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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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.

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

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

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 is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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?

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

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

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

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

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

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?

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.

Build up the concept of the Taylor series

Get some practice using big and small numbers in chemistry.

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

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

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

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?

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

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

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

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

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

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

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

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

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

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