# USING DIFFERENTIAL ENTROPY (SHANNON INFORMATION) AND IQ CURVE TO DEFINE HOW AN EXAM SUCCESS: APPLICATION TO VIETNAM NATIONAL EXAMS 2012-2016

T.A. Chu^{1},

T.T.H. Pham^{2},

T.L. Nguyen^{1},

C.P. Tran^{3},

A.V. Nguyen^{1}^{ 1}Institute of Physics, Vietnam Academy of Science and Technology (VIETNAM)

^{ 2}Le Hong Phong High School, Hai Phong, Viet Nam; Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Vietnam (VIETNAM)

^{ 3}The Vietnam Institute of Educational Sciences (VIETNAM)

To enter the universities, the students in the many eastern Asia countries such as China, Japan, Korea, Vietnam ... have to pass the national selection exam. This exam usually is hard and very competitive so is a big even of the year for many families and courses a high tension for one of tenth national population. Opinion about the exams in the newspapers often have big disagreements on estimation the exams are performed good or not. For this purpose, in this work we develop a new method to define how the exam was success. In statistical physics and information theory there is a useful concept of differential entropy (Shannon information or Shannon entropy). Our method is based on the relative differential entropy (Shannon relative information) and IQ curve. From the published official governmental statistical data, the exam score distribution curves are defined and their corresponding Shannon relative entropy in information can be calculated. Considering the exam result is good if the shape of the score distribution functions is closed to the standard IQ curve (that mean the information constrain function is the IQ curve), we can develop a grading tool for success of exams. As an example, we apply our method for investigation and grading the Vietnam national exams in the period 2012-2016.