For year 11 pupils who want to go on to study maths at A-level, the most important thing is not to forget everything you have already learned! Many of the skills you have worked hard to master in your GCSE studies are used frequently in the higher level maths you study at A Level. So during these months you should keep practicing to keep your skills sharp. Here are some ideas for you:
This is not about teaching yourself anything new (unless you really want to!) so you can skip out the sections on Calculus and Matrices. There are also some bits you can skip out from Algebra (Domains and ranges, Drawing functions, Pascal’s triangle, Factor theorem, Cubics), Co-ordinate Geometry (Equation of a circle (centre not the origin), Equation of a tangent to a circle) and Geometry (Trig identities, Other Trig ratios, Trigonometric equations).
There are plenty of excellent books to read. These are not maths text books, but stories about the history of bits of mathematics, how it was developed and how it was (and is) used. Here is a small selection: