Which of these infinitely deep vessels will eventually full up?

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

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.

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

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Use vectors and matrices to explore the symmetries of crystals.

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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

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.

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

Build up the concept of the Taylor series

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

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

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

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.

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?

Which line graph, equations and physical processes go together?

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

Get some practice using big and small numbers in chemistry.

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

Can you match the charts of these functions to the charts of their integrals?

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

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

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

Explore the relationship between resistance and temperature

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

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