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?

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

Which line graph, equations and physical processes go together?

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.

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

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

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

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

How would you go about estimating populations of dolphins?

Get further into power series using the fascinating Bessel's equation.

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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

Build up the concept of the Taylor series

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

Explore the relationship between resistance and temperature

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

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.

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

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

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?

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

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.

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

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.

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

Which dilutions can you make using only 10ml pipettes?

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