Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

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

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

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

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

Work out the numerical values for these physical quantities.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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.

Get some practice using big and small numbers in chemistry.

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

How would you go about estimating populations of dolphins?

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?

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

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?

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

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

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

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

Explore the relationship between resistance and temperature

Build up the concept of the Taylor series

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.

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.

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

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

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

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.

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