Research On The College Entrance Examination Derivative And The Definite Integral Content

Derivative and definite integral, a necessary component of mathematical theory, is an important instrument and means of studying the function. It plays a vital role in mathematics teaching in senior middle school and is considered as the key part in the College Entrance Examination. The related study of problem-solving strategy and method of derivative and definite integral has the realistic significance in mathematics derivative and definite integral teaching in senior middle school.According to the ordinary higher school enrollment unified national examination (NCEE) mathematics test from 2005 to 2015, respectively on the volume, Shaanxi Province and Shandong Province exam questions, from the test in the derivative and integral knowledge about the test proportion analysis, and the test points with knowledge situation of examining the statistical analysis. This paper mainly from the following three aspects of research.The study carried out a statistical analysis of the proportions of derivative, definite integral and its detailed knowledge in NCEE(National College Entrance Entrance) mathematics papers from 2005 to 2015, including the national, Shaanxi and Shandong papers, mainly studying on the following aspects:Firstly, through analyzing the assessment score and proportions of the derivative and definite integral knowledge in mathematics papers, and the ratio of its related knowledge appeared in 2005-2015's NCEE papers, the study concluded the seven high-frequency testing points relating to the derivative and some related points concerning with the derivative and about integral module.Secondly, the study analyzed four major factors affecting the difficulty of the derivative item in mathematics paper, including the number of the knowledge points, the number of operation reasoning procedure, the abstractness of the problem and concealment. It also established the model of paper's difficulty through the analytic hierarchy process and found out that the difficulty for the liberal arts were higher than the one for the science in the same year.Thirdly, based on the above analysis, the study gave some suggestions for learning derivative and definite integral in senior middle school:(1) strengthening the basic knowledge learning of derivative and definite integral, (2) focusing on the connection of knowledge points, (3) focusing on the penetration of mathematical thinking.