This problem explores the biology behind Rudolph's glowing red nose.

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

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

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

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

How would you go about estimating populations of dolphins?

Get some practice using big and small numbers in chemistry.

Which units would you choose best to fit these situations?

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?

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

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

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

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

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

Build up the concept of the Taylor series

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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.

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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?

Explore the relationship between resistance and temperature

Which dilutions can you make using only 10ml pipettes?

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

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

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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

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