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.

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.

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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

Have you ever wondered what it would be like to race against Usain Bolt?

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Work out the numerical values for these physical quantities.

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

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

Which line graph, equations and physical processes go together?

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

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

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?

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

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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?

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

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

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

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?

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

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.

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...

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

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

Use your skill and judgement to match the sets of random data.

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

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

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