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.

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

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.

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

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

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.

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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?

Build up the concept of the Taylor series

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?

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

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

Which units would you choose best to fit these situations?

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

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

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.

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

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?

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.

Explore the relationship between resistance and temperature

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

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?

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

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