Nowadays along with changing of understanding of the teaching process individual responsibility of every student for results of his/her learning is becoming more and more important. Therefore changes in the teachers’ didactic approach which are directed on involving of the student in the assessment process of his/her knowledge by means of individualization of assessment itself are required. Computerized solutions can assist on this field. The paper describes refinement of the previously developed the concept-map based knowledge assessment system towards changing of the difficulty degree of task given to the student. Two approaches are offered, which allow to assess a student’s knowledge level more accurate: changing the degree of task difficulty by additionally inserting concepts and changing the degree of task difficulty by offering different tasks. In the first approach the system additionally inserts concepts into the structure of the concept map when the task for the student is to fill a teacher-prepared concept map structure by a given list of concepts. The second approach provides five-tasks which cover both "fill-in" and "construct-a-map" tasks and are ranged from the easiest to the most difficult. Both approaches are described in detail and results of experimental evaluation of the corresponding versions of the concept-map knowledge assessment system are given