Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Where should runners start the 200m race so that they have all run the same distance by the finish?

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

Have you ever wondered what it would be like to race against Usain Bolt?

Was it possible that this dangerous driving penalty was issued in error?

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Get further into power series using the fascinating Bessel's equation.

Why MUST these statistical statements probably be at least a little bit wrong?

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Which dilutions can you make using only 10ml pipettes?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Get some practice using big and small numbers in chemistry.

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Invent scenarios which would give rise to these probability density functions.

How would you go about estimating populations of dolphins?

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Go on a vector walk and determine which points on the walk are closest to the origin.

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

When you change the units, do the numbers get bigger or smaller?

Match the descriptions of physical processes to these differential equations.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Explore the relationship between resistance and temperature

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Analyse these beautiful biological images and attempt to rank them in size order.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Build up the concept of the Taylor series

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Look at the advanced way of viewing sin and cos through their power series.

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

Here are several equations from real life. Can you work out which measurements are possible from each equation?