# 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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• Clear

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 Level
##### Wiring up a Net-Zero Home
A homeowner decides to make their house carbon-neutral. They place solar panels on the roof, which then connect o their mains circuit via a
A Level
##### A Hurricane Direction Shift
The movement of a hurricane is modelled by vector h.  It is moving at a speed of 20 kph, with the direction of 165˚
A Level
##### Monitoring Currents
In this question, all distances are measured in kilometres. 2 deep sea ocean current monitors, A and B, have position vectors (-1, 7, k)
A Level
##### Mountainside Monitoring
3 CO₂ monitors K, L and M are placed on a mountain side The vector (overrightarrow{text{KL}} = 3mathbf{i -}6mathbf{k}) and (overrightarrow{text{LM}} = 2mathbf{i} +
A Level
##### Colliding Currents
2 deep sea ocean currents meet. By modelling one current as the positive y axis. a) Find the angle that the second current, with
A Level
##### A Climate Aware Citizen
A person decides in 2020 that they want to completely eradicate their carbon footprint in 20 months. Following this decision, they begin to use
A Level
##### City Emission Levels
The emissions of a city from 2000 to 2012 are modelled by the equation (pleft( t right) = frac{1}{10}lnleft( t + 1 right) –
A Level
##### A Carbon Conscious Company
The curve [y = e^{-0.5x} + 4x – 0.1x^{2} + 2] Can be used to describe a company’s net emissions, in tons of CO2,
A Level
##### UK Carbon Dioxide Emissions
The rate of CO2 emissions for the UK was measured every 5 years, from 1990 to 2015. The results are given in the table
A Level
##### Finding the Total Carbon Dioxide Emissions from 1850
The graph below shows how the rate of CO2 emissions varies from 1800 to 2017. This curve can be approximated as (E = 1.5e^{0.02t})
A Level
##### A Regrowing Reef
a) Use the substitution (u = 4 – sqrt{s}) to show that [int_{}^{}frac{text{dh}}{4 – sqrt{s}} = – 8lnleft| 4 – sqrt{s} right| – 2sqrt{s}
A Level
##### 50 Years to Net-Zero
A country wishes to achieve net-zero CO2 emissions in 50 years.  At the start of the program their emissions are 800MtCO2 year-1.  They decide
A Level
##### Deep-Sea Bubbles
Deep sea vents can emit harmful gases, such as hydrogen sulphide. Since these bubbles are small, they shrink once they leave the vent, as
A Level
##### Filling a Weather Balloon
The height (h km) that a weather balloon can reach is related to the volume (v m₃) of helium in it at sea level
A Level
##### Storing Sequestrates
A manufacturer produces a tank for storing liquid CO2 underground. The tank is modelled in the shape of a hollow vertical circular cylinder closed
A Level
##### 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
A Level
##### Shrinking Species
Since 1800, the number of amphibian species, N, has been decreasing over time, t.  A simple model shows that the rate of decrease of
A Level
##### The Swelling Sahara
Human-induced global warming is causing deserts such as the Sahara to increase in surface area. In 1950 the area of the Sahara Desert was
A Level
##### A Shrinking Rainforest
In a simple model, the surface area, S km2, of a shrinking rainforest depends on the time, t, in years since 1980. The following
A Level
##### A Speedy Sea Current
An ocean current separates into 2 different currents at a small island that can be modelled as the origin. Current A heads due south