratio of the money that Siobhan receives to the money that Iwan receives.
Liu has a bag only containing red grapes and green grapes. 
of the grapes are red.
If there are 8 red grapes in the bag, how many grapes are green?
Sophia has a different bag only containing red grapes and green grapes.
She picks out a red grape from her bag and eats it.
How many of the remaining grapes in her bag are red and how many are green?
Calculate.
Give your answer as a mixed number in its simplest form.
Work out.
5 × 104 – 1.6 × 103
Give your answer in standard form.
Calculate.
Give your answer as a mixed number in its simplest form.
Work out.
Give your answer in standard form.
A box contains only red, blue and green pens. The ratio of red pens to blue pens is 5: 9. The ratio of blue pens to green pens is 1: 4.
Calculate the percentage of pens that are blue.
72 students each took a theory test followed by a practical test. They either passed or failed each test.
This frequency tree shows some of the results.
How many students passed both tests?
Complete the frequency tree.
Which test was passed by more students? Explain your reasoning.
Write 0.26 as a fraction. Give your answer in its simplest form.
Write down all the possible values of n.
Also involves Forming and solving equations
Two bags each contain only red counters and yellow counters.
In Bag A, the ratio of red counters to yellow counters is 1: 4.
Sharon says
The proportion of the counters that are red is the same in both bags.
Explain why Sharon is not correct.
The number of counters in the two bags is the same.
Complete the table below to show how many counters of each colour could be in the bags.
In another bag, Bag C, the ratio of red counters to yellow counters is 3: 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3: 5.
How many yellow counters are in Bag C?
Diners choose one starter and one main from the options given in the table below. Vegetarian dishes are indicated with a (v).
| Starter | Main |
| Cheese salad (v) | Steak and chips |
| Prawn cocktail | Fish and chips |
| Mozzarella sticks (v) | Tomato pizza (v) |
| Pork chops | |
| Nut cutlet (v) |
Work out the fraction of all the meal combinations which have at least one vegetarian option.
Diners also choose one of 6 dessert options.
How many different three-course meal combinations are available?
Also involves The four operations
Here are the results of a survey of 437 people in a town.
• 62 males speak Spanish.
• 153 females do not speak Spanish.
• 280 people do not speak Spanish.
Jeff says
At least 2 out of every 5 females in the town can speak Spanish.
Is he correct? Show clearly how you reached your decision.
Also involves Forming and solving equations
Two bags each contain only red counters and yellow counters.
In Bag A, the ratio of red counters to yellow counters is 1: 4.
Sharon says
The proportion of the counters that are red is the same in both bags.
Explain why Sharon is not correct.
The number of counters in the two bags is the same.
Complete the table below to show how many counters of each colour could be in the bags.
In another bag, Bag C, the ratio of red counters to yellow counters is 3: 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3: 5.
How many yellow counters are in Bag C?
Also involves Fractions, decimals and percentages
Karen made 40 cakes. She gives 
of the cakes to Andrew. She gives 10% of the 40 cakes to Chris.
What fraction of the 40 cakes does she have left?
Also involves Converting between units
The ratio 20 minutes to 1 hour can be written in the form 1: n.
Find the value of n.
The scale on a map is 1: 25 000.
How many kilometres on the ground is represented by 6 cm on the map?
Kiri and Peter share some sweets in the ratio 6: 7.
What fraction of the sweets does Kiri receive?
Work out.
Also involves Forming and solving equations
There are 20 coins in a pot. The coins are 1p, 2p, 5p and 10p.
A coin is taken at random from the pot.
• The probability that it is a 1p coin is 
• The probability that it is a 2p coin is 
The total value of the coins in the pot is 57 pence.
Work out how many of each type of coin there are in the pot.
1p........, 2p........, 5p........, 10p........
Give your answer in its lowest terms.
Last year, Katie earned £16 200. Her total loan repayments were £6400.
Katie estimates that the ratio of her loan repayments to her earnings is approximately 3: 8.
Is she correct? Show your reasoning.
George is the manager of a shoe shop. He samples 50 of his customers and asks them about the one style of shoe they would buy next. The table shows his results.
| Style of shoe | Number of customers |
| Laced shoes | 18 |
| Boots | 15 |
| Sandals | 8 |
| Trainers | 5 |
| Other | 4 |
George buys 1000 pairs of shoes with the number of each style based on his survey results.
How many pairs of sandals should he buy? Write down any assumption you make about his sample.
Give your answer in its lowest terms.
George is the manager of a shoe shop. He samples 50 of his customers and asks them about the one style of shoe they would buy next. The table shows his results.
| Style of shoe | Number of customers |
| Laced shoes | 18 |
| Boots | 15 |
| Sandals | 8 |
| Trainers | 5 |
| Other | 4 |
George buys 1000 pairs of shoes with the number of each style based on his survey results.
How many pairs of sandals should he buy? Write down any assumption you make about his sample.
Of those students who study a language, 
study Spanish. Find the ratio of students who study Spanish to students who do not study Spanish.
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