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?

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?

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

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

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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

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

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

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

Which countries have the most naturally athletic populations?

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Which line graph, equations and physical processes go together?

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

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

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

Get some practice using big and small numbers in chemistry.

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?

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

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

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.

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

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

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

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

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

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.

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

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

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