Those distinctions are irrelevant. Education was free in USSR. Access to math circles and specialized math schools was also free. It was not necessary to hire a tutor or pay for advanced classes to get admitted, unless we’re talking about the Conservatory or MGIMO.
Source: I was born and received education in USSR, so can tell Soviet propaganda from reality.
Despite Soviet propaganda to the contrary, social class continued to exist in the USSR.
At the top of the class hierarchy, were senior party officials and their families.
Next rung down were university-educated professionals (doctors, engineers, scientists, etc)
Then came skilled factory workers, etc
Unskilled labourers were near the bottom of the Soviet class hierarchy