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

Where should runners start the 200m race so that they have all run the same distance by the finish?

Look at the advanced way of viewing sin and cos through their power series.

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

How would you go about estimating populations of dolphins?

Get further into power series using the fascinating Bessel's equation.

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

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

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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. . . .

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

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

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

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

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

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

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?

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

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.

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?

Which dilutions can you make using only 10ml pipettes?

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

Get some practice using big and small numbers in chemistry.

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.

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

Work out the numerical values for these physical quantities.

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...