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?

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

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.

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

How would you go about estimating populations of dolphins?

Which of these infinitely deep vessels will eventually full up?

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.

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

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.

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.

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?

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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

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?

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

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

Get some practice using big and small numbers in chemistry.

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

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

Match the descriptions of physical processes to these differential equations.

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

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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

When you change the units, do the numbers get bigger or smaller?

Build up the concept of the Taylor series

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

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

Which units would you choose best to fit these situations?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Explore the relationship between resistance and temperature

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

Where should runners start the 200m race so that they have all run the same distance by the finish?

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