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

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

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.

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

Get some practice using big and small numbers in chemistry.

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

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

Which line graph, equations and physical processes go together?

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

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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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.

Which units would you choose best to fit these situations?

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

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 properties of matrix transformations with these 10 stimulating questions.

Build up the concept of the Taylor series

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.

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

Explore the relationship between resistance and temperature

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

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?

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.

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

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

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

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?

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

Match the descriptions of physical processes to these differential equations.

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?

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.

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