Work out the numerical values for these physical quantities.

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

Explore the relationship between resistance and temperature

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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.

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

Build up the concept of the Taylor series

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

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

Which dilutions can you make using only 10ml pipettes?

Which units would you choose best to fit these situations?

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.

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

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

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.

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

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

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

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

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

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.

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

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

How would you go about estimating populations of dolphins?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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