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.

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

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

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

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

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

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

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

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.

Which units would you choose best to fit these situations?

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

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

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

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

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

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

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?

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.

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.

Use vectors and matrices to explore the symmetries of crystals.

Is it really greener to go on the bus, or to buy local?

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

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

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?

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

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

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

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

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

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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?

Which line graph, equations and physical processes go together?

How would you go about estimating populations of dolphins?

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