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.

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

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

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

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?

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

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

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

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.

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. . . .

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?

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

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

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

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

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

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

Build up the concept of the Taylor series

Explore the relationship between resistance and temperature

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.

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

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

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

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

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

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

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

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

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.

Get some practice using big and small numbers in chemistry.

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.

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?