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?

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.

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

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

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

Get some practice using big and small numbers in chemistry.

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

Use your skill and judgement to match the sets of random data.

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

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

Work out the numerical values for these physical quantities.

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

How do you choose your planting levels to minimise the total loss at harvest time?

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.

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

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

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

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

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

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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

Use vectors and matrices to explore the symmetries of crystals.

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.

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

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

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.

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. . . .

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

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

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

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?

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

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

Which line graph, equations and physical processes go together?

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

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

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

Explore the shape of a square after it is transformed by the action of a matrix.