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

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

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

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

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

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

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

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.

Which line graph, equations and physical processes go together?

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?

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.

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

Explore the relationship between resistance and temperature

Get some practice using big and small numbers in chemistry.

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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

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

How would you go about estimating populations of dolphins?

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.

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

Work out the numerical values for these physical quantities.

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

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

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?

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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

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