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

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

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.

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

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

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.

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

Get some practice using big and small numbers in chemistry.

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

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

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

Build up the concept of the Taylor series

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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.

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

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

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

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

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.

Which dilutions can you make using only 10ml pipettes?

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

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

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.

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

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

Explore the relationship between resistance and temperature

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

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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