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

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?

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

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?

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

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

Can you match the charts of these functions to the charts of their integrals?

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

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?

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

Use vectors and matrices to explore the symmetries of crystals.

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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

This problem explores the biology behind Rudolph's glowing red nose.

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 calulate various quantities in biological contexts.

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

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

Get some practice using big and small numbers in chemistry.

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.

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

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

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.

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?

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.