Critical Analysis of Data & Models (AQA Level 3 Mathematical Studies (Core Maths): Paper 2B: Critical Path & Risk Analysis): Exam Questions

Pete wants to buy a house.

His annual salary is £66 000

The bank will lend him three times his annual salary for a mortgage.

This is 90% of the house price.

He makes these notes:

Critically analyse Peter’s notes making corrections where necessary.

Use Positive spin on the Preliminary Material.

The editor of the local newspaper received a letter of complaint to say the data had been badly presented.

Was the complaint justified?

The newspaper headline for the 2014 by-election result said:

Does the data support these claims?

Comment on the validity of each of the statements made by the three candidates on Page 3 of the following Preliminary Material.

Show working to justify your comments.

Use Economics of music streaming from the Preliminary Material.

Use the information in Graph 2 to estimate the number of premium Google (including YouTube Music) subscriptions there were in the UK in January 2020

Which is the best estimate?

Suggest two improvements that could be made to the graphs on pages 2 and 3 of the Preliminary Material.

Readers of the extract commented that it was difficult to follow Diagram 1

Give one reason why they might have said this.

In a sports club,

     20 players are daily active users of BBC Sounds
     27 players are weekly active users of BBC Sounds.

Compare

     the proportion of listeners at the sports club who are daily active users
     with
     the proportion of all consumers who are daily active users.

Use the information in Graph 1 to justify your comparison.

Two music websites commented on the report.

The Recorder

Waxing Lyrical

Using the Preliminary Material, comment on the validity of each website’s claim. You must show your working.

Another music website made this claim.

The Daily Fret

Is the website’s claim correct?

Use Graph 1 to justify your answer.

Use Economics of music streaming from the Preliminary Material.

Molly is researching how the income from Spotify was shared out in 2020 In 2020, the price of a Spotify premium subscription was £9.99 per month in the UK

Molly disagreed with the report, saying,
    “As VAT is 20%, the Government should receive almost £2 for each monthly subscription, not £1.67”

Is Molly correct?

Show working to justify your answer.

Molly used the following method to estimate the total amount of Spotify’s UK subscription revenue that should have been received by recording artists in 2020

Identify two mistakes in Molly’s calculation.

You do not need to carry out any calculations.

The table shows some information about the number of students who took GCSE French and GCSE Spanish in 2012 and 2022

Write a brief report to summarise the information in the table.

Your brief report should include

• how the number of students who took each qualification has changed from 2012 to 2022   

• how the proportions of students who were male compared for the two qualifications in 2022

The table shows information about the top four teams in the 2020 Olympic Games.

Work out the ratio of gold medals to bronze medals for the United States.

A British newspaper made the following claim.

Does the data support this claim?

Show working to support your answer.

Use Online Nation from the Preliminary Material.

Suggest two improvements that could be made to the graphs in the Preliminary Material.

Graph 1 in the Preliminary Material is based on the results of a survey.
35 children aged 7 said they use messaging or social media.

Estimate the number of children aged 7 that took part in the survey.

Mark works for a children’s charity.

The charity is concerned by the amount of time that children spend online.

He calculates the percentage increase in time that children aged 15–16 spend online compared to children aged 7–8

Here is his calculation, which uses information from the last sentence in the Preliminary Material.

Identify one mistake in Mark’s calculation and work out the correct percentage increase.

Mistake___________________________________________________

Correct calculation and answer_________________________________

Ayesha, a radio journalist, produces a report based on the Online Nation extract in the Preliminary Material.

The report used Graph 1 to make the claim,

“There are more 13-year-olds using messaging or social media than 12-year-olds.”

Give one reason why this might not be true.

Ayesha commented that the Online Nation extract was difficult to follow in places.

Give two reasons why she might have said this.
You should not comment on the graphs.

Ayesha wants to comment on how much money social media companies make from children in the UK

She finds the following information for 2020

• There were approximately 3.2 million children aged 12–15 in the UK

• Instagram made $24 billion from their 1.41 billion users around the world.

• The average exchange rate was £1 = $1.28

Use this information, together with the data from the Preliminary Material, to estimate how much Instagram made from children aged 12–15 in the UK

Give your answer to the nearest million pounds.

