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

Use your skill and judgement to match the sets of random data.

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

Which line graph, equations and physical processes go together?

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

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

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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

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

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

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.

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

Match the descriptions of physical processes to these differential equations.

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

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

Explore the relationship between resistance and temperature

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

Build up the concept of the Taylor series

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.

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

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

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

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

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

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

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?

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.

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

Where should runners start the 200m race so that they have all run the same distance by the finish?

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