## Scotland’s Curriculum – EVolution of vehicle sales

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

• Explore the infographic – what can be worked out from this information and what questions does it raise?
• Look at trends in vehicle registrations
• Look at proportions of types of newly registered vehicles over time – why has the percentage of petrol cars being registered increased from 2015 to 2020?
• Do some calculations to show that the number of petrol cars being registered has decreased from 2015 to 2020.
• Reflect upon the implications for misleading representations of data
• Consider the implications of the ban on new petrol and diesel cars by 2035 – what affect will this ban have on the proportions of car types being registered?
•  What questions does the increase in electric vehicles raise?

Mathematical opportunities offered

• Interpretation of data, statistics, graphs, infographics in context
• Critiquing graphs
• Calculating percentages
• Exploring proportions of quantities over time
• Making conjectures about future proportions given available data
• Analysing and comparing data in order to develop and present a conclusion.

## Scotland’s Curriculum- EVolution of vehicle sales

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

• Explore the infographic – what can be worked out from this information and what questions does it raise?
• Look at trends in vehicle registrations
• Look at proportions of types of newly registered vehicles over time – why has the percentage of petrol cars being registered increased from 2015 to 2020?
• Do some calculations to show that the number of petrol cars being registered has decreased from 2015 to 2020.
• Reflect upon the implications for misleading representations of data
• Consider the implications of the ban on new petrol and diesel cars by 2035 – what affect will this ban have on the proportions of car types being registered?
• What questions does the increase in electric vehicles raise?

Mathematical opportunities offered

• Interpretation of data, statistics, graphs, infographics in context
• Critiquing graphs
• Calculating percentages
• Exploring proportions of quantities over time
• Making conjectures about future proportions given available data
• Analysing and comparing data in order to develop and present a conclusion.

## Core Maths – EVolution of vehicle sales

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

• Explore the infographic – what can be worked out from this information and what questions does it raise?
• Look at trends in vehicle registrations
• Look at proportions of types of newly registered vehicles over time – why has the percentage of petrol cars being registered increased from 2015 to 2020?
• Do some calculations to show that the number of petrol cars being registered has decreased from 2015 to 2020.
• Reflect upon the implications for misleading representations of data
• Consider the implications of the ban on new petrol and diesel cars by 2030 – what affect will this ban have on the proportions of car types being registered?
• What questions does the increase in electric vehicles raise?

Mathematical opportunities offered

• Interpretation of data, statistics, graphs, infographics in context
• Critiquing graphs
• Calculating percentages
• Exploring proportions of quantities over time
• Making conjectures about future proportions given available data
• Analysing and comparing data in order to develop and present a conclusion.

## Key Stage 3 – EVolution of vehicle sales

Resource produced in collaboration with MEI

Brief overview of session ‘logic’

• Explore the infographic – what can be worked out from this information and what questions does it raise?
• Look at trends in vehicle registrations
• Look at proportions of types of newly registered vehicles over time – why has the percentage of petrol cars being registered increased from 2015 to 2020?
• Do some calculations to show that the number of petrol cars being registered has decreased from 2015 to 2020.
• Reflect upon the implications for misleading representations of data
• Consider the implications of the ban on new petrol and diesel cars by 2030 – what affect will this ban have on the proportions of car types being registered?
•  What questions does the increase in electric vehicles raise?

Mathematical opportunities offered

• Interpretation of data, statistics, graphs, infographics in context
• Critiquing graphs
• Calculating percentages
• Exploring proportions of quantities over time
• Making conjectures about future proportions given available data
• Analysing and comparing data in order to develop and present a conclusion.

## Internal combustion engines

A country’s government wants to reduce the number of cars using internal combustion engines by encouraging the purchase of electric vehicles.

The total number of cars using internal combustion engines in a country at time t can be modelled by the equation

$N\left( t \right) = \left( 3.5 \times 10^{7} + E \right)e^{- \frac{1}{10}t} – E$

Where N(t) is the number of cars using internal combustion engines at time t years after the program was introduced and E is the number of electric vehicles on the roads before the government initiative.

Using the equation for this model,

a) Explain the significance of the number 3.5 x 107.

[1 mark]

b) Explain why the initial number of cars using internal combustion engines is independent of the initial number of electric vehicles.

[2 marks]

c) Calculate the number of cars using internal combustion engines after 10 years if the initial number of electric vehicles is 2 x 106.

[2 marks]

d) Analyse the suitability of this model by evaluating it for large values of t.

[2 marks]

## Net-Zero Buses

15 cities, each of varying sizes, decide to have carbon-neutral public transport systems.

When the cities are arranged in size order from smallest to largest, the number of new electric buses they need follows an arithmetic sequence with first term (representing the smallest amount of buses needed for the smallest city) a buses and common difference d buses.

The 7ᵗʰ city in this progression needs 580 new electric buses and the largest city needs 1020 new electric buses.

Find the value of a and the value of d.

[5 marks]

## EV Increase

A country decides to subsidise the purchase of electric vehicles, causing more people to buy them.

Initially, the country used an equivalent of 56 million tonnes of oil for transport.

Since the government subsidy, the transport sector in each subsequent year has required 80% of the amount of oil that the previous year required.

a) Write a recurrence relation to model the amount of oil used, in million tonnes, in each subsequent year.

[2 marks]

b) Find the amount of oil needed for the transport sector after the fifth year.

[2 marks]

c) Find the total amount of oil used until the transport sector requires no more oil.

[4 marks]

d) State one limitation with the model.

[1 mark]