Pupils from one primary school and one secondary school in Rochdale were asked,

“What is the main type of transport you use to travel to school?”

The table shows the results.

One secondary school pupil is chosen at random.

Write down the probability that the pupil travels to school by bicycle.

One pupil is chosen at random from each school.

Work out the probability that both pupils travel to school by car.

In Rochdale,

22650 pupils attend primary school
13721 pupils attend secondary school.

Using the information in the table, estimate how many pupils in Rochdale travel to school by bicycle.

Give one reason why your answer to Question 4(c) might not be a good estimate.

The plans for a new housing estate include 80 properties of different types.

The table shows the planned number of each type of property.

Work out the ratio of houses to flats.

The local council must approve the plans for the housing estate.
To be approved, the plans must meet some minimum requirements.

Here are the minimum requirements for the number of cycle parking spaces.

The plans for the housing estate include 185 cycle parking spaces.

Do the plans meet the minimum requirements?

You must show your working.

The developers building the housing estate want to change their plans.

They make more profit on 2-bedroom houses than on 2-bedroom flats.

To approve the plans, the local council insists that

• there must still be 80 properties

• at least 23% of the properties are classified as ‘affordable housing’.

The table shows which properties are classified as ‘affordable housing’.

Use Electricity generation from the Preliminary Material.

The bar chart shows how each of the four nations of the United Kingdom generated electricity in 2019

Suggest two improvements that could be made to the bar chart.

Two newspapers reported on electricity generation in England in 2019.

Morning Record

Daily Bulletin Review

Using Table 1 in the Preliminary Material, comment on the validity of each newspaper’s claim. You must show your working.

Morning Record____________________________________________

Daily Bulletin Review_________________________________________

In 2019, Northern Ireland generated 4189 GWh of electricity by renewables.

The average cost of electricity was 14.4p per kWh

1 GWh = 1 000 000 kWh

Anna says,

“In 2019, Northern Ireland generated electricity by renewables worth over 600 million pounds.”

Is she correct?

You must show your working.

In 2019, Wales generated 7700 GWh of electricity by renewables.

Work out the total amount of electricity generated in Wales from all fuels.

Answer __________________________ GWh

Bobby wants to work out the mean percentage of electricity generated by renewables in the UK.

Here is his calculation, which uses the values from Chart 1 in the Preliminary Material.

The article states that 37.1% of energy generated in the UK in 2019 was by renewables.

Critically analyse Bobby’s method, explaining why his percentage does not agree with the article.

You do not need to carry out any calculations.

Between January and March 2020, 97.4% of trains were early or on time in the UK.

The rest of the trains were late.

Trains were late for one of three reasons.

The table shows the reasons why trains were late.

In Scotland, between January and March 2020, approximately 3370 trains were late due to rail infrastructure.

Estimate, for the same period, how many trains were late due to train operation.

State one assumption you made in part (a).

Eva is a newspaper reporter.

She collected data about the degree results achieved by students at a university over 3 years.

Some students failed their course and were not awarded a degree. Eva recorded the results in this table.

Work out the ratio of students in 2019 awarded an Upper Second class degree to the total number of students completing their course that year.

Circle your answer.

1 : 2 2 : 1 1 : 3 3 : 1

In an article on the data Eva made the following statements.

Statement 1

‘The average amount a student paid for a degree course was £27000. This means that the university collected more than half a billion pounds from these students.’

Statement 2

‘The percentage of students in the year group awarded a First class degree increased by more than half from 2018 to 2020’

Does the data support these statements? Show working to support your answers.

Use Plastic waste from the Preliminary Material.

Suggest two improvements that could be made to the charts in the Preliminary Material.

Readers of the extract from the briefing paper commented that it was difficult to follow in places.

Give three reasons why they might have said this.

You should not comment on the charts.

The following statements were made about the data on two online forums.

Ecofriends

Greenusers

Using the data given, comment on the validity of these statements.

The bar chart shows information about the exports of plastic waste from the UK in 2018

State two errors in the bar chart.

Eva is a newspaper reporter.

She collected data about the degree results achieved by students at a university over 3 years.

Some students failed their course and were not awarded a degree. Eva recorded the results in this table.

