Warning: this page contains unfettered political opinion, so if you'd rather not be bothered with my blether, do go down to the list of interesting websites further down the page.
The invention of the Internet has provided would-be learners with a huge wealth of information that was never available to previous generations. However, it is sometimes hard to separate the wheat from the the chaff and there is a great deal of both out there. The problem for many is figuring out which may be valuable and which (to quote the current American president) is fake news.
There is a lot of misinformation out there. But you should always challenge it by checking with primary sources. You will find websites and Youtube videos to suit every crackpot idea out there, but it is your job, as a serious student, to check facts and test opinions (yes, mine too!). That is what your brain is for, so use it, please!
Favorite quote on this from Henry Ford. (No, not that one!)
"Thinking is the hardest work there is, which is probably the reason why so few engage in it."
Wikipedia can divide a room. The standard detractor's cry, "But it's written by ... anybody." doesn't really hold up as that applies to just about anything written by anyone, ever. If you want to read some real trash, try looking up the word "Negro" in an early 20th century edition of those august volumes, The Encyclopedia Britannica, and then come and talk to me about Wikipedia and those vague inaccuracies that people talk about. If you ask people to be specific aboput these inaccuracies, they start to bluster and get offended. (Unless you are one those white supremacist types in which case, just go away please. I told you to leave in the last but one paragraph. Go away!). Remember, Wikipedia is a secondary source and in common with all secondary sources, it needs checking with other (primary) sources, if you are going to become an intelligent, considered human being and not an ignorant brute. In terms of maths stuff, Wikipedia has a great deal of excellent material, much of which, I confess, is beyond my ability to comprehend. But if you want to know what a 42 sided polygon is properly called or you are interested in the many proofs of Pythagoras' Theorem (which probably wasn't discovered by Pythagoras), then Wikipedia has the correct answer for you.
This is a subscription only website, but as many, if not most schools in the UK have a subscription to it, it is likely that you (if you are a student) or your child (if you are a parent) will have a subscription. There is a wealth of material here: the entire GCSE, AS & A level courses are here in lessons when you get stuck and exercises with instant feedback when you want to figure out if you've "got it".
Nrich is a free to use website and is a Cambridge University project, but it is not all very high brow stuff. There are puzzles and problems for all ages and all levels. Many of those pesky (and difficult) UK Maths Challenge questions end up here and you will find hints to get you going and solutions so you can check yours. This is a brilliant resource for both students and teachers alike.
- Wolfram Alpha
Wolfram Alpha is another order of extraordinary. You can (and I do) subscribe to get extra stuff, but the basic thing is available to all. Ask it any question from "What is the poulation of Leamington Spa?" to "Integrate the square of coth cubed x wrt x", and all points in between and it will give you the right answer pretty regularly. I have it open most of the time if I'm doing anything difficult, so I can check my results. Very useful indeed! However, you can't take it into an exam, I'm afraid.
Euclidea has been this year's obsession for me. It is so simple to use and it will keep you puzzling for hours. It is a website, but also an Android and iOS app. It is free to use, though they ask people to contribute at certain stages and I hope people will do that as the developers deserve our thanks and our money. All of the puzzles on the app can be solved using a pair of compasses and a straight edge (an unmarked rule) though as you progress, certain commonly used combinations, like angle and perpendicular bisectors become available to you. Utterly brilliant and the user interface is peerless.
I will supplement this page with other sites as I remember or come across them.