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

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

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

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.

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

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

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.

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

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?

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

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

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

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

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

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

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

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.

Which line graph, equations and physical processes go together?

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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

Which dilutions can you make using only 10ml pipettes?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

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