First of all, in terms of progress:
It is very important to learn all the mathematics contents of the whole high school in the summer vacation before the start of senior one, and to complete two rounds of review last semester like senior three. The initial test scores 150, which should not be underestimated. Then, it is the content of the game. Don't think that reading a few competition books is enough, because those books are too rough; At this time, the requirements for teachers are even higher. Teachers should not only be very familiar with the content of the competition, but also constantly sum up important thinking methods so that students can use them flexibly.
Second, the required reading list:
Initial stage (special topic):
0 1, * combinatorial geometry (single bottle) 02, * function equation
03, * "How to Prove Trigonometric Identities" 04, * "Cauchy Inequalities and Ranking Inequalities" (Nanshan)
05, * "pigeonhole principle and Coloring Problems" 06, * "Covering" (single bottle)
07, *' Elementary Number Theory' (three volumes) 08,' Interesting Number Theory'
09.* "Solving 300 Typical Problems of Basic Number Theory" (Wang Yuan et al.) 10, * "Geometric Inequalities"
1 1, interesting graph theory problem (single bottle) 12, * graph theory method in mathematics contest.
13, * Count 14, * Combinatorial Mathematics Theory and Problem Solving.
15, combinatorial counting method and its application 16, principles, methods and skills of combinatorial analysis.
17, * set and its subset (single bottle) 18, * geometric transformation and geometric proof (Xiao Zhenggang)
19, modern Euclidean geometry (R.A.Johnson) 20, small flowers in plane geometry (single bottle)
Review stage (synthesis, aiming at thinking methods):
2 1, * Looking at the problem from the particularity (Su Chun) 22. Combinatorial identity (Shi Jihuai)
23. Analytic geometry skills (single bottle) 24. * Calculate twice (single bottle)
25.* Solving problems with structural methods (Yu, Yan Zhenjun) 26. * Talking about mathematical induction (Su Chun)
The above books (basically written by mathematicians) should be read (especially those marked with *); Although there are several books, these books are really good and explain many problems thoroughly. Then, it's time to read some competition books. Of course, it will be easy to read at this time. "Information of the First Mathematical Olympiad National Training Team" is a good material.
Recommend some very useful extracurricular reading materials:
27. Mathematical Games and Translation Appreciation of Popular Mathematical Masterpieces (Bauer)
28. Mathematical entertainment in the translation of popular mathematical masterpieces (J.A.H Hunter J.S. Madge)
29. Geometric Properties of Conic Curves Translated from Popular Mathematical Masterpieces (Cockshott Walters)
30. "conic curve"
3 1, Circle and Ball (W. Brasuke)
32. Combinatorial Mathematics on the Chessboard (Feng Yuefeng)
33. Geometry (Descartes)
34. The famous geometric theorem (Yano Kentaro)
For the competition coach, I think the above books should be familiar, so a direct benefit is to know the background of the topic. Of course, the math level will also be by going up one flight of stairs. For those who take part in the competition, it is also very demanding to learn so many books in a short time. If the time is well arranged, after reading these books (or basically reading them), the league will start immediately, about one month after the start of the second year of high school (some provinces have already set up preliminary competitions, which may be earlier). Even if the exam is not ideal, I don't think it is a big problem to win the second prize. Don't be discouraged and don't be too pessimistic, because there is still one chance in senior three, and there is still a whole year to prepare carefully, until one year later.