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?

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

Can you draw the height-time chart as this complicated vessel fills with water?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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?

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.

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

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 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.

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

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.

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

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?

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

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?

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

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

Which dilutions can you make using only 10ml pipettes?

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

Get some practice using big and small numbers in chemistry.

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.

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.

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

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

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