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

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.

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

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

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

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

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

How would you go about estimating populations of dolphins?

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?

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

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

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?

Use vectors and matrices to explore the symmetries of crystals.

Which dilutions can you make using only 10ml pipettes?

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?

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.

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?

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

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

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

Match the descriptions of physical processes to these differential equations.

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 biological contexts.

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

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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

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

Get some practice using big and small numbers in chemistry.

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

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

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

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.