Use vectors and matrices to explore the symmetries of crystals.

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

Which of these infinitely deep vessels will eventually full up?

How would you go about estimating populations of dolphins?

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.

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

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

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 visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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.

Work with numbers big and small to estimate and calulate 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.

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

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

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. . . .

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

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?

Match the descriptions of physical processes to these differential equations.

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

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

Invent scenarios which would give rise to these probability density functions.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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.

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.

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

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

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

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

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

Which dilutions can you make using only 10ml pipettes?