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

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

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

Work out the numerical values for these physical quantities.

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Which units would you choose best to fit these situations?

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

Get some practice using big and small numbers in chemistry.

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 properties of matrix transformations with these 10 stimulating questions.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

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

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

Build up the concept of the Taylor series

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

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

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

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

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.

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

How would you go about estimating populations of dolphins?

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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

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

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

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?

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