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.

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

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.

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

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

Which countries have the most naturally athletic populations?

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

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

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

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

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

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

How would you go about estimating populations of dolphins?

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

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

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?

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

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.

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

Which line graph, equations and physical processes go together?

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.

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

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. . . .

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

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Explore the properties of matrix transformations with these 10 stimulating questions.

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

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

Use vectors and matrices to explore the symmetries of crystals.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Can you sketch these difficult curves, which have uses in mathematical modelling?

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

Can you make matrices which will fix one lucky vector and crush another to zero?

Explore the meaning of the scalar and vector cross products and see how the two are related.

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Which dilutions can you make using only 10ml pipettes?

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Can you work out which processes are represented by the graphs?

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

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.