Treaty Atlas
A treaty here is an agreement between the member states themselves, and it is the closest thing the Union has to a constitution: nothing the institutions do can override it, and every power they have comes out of it. Which is also why there are seven of them rather than one — amending a treaty needs every government to agree and then every national ratification, so when the Union has needed to change, it has done it by negotiating a new treaty rather than by editing the old one. Each one on this timeline is a settlement somebody had to be talked into.
The Union was not designed and then built. It was negotiated repeatedly, by people who disagreed, and its awkward parts are settlements from particular years that nobody has since been able to reopen: three seats for the Parliament, a veto on foreign policy, a currency a fifth of the members do not use. Almost every argument in the other eleven explainers is an argument about something on this timeline.
Below, two things at once against the same date: the treaties on the rail, and who was a member state on the map. Seven treaties, eight enlargements, and one departure. Walk it with the arrows, or click any node.
Sources & caveats
Country outlines: Natural Earth 1:110m, projected in Lambert conformal conic (standard parallels 43°N / 62°N). Boundaries are drawn as they are today, not as they stood at each date — West and East Germany are not shown separately, and the map does not attempt to render the USSR, Yugoslavia or Czechoslovakia. Read the shading as "which states were in, by today's borders", which is what the exam asks about.