Schools run by local authorities have an annual budget which is calculated by formula. The formula used for funding my school is quite easy to understand and its components all seem reasonable, yet it can cause some unexpected problems for an unwary manager.

Most of the funding depends on the number of pupils, each being worth an annual amount according to his or her age. If a comprehensive school has fewer than 750 pupils it is regarded as being small, needing extra money to provide an adequate curriculum. This extra is given as a bonus for each pupil; and tapers to zero as the numbers reach 750.

Cheryl Maiden is director of the Maths 100 Foundation, which is based in Henley-on-Thames.

The day begins before 9.00 a.m. and it’s a relaxed time opening mail over breakfast, punctuated by the occasional call. This morning it’s a query from the printers about the paper for Part 3, and the Yellow Pages again. I enjoy the post as it has become increasingly varied, bringing interesting new people into the Maths 100 project.

The cubic holds a double fascination, since not only is it interesting in its own right, but its solution is also the key to solving quartics. This article describes five fundamental parameters of the cubic (δ, λ, h, xN, and yN), and shows how they lead to a significant modification of the standard method of solving a cubic, generally known as Cardan’s solution.