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

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

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

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

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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.

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

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

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

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

Is it really greener to go on the bus, or to buy local?

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

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.

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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.

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?

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.

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

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.

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

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?

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

Use vectors and matrices to explore the symmetries of crystals.