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

Can you draw the height-time chart as this complicated vessel fills with water?

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

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

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

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

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

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. . . .

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

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

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 work out which processes are represented by the graphs?

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

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

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.

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

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.

Explore the relationship between resistance and temperature

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

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

Build up the concept of the Taylor series

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

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?

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

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.

Get some practice using big and small numbers in chemistry.

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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

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

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.

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

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

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

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.

Which dilutions can you make using only 10ml pipettes?

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

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