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

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

Which line graph, equations and physical processes go together?

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

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

Build up the concept of the Taylor series

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

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

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

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

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

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

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

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

Work out the numerical values for these physical quantities.

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

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?

How would you go about estimating populations of dolphins?

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?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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?

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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.

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

Which units would you choose best to fit these situations?

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

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

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

Match the descriptions of physical processes to these differential equations.

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