Which of these infinitely deep vessels will eventually full up?

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

How would you go about estimating populations of dolphins?

Use vectors and matrices to explore the symmetries of crystals.

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.

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

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

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

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

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

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

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

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

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.

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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?

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

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.

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

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

Explore the relationship between resistance and temperature

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?

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

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?

Build up the concept of the Taylor series

Match the descriptions of physical processes to these differential equations.

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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

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?

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

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