高考数学压轴题是高考数学中考察数学能力最综合、难度最大、区分度最大的一类题型，是否能够解决压轴题是学生数学核心素养的有力体现。本研究通过整理近五年全国I卷和全国甲卷高考数学真题，基于统计分析法和个案分析法，从微观层面对高考试题中的压轴题进行比较研究，并基于当前研究提出相应的教学启示和建议。

以2019-2023年的全国I卷和全国甲卷高考题为研究对象，本研究旨在通过建立难度模型，分析高考题中压轴题的综合难度；并通过个案分析，结合问题分析压轴题的能力考察情况，进而对试卷中的压轴题进行整体比较，研究发现：

（1）通过统计分析法，结合鲍氏难度模型，得到近五年全国I卷的综合难度为9.0449，近五年全国甲卷（包括20年前的全国III卷）的综合难度为8.5368，从数据上可以看出，全国I卷的综合难度高于全国甲卷。

（2）通过个案分析法，结合高中数学六大核心素养，将2023年全国I卷和全国甲卷解析几何大题和2022年全国I卷和全国甲卷导数大题进行两两比较，研究结果表明，全国I卷对于核心素养的考察综合程度远超全国甲卷，重点表现在数学建模和数据分析上，全国I卷的计算难度较全国甲卷较低，但是思维难度较高，更加考察学生的数学阅读能力。

基于以上研究结论，结合新课程改革理念和《普通高中数学课程标准》，本文从命题方面和教学方面各提出三条建议。

在命题方面，建议降低压轴题难度，着重考察核心素养，可以适当加入竞赛数学，并且结合科学或生活背景，设计更加新颖的题设背景。

在教学方面，用高等数学指导中学数学教学，做好命题——教学桥梁，同时积极参与教研活动，与时俱进。

The final question of college entrance examination is the most comprehensive, the most difficult and the most differentiated type of question in college entrance examination. Whether the final question can be solved is a powerful reflection of the core quality of students' mathematics. Based on statistical analysis and case analysis, this study conducted a comparative study on the final questions in the college entrance examination from the micro level by sorting out the national I paper and National A paper math real questions in the recent five years, and put forward corresponding teaching enlightenment and suggestions based on the current research.

Taking the national college entrance examination of I papers and A papers from 2019-2023 as the research object, this study aims to establish a difficulty model to analyze the comprehensive difficulty of the final questions in the college entrance examination. And through case analysis, combined with the ability to analyze the final question, and then the overall comparison of the final question in the test paper, the research finds:

(1) Through statistical analysis, combined with Bao's difficulty model, the comprehensive difficulty of the national I paper in the past five years is 9.0449, and the comprehensive difficulty of the National A paper in the past five years (including the National III paper 20 years ago) is 8.5368. It can be seen from the data that the comprehensive difficulty of the national I paper is higher than that of the national A paper.

(2) Through case analysis, combined with the six core literacy of high school mathematics, this paper makes a ptwo comparison between the analytical geometry of 2023 National Paper I and National paper A and the derivative of 2022 National paper I and National paper A. The research results show that the comprehensive degree of examination of the core literacy of national paper I is far higher than that of national paper A, with emphasis on mathematical modeling and data analysis. The calculation difficulty of the national I paper is lower than that of the national A paper, but the thinking difficulty is higher, and the students' math reading ability is more examined.

Based on the above research conclusions, combined with the new curriculum reform idea and the mathematics curriculum Standards of ordinary high school, this paper puts forward three suggestions from the proposition and teaching aspects.

In terms of proposition, it is suggested that the difficulty of the final question should be reduced, the core quality should be examined, the mathematics of the competition can be properly added, and the background of science or life should be combined to design a more novel background of the question.

In terms of teaching, we should use higher mathematics to guide middle school mathematics teaching, do a good job of proposition - teaching bridge, and actively participate in teaching and research activities to keep pace with The Times.