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

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

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

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.

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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

Explore the relationship between resistance and temperature

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

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

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

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

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

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

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

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

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

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.

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

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

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