As for the choice of training books in peacetime, The Graphic Album of Special Lecture of Senior High School Mathematics Competition published by Zhejiang University Press is a good choice, with classic examples and reasonable distribution of exercise difficulty. It is also realized step by step and is suitable for self-study.
In terms of training methods, if we hurry to prepare for this year's championship, after all, there are still some sectors to be trained, such as number theory, combination and algebra. When there is not much time, we can set a shorter time limit, such as 20 minutes, or you can answer questions for half an hour. It is best to write wonderful proofs or good conclusions in a special notebook, so that you can accumulate some conclusion skills and experience and improve your problem-solving ability quickly in a short time.
But if you want to go further, long-term training methods can't solve problems by accumulating conclusions from experience like this. In this case, we will have no creativity when solving problems, and we will have no clue when encountering real problems. Only when we have enough time can we come up with a solution on our own, which will not only impress the topic more deeply, but also really improve our analytical ability. If you ignore thinking and pay too much attention to increasing experience and accumulating conclusions, you will try to find a shortcut to solve the problem every time (that is, rely too much on lemma to prove the problem). Of course, this does not mean that you will never ask the answer. It just means that you have to think hard to solve them.
The necessary experience can be obtained by reading examples and analyzing the problems in the training paper with the teacher. The difficulty of teachers' competition training papers is generally reasonable. Knowing what kind of questions are suitable for your current level, I suggest taking the above methods to deal with the teacher's problems, and don't give up until you figure it out. This not only exercised my ability, but also gradually solved many problems by myself, and my confidence will gradually increase. It is much better to gradually increase the difficulty and practice in a down-to-earth manner than to study some difficult problems such as cmo at the beginning, and finally have to look at the answers, but I don't know how to think about this auxiliary line for a long time (for example, beginners can draw a conclusion according to the answers on the first day of the national team selection examination in 2008, but they just don't understand why they should do this, and later they know that it is related knowledge of harmonizing acupoints, which belongs to a topic that is not suitable for them).
Too difficult questions will not only cost you a lot of time, but also improve your ability, get twice the result with half the effort, and waste good questions and give you a sense of frustration. How to grasp the difficulty of the topic? I suggest you train with the competition coach now, read some books on special lectures after class, or ask the coach to recommend some topics to think about. When a powerful ability is formed, you can certainly overcome some difficult problems.
These are just personal suggestions. Everyone's situation is different. Only by summing up the methods that suit you can you go further. Finally, I wish you good luck in the exam and climb the peak of the math competition.