Percentages

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.

The bar chart shows the number of hours per month Riley spends at the gym in each of January, February and March.

How many hours did Riley spend at the gym in February?

Find how many more hours Riley spent at the gym in January compared to March.

In April, Riley spent a total of 18 hours at the gym.

Complete the bar chart for April.

Riley says,

I spent 50% less time at the gym in April than in March.

Is Riley correct? Show how you decide.

Riley is........ because........

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.

A school has three terms, Autumn, Spring and Summer.

In class A there were 90 absences in the Autumn term, 120 absences in the Spring term and 40 absences in the Summer term.

Compared to class A, class B had:

• fewer absences in the Autumn term

• 5% more absences in the Spring term

• 7 more absences in the Summer term.

Design and complete a two-way table to show this information.

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.

A student thinks of a number. The student takes 16 from the number and then divides by 4. The answer is 8.

What number is the student thinking of?

A teacher thinks of a number. 150% of the number is 36.

What number is the teacher thinking of?

The price of a laptop is reduced in a January sale from £450 to £382.50.

Work out the percentage reduction in the price of the laptop.

The graph shows the price of the laptop in the months before the January sale.

Explain why this graph is misleading.

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.

A school has three terms, Autumn, Spring and Summer.

In class A there were 90 absences in the Autumn term, 120 absences in the Spring term and 40 absences in the Summer term.

Compared to class A, class B had:

• fewer absences in the Autumn term

• 5% more absences in the Spring term

• 7 more absences in the Summer term.

Design and complete a two-way table to show this information.

The price of a laptop is reduced in a January sale from £450 to £382.50.

Work out the percentage reduction in the price of the laptop.

The graph shows the price of the laptop in the months before the January sale.

Explain why this graph is misleading.

Each member of a tennis club is classed as a junior, an adult or a senior.

• 16% of the members are seniors.

• The ratio of the number of juniors to the number of adults is 9: 5.

• There are 95 more juniors than seniors.

Work out the total number of members of the tennis club. You must show your working.

Amit invests some money at a rate of 4% per year compound interest. After 2 years the value of Amit’s investment is £1352.

Work out how much money Amit invested.

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.

The cost of sending a child to nursery is £5.80 per hour on each weekday. On Saturday the cost is times the weekday hourly rate.

A child goes to nursery for:

• 6 hours on Wednesday

• 5 hours on Thursday

• 4 hours on Saturday.

The total cost for the three days is reduced by 5% as a special offer.

Work out the cost for the three days after the 5% reduction. You must show your working,

The graph shows the time, in minutes, taken by some pupils to travel to school on Tuesday.

Less than 10 10 to 30 More than 30

Time (minutes)

Find the percentage of these pupils that took more than 30 minutes to travel to school.

On Tuesday the number of pupils taking 10 to 30 minutes to travel to school was 25% less than on Monday.

Find the number of pupils taking 10 to 30 minutes to travel to school on Monday.

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.

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?

The price of a holiday increases from £320 to £340.

Work out the percentage increase in the price of the holiday.

The graph shows the time, in minutes, taken by some pupils to travel to school on Tuesday.

Less than 10 10 to 30 More than 30

Time (minutes)

Find the percentage of these pupils that took more than 30 minutes to travel to school.

On Tuesday the number of pupils taking 10 to 30 minutes to travel to school was 25% less than on Monday.

Find the number of pupils taking 10 to 30 minutes to travel to school on Monday.

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.

Sam eats 30% of a 600 g pack of cereal every day.

Sam has no cereal left. The cereal is no longer sold in 600 g packs. Instead, the cereal is now sold in 400 g packs.

Sam wants to continue to eat the same amount of cereal every day.

Work out the minimum number of 400 g packs of cereal that Sam must buy to have enough for 7 days. You must show your working.

Increase £95 by 16%.

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.

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).

The scatter diagram shows the test scores for 20 pupils in Science and Mathematics.

Describe the type of correlation shown in the scatter diagram.

One pupil took the Science test but was then ill during the Mathematics test and had to leave early.

On the scatter diagram, circle the point that is most likely to represent this pupil.

