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

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

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

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

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

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

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

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

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

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?

Use vectors and matrices to explore the symmetries of crystals.

Which of these infinitely deep vessels will eventually full up?

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

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

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?

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.

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

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.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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

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

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?

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.

Which line graph, equations and physical processes go together?

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

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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