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

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

How would you go about estimating populations of dolphins?

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

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

Use vectors and matrices to explore the symmetries of crystals.

Analyse these beautiful biological images and attempt to rank them in size order.

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

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

Work out the numerical values for these physical quantities.

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.

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?

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

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

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 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.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

When you change the units, do the numbers get bigger or smaller?

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?

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

Which units would you choose best to fit these situations?

Build up the concept of the Taylor series

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

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

Match the descriptions of physical processes to these differential equations.