Which line graph, equations and physical processes go together?

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

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

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

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 physical contexts.

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

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?

Work out the numerical values for these physical quantities.

Get some practice using big and small numbers in chemistry.

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.

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

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

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

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?

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

Match the descriptions of physical processes to these differential equations.

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

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 relationship between resistance and temperature

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?

How would you go about estimating populations of dolphins?

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.

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

Can you work out which processes are represented by the graphs?

Which units would you choose best to fit these situations?

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

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

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

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?

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.

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

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

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

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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