Work out the ratio of students in 2019 awarded an Upper Second class degree to the total number of students completing their course that year.

Circle your answer.

1 : 2 2 : 1 1 : 3 3 : 1

In an article on the data Eva made the following statements.

Statement 1

‘The average amount a student paid for a degree course was £27000. This means that the university collected more than half a billion pounds from these students.’

Statement 2

‘The percentage of students in the year group awarded a First class degree increased by more than half from 2018 to 2020’

Does the data support these statements? Show working to support your answers.

Use Plastic waste from the Preliminary Material.

Suggest two improvements that could be made to the charts in the Preliminary Material.

Readers of the extract from the briefing paper commented that it was difficult to follow in places.

Give three reasons why they might have said this.

You should not comment on the charts.

The following statements were made about the data on two online forums.

Ecofriends

Greenusers

Using the data given, comment on the validity of these statements.

The bar chart shows information about the exports of plastic waste from the UK in 2018

State two errors in the bar chart.

Helen is researching the amount of fat in 25-gram packets of ready salted and prawn cocktail crisps for three brands, A, B and C.

The table shows the amount of fat for each of the six packets.

Draw lines below to match each box on the left to the correct box on the right.

Helen produces a bar chart to show the information for the six packets.

Identify two errors in the bar chart.

Helen buys a packet of brand B’s prawn cocktail crisps weighing 160 grams.

This packet costs £2.30

Helen thinks that for every 10 pence worth of crisps in this packet, there are approximately 3 grams of fat.

Is Helen correct?

Assume that this packet and brand B’s 25-gram packet of prawn cocktail crisps have the same fat content per gram.

Show working to support your answer.

Use PISA from the Preliminary Material (opens in a new tab).

Suggest three improvements that could be made to the article in the Preliminary Material, including the graphs.

A research assistant is comparing the UK average science score with the overall OECD average science score.

She wants to find out how many per cent higher the UK average is than the overall average.

Here is her calculation

Critically analyse her calculation, making corrections where necessary.

The following comments were made on social media after the 2015 results were published.

‘For PISA maths in 2015, the range of average scores of the four UK nations is above 10’

Simon

‘If Scotland’s percentage decline in reading score from 2012 to 2015 is repeated in the next PISA test, the score will drop below 485’

Rukshana

(i) Is Simon correct? Show working to support your answer.

[2]

(ii) Is Rukshana correct?

Show working to support your answer.

[3]

Use Brexit from the Preliminary Material.

The UK population was 65 million in June 2016 What percentage of the population, correct to one decimal place, were eligible voters for the EU membership referendum?

One improvement that could be made to each graph in the Preliminary Material would be to label the axes.

Suggest two other improvements that could be made to each graph.

Graph 1: EU immigration in the UK

Graph 2: Brexit’s impact on the pound

For 2015, the UK paid the EU £14.6 billion.

During the campaign, Vote Leave claimed that the EU costs the UK over £350 million every week.

Is Vote Leave’s claim justified?

You must show your working.

Many people made comments on social media about the referendum.

Here are three of the comments.

Using the table on page 2 of the Preliminary Material, check the validity of these comments.

You must show your calculations

Tim’s comment______________________________________________

Kelly’s comment_____________________________________________

Larissa’s comment___________________________________________

Maria is planning to move to Spain. She wants to buy a house which, including all associated fees, will cost €327 500

In May 2014 she opened a Spanish bank account with a deposit of £17 000 The account pays no interest.

The current exchange rate is £1 = €1.08

This is a decrease of 10% from the May 2014 rate.

Maria owns a house in England which she bought for £253 000. She has no mortgage. The house is now worth 12.5% more than she paid for it.

Advise Maria on whether the money she gets from selling her house in England, together with the money in her Spanish bank account, will be enough to buy the house in Spain.

You must show your working.

A company has two offices, Office A and Office B, at different locations.

The company carries out a survey into the main ways of travelling to work by employees at both offices.

The results are shown in the table below.

An employee is chosen at random from all employees who travel to work by bus or train.

Calculate the probability that the employee is from Office A.

One of the offices is in the centre of a town. The other office is in a business park, 10 miles outside the town.

State which office, A or B, is more likely to be in the centre of the town.

Give a reason for your answer.