You may have known the answers before taking the exam, but if you had forgotten them by the time of the exam, then you would have had to read the passage text. The reason you didn't need to read the passage text was that you knew them at the time of the exam.
This is because "know" in English doesn't usually mean "learn"; it usually (and in your example) has a meaning closer to "currently remember". So when you say "had already known", you're saying there had been a moment earlier when you knew. This might be true! But many true things are still not what you're intending to say.
If you want to talk about the process or moment when someone starts to know something, and really want to use the word "know" instead of "learn", "find out", etc., there's the phrase "come to know". But it doesn't really fit in your example.