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?

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

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?

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

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

Which line graph, equations and physical processes go together?

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

How would you go about estimating populations of dolphins?

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

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

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?

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.

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?

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

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

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

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

Build up the concept of the Taylor series

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

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.

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

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

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?

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

Which units would you choose best to fit these situations?

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.

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

Explore the relationship between resistance and temperature

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. . . .

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

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