Can you construct a cubic equation with a certain distance between its turning points?

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

Explore the relationship between resistance and temperature

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

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

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

How would you go about estimating populations of dolphins?

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?

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

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?

Get some practice using big and small numbers in chemistry.

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?

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

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

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

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.

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

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

Work out the numerical values for these physical quantities.

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

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

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.

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.

Build up the concept of the Taylor series

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

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 calulate various quantities in biological contexts.

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

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

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

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Which dilutions can you make using only 10ml pipettes?

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

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

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

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