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?

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

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 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.

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

Which dilutions can you make using only 10ml pipettes?

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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.

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

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

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.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

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.

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

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

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

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

Get further into power series using the fascinating Bessel's equation.

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

Which units would you choose best to fit these situations?

Explore the relationship between resistance and temperature

Analyse these beautiful biological images and attempt to rank them in size order.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Build up the concept of the Taylor series

Look at the advanced way of viewing sin and cos through their power series.

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

When you change the units, do the numbers get bigger or smaller?

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

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

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

Here are several equations from real life. Can you work out which measurements are possible from each equation?

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

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

Match the descriptions of physical processes to these differential equations.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.