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.

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

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?

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

Get some practice using big and small numbers in chemistry.

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

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

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?

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

Work out the numerical values for these physical quantities.

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

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

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

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

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

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.

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

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.

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

Explore the relationship between resistance and temperature

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?

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

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

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

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?