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

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

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

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

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

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.

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

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?

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

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

Which of these infinitely deep vessels will eventually full up?

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

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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

Work out the numerical values for these physical quantities.

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

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

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?

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

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

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?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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.

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.

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

Match the descriptions of physical processes to these differential equations.

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

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

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