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.

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

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 Jo make a gym bag for her trainers from the piece of fabric she has?

Simple models which help us to investigate how epidemics grow and die out.

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.

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.

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

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

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

Match the charts of these functions to the charts of their integrals.

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

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

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?

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

Get some practice using big and small numbers in chemistry.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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.

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

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

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

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

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.

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

Which units would you choose best to fit these situations?

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

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?

Build up the concept of the Taylor series

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

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