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 vectors and matrices to explore the symmetries of crystals.

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.

How would you go about estimating populations of dolphins?

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

Match the charts of these functions to the charts of their integrals.

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

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?

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

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?

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

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

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

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

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.

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 biological contexts.

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

Build up the concept of the Taylor series

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

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?

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

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?

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

Explore the relationship between resistance and temperature

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

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

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

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

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

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

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

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