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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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

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

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

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

Explore the relationship between resistance and temperature

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

Which line graph, equations and physical processes go together?

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Build up the concept of the Taylor series

Match the descriptions of physical processes to these differential equations.

Work out the numerical values for these physical quantities.

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

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

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

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

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

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?

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.

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

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

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

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

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

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

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?