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  • I knew that class test would be held at 11:00 AM.
  • I knew that there was class test at 11:00 AM.

What are the differences between them? Do they mean same meaning?

  • Using "was" does not indicate probability. BTW, "the/a class test". – user3169 Dec 2 '15 at 5:06
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(Firstly - class test requires an article: the definite article, "the"; or the indefinite article, "a".)

I knew that the class test would be held at 11:00 AM.

This is in essence a statement of what you believed in the past. In the past, you believed that, at a moment which was then in the future but which is now in the past, a class test was going to be held.

I knew that there was [going to be] a class test at 11:00 AM.

Back in the past I was certain either that a class test was happening at that same time, or that a class test had already happened at an even earlier moment in time

I knew that there would be a class test at 11:00 AM.

I knew, back in the past, that there was going to be a class test in my then future, which is now also the past.

The British Council's web site (link) says

... would is the past tense form of will. Because it is a past tense it is used:

to talk about the past.
to talk about hypotheses – things that are imagined rather than true.
for politeness.

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