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

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

Use vectors and matrices to explore the symmetries of crystals.

How would you go about estimating populations of dolphins?

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?

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

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

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

Which of these infinitely deep vessels will eventually full up?

How do you choose your planting levels to minimise the total loss at harvest time?

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?

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

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

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

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

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

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

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.

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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

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

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.

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

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

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

Build up the concept of the Taylor series

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.

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

Match the descriptions of physical processes to these differential equations.

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

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.

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

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 dilutions can you make using only 10ml pipettes?

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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