It struck me that it might be useful to think about my top recommendations for students. Using some categories again gives me the excuse to mention more than 10! All these resources are free to use.
Francesco Bondi’s art work on Desmos. Click the image to see the graph on Desmos.
For an online graph plotter try the excellent Desmos graphing calculator, it is very easy to use and allows you to save your graphs if you sign up. (Facebook is one option you can use to sign in to Desmos). You can see more examples of Desmos graphs here and there is a helpful user manual you can download from Desmos. There are many creative users of Desmos, have a look at the selection of art work! Make sure you get Desmos on your phone and/or tablet too.
For checking your work WolframAlpha is so useful, it is free to use for checking answers for as many queries as you want (step by Step solutions require a subscription). The set of slideshows here show you the syntax for a variety of queries.
For more excellent calculators and tools for checking your work, try this collection.
Calculus workbook from Plymouth University
There are many sites with useful notes and examples online for all ages, you will find several on the Notes page, this Evernote shared notebook, Mathematics notes includes many links, several universities have very helpful resources which they have made available to all students. You do not have to be an Evernote user (though I’d recommend it highly), just select ‘View’ to access the notebook.
For reference materials see the various resources on the Reference page which includes links to online dictionaries.
If you like to watch videos to help you learn then you may find some useful resources on the Videos page. Though of course you need to actually do lots of questions!
The best way to learn Mathematics is of course to do Mathematics and there are some excellent sources of problems for students of all ages to try.
Underground Mathematics has an extensive collection of questions to get you really thinking about your Mathematics. Suggestions and full solutions are provided but as always make sure you really do everything you can first with the question.
There are several sites with questions and examples for students of all ages. See more posts with many more resources in the Questions Category.
For revision you can use questions and examples already mentioned, Underground Mathematics includes examination questions for students age 16+. Note the above question comes from an Oxford University Mathematics aptitude test; it is one of the many Review Questions.
The Revision pages include questions from UK 15-18 Mathematics Examinations. These all include very challenging questions as well as more routine practice.
For 17-18 Year olds, MadAsMaths includes some very challenging questions for those aiming at the top grades. My student who recommended the site went on to achieve an A* grade!
If your teacher is not using Diagnostic Questions shown here, you can sign yourself up as a student. Note the many Collections of Questions as well as questions by topic. (You need to be signed in for the link to work).
Brilliant – Level 5 example
On the Challenges page you can see resources such as the UK Maths Challenges, Nrich, Underground Maths and Brilliant. Signing up to Brilliant (including an easy option for sign in for Facebook users) will allow you to join an international community and get free weekly, personalised problems. Questions at various levels are available. Follow Brilliant on Facebook.
We all like to play Games, many games are available to help you practise Mathematics, you can see a whole collection on Mathematics Games.
Try Bart Bonte’s logic game ‘Think Outside the Flock’. The game is on Math Playground which I know has many games students enjoy. For more logic games and puzzles try the Logic page.
Make a badge!
Are you wandering what mathematicians do or are thinking about a career in Mathematics? Aimed at anyone from age 11 to adult the Maths Careers site will answer your questions.
The Maths Careers site offers you many articles to read, for further reading materials try Plus Magazine from The Millennium Mathematics Project – University of Cambridge or perhaps Math in the News from the Mathematical Association of America or Mathematical Moments from the American Mathematical Society.
The 11 Commandments of Mathematics is perhaps a good way to end this post – and note 10 on Learning Mathematics – think about how you learn not just what you learn. Have a look at these Study Strategies from The Learning Scientists.
For valuable resources to support the techniques described here see the excellent downloadable materials on study strategies. Note how each strategy is backed up by research.
Obviously all these sites are those that I think are particularly good, I do know that many of my students use a lot of the sites I have mentioned here. You will find more recommendations on the Useful links pages. Students do let me know your own particular favourites.