Estimation & Modelling (AQA Level 3 Mathematical Studies (Core Maths): Paper 1: Data, Finance, Estimation & Modelling): Exam Questions

Each year the European Union asks each member country to provide data for the volume of landfill waste per person.

What type of data is collected by the European Union?
Tick all boxes that apply

You may use Waste on pages 4 and 5 of the Preliminary Material.

In recent years people have been encouraged to recycle where possible. However, if waste cannot be recycled it is put into a landfill site.

• A new landfill site is to be built for a small town.

• The site will have a hole in the ground and the town’s waste will be put into the hole.

• The site needs to be used for a minimum of 15 years.

Estimate the dimensions of the hole.

Show details of your assumptions and calculations.

A person’s heart rate is the number of times their heart beats per minute.

Estimate the number of times an average person’s heart beats in their lifetime.
State any assumptions you make.

Use Household Waste in the Preliminary Material.

A new housing estate is being planned.

There will be a total of 500 new homes on the estate.

     150 homes will be 4-bedroom houses.
     200 homes will be 3-bedroom houses.
     90 homes will be 2-bedroom houses.
     60 homes will be flats for one person.

The local council wants to estimate the amount of residual waste the new housing estate will produce that needs to be sent to the landfill site.

Estimate the number of kilograms of residual waste that will be produced per week from the new housing estate.

State any assumptions you make.
You must show your working.

Explain how your answer may have been affected by an assumption you made.

Estimate the number of hours an average Year 10 student spends doing homework in a year.

State any assumptions you make.

You must show your working

Use Christmas Trees in the Preliminary Material.

During 2023, tree growers will plant seedlings to replace trees sold at Christmas 2022 and allow for growth in demand.

They will plan for the trees to have time to grow to a height of 6 feet before cutting them.

Estimate the total number of acres of land needed to be newly planted with Nordmann firs in 2023 in the UK

Use 1 acre = 43560 square feet

State any assumptions you make.

You must show your working

Explain how your answer may have been affected by one assumption you made.

Estimate the number of hours in a year that a washing machine is in use in an average household.

State any assumptions you make.

You must show your working.

Use Sweet Factory in the Preliminary Material.

You may also use the Formulae Sheet.

The factory is making a new sweet.

The sweet will be a sphere of radius 0.8 cm

The sweets will be packaged into cylindrical tubes of radius 2 cm and height 10 cm

One machine will be used for these new sweets.

It will take an hour and a half before the first sweets are produced and packaged.

Once the first sweets come off the production line in their tubes the production is continuous until the end of the day.

Estimate how many tubes of sweets can be filled in one working day.

Give your answer to a suitable degree of accuracy.

State any assumptions you make. You must show your working.

Explain how your answer may have been affected by one assumption you made.

Estimate the number of school meals served each year in a large secondary school.

State any assumptions you make. You must show your working.

Use Building Plot from the Preliminary Material.

A housing estate is to be built on a plot of land.

The plot of land has an area of 20 hectares.

The total length of the roads on the estate will be between 800 m and 1200 m
At least 25% of the plot must be used for 2-bedroom houses.
The rest of the plot will be shared between 3-bedroom and 4- bedroom houses.

Estimate the total number of houses that will be built on the plot.
State any assumptions you make.
You must show your working.

Explain how your answer may have been affected by an assumption you made.

Estimate the total amount of time per year taken by all the students in an average year 10 class to get ready to go to school in the morning.

State any assumptions that you make.

You must show your working.

Use Great Britain’s motorways from the Preliminary Material.

Here is a map of the M1 motorway

The motorway has three lanes each way for just over half its length.

Nearly all of the remainder of the motorway is four lanes each way.

The distance from Northampton to Luton along the motorway is 36 miles.
The cost of resurfacing a motorway is £15 per square metre.
1 mile ≈ 1600 metres.

Estimate the cost of resurfacing the whole of the M1 motorway.

Your estimate should include the hard shoulder.

State any assumptions you make. You must show your working.

Explain how your answer may have been affected by an assumption you made.

Estimate how many hours of sleep the average person in the UK has in their lifetime.

State any assumptions you make.
You must show your working.

Use Making food and drink cans in the Preliminary Material (opens in a new tab).

A food company is making a new soup product.
The soup will be put into a new size of can.

In a trial run, the food company produced between 1900 and 2150 litres of soup per hour.

The company manager asks a can manufacturer to supply three-piece cans with diameter 7 cm and height 9 cm

The can manufacturer must buy 1 m by 1 m sheets of steel to make the cans.

Estimate how many sheets of steel the can manufacturer will need to make enough cans for one week of soup production.

Give your answer to the nearest 10 sheets.

State any assumptions you make. You must show your working.

Explain how your answer may have been affected by one assumption you made.