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?

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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?

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

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

Was it possible that this dangerous driving penalty was issued in error?

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

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

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

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

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

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

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

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

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

Explore the relationship between resistance and temperature

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

Get some practice using big and small numbers in chemistry.

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

This problem explores the biology behind Rudolph's glowing red nose.

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

How would you go about estimating populations of dolphins?

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 physical contexts.

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

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...

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

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

Explore the shape of a square after it is transformed by the action of a matrix.

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

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

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