Which countries have the most naturally athletic populations?

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.

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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.

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.

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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

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

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

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

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

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 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?

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

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. . . .

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

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

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

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

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?

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