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.

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.

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

Build up the concept of the Taylor series

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

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

How would you go about estimating populations of dolphins?

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

Get some practice using big and small numbers in chemistry.

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

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

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

Which units would you choose best to fit these situations?

Explore the relationship between resistance and temperature

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

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?

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

Match the descriptions of physical processes to these differential equations.

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

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?

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

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

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

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

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

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. . . .

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

Which dilutions can you make using only 10ml pipettes?

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

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

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?