By drawing a line of best fit, estimate the test score in Mathematics for a pupil who scored 28 in the Science test.

Explain why using the scatter diagram to estimate the test score in Mathematics for a pupil who scored 60 in Science may be unreliable.

Find the percentage of the 20 pupils who scored less than 30 marks in both Science and Mathematics.

At an adventure park, all children participate in three activities, choosing exactly one activity from each of three options.

On one Monday morning, 100 children visited the adventure park.

The frequency tree shows the number of children choosing some of the activities.

Option 1
Option 2
Option 3

........

Complete the frequency tree.

Which was the most popular activity out of rafting, swimming and tennis? Show how you decide.

One of the 100 children is picked at random.

Find the probability that this child chose bowling.

Alex says

45% of all children coming to the adventure park choose football.

What assumption has Alex made?

The price of a television is increased by 35%. In a sale, the new price of the television is decreased by r %.

The overall percentage increase in the price of the television is 16.1%.

Find the value of r. You must show your working.

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.

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........

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).

The scatter diagram shows the test scores for 20 pupils in Science and Mathematics.

Describe the type of correlation shown in the scatter diagram.

One pupil took the Science test but was then ill during the Mathematics test and had to leave early.

On the scatter diagram, circle the point that is most likely to represent this pupil.

By drawing a line of best fit, estimate the test score in Mathematics for a pupil who scored 28 in the Science test.

Explain why using the scatter diagram to estimate the test score in Mathematics for a pupil who scored 60 in Science may be unreliable.

Find the percentage of the 20 pupils who scored less than 30 marks in both Science and Mathematics.

The diagram shows a shaded sector inside a parallelogram. The sector has an angle of 30°. The parallelogram, ABCD, has length BC = 20 cm and AB = 12 cm. The perpendicular distance between BC and AD is 6 cm.

Show that the area of the sector is 37.7 cm², correct to 3 significant figures.

Work out the percentage of the parallelogram that is not shaded.

A climber is in a competition.

Here are their scores after two events.

Event 3 is out of 52 points.

The climber’s overall score is found by adding the three scores together.

Find the score the climber needs in event 3 to achieve 85% of the total points.

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.

A motorist wants to buy a new car but does not have enough money.

The price of the car is £16 000.

The motorist sees this notice for a deal on the car they want to buy. The number of equal monthly payments is hidden.

Pay 15% of the price of the car now

Work out the number of monthly payments if the total cost of the car to the motorist is £17 400. You must show your working.

A box contains only red, green and black pens. The ratio of red pens to green pens to black pens is 1: 4: 11.

Work out the percentage of the pens that are green.

There are 24 more green pens than red pens.

Work out the total number of pens in the box.

Decrease 480 by 20%.

Alex buys a new phone with 10.5 Gb (Gigabytes) of data. This is 40% more data than on Alex’s old phone.

Work out the amount of data Alex had on the old phone.

A restaurant menu has 4 main courses and 3 side dishes. For their meal, each customer chooses 1 main course and 1 side dish.

Work out the percentage of possible meals that cost less than £8.

The price of a phone increases from £240 to £262.80.

Calculate the percentage increase in the price of the phone.

A biologist assumes the population, P, of birds on an island can be predicted using the formula

P = 3800 × 1.042ⁿ

where n is the number of years after the start of 2020.

Write down the percentage increase per year that is used in the formula.

Calculate the predicted population at the start of 2024.

Show that the number of birds is predicted to exceed 7000 during 2034.

A researcher says that between 2022 and 2030 the percentage increase per year in the population will be 2.8%.

If the researcher is correct, explain how this new information will affect the answer in part (c)(i).

A motorist wants to buy a new car but does not have enough money.

The price of the car is £16 000.

The motorist sees this notice for a deal on the car they want to buy. The number of equal monthly payments is hidden.

Pay 15% of the price of the car now

Work out the number of monthly payments if the total cost of the car to the motorist is £17 400. You must show your working.

A box contains only red, green and black pens. The ratio of red pens to green pens to black pens is 1: 4: 11.

Work out the percentage of the pens that are green.

