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Maths for Planet Earth: Climate Based Questions for students and teachers

A team of students, Madeleine Ratcliffe, Lucy Fellingham and John Allen, and academics at the Environmental Change Institute, School of Geography and the Environment, and Department of Physics, University of Oxford, developed the Maths for Planet Earth questions. They work on climate and energy issues and are passionate about inspiring young people to join the fight against climate change.

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The world needs brainy mathematicians to help tackle climate change.

The aim of these questions is to integrate climate change into the school curriculum beyond the usual suspects of geography and environmental science.

These questions closely follow example problems from GCSE and A level past exams and were developed using existing exam questions. The maths skills tested in the question remained unchanged, but the context of the question was adapted to a climate change theme.

A Solar Sine Curve
A Level
A Solar Sine Curve
You are given the equation [fleft( x right) = 5costheta – 8sintheta] a) Express f(x) in the form (Rcos{(theta + alpha})) where (R >
A New Renewable
A Level
A New Renewable
A scientist wishes to develop a new way of generating renewable energy. They decide to use a large magnet on a large spring, oscillating
Net-Zero Buses
A Level
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
Arithmetic Afforestation
A Level
Arithmetic Afforestation
A country decides to begin a reforestation program, starting in 2020, gradually increasing the number of trees planted per year by the same amount
EV Increase
A Level
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
A Total Emissions Goal
A Level
A Total Emissions Goal
The warming caused by carbon dioxide (CO₂) emissions over any given period is proportional to the total amount of CO₂ emitted over that period.
A Nuclear Disaster
A Level
A Nuclear Disaster
Chernobyl is the site of a nuclear disaster that happened in 1986. Due to the slow decay of radioactive elements, the site is still
An Advancing Hurricane
A Level
An Advancing Hurricane
A hurricane is heading from the Atlantic Ocean to Miami, Florida. If the centre of the hurricane goes within a 50 kilometre radius of
A Carbon negative company
A Level
A Carbon Negative Company
A small company’s carbon dioxide (CO₂) emissions since 2000 can be modelled using the parametric equations [12x = t, y = 8t – 4.9t^{2}
Separated Satellites
A Level
Separated Satellites
2 weather-monitoring satellites orbit the earth. One is in a circular orbit C₁, the other orbits in an extreme ellipse, C₂ so that it can
A Quadratic Emissions Model
A Level
A Quadratic Emissions Model
The graph shows the rate of CO2 emissions per year since 1800. A climate scientist thinks that a quadratic curve could be fitted to
Warming Up A Solar Cell
A Level
Warming up a Solar Cell
The temperature T˚C of a solar cell during a 24 hour period is modelled as  [T = 20 – kleft( 15 – frac{5t}{4} right)^{2}
A Ferocious Forest Fire
A Level
A Ferocious Forest Fire
During a particularly hot summer, the area of a small forest was reduced by fire. The area, Akm2, of the surviving forest is modelled
Profiting from Reforestation
A Level
Profiting from Reforestation
A small company is planting trees in areas of the Amazon rainforest that have been affected by forest fires. On any day, the cost
surviving species
GCSE
Surviving Species
Climate change affects the habitats and environments of many species, some of which won’t be able to adapt fast enough to survive in their
climate striking students
GCSE
Climate Striking Students
The pie chart shows information about students going to a ‘Fridays for Future’ climate strike. 3360 more female students went to the strike than
annual carbon dioxide emissions
GCSE
Annual Carbon Dioxide Emissions
The table below shows information about the annual CO2 emissions from 140 cities. a) Work out an estimate for the mean CO2 emissions across
there is no planet B
GCSE
There Is No Planet B
Here is a pie chart taken from Mike Berners-Lee’s book There is no Planet B.  a) Calculate angle x. (shown on graph in the
reducing biodiversity loss
GCSE
Reducing Biodiversity Loss
The graph from the IPBES Global Assessment Report on Biodiversity and Ecosystem Services shows 3 different scenarios for how we could reduce biodiversity loss
a council questionnaire
GCSE
A Council Questionnaire
Sean works for a town council. He wants to find out how often people use recyling bins when throwing away paper. He is going
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