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.

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.

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

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

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

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

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

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

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

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

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

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?

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

Which line graph, equations and physical processes go together?

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

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

Match the descriptions of physical processes to these differential equations.

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

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

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

Build up the concept of the Taylor series

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

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

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

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.

Which dilutions can you make using only 10ml pipettes?

Formulate and investigate a simple mathematical model for the design of a table mat.

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.

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.