The method of ensuring the proper preparation of senior pupils for undergoing of external independent assessment is an extremely topical pedagogical problem. For the time being, the Math test of EIA contains four forms of items: with alternatives, with a short answer, setting matches and open form with full explanation. At the same time, the tasks of the last form were absent for a long time in the external testing of mathematics, and therefore there was a need for the development of methodological recommendations concerning the particularities of solving these test tasks. The purpose of the article is to highlight the peculiarities of the structure of items with full explanations, which are part of the standardized tests, the formulation of general recommendations for preparation for their solution, as well as demonstration of concrete examples of their solutions. When they are included in standardized tests, tasks with full explanation try to construct in such way, that they are mostly solved in the same way, using explicit and indirect guidance for this purpose. Such structure of the items of this form limits the mathematical creativity of the test participants to some extent, but is justified, because it provides the opportunity for most pupils to evaluate the correctness of the solutions given by them based on common positions. During solving the item with full explanation, pupils should take into account the above-mentioned tips and identify the stages of the decision that will be assessed during the review. At the same time, it is important at each particular stage to understand what particular facts need to be thoroughly proved, and which to be only to formulated, since excessive detail when making a decision only complicates the work of a specialist during the inspection. In order to ensure the proper quality of preparation for solving tasks with full explanation, coordinated work is required both by the testing participant and by the specialists who prepare him for external testing. If the first one, for the most part, requires the execution of large number of training test items, then the latter requires understanding of what the structure should be these training tasks, how to break their decision on the stages and how to arrange the solution so that it was mathematically literate and concise at the same time.