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

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

Match the descriptions of physical processes to these differential equations.

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

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

How would you go about estimating populations of dolphins?

Which line graph, equations and physical processes go together?

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

Work out the numerical values for these physical quantities.

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

Which of these infinitely deep vessels will eventually full up?

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

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?

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

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

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

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

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

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.

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

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

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

Which dilutions can you make using only 10ml pipettes?

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