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

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.

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

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

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

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

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

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

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?

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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?

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

Which units would you choose best to fit these situations?

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

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

Build up the concept of the Taylor series

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

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

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.

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

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

Match the descriptions of physical processes to these differential equations.

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?

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