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

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

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

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?

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

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

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

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

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.

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

Which of these infinitely deep vessels will eventually full up?

How would you go about estimating populations of dolphins?

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

Can you draw the height-time chart as this complicated vessel fills with water?

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

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

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?

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

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.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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?

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

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

Explore the relationship between resistance and temperature

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

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

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.

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

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.

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

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