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

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

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

Explore the relationship between resistance and temperature

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

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

Get further into power series using the fascinating Bessel's equation.

Match the charts of these functions to the charts of their integrals.

Which line graph, equations and physical processes go together?

How would you go about estimating populations of dolphins?

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

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.

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

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?

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.

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?

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

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

Use vectors and matrices to explore the symmetries of crystals.

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

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.

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

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?

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

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

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

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

Get some practice using big and small numbers in chemistry.

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?

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