Studying for maths isn’t just about practice makes perfect. You have to be correct!
Every now and then, some students pick up the habit of doing, but not checking. After you finish a question, you should always verify that your answer is valid. For textbooks, this basically means bookmark the answers page, and refer back to them every five questions or so.
Obviously, it’s not so easy for proof-work and algorithms. For proofs, naturally you’d expect to arrive at the given result. But you should still check that your flow of logic is still correct! For algorithm work, see if the end result matches what the answers give, at least.
But also, when studying with sample exams, keep in mind that many of them come with solutions! If your answer is correct, you should still compare your method to the solutions, and see if they match up. If they don’t, check if your method had a flaw, but potentially ran into ‘two-wrongs-make-a-right’. (That is, a correct answer from incorrect working.) Otherwise, see if their approach was easier! You may pick up a new little trick that way!
Also, on the other hand, you should never fall reliant on solutions and answers. Remember, they’re there to help you revise, not do the task for you. If you’re always using answers without thinking, unfortunately you’re not going to learn!
Everyone’s bound to make a mistake somewhere whilst revising for mathematics. Or run into a roadblock where something no longer makes sense. This could happen when you first start preparing for an exam, or just doing homework, or elsewhere. The hard thing is going back to fill in the gaps later on. Or even worse, deciding to go back, only to forget where the issues even were!
All you have to do here is start compiling a small list of these difficulties and mistakes. Keep everything you record on it short and succinct. (For example textbook, question number, 5 sentence annotation on why it’s there.) Keep adding to the list, and start going back to it when you feel the time is right. That could be after a few days, or during the lead-up to an exam, or following enough questions from other papers/topics.
Also, update the list as appropriately as you can. For example, you might cross something off when you’re at least soundly confident on the issue. (Doesn’t necessarily have to be a perfect understanding if it’s hard – just consider if it’s adequate!) But you might highlight or just leave alone something that you’re still struggling to get. That may be something you’d note to ask your teacher, considering you had the same trouble twice!
Obviously, it’s up to you if you want to record your mistakes to the finest detail. I only recommend listing the ones you see appropriate! After all, it starts becoming a drain when you see a HUGE list of things to revisit. It risks de-motivation, and it’s likely you actually don’t have time for that!
Many high achievers like to keep a mental note of what stuff takes them minimal brainpower. There’s no point listing that out; they just know that ‘this is easy’.
Knowing what’s easy for you comes with two small advantages. The first is that you know you can always handle that kind of concept. Come exam time, you can always momentarily skip all the hard problems, and get the easy stuff done first. (Funnily enough, it’s an easy way to know you’ll likely bag these marks!)
The second is being wary of the overconfidence trap. You become aware of what questions (or parts) you’d be more susceptible to rushing. That means you know where you’d be more prone to silly mistakes! I.e., a minor accident such as error in basic arithmetic and algebra, or mixing up some variables in an equation. Or even just a calculator mistake. This is why checking your answers can be really valuable in saving marks!