Match the descriptions of physical processes to these differential equations.

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.

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

How would you go about estimating populations of dolphins?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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?

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?

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

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

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?

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.

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.

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

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?

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

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

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.

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

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

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

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

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.

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

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Build up the concept of the Taylor series

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

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