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

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

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

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?

Which line graph, equations and physical processes go together?

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

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

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

How would you go about estimating populations of dolphins?

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

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.

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

Which dilutions can you make using only 10ml pipettes?

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.

Get some practice using big and small numbers in chemistry.

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Explore the relationship between resistance and temperature

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

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

Build up the concept of the Taylor series

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

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

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

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

Which units would you choose best to fit these situations?

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...

Work out the numerical values for these physical quantities.

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

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

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

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.

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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?

Can you construct a cubic equation with a certain distance between its turning points?

Match the charts of these functions to the charts of their integrals.