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?

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

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

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

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

Which line graph, equations and physical processes go together?

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

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

Get some practice using big and small numbers in chemistry.

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

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

Match the charts of these functions to the charts of their integrals.

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

Work out the numerical values for these physical quantities.

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

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

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

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.

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

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.

Build up the concept of the Taylor series

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

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

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.

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

Explore the relationship between resistance and temperature

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

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

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

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

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

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

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

How would you go about estimating populations of dolphins?

Which units would you choose best to fit these situations?

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.

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.

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