There are 24 more green pens than red pens.

Work out the total number of pens in the box.

A restaurant menu has 4 main courses and 3 side dishes. For their meal, each customer chooses 1 main course and 1 side dish.

Work out the percentage of possible meals that cost less than £8.

Casey’s mobile phone gives a weekly report showing the amount of time they use their phone.

This week the report says that the phone was used

• for 217 minutes

• 24% more than last week.

Calculate Casey’s phone usage last week.

Hiro invests £2500 for 2 years in a bank account paying r % per year compound interest. At the end of 2 years, the amount in the bank account is £2704.

Calculate r.

Finley has 72 sweets. Finley gives

• 25% of the sweets to Alex

The price of petrol decreases from £1.32 per litre to £1.02 per litre.

Calculate the percentage decrease in the price.

The diagram shows a circle inside a square of side 12 cm.

Work out the percentage of the square that is shaded. You must show your working.

Increase 200 by 15%.

The price of petrol decreases from £1.32 per litre to £1.02 per litre.

Calculate the percentage decrease in the price.

The diagram shows a circle inside a square of side 12 cm.

Work out the percentage of the square that is shaded. You must show your working.

A zoo counts its animals. The ratio of antelope to zebra is 3: 2. The ratio of meerkats to zebra is 7: 3.

Write the number of antelope as a percentage of the number of zebra.

There are 15 more meerkats than antelope.

Work out the number of zebra in the zoo.

y is directly proportional to the square of x.

Find the percentage decrease in y when x is decreased by 30%.

At the end of each year, a driver records how many kilometres they have driven.

In 2021, they drove 18% more kilometres than in 2020. In 2022, they drove 25% more kilometres than in 2020.

In 2022, they drove 3500 km.

Kai says

I can work out how many kilometres were driven in 2020 by reducing 3500 by 25%. 3500 × 0.75 = 2625 km.

Explain why 2625 is not the correct number of kilometres driven in 2020.

Calculate the number of kilometres driven in 2021.

Eve is counting the photos on her phone. The ratio of the number of photos of her family to photos of her friends is 3: 7. She has 450 photos of her family. 80% of the photos of her friends include Jack.

Work out how many of the photos of her friends include Jack.

An examination has three papers. Paper 1 is marked out of 60. Paper 2 is marked out of 40. Paper 3 is marked out of 100. The three marks are added together to form the total mark out of 200.

A student scored 65% on Paper 1 and 70% on Paper 2.

Find the mark they need to get on Paper 3 to achieve 64% of the total marks. You must show your working.

Write 65% as a fraction in its simplest form.

25 people entered a competition. 4 of them won a prize.

Work out the percentage of people that won a prize.

Increase 250 by 20%.

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.

Two supermarkets, A and B, have special offers on the same packet of biscuits.

Dan buys one packet of these biscuits.

Which supermarket is best value for Dan? Show how you decide.

Supermarket........ because........

Darcy buys three packets of these biscuits.

Which supermarket is best value for Darcy? Show how you decide.

Supermarket........ because........

A child has four identical wooden cubes of side length 6 cm.

They arrange the cubes in a 2 by 2 by 1 arrangement to form a cuboid.

Show that the surface area of the cuboid is 576 cm².

The child rearranges the cubes in a 4 by 1 by 1 arrangement to form a different cuboid.

Calculate the percentage increase in surface area for this cuboid compared with the 2 by 2 by 1 cuboid.

An examination has three papers. Paper 1 is marked out of 60. Paper 2 is marked out of 40. Paper 3 is marked out of 100. The three marks are added together to form the total mark out of 200.

A student scored 65% on Paper 1 and 70% on Paper 2.

Find the mark they need to get on Paper 3 to achieve 64% of the total marks. You must show your working.

Jamie was paid £14.00 per hour. Jamie receives a pay increase of 20%.

Work out how much Jamie is now paid per hour.

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.

In 1980, Ling’s flat was worth £23 000. Today, Ling’s flat is worth 1200% of its value in 1980.

Calculate the value of Ling’s flat today.

A child has four identical wooden cubes of side length 6 cm.

