Mountainside Monitoring

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]

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 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]

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 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]

Past Climate Teaching Resources

wordleThese 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.


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.

geographical association publishers awardThese 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.

Past Climate Changes – Module 4

Past Climate Changes – Module 3

Module 3 – the last 2000 years

Core Resources

Climate graph, 1,500 years, without uncertainty

Climate graph, 1,500 years, with uncertainty


Past Climate Changes – Module 2

Module 2 – the last 11000 years (The Holocene)

Core Resources

Climate graph, 11,000 years, without uncertainty


Climate graph, 11,000 years, with uncertainty


Past Climate Changes – Module 1