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

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?

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

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

Explore the relationship between resistance and temperature

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

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

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

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

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

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

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

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

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

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

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.

Work out the numerical values for these physical quantities.

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?

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

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

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

Get some practice using big and small numbers in chemistry.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

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

Build up the concept of the Taylor series

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

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

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

Is it really greener to go on the bus, or to buy local?

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

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

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

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

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

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

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

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

Which line graph, equations and physical processes go together?