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

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

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

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

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?

Which countries have the most naturally athletic populations?

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

How would you go about estimating populations of dolphins?

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

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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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.

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

Which units would you choose best to fit these situations?

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

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

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

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

Build up the concept of the Taylor series

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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.

Explore the relationship between resistance and temperature

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

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.