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

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.

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

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

Which countries have the most naturally athletic populations?

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

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?

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

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

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?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

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

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

Simple models which help us to investigate how epidemics grow and die out.

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?

Which dilutions can you make using only 10ml pipettes?

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

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.

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

How would you go about estimating populations of dolphins?

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

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

Get some practice using big and small numbers in chemistry.

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

Build up the concept of the Taylor series

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

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

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

Use your skill and judgement to match the sets of random data.

Which units would you choose best to fit these situations?

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 biological contexts.

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

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