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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Which countries have the most naturally athletic populations?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

How would you go about estimating populations of dolphins?

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Which line graph, equations and physical processes go together?

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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

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

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

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?

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.

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

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

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

Formulate and investigate a simple mathematical model for the design of a table mat.

Build up the concept of the Taylor series

Explore the relationship between resistance and temperature

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Simple models which help us to investigate how epidemics grow and die out.

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

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

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

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

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

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

Get some practice using big and small numbers in chemistry.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

Which dilutions can you make using only 10ml pipettes?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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 calculate various quantities in physical contexts.

Which units would you choose best to fit these situations?

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

Match the descriptions of physical processes to these differential equations.

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