Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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

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

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

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

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

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

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

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

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

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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?

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

Which units would you choose best to fit these situations?

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?

Match the descriptions of physical processes to these differential equations.

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

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

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