What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

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

Where should runners start the 200m race so that they have all run the same distance by the finish?

Get some practice using big and small numbers in chemistry.

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

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.

Work out the numerical values for these physical quantities.

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

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

Explore the relationship between resistance and temperature

Match the descriptions of physical processes to these differential equations.

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

Build up the concept of the Taylor series

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?

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

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

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

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

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

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

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

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

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

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

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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

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