They arrange the cubes in a 2 by 2 by 1 arrangement to form a cuboid.

Show that the surface area of the cuboid is 576 cm².

The child rearranges the cubes in a 4 by 1 by 1 arrangement to form a different cuboid.

Calculate the percentage increase in surface area for this cuboid compared with the 2 by 2 by 1 cuboid.

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.

Here are the ticket prices for a zoo when bought at the gate.

Mr and Mrs Khan take their four children to the zoo. They buy their tickets at the gate.

How much do Mr and Mrs Khan save by buying a family ticket?

All ticket prices are reduced by 15% if bought online rather than at the gate. Mr and Mrs Morris take their one child to the same zoo. They buy their tickets online.

What is the lowest possible total cost of their tickets?

A coat is on sale in a shop at a special price of £149.40. The shop says this is a saving of 17% on their normal price.

Work out the shop’s normal price for the coat.

The scatter diagram shows the midday temperature at 13 different heights on a mountain.

The table has the information for 2 more heights.

Plot these on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

By drawing a line of best fit, estimate the temperature at 1000 m.

Circle the outlier on the scatter diagram.

Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.

Find the percentage of the 15 temperatures which are below 6 °C.

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.

Taylor has collected data on the number of students who were absent from their school last week. The bar chart shows the results for the first four days.

On Friday there were 54 students who were absent from the school.

Show this information on the bar chart.

Taylor says

On Monday 150% of the students were absent from my school.

Could this be true? Explain how you decide.

There are 600 students in Taylor’s school. Find the percentage of students who were absent from Taylor’s school on Thursday.

A test has 20 questions.

Amaya attempts all of the questions. She gets 65% of the questions correct. Kai gets six of the questions wrong.

Who has the smallest number of questions wrong? Show working to support your answer.

A sports club has 250 members.

Some of the members wish to change a club rule. To change a club rule, at least 70% of all the members must vote ‘yes’.

At a meeting of the sports club, 10 members were absent and did not vote. The other members voted yes: no: don’t know in the ratio 11: 3: 1.

Did enough members vote ‘yes’ to change the rule? Show how you decide.

A garage is trying to sell a car. The price of the car is normally £18 000.

In a sale, the price of the car is reduced by 30%. As a special offer, the sale price is then reduced by r %. The special offer price is £9450.

Find the value of r. You must show your working.

In January 2018, an art collector bought an antique painting. In January 2020, he sold it for £17 640.

Assume the value of the painting increased by 5% each year.

Calculate the art collector’s profit. You must show your working.

The scatter diagram shows the midday temperature at 13 different heights on a mountain.

The table has the information for 2 more heights.

Plot these on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

By drawing a line of best fit, estimate the temperature at 1000 m.

Circle the outlier on the scatter diagram.

Explain why using the scatter diagram to estimate the temperature at 1800 m may be unreliable.

Find the percentage of the 15 temperatures which are below 6 °C.

Two pupils are given data that shows the estimated number of computer tablet users worldwide from 2014 to 2018.

Li creates this pie chart to show the data.

Number of computer tablet users (billions)

Write down two reasons why Li’s pie chart is not suitable to represent the data.

Amaya creates this line graph to show the same data.

Work out the percentage increase in the number of computer tablet users from 2014 to 2018.

A garage is trying to sell a car. The price of the car is normally £18 000. In a sale, the price of the car is reduced by 30%. As a special offer, the sale price is then reduced by r %. The special offer price is £9450.

Find the value of r. You must show your working.

The price of a plane ticket is increased by 15% to £1426.

Find the original price of the plane ticket.

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.

The table shows the marks obtained by 10 students in spelling tests in January and February.

The marks for the first six students are plotted on the scatter diagram.

Plot the marks for the remaining four students.

Describe the type of correlation shown in the completed scatter diagram.

On the scatter diagram, circle the student that made the greatest improvement in their

marks from January to February.

Work out the percentage change in this student’s marks from January to February.

Another student, Kai, scored 79 marks in the test in January but was absent for the test in February.

Kai says

I could use a line of best fit on the scatter diagram to estimate the marks I may have achieved in the test in February.

