Maths

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:

• GCSE papers – if you have got (or can download) GCSE Higher maths papers, then keep doing them. The mark schemes are usually available as well.
• Online learning – use whatever logins you have (Hegarty, MyMaths, Pixl, BBC Bitesize, etc.) to carry on with GCSE work from their resources. To be accessing A-level maths you will need to be confident at grade 6 work and familiar with work at higher grades than that.
• Corbett Maths (https://corbettmaths.com/more/further-maths/) has an excellent section for the Level 2 Further Maths qualification (one which bridges the gap between GCSE and A-level) with video tutorials, practice questions and those all-important answers. Work through these sections:

1. Number
2. Algebra
3. Co-ordinate Geometry
4. Geometry

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).

• Puzzles and problem-solving: there are a lot of good sources of puzzles on the internet.

1. nrich: https://nrich.maths.org/secondary has a range of problems, activities, games and articles for 11-18 pupils.
2. Alex Bellos writes a fortnightly puzzle column for The Guardian which is published on their website: https://www.theguardian.com/science/series/alex-bellos-monday-puzzle
3. BBC Radio 4’s Today programme broadcasts a puzzle every morning at around 6:50am. You can find the archive on their website here: https://www.bbc.co.uk/programmes/articles/w9qwf7cQ01vBHCSwHK7mp/the-today-quizThe New Scientist website has a puzzle page here: https://www.newscientist.com/article-type/puzzles/
4. Plus magazine (https://plus.maths.org/content/) has a great range of puzzles and maths articles, including some very topical ones on Coronavirus!

Wider reading

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:

• The Code Book – Simon Singh
• The Calculus Wars – Jason Bardi
• How Long is a Piece of String? – Rob Eastaway and Jeremy Wyndham
• Why do buses come in threes? – Rob Eastaway and Jeremy Wyndham
• The Hidden Mathematics of Sport – Rob Eastaway and John Haigh
• Maths on the back of an envelope – Rob Eastaway
• Alex’s Adventures in Numberland – Alex Bellos
• The Simpsons and their Mathematical Secrets – Simon Singh
• 1089 and All That: A Journey into Mathematics – David Acheson
• Taking Chances – John Haigh
• e: the Story of a Number – Eli Maor
• An Imaginary Tale – The Story of √−1 – Paul J. Nahim
• Does God play dice? – Ian Stewart
• 17 Equations that Changed the World – Ian Stewart
• The Music of the Primes – Marcus du Sautoy
• Why Beauty is Truth – Ian Stewart
• Fermat’s Last Theorem – Simon Singh
• Leonardo, the first scientist – Michael White
• Longitude – Dava Sobel
• The curious incident of the dog in the night-time – Mark Haddon
• Uncle Petros and Goldbach’s Conjecture – Apostolos Doxiadis