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

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.

How would you go about estimating populations of dolphins?

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

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

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

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

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.

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

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

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

Which of these infinitely deep vessels will eventually full up?

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?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Can you sketch these difficult curves, which have uses 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.

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?

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

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

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

Is it really greener to go on the bus, or to buy local?

Have you ever wondered what it would be like to race against Usain Bolt?

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Which dilutions can you make using only 10ml pipettes?

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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

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

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

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.

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

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?

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