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

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

Which countries have the most naturally athletic populations?

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

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

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.

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

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?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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?

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

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.

Get some practice using big and small numbers in chemistry.

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

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?

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

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

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

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

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

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

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

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

Can you draw the height-time chart as this complicated vessel fills with water?

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

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

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

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

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