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 the number of species is proportional to the remaining number of species.

Given that the initial number of amphibian species is N0, and t is the number of years since 1800,

a) Show that \(N = N_{0}e^{- kt}\)

[4 marks]

In 2000 the number of amphibian species is 0.9N₀.

b) Find the exact value of k.

[3 marks]

c) Using the model, in what year will 20% of amphibian species be

[3 marks]

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 9,200,000 km2, whereas in 2000 the area of the Sahara Desert had increased to 9,930,000 km2 due to human-induced global warming.

A model could be used to relate the surface area of the Sahara Desert, S km2, to the time, t, in years since 1950.

a) By first forming an exponential model for the surface area of the Sahara Desert relating S and t, show that the increase in the surface area of the Sahara Desert is approximately 0.15% per year.

[5 marks]

b) Use the model formed in (a) to estimate the size of the Sahara Desert in 2050. Give your answer in km2 to 3 s.f.

[1 mark]

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 new habitats.

The graph shows the percentage of species driven extinct since 1500. Of the species that were around in 1500

Diagram showing Extinctions since 1500

a) Calculate the probability of a reptile species having gone extinct by 1900. 

[1 marks]

b) Calculate the probability of an amphibian species not having gone extinct by 2018. 

[1 marks]

c) Of a sample of 60,000 species alive in 1500, assuming equal numbers of amphibian, mammal, bird, reptile and fish species are included, find, by first taking an average, how many species you would expect to have not gone extinct by 2018.

[3 marks] 

Climate Striking Students

The pie chart shows information about students going to a ‘Fridays for Future’ climate strike.

climate strike chart

3360 more female students went to the strike than male students.

a) Work out the total number of students at the climate strike.

[3 marks]

At the next ‘Fridays for Future’ climate strike, 20% more male and 12% more female students attended.

b) How many more students attended this strike?

[2 marks]

c) Draw an accurate pie chart representing the ratio of male to female students in the second climate strike, giving the angles subtended by the segments to the nearest degree.

[4 marks] 

Annual Carbon Dioxide Emissions

The table below shows information about the annual CO2 emissions from 140 cities.

 table shows information about the annual CO2 emissions from 140 cities.

a) Work out an estimate for the mean CO2 emissions across the 140 cities.

[3 marks]

b) Estimate the total amount of CO2 emitted from the 140 cities by using the mean value.

[1 mark]

c) Draw a frequency polygon representing the table.

[3 marks]

There Is No Planet B

Here is a pie chart taken from Mike Berners-Lee’s book There is no Planet B. 

no planet b pie chart

a) Calculate angle x. (shown on graph in the fossil fuel section) 

[2 marks]

b) The ratio of the percentages of manure and CH4 to methane and paddy fields to enteric emissions is 7:3:8. Complete the pie chart.

[3 marks]

UK Energy Usage

The table gives information about how the UK used its energy in 2017.

CREDS calculations based on BEIS (2018)


Percentage of UK energy used by sector (%)









a) Draw an accurate pie chart to show this information. 

[3 marks]

In 2017, the UK used the equivalent of 141 million tonnes of oil for energy.

One year the government develops a new initiative to get more people to use electric buses. 

The energy used by transport decreased by 15%.

The UK will use the same total amount of energy.

b) Express the amount of energy the UK will use for transport as a percentage of 141 million tonnes of oil equivalent. 

[3 marks]

A New Power Station

A new kind of gas-fired power station releases on average 1.73×104 kg of pure carbon dioxide (CO2) every day. It also uses the heat of exhaust gases to provide community heating so the carbon dioxide leaving the power station is at same temperature as the environment. The density of CO2 as it leaves the power station is 1.98 kg/m³.


a) What volume of pure CO2 will be emitted from the power station each day? 

[2 marks]

The CO2 now enters the atmosphere and is ‘diluted’ by other air molecules and therefore occupies a larger volume. In the atmosphere, for every million (1000000) air molecules, there are 400 CO₂ molecules. 

b) Work out the volume that the diluted CO2 will now take up in the atmosphere. Give your answer to 3sf.

[2 marks]

A new technology is added to the power station to capture this carbon dioxide and store it as a liquid.

c) The density of liquid carbon dioxide is 1100kg/m³. 

Work out the volume that the amount carbon dioxide produced every day will occupy if stored as a liquid. 

[2 marks]

A depleted oil field contains a reservoir of area 1150 m2 which is 150m deep. This reservoir could be used to store the liquid carbon dioxide.

d) Evaluate how many years’ worth of carbon dioxide emitted from the power station could be stored in this oil field. Give your answer to two significant figures. 

[3 marks]

The Rates of Sea Level Rise

The graph shows satellite measurements of global sea level rise since 2000. 

(mm = millimetres)

the rates of sea level rise chart

a) Draw a line of best fit through the data between 1993 and 2010, and work out the rate of global sea level rise.

[3 marks]

b) Draw a line of best fit through the data between 2010 and 2018, and work out the rate of global sea level rise. 

[3 marks]

c) What does the difference between the rate in part b) and the rate in part c) tell us about how global sea level rise is changing? 

[1 mark]

Arctic Ice Melting

The increasing global temperature due to human-induced climate change is causing ice in the Arctic to melt, particularly over the summer season, July to September.

Arctic Ice Melting Diagram

In September 1999, there was 6.2 million km2 of Arctic sea ice.

In September 2015, there was 4.6 million km2 of Arctic sea ice.

Work out the percentage decrease in Arctic sea ice from September 1999 to September 2015. 

[3 marks]