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

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

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

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?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

Work out the numerical values for these physical quantities.

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

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?

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

Use vectors and matrices to explore the symmetries of crystals.

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

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

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

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

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 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?

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

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

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

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?

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

Can you draw the height-time chart as this complicated vessel fills with water?

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

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

Build up the concept of the Taylor series

Look at the advanced way of viewing sin and cos through their power series.

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

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

Match the descriptions of physical processes to these differential equations.

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

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.

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?

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

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?