For maths, by far the most efficient strategy I found for studying was doing practice questions. As many as reasonably possible. This not only builds up your ability to sort of act like a "human computer", completing a set of instructions consistently and quickly, but also exposes you to a ton of different ways that questions can be phrased, so you're not caught off guard by a weirdly communicated question.

It's also just a great way of overcoming the "yeah, I think I know it" trap. You see this kind of thing all the time - where people are like "Before the exam, I thought I had a pretty good grasp of the subject, but then I sat down to take the exam and looked at the questions and I just had no idea how to figure it out/write down a good response, as if all the things I studied left my brain in an instant. What the hell?!" That's a good indicator that you convinced yourself that you knew the material - you could sit down, read a key word like "osmosis" or whatever, and go "oh, I know that's a key word!" but didn't actually know the material, you were just recognizing it and reading the explanation for it and saying "yeah, I recognize this definition, I've read it before". There's a lot of ways to do the process of reproducing the material in your head, such as creating flashcards or posters (another comment here is about teaching it to other people, or at least imagining that you are) or indeed, practice questions, and all of them are better than passively reading and recognizing it. Just pick your favourite.

Other than that, make sure you realize the value of breaks - they are just as important as the time spent studying, as it gives you time for your mind to rest and organize what you've learned before pushing on. There's a lot of different ways of organize taking breaks which work for different people, but pomodoros are among the most popular (25 minutes of work, 5 minute break. Do that four times and you get a 30 minute break. Then repeat from the beginning). There's others, like one where you work for 50 minutes and take a break for 15/20 minutes, as well as one where you work for about two hours and then take a half-hour break. Whichever one works, works.

6 months is plenty of time if properly utilized; usually when people start panicking about exams, it's like "oh yeah, it's in 2 weeks" and that involves very different strategies. As long as you start now and use the time well, you should be totally fine.

There's a short book called "A Mind For Numbers: How to Excel at Math and Science" that I recommend. It's about learning and studying in general, not just math and science. It's worth taking the time to read it to develop some strategies for your studying.

I also used to use flash card programs like Anki, not sure if that's still a popular one or not.

I often learn by teaching so I'll find other people who want to learn it and explain the things I'm learning to them. Or if it's something really boring I'll explain it to someone who's willing to listen to it. I'll also explain and narrate in my head imagining an old roommate or something. People I've given this strategy to IRL say they pretend they're streaming, but I don't do that because I don't really watch streamers very much. The trick to it is to relate it to things you know, but not turn it into explaining capitalism because the test probably doesn't have questions about labor valorization etc etc.

I think someone on hexbear at one point posted a 'focus hack' video that suggested putting on headphones with no music playing as though you've listened to music which ended, but you were focused so you didn't notice. I don't do this, but it makes sense to me. The video had a bunch of stuff like that, I think one was a plugin that removes recommendations from youtube so the website is just a search bar and it tricks people into realizing that they're watching for convenience rather than looking for stuff and information.

For, like, exam trick questions, they usually fall into two categories:

• Specific methodology trick: you basically cannot do these by hand in enough time if you don't know the trick.

Multiply 503 by 497.

Factor out a 3 and make it (500+3)*(500-3). Then it's (250,000 - 9). (Doing this longhand would take forever even if you could obviously do it.)

• Specific knowledge trick: you basically cannot do these efficiently without just knowing from some other source.

The cube root of 64 is 4, because 4x4x4 is 64. What is the cube root of 1,728?

1,728 is a cubic foot so the answer is 12. (You'd have to test factors or do cube root division which is hard and takes a long time.)

Either way, look at old exam questions and example questions and figure out what the these tricks are for the test you're taking.

Also, good luck. You probably know and remember much more than you think.

Do you exam well? Like are you calm sitting them, do you know how to keep track of time and avoid sunk costing on questions you can't answer etc?

If no you'll want to address that.

Otherwise work through textbooks of the appropriate material. Find some and work through, I mean work through. Not speed read and nod along. Write notes and do the practice problems. Do it regularly, to learn how to do a skill you have to regularly practice. You'll need a schedule that has you setting aside time at least a couple of times a week.

You have to regularly practice things in short sessions to learn well, and once learned repeat less frequently to maintain that knowledge. So you might spend 1 hour on the current topic, and close with 15 minutes of some practice questions on topics you already covered.

Keep notes of what you've done, by hand! it activates more brain shit. Talking aloud through problems can help too, or pretending you're explaining what you just learned to a nearby prop or very patient person. If you're struggling with a topic in your revision questions do more of it till it's easy again.

Also I don't exactly recommend this but amusingly prompting an llm to be an inquisitive listener and trying to explain topics and answer its "questions" might be helpful? NEVER try to learn from one though, they lie really convincingly.