What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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?

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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

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

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

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

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

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

Build up the concept of the Taylor series

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

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

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

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

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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.

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

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

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

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?

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

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

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

Explore the relationship between resistance and temperature

How would you go about estimating populations of dolphins?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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