Is Kai’s method reliable? Give a reason for your answer.

A worker received a 10% pay increase in 2017 and a further 10% pay increase in 2018. The worker says

Over these two years, my pay increased by 10% + 10% = 20%.

The worker is incorrect.

Work out the correct percentage increase. You must show your working.

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.

Increase 600 by 17%.

The price of a plane ticket is increased by 15% to £1426.

Find the original price of the plane ticket.

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.

The table shows the marks obtained by 10 students in spelling tests in January and February.

The marks for the first six students are plotted on the scatter diagram.

Plot the marks for the remaining four students.

Describe the type of correlation shown in the completed scatter diagram.

On the scatter diagram, circle the student that made the greatest improvement in their

marks from January to February.

Work out the percentage change in this student’s marks from January to February.

Another student, Kai, scored 79 marks in the test in January but was absent for the test in February.

Kai says

I could use a line of best fit on the scatter diagram to estimate the marks I may have achieved in the test in February.

Is Kai’s method reliable? Give a reason for your answer.

A worker received a 10% pay increase in 2017 and a further 10% pay increase in 2018. The worker says

Over these two years, my pay increased by 10% + 10% = 20%.

The worker is incorrect.

Work out the correct percentage increase. You must show your working.

James is taking three examination papers in Spanish. Here are his first two results.

Paper 3 is out of 95. The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

Lily buys and sells microwaves.

She buys each one for £32 and sells it for £60. She also pays £7 for the delivery of each microwave she sells.

If she sells a microwave that is faulty then Lily must pay for its repair and redelivery. This costs her another £25 for each faulty microwave.

Last month, 6 out of the 80 microwaves Lily sold were faulty.

This month she has orders for 133 microwaves.

Calculate her expected percentage profit on this month’s order. Showing your working in the boxes below may help you present your work.

A jacket has its price reduced by 20% in a sale. The sale price is £56.

Work out the price of the jacket before the sale.

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

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.

James is taking three examination papers in Spanish. Here are his first two results.

Paper 3 is out of 95. The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

Lily buys and sells microwaves.

She buys each one for £32 and sells it for £60. She also pays £7 for the delivery of each microwave she sells.

If she sells a microwave that is faulty then Lily must pay for its repair and redelivery. This costs her another £25 for each faulty microwave.

Last month, 6 out of the 80 microwaves Lily sold were faulty.

This month she has orders for 133 microwaves.

Calculate her expected percentage profit on this month’s order. Showing your working in the boxes below may help you present your work.

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.

Each day, Eve records how long it takes her to complete a puzzle.

On Friday, she took 50% less time than on Thursday. On Saturday, she took 20% less time than on Friday. On Saturday, she takes 36 minutes to complete the puzzle.

How many minutes did she take to complete the puzzle on Thursday? Show your working.

Show that Nina’s answer is 64.

Calculate the error in her estimated answer as a percentage of the exact answer.

Paintings are sold in an art gallery. The cost of a painting has k % commission added to it. Tax of 15% is then added to the total cost to give the price to pay.

Layla correctly calculates the price to pay by multiplying the cost of the painting by 1.403.

Work out the value of k.

A theme park asked 900 people to choose their favourite activity from a list of five. The pictogram shows the results for four of the activities.

How many people chose entertainment?

How many more people chose water rides than family rides?

All 900 people chose one of the five activities.

Complete the pictogram for children’s rides.

Will plays a game at the theme park. There are 20 cards numbered from 1 to 20. Will takes a card at random. He wins if the card he chooses shows a prime number.

Work out the probability that Will wins. Give your answer as a fraction in its simplest form.

A family ticket for the theme park costs £68. If the ticket is bought online it costs 15% less.

How much does it cost to buy a family ticket online?

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1: 2: 3 by weight. He buys the cement, sand and stone in bags as shown in this table.

He packs the dry concrete into 30 kg bags.

Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.

Show that Bob buys 500 kg of sand.

Bob sells the 50 bags of dry concrete for a total of £396.

Calculate Bob’s percentage profit.

12 students take two tests. Each test is out of 60. The scatter diagram shows the results for 10 of the students.

