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.

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?

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.

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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.

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 properties of matrix transformations with these 10 stimulating questions.

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?

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

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 calulate various quantities in biological contexts.

Build up the concept of the Taylor series

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

Match the descriptions of physical processes to these differential equations.

Work with numbers big and small to estimate and calculate 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.

Explore the relationship between resistance and temperature

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

Which line graph, equations and physical processes go together?

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

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?