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.

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

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.

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

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

Get some practice using big and small numbers in chemistry.

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

Build up the concept of the Taylor series

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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 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.

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.

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

How would you go about estimating populations of dolphins?

Which units would you choose best to fit these situations?

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

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.

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

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?

Match the descriptions of physical processes to these differential equations.

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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.

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

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