The table shows the results for the other 2 students.

Plot these results on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

Draw a line of best fit on the scatter diagram.

Another student was absent for Test 2. The student scored 40 marks on Test 1.

Use your line of best fit to estimate a result for this student on Test 2.

Work out the percentage of the 12 students whose result on Test 1 is lower than their result on Test 2.

Tom buys a radio for £40. Later he sells it and makes a profit of 20%.

Tom says

The ratio of the price I paid for the radio to the price I sold the radio is 5: 6.

Show that Tom is correct.

The midpoints of the sides of a rectangle are joined by straight lines as shown.

Work out the percentage of the rectangle that is shaded.

Write down the multiplier for an increase of 140%. Give your answer as a decimal.

Ali invests £1500 in October. The investment increases in value by 10% in November. It then decreases in value by 20% in December.

Ali says

10% – 20% = - 10%, so the £1500 has lost exactly 10% of its value.

Explain what Ali has done wrong.

Work out the correct percentage loss.

Amrit’s income is 32% more than Bethan’s income. Amrit and Bethan’s combined income is £54 868.

Calculate Amrit’s income.

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1: 2: 3 by weight. He buys the cement, sand and stone in bags as shown in this table.

He packs the dry concrete into 30 kg bags.

Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.

Show that Bob buys 500 kg of sand.

Bob sells the 50 bags of dry concrete for a total of £396.

Calculate Bob’s percentage profit.

12 students take two tests. Each test is out of 60. The scatter diagram shows the results for 10 of the students.

The table shows the results for the other 2 students.

Plot these results on the scatter diagram.

Describe the type of correlation shown in the scatter diagram.

Draw a line of best fit on the scatter diagram.

Another student was absent for Test 2. The student scored 40 marks on Test 1.

Use your line of best fit to estimate a result for this student on Test 2.

Work out the percentage of the 12 students whose result on Test 1 is lower than their result on Test 2.

In 2017, a chocolate bar had a mass of 250 g. In 2018, the mass of the chocolate bar was reduced to 220 g.

Work out the percentage decrease in the mass of the chocolate bar from 2017 to 2018.

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.

Amrit’s income is 32% more than Bethan’s income. Amrit and Bethan’s combined income is £54 868.

Calculate Amrit’s income.

Jack and Alex take rubbish to be recycled. Jack takes 520 kilograms, 87% of which can be recycled. Alex takes 750 kilograms, 61% of which can be recycled.

Calculate who takes the greatest amount of rubbish that can be recycled and by how much.

Ed has a card shop.

He buys a particular card for £1.20 and sells it for £1.68.

Calculate his percentage profit on this card.

Ed’s profit on “Good Luck” cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.

Work out Ed’s profit on “Good Luck” cards in 2017.

Adam buys 2 adult tickets and 1 child ticket at the sale price. A 2% booking fee is then added to the total cost of the tickets.

Calculate the total amount that Adam must pay.

Work out 20% of 40.

Sophie is organising a raffle.

• Each raffle ticket costs 50p.

• She sells 400 tickets.

• The probability that a ticket, chosen at random, wins a prize is 0.1.

• Each winning ticket receives a prize worth £3.

Sophie says

I expect the raffle to make over £100 profit.

Show that Sophie is wrong.

Ed has a card shop.

He buys a particular card for £1.20 and sells it for £1.68.

Calculate his percentage profit on this card.

Ed’s profit on “Good Luck” cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.

Work out Ed’s profit on “Good Luck” cards in 2017.

Adam buys 2 adult tickets and 1 child ticket at the sale price. A 2% booking fee is then added to the total cost of the tickets.

Calculate the total amount that Adam must pay.

In 2017, the value of a house increased by 4%. In 2018, the value of the house then decreased by 3%.

Teresa says

Over the two years the value of the house increased by exactly 1% because 4 – 3 = 1.

Show that Teresa is wrong.

Shari buys a box of 60 candles for £125. She sells the candles for £2.25 each.

Calculate her percentage profit.

Emily spent £2400 on holiday in 2017. This was 20% more than she spent on holiday in 2016.

