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

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

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

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.

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

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

Which countries have the most naturally athletic populations?

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?

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

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

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?

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

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.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

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

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?

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

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.

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

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

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.

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.

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?

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

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

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

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.

Get some practice using big and small numbers in chemistry.

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

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

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?

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

Match the descriptions of physical processes to these differential equations.

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