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

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?

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

Get some practice using big and small numbers in chemistry.

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

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

Work out the numerical values for these physical quantities.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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 physical contexts.

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

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.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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.

Explore the relationship between resistance and temperature

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

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

Match the descriptions of physical processes to these differential equations.

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

Which units would you choose best to fit these situations?

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

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

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

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

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

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?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

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

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?

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

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

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