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

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

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?

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

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

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?

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

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

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

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

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?

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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?

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

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.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

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.

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Which dilutions can you make using only 10ml pipettes?

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

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

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...

Get some practice using big and small numbers in chemistry.

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?

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.