Physics state matriculation exam is an optional written exam, that students take after finishing the fourth grade of high school. The state matriculation exam in physics is standardized and is conducted on a large sample of high school graduates, so it is one of the best indicators of knowledge and understanding of physics of high school graduates in the Republic of Croatia. Analyzed exams for this thesis consisted of 25 closed-ended questions and 12 open-ended questions. Most of the closed-ended questions are also conceptual and important for the analysis of student understanding of physics content. In this thesis, based on the data from several physics state matriculation exams, students' answers to conceptual questions and their errors in understanding the concepts encountered during physics classes are identified and analyzed. The physics problems are divided by areas of physics and educational outcomes, and the problems that best indicate the high school graduate's understanding of the concepts and the possible difficulties that may arise with them are discussed. According to the students' results on individual tasks, an attempt will be made to give reasons for the observed degree of success and related student difficulties, and to provide guidelines for teaching physics that can result in a better student understanding of concepts in physics and better results at the state matriculation exam in physics.