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

Which line graph, equations and physical processes go together?

How would you go about estimating populations of dolphins?

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.

Work out the numerical values for these physical quantities.

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

Get some practice using big and small numbers in chemistry.

Where should runners start the 200m race so that they have all run the same distance by the finish?

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

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

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

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.

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?

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

Explore the relationship between resistance and temperature

Match the descriptions of physical processes to these differential equations.

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

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

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

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?

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

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

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

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

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

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

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

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

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

Which units would you choose best to fit these situations?

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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

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

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

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.

Can you draw the height-time chart as this complicated vessel fills with water?

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

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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?