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?

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

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

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

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?

Which of these infinitely deep vessels will eventually full up?

Was it possible that this dangerous driving penalty was issued in error?

How would you go about estimating populations of dolphins?

Can you construct a cubic equation with a certain distance between its turning points?

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

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.

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

Can you sketch these difficult curves, which have uses in mathematical modelling?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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.

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...

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

Explore the relationship between resistance and temperature

Get some practice using big and small numbers in chemistry.

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

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

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.

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

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

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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?