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

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

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?

Work out the numerical values for these physical quantities.

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

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

Which dilutions can you make using only 10ml pipettes?

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

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?

Get some practice using big and small numbers in chemistry.

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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

Explore the relationship between resistance and temperature

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

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?

Which line graph, equations and physical processes go together?

Match the descriptions of physical processes to these differential equations.

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.

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?

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

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

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

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

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

Can you match the charts of these functions to the charts of their integrals?

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

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

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

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

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

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

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

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

Build up the concept of the Taylor series

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