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

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

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

Can you match the charts of these functions to the charts of their integrals?

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

Which units would you choose best to fit these situations?

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

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.

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

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

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

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

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

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.

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

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?

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

Explore the relationship between resistance and temperature

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

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

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

How would you go about estimating populations of dolphins?

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

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

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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

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