3 CO₂ monitors K, L and M are placed on a mountain side
The vector \(\overrightarrow{\text{KL}} = 3\mathbf{i -}6\mathbf{k}\) and \(\overrightarrow{\text{LM}} = 2\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}\), relative to a fixed origin.
Show that \(\angle KLM = 66.4°\) to one decimal place
[7 marks]
Hence find \(\angle LKM\) and \(\angle LMK\)
[3 marks]
The height (h km) that a weather balloon can reach is related to the volume (v m₃) of helium in it at sea level by the equation:
\[h = \frac{8v^{2}}{5} – \frac{32v^{3}}{255}\ ,\ v \leq 12\]
a) Find the volume of helium required to achieve the maximum height and state this height.
[5 marks]
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 get closer to the surface.
These orbits can be modelled by the equations below:
\[C_{1}:\left( x + 2\sqrt{17} \right)^{2} + y^{2} = 66\]
\[C_{2}:x = 10\cos t,\ y = 4\sqrt{2}\sin t,\ 0 \leq t \leq 2\pi\]
Give the x coordinate of the points of intersection of the curves C₁ and C₂, given that
\(- 5 \leq x \leq 0\). Give an exact answer in the form
\[A\sqrt{1122} + B\sqrt{17}\]
[7 marks]
These resources explore the climate of five different scale periods of the past 2.6 million years. Within each, some of the basic processes affecting the climate are investigated. Please feel free to adapt the resources to the level and ability of the students you teach.
Module 1 – the last 2.6 million years: Milankovitch Cycles, Supervolcanoes
Module 2 – the last 11000 years: The Holocene
Module 3 – the last 2000 years: the Medieval Warm Period and the Little Ice Age
Module 4 – the last 500 years: Volcanoes
Module 5 – the last 200 years: the Sun, the Anthropocene and the Greenhouse Effect
Notes on the sources of data used.
Guide to sources of paleo-climate data.
Acknowledgements
These resources were jointly produced by Dr Kathryn Adamson (Manchester Metropolitan University), Dr. William Roberts (Bristol University), Dr. Chris Brierley (University College London) and the Royal Meteorological Society.
These resources were Highly Commended by the Geographical Association, who noted that they give teachers structured access to curriculum topics that are otherwise not readily found with up-to-date data from paleo-climate experts.
Climate graph, 500 years, without uncertainty
Climate graph, 500 years, with uncertainty
PowerPoint explanation of the impact of Volcanoes on Climate
Investigation – the Year With No Summer and corresponding
PowerPoint
Using tree rings to teach past climate change
How Do Volcanic Eruptions Affect Climate and Our Ability to Predict Climate? IPCC WG1 FAQ11.2
1816 – the year without summer: the experience of Newcastle-upon-Tyne
Situating 1816, the ‘year with no summer’, in the UK
< Module 3 – the last 2000 years | All Modules | Module 5 – the last 200 years >
Climate graph, 1,500 years, without uncertainty
Climate graph, 1,500 years, with uncertainty
PowerPoint explanation of Medieval Climate Anomaly and the Little Ice Age
Did the European Conquest of the Americas Contribute to the Little Ice Age?, Teaching Geography, 2019
KS3/ 4 Causes of Climate Change in the Little Ice Age Worksheet and Teachers’ Notes
A Level – The Impact of the arrival of Europeans in the Americas on the Carbon Cycle –Worksheet and Teachers’ Notes.
Investigation – Little Ice Age in London
Case study – Medieval Climate Anomaly and the Vikings
IPCC 2001: Was there a “Little Ice Age” and a “Medieval Warm Period”?
Little Ice Age scientific summary paper
The Great Snow of winter 1614/ 1615 in England: a paper looking at contemporary reports of extreme weather.
< Module 2 – the Holocence | All Modules | Module 4 – the last 500 years >
Climate graph, 11,000 years, without uncertainty
Climate graph, 11,000 years, with uncertainty
A Timeline of Earth’s Average Temperature
Interpreting a temperature graph
< Module 1 – the last 2.6 Million years | All Modules | Module 3 – the last 2000 years >
Climate graph, 2.6 million years, without uncertainty
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