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 simple trigonometry to calculate the distance along the flight path from London to Sydney.

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.

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

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

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

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.

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

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 biological contexts.

Build up the concept of the Taylor series

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

Explore the relationship between resistance and temperature

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

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

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?

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

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?

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

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

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

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

Which line graph, equations and physical processes go together?

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

How would you design the tiering of seats in a stadium so that all spectators have a good view?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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?

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

Use vectors and matrices to explore the symmetries of crystals.