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?

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

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

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

Which of these infinitely deep vessels will eventually full up?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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?

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Which dilutions can you make using only 10ml pipettes?

Work out the numerical values for these physical quantities.

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

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?

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.

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

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

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.

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

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.

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?

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

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

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

Get some practice using big and small numbers in chemistry.

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.

Match the descriptions of physical processes to these differential equations.

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

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