Which countries have the most naturally athletic populations?

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?

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

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.

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

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

Get some practice using big and small numbers in chemistry.

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

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

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?

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

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

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

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

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

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

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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?

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

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.

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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.

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 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?

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

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

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.

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

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.