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

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

Use vectors and matrices to explore the symmetries of crystals.

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

How would you go about estimating populations of dolphins?

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

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

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.

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?

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

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

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

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.

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

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

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

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?

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

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?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Which line graph, equations and physical processes go together?

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

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.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Match the descriptions of physical processes to these differential equations.

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

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

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

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.

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

Build up the concept of the Taylor series

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

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

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.