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.

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

Work out the numerical values for these physical quantities.

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

Which dilutions can you make using only 10ml pipettes?

Get some practice using big and small numbers in chemistry.

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

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?

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

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

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

Which line graph, equations and physical processes go together?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Which units would you choose best to fit these situations?

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

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

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.

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

Build up the concept of the Taylor series

Explore the relationship between resistance and temperature

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

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

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?

Where should runners start the 200m race so that they have all run the same distance by the finish?

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?

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

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

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

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

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

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.

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

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?

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

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

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

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