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. . . .

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.

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

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.

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

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

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

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

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

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

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?

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?

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

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

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.

Build up the concept of the Taylor series

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

Explore the relationship between resistance and temperature

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

Get some practice using big and small numbers in chemistry.

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

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

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.

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.

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

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.

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

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.

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

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.

Which dilutions can you make using only 10ml pipettes?

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