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

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

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

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

Which line graph, equations and physical processes go together?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

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.

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?

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

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?

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.

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.

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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?

Work out the numerical values for these physical quantities.

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

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.

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.

Get some practice using big and small numbers in chemistry.

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

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

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

Which dilutions can you make using only 10ml pipettes?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

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

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

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Build up the concept of the Taylor series