Calculate the amount she spent on holiday in 2016.

This table shows the ticket price for each person to visit a zoo in winter.

A family of two adults, one child aged 8 and one child aged 1 visit the zoo in winter.

What is the total cost of the tickets?

In summer, the zoo increases the prices.

An Adult ticket increases by 20%. A Child ticket increases by 15%.

How much more does it cost the family to visit in the summer than in the winter?

Shari buys a box of 60 candles for £125. She sells the candles for £2.25 each.

Calculate her percentage profit.

In a village the ratio of males to females is 2: 1.

40% of the people in the village are right-handed males. 25% of the people in the village are right-handed females.

Show that the proportion of females who are right-handed is greater than the proportion of males

who are right-handed.

Emily spent £2400 on holiday in 2017. This was 20% more than she spent on holiday in 2016.

Calculate the amount she spent on holiday in 2016.

The price of a washing machine is reduced by 20% for a sale. Afterwards, the sale price is increased by 30%.

Joachim says

The washing machine is now 10% more expensive than before the sale.

Explain Joachim’s error and work out the correct percentage change in the price of the washing machine from before the sale to after the sale.

Joachim’s error is........

Correct percentage change is........ %

Write 48 as a percentage of 200.

Decrease 650 by 40%.

Pippa owns a snack bar.

Spread costs £3.20 for a 1 kilogram tub and £6.15 for a 2 kilogram tub.

Pippa buys enough spread to last for 14 days.

What is the lowest price Pippa can buy this spread for? Show your working.

In 2016, Pippa paid £1650 rent. In 2017, the rent increased by 14%.

Calculate the amount of rent she paid in 2017.

Lee wishes to find out if there is a relationship between a person’s age and the time it takes them to complete a puzzle.

Lee decides to conduct an experiment. She asks 12 people to complete the puzzle. She records each person’s age and the time taken to complete the puzzle.

Make one criticism of Lee’s method.

This scatter diagram shows the results for ten of the people in Lee’s experiment.

Here are the other two results.

Plot these results on the scatter diagram.

What type of correlation is shown in the scatter diagram?

Estimate the time it would take a person aged 35 to complete the puzzle. Show your working to justify your answer.

Lee says that at least 80% of the 12 people completed the puzzle in under 30 seconds.

Is Lee correct? Show working to support your answer.

The price of a computer was £750.

In a sale the price is reduced by 20%. On the final day the sale price is reduced by a further 12%.

How much is saved in total by buying the computer on the final day of the sale?

This bar chart shows the average monthly expenditure, by category, of households in a particular town in 2005 and 2015.

Utility bills Transport Housing Entertainment Food

In which category was there a decrease in the average monthly expenditure between 2005 and 2015?

How much more was the average monthly expenditure on housing in 2015 than in 2005?

The total average monthly expenditure in 2005 was £1200.

What percentage of this was spent on transport?

In July the price of a holiday is £500. In August the price increases by 25%. In September the price drops to £500 again.

Work out the percentage decrease from the August price to the September price.

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.

60% of the people in a town are males. 20% of the males are left-handed. 21.6% of all the people are left-handed.

Work out the percentage of the people who are not male who are left-handed.

y is directly proportional to the square of x.

Find the percentage increase in y when x is increased by 15%.

The value of a car, £ V, is given by

V = 16 500 × 0.82ⁿ

where n is the number of years after it is bought from new.

Write down the value of the car when new.

Write down the annual percentage decrease in the value of the car.

Show that the value of the car after 4 years is less than half its value when new.

Jack sent 15% more text messages in March than in February. Jack sent 460 text messages in March.

How many more texts did Jack send in March than in February?

Ceri records the time taken, t minutes, to travel to school for a sample of 168 students at her

Draw a histogram to represent this information.

Ceri says

The longest time that any of these students took to travel to school was 80 minutes.

Is she correct? Give a reason for your answer.

Ceri also claims that 25% of all of the students at this Academy took more than 30 minutes to travel to school.

Show how Ceri might have worked out her claim.

State one assumption that Ceri has made in making her claim.

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.

