The age peculiarities dynamics of the intellectual abilities of schoolchildren (IAS) in solving problems of various difficulties is studied, as well as the analysis of a computer database is provided, which allows obtaining information on various IAS indicators, both at the student's level (individual student's characteristics) and at the level of other parties concerned. Only those IAS indicators, the development level of which adequately reflects the whole picture of the student's intellectual development, have been highlighted. The indicators are conditionally divided into two groups: (I) indicators of mental development, which the school education is focused on and (II) indicators characterizing the students' ability to solve heuristic challenging tasks. A qualitative distinction between the intellectual development of two students' groups -6-9 and 10-11 grades, has been determined, as well as a quantitative difference in IAS indicators between all the surveyed schoolchildren age groups. The difference in the effectiveness of solving problems of different difficulty has been revealed. The problems for the solution of which it is required to "go beyond" the initial level of mental support of educational activities, to involve new intellectual "layers", "plans" and a special mental subject organization, i. e. everything which is defined in the study as untapped intellectual potential, are, in general, solved worse. The study demonstrates the importance of knowing the IAS indicators age dynamics for the learning management individualization.