Study on Solving Problems of Conic Sections in the New College Entrance Examination — Take the National Test in 2019-2024 as an Example

With the gradual implementation of the new college entrance examination, Sichuan, as the fifth echelon of the reform, will also officially open the first new college entrance examination this year. However, the change of question type and the increase of difficulty of test questions also follow. The conic curve test is one of the key and difficult points in high school mathematics, and it is also the pride of the new college entrance examination. The knowledge of conic curve is an important part of plane analytic geometry, and it is also a typical combination of number and shape. It is self-evident that it contains mathematical ideas. Based on the existing relevant research, this paper studies the conic curve test questions in the national volume of the new college entrance examination from 2019 to 2024. The content of this paper can be divided into three parts: The first part introduces the research background, research questions, and expounds the purpose and significance of the research. This paper introduces the related research of many scholars, including the content of conic curve teaching materials, problem-solving errors, problem-solving strategies, teaching and so on. It also expounds Polya s problem-solving theory and the conic curve content of the new college entrance examination, based on which the analysis is carried out. The second part, as the core part of this paper, studies the six-year conic curve test questions from two perspectives. Firstly, it is the requirement of mastering the conic curve in the new curriculum standard. Secondly, it is the analysis of the proportion of test questions and scores, the test points and difficulty of the test questions. Finally, it is a comprehensive analysis. The collected real questions are sorted out, classified and summarized into the corresponding questions, and the corresponding problem-solving analysis and strategies are given. The third part summarizes the work of this paper, and puts forward some suggestions for teachers teaching and students learning.