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.

Match the descriptions of physical processes to these differential equations.

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

Get some practice using big and small numbers in chemistry.

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

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

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?

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

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

Explore the relationship between resistance and temperature

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?

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

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

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

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

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

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

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

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?

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

Which dilutions can you make using only 10ml pipettes?

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?

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.

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

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. . . .

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

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.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.