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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

Get some practice using big and small numbers in chemistry.

Build up the concept of the Taylor series

Work out the numerical values for these physical quantities.

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

Explore the relationship between resistance and temperature

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.

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?

How would you go about estimating populations of dolphins?

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

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

Which units would you choose best to fit these situations?

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

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

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

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.

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

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

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

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Use vectors and matrices to explore the symmetries of crystals.

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

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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?

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

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

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

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

Can you sketch these difficult curves, which have uses in mathematical modelling?

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

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

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

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

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.

Can you construct a cubic equation with a certain distance between its turning points?