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.

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

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

How would you go about estimating populations of dolphins?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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.

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

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

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

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

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

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

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

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.

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.

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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?

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

Match the descriptions of physical processes to these differential equations.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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. . . .

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?

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

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

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

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.

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

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

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.