Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

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?

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

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.

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

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

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

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

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

How would you go about estimating populations of dolphins?

Match the descriptions of physical processes to these differential equations.

Get some practice using big and small numbers in chemistry.

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

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

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

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

Explore the relationship between resistance and temperature

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

Use vectors and matrices to explore the symmetries of crystals.

Have you ever wondered what it would be like to race against Usain Bolt?

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

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

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

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

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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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

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

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

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

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

Build up the concept of the Taylor series