One of the most popular posts on my blog for teachers is Top >10 Mathematics Websites. It struck me that it might be useful to think about my top recommendations for students. Using some categories here again gives me the excuse to mention more than 10! All these resources are free to use.
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!
For checking your work WolframAlpha is so useful, it is free to use for as many queries as you want; additionally with free use you can get step-by-step solutions for three problems a day. 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.
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.
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. On the Challenges page you can see resources such as the UK Maths Challenges, Nrich, 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. (See this post for further information).
Continuing with the theme of doing Mathematics, applets can help you explore the subject. Try some of the Wisweb Applets, see for example these challenging Plans and Elevations applets. (Note that these require Java – Chrome and Java don’t always seem to get along – try IE with Java). On the notes page I have mentioned Craig Barton’s site, also from Craig you could try his Autograph activities (which only require the free Autograph viewer to work). Ron Barrow has an extensive collection available for you to try on Waldomaths. You could for example practise solving equations (note the 5 levels of difficulty) or older students could try the resources on Matrices, Complex Numbers or Polar Coordinates available in his Further Mathematics collection.
We all like to play Games, many games are available to help you practise Mathematics, you can see a whole collection on Mathematics Games. See for example
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.
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 many more recommendations on the Useful links pages. Students do let me know your own particular favourites.