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

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

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

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

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 calculate various quantities in biological contexts.

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

How would you go about estimating populations of dolphins?

Use vectors and matrices to explore the symmetries of crystals.

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

Explore the shape of a square after it is transformed by the action of a matrix.

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.

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

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

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

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

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?

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

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

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?

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

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Which line graph, equations and physical processes go together?

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

Looking at small values of functions. Motivating the existence of the Taylor expansion.

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

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

Why MUST these statistical statements probably be at least a little bit wrong?

Here are several equations from real life. Can you work out which measurements are possible from each equation?

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

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

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