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

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

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?

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?

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.

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.

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

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

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

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?

Which units would you choose best to fit these situations?

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

How would you go about estimating populations of dolphins?

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

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

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

Get some practice using big and small numbers in chemistry.

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

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.

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

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

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

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

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.

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

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.

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

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

Build up the concept of the Taylor series

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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

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

Explore the shape of a square after it is transformed by the action of a matrix.

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.

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

Which dilutions can you make using only 10ml pipettes?

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Explore the relationship between resistance and temperature

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

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