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

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

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

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

Which line graph, equations and physical processes go together?

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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?

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

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

Get some practice using big and small numbers in chemistry.

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

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

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

Explore the relationship between resistance and temperature

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.

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

How would you go about estimating populations of dolphins?

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

Which units would you choose best to fit these situations?

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

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

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

Build up the concept of the Taylor series

When you change the units, do the numbers get bigger or smaller?

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

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?

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

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

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

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

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

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