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

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

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

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

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

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.

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

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

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

Which line graph, equations and physical processes go together?

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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.

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

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?

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

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

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.

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

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

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?

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

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

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?

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?

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

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

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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?