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

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.

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

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

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

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.

Use vectors and matrices to explore the symmetries of crystals.

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

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

Explore the relationship between resistance and temperature

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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

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

Can you make matrices which will fix one lucky vector and crush another to zero?

Can you sketch these difficult curves, which have uses in mathematical modelling?

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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.

Explore the properties of matrix transformations with these 10 stimulating questions.

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

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

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

How do you choose your planting levels to minimise the total loss at harvest time?

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