Match the descriptions of physical processes to these differential equations.

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

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

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

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

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?

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

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

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.

Get some practice using big and small numbers in chemistry.

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

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

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.

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

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

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

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

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?

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

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.

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

Explore the relationship between resistance and temperature

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?

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

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

Which units would you choose best to fit these situations?

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

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

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

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

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

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

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

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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

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

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