As we come to the end of an academic year and look to a new one, it will be a time of change for many students. Perhaps you have completed GCSEs or equivalent qualifications (UK age 15-16) and are about to start on your A Levels or perhaps you have completed those and are about to start studying Mathematics at university.

To be in a position to begin your new courses well you should be thoroughly familiar with the essentials of the work you have studied to date. At whichever level you are studying your Algebra should be at a standard where you can manipulate expressions with ease.

Some resources to help you prepare and will be useful reference material for you during your course…

For students going on to A Level then a really useful publication is use OCR’s brilliant guide for students **Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide**. With sections on Algebra, Trigonometry and graphs including examples, question practice on key topics and suggested reading before starting the A Level this is so valuable for students.**pdf format: bridging-the-gap-between-gcse-and-as-a-level-mathematics-a-student-guide**

**Dr Frost Maths** is used by millions of students round the world. Amongst the extensive **library of resources** are **videos for students age 8-18** explaining topics from scratch. There are longer Exam-topic videos, average length 10 minutes and shorter Key Skill videos which are about 2-4 minutes in length.

Free lessons from Colin Hegarty **recorded on YouTube** are available to help GCSE students prepare for A Level Maths.

These **Transition Takeaways** from Mohammed Ladak have been specifically chosen to help with A Level Maths preparation.

You could also look at **Step Up to A Level Maths** from The Centre of Innovation in Mathematics Teaching which helpfully lists skills you should be confident with and provides resources to support your study of these skills.

From AMSP – check **Transition to A Level Mathematics **– Essential Skills.

As you study your A level (16-18) course you may find some of the material in the section below useful.

For many challenging questions to really get you thinking, try the brilliant **Underground Mathematics** site.

Make sure you have some useful apps on your phone if you don’t have them already. **Mathscard app from Loughborough university** is free and a handy reference guide of mathematical facts and formulae. Every student should have the **Desmos **app (free) and you could also get the **WolframAlpha** app (low cost).

If you are preparing for university, then make sure your A Level knowledge is secure – perhaps check the **Algebra Refresher** from **The Mathcentre** which has many questions and the answers are at the end of the document. The Mathcentre has an extensive collection of helpful resources for students of Mathematics.

For a collection of forty mathematics activities bridging between A Level and University, try **Carom Maths **from Jonny Griffiths.

Check the **List of Activities**, how much do you know about Inequalities for example? For a complete PowerPoint with information and questions on Inequalities, choose Carom 1-2: Inequalities.

For older students, **AJ Hobson’s Just the Maths** (individual pdfs hosted by UEA) (or a complete pdf from the Math Centre: **AJ Hobson’s ‘Just the Maths’) **is very useful as is the excellent **Math Centre site** which includes extensive resources. The **quick reference leaflets** which are available on numerous topics are very clearly written and succinct, see these for example on the **Product Rule** and the **Quotient Rule**. There are also teach yourself booklets, revision booklets, videos and diagnostic tests. See also these **very clear notes with exercises from Plymouth University**. There are many free courses available from **The Open University **and **MIT** .

If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include very clear worked examples. For easy access to these resources, the **HELM Project Workbooks** are hosted by **Loughborough University’s Mathematics Learning Support Centre**. Alternatively, the **complete set is hosted by the Open University**. To access the Open University resources you will need to **create an account** (easy and free), this will also give you access to the numerous free online courses.

If you are studying or about to study at university then have a look at Kevin Houston’s ‘**How not to get a good mathematics degree**‘ and ‘**How to get a good mathematics degree**‘. He also has provided a pdf file you can download: **10 Ways to Think Like a Mathematician**. Kevin Houston works at the University of Leeds in the UK.

From Professor Stephen Chew of Samford university, this series of 5 videos looks at how to get the most out of studying (any subject, not just maths). Part 1 includes ‘beliefs that make you stupid’!**How to get the most out of studying (Part 1), ****Part 2, ****Part 3, **** Part 4, ****Part 5**

The Open University has several **helpful publications** for students of Mathematics. Many of these resources would be helpful for students still at school.

From John Kerl – see these excellent **tips for mathematical handwriting**.

For older students Peter Alfeld wrote this guide on **Understanding Mathematics** for his students at Utah University.

And finally – check the 11 Commandments of Mathematics!

Remember these ~~ten~~ eleven commandments for mathematicians!

Alternatively – a pdf file, the links can work faster from pdfs.

Also available as a poster: **11-commandments-mathematics**

Wishing Mathematics students everywhere – whatever stage you are at a very successful next stage.