A-level courses and examinations are with us for some time to come. Even if Mevel is introduced, for most pupils who spend two years in the I sixth form A-levels will remain the basis of their studies. It seems to me that we need a major debate about A-level mathematics; we need to review it as it is and try to decide what developments are necessary. The discussion I paper ‘Mathematics at A-level’ has already raised a number of points, some of which are touched on here. This article is not a statement of official SMP policy; any opinions expressed in it are my own. The aim is to provoke discussion. I shall consider a number of issues which seem to me to be important, hoping that others will be stimulated to contribute comments and suggest other topics which need attention.

In teaching Analytical Geometry very little attention is often given to the interpretation of the form of an equation, although this may often convey a good deal of information; by grouping the terms of an equation in different ways, a variety of useful and interesting results may be obtained with very little labour.

Some suggestions as to the possibilities of this method may be afforded by the cases given below. A considerable number of results are obtained, purely by simple manipulation of the general equation of the conic section in point and line co-ordinates. Except in one instance, no reference has been made to infinite elements; if we include the notions of infinite points and lines, and of the circular points, the power of the method increases very greatly. The only knowledge that has been assumed is that which is quite fundamental in point and line co-ordinates, and the meanings of certain simple typical forms.

E. H. Neville was Librarian of the Mathematical Association for over thirty years, from 1923 to 1954.For more than half of that time Neville was not only Librarian but custodian of the books which were handsomely shelved and displayed in his own home, first in his house on Castle Hill, Reading, and then in his first house in Sonning.

The best separation of substances by adsorption chromatography requires a de-sorbing solvent whose concentration-volume graph is concave. Various methods have been devised to achieve this, sometimes ignoring the density difference between the dilute and concentrated solvents. A particular method of mathematical interest is that of Baker, Ellis and Hawley [1] where standard components can be used and density differences are reduced by using a floating siphon.