Calculate the volume of a sphere with radius 6 cm.

An ornament is made from a solid glass square-based pyramid. The base has side length 15 cm. A hemisphere with radius 6 cm is cut out of the base of the pyramid. This reduces the volume of glass contained in the ornament by 30%.

Calculate the perpendicular height of the pyramid. [The volume of a pyramid is × area of base × perpendicular height. A hemisphere is half a sphere.]

State the median salary.

Find the interquartile range.

Make two different comparisons between the distribution of the salaries at Bexbridge Biscuits and the salaries at Camford Cookies.

Write 62 as a percentage of 500.

Increase £196 by 9%.

The scatter diagram shows the results of 17 students in their French test and their German test. Both tests are out of 100.

Here are the results of another 4 students.

Plot these results on the scatter diagram.

Describe the type and strength of the correlation shown in this diagram.

Work out the percentage of the students whose German result was higher than their French result.

Jack carries out a survey in his school. He selects 50 students, at random, and asks them

Do you think that it is a good idea to have women-only railway carriages?

These are his results.

What percentage of the students in Jack’s survey answered ‘Yes’?

Jack says

My survey shows that people in England think that it is a good idea to have women-only railway carriages.

Explain why Jack may be wrong.

Luka invests £1500. At the end of the first year, 2% interest is added. At the end of the second year, after interest has been added, the investment is worth £1606.50.

Show that 5% interest has been added at the end of the second year.

The scatter diagram shows the results of 17 students in their French test and their German test. Both tests are out of 100.

Here are the results of another 4 students.

Plot these results on the scatter diagram.

Describe the type and strength of the correlation shown in this diagram.

Work out the percentage of the students whose German result was higher than their French result.

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.

Naomi is given a 10% pay decrease. Her new wage is £252 per week.

What would be her weekly wage if, instead, she had received a 10% pay increase?

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?

Work out 17% of 54. Give your answer correct to 1 decimal place.

The pass mark for a test is 86%. Steve scores 52 out of 61 marks.

Does he pass the test? Explain your answer.

Mo’s tyre pressure gauge shows a reading which is 12% higher than the actual pressure.

What is the actual pressure when Mo’s gauge shows 38.64?

George recorded all the different types of tree in a wood.

His results are shown in this table.

Complete the table.

Complete the bar chart to show George’s results.

George found 60 trees altogether in the wood.

What percentage of the trees were oak trees?

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?

Students at a school must choose one subject from Option 1 and one from Option 2. The school offers two languages, French and Spanish.

The subjects are given in this table.

Work out the percentage of all the subject combinations which have exactly one language.

Mo’s tyre pressure gauge shows a reading which is 12% higher than the actual pressure.

What is the actual pressure when Mo’s gauge shows 38.64?

On 1^st November 2015 there were 4200 trees planted in a wood. On 1^st November 2016, only 3948 of these trees were still alive.

It is assumed that the number of trees still alive is given by

N = ar^t

where N is the number of trees still alive t years after 1^st November 2015.

Write down the value of a.

Show that r is 0.94.

Show that on 1^st November 2030 the number of trees still alive is predicted to have decreased

by over 60% compared with 1^st November 2015.

The cumulative frequency graph shows the speeds, in miles per hour (mph), of vehicles passing a 40 mph speed limit sign on a road.

A speed camera will be installed if more than 30% of vehicles go over the speed limit of 40 mph.

Use information from the graph to decide if a speed camera should be installed.

Helen delivers parcels. On Tuesday, Helen delivered 20% more parcels than on Monday. On Wednesday, Helen delivered 50% fewer parcels than on Tuesday. On Wednesday, Helen delivered 72 parcels.

Calculate the number of parcels that Helen delivered on Monday.

This table shows the populations of the four countries of the UK in 2012. All values are given correct to 3 significant figures.

Write the population of England as an ordinary number.

Work out the total population of Wales, Scotland and Northern Ireland. Give your answer in standard form.

The total population of the UK is predicted to reach 73.3 million in 2037.

Calculate the predicted percentage increase in the UK population from 2012 to 2037. Give your answer correct to 2 significant figures.