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

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

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

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

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

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

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

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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

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

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. . . .

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

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

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

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.

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.

Build up the concept of the Taylor series

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

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

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.

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

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

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.

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

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

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

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

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

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

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.

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

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.

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

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.

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

Which dilutions can you make using only 10ml pipettes?

Explore the relationship between resistance and temperature

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

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

How would you design the tiering of seats in a stadium so that all spectators have a good view?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?