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.

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

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

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?

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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.

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.

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

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

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.

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

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

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

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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