(When I was in middle school, I usually talked about proof questions and geometry questions.)
1, see the problem.
2. What should I do? In other words, it is necessary to understand what this topic really requires.
3, assuming that the topic is absolutely correct, then the required answer is equivalent to a known condition.
4. Since this condition holds, a series of conditions are bound to hold and gradually approach the known conditions in the topic.
5. What is deduced from the known conditions is a clue, and what is deduced from the required answers is also a clue. Look for the intersection of the two.
It seems very troublesome to say, but it is actually very simple to get used to it, especially for general proof problems, geometric problems and some algebraic problems. This should be the so-called reverse thinking.
As for carelessness, it is hard to say. There is a saying that it may be a reference, that is, to synthesize the previous wrong questions, summarize the reasons for the mistakes, and then classify them. This should be helpful. Learning math well means spending more time summing up. When you read all kinds of topics and make all kinds of mistakes, there is nothing to be afraid of. Mistakes are also wealth.
This is my experience. I don't know if it will help you. I wish you success!