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.

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

Can you construct a cubic equation with a certain distance between its turning points?

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

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

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

Which line graph, equations and physical processes go together?

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

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.

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

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

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

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

Can you match the charts of these functions to the charts of their integrals?

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

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

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

Explore the relationship between resistance and temperature

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

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

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?

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

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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

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

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

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

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

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

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.

Have you ever wondered what it would be like to race against Usain Bolt?

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.