The existing system of holding of external independent assessment (EIA) in mathematics does not satisfy the needs of society, because it does not take into account the profile of training of Ukrainian pupils and the domain of their professional implementation in future. To solve this problem, we propose to introduce two-level testing in mathematics, taking the following steps: 1) to take principled decision on the transition to two-level system with indication of precise period of its implementation and create a working group of specialists for this; 2) to develop and publish in the press a draft concept of transition to two-level testing; 3) to discuss this project at conferences, seminars and in social networks; 4) summarize the discussion, form and approve at the state level a package of documents regulating the transition to a two-level EIA in mathematics.