A Grammar Problem
Ms.Lin's class used to be a headach because the students were disrespectful to each other. ____ her efforts to build team spirit proved fruitless, she decided to try something new.....

What is the blank should be filled?
A.With
B.As
C.Despite
D.Since

Answer: A
But isn't "with" a preposition?
Why it can be followed with "proved",a verb?

Question

A Grammar Problem
Ms.Lin's class used to be a headach because the students were disrespectful to each other. ____ her efforts to build team spirit proved fruitless, she decided to try something new.....

What is the blank should be filled?
A.With
B.As
C.Despite
D.Since

Answer: A
But isn't "with" a preposition?
Why it can be followed with "proved",a verb?

Answer

I have looked again,and "A" is the right answer.
But my teacher say, "A.B.D can all be the answer."

Answer

Actually, it is "A".  "Proved" works as a participle here (the past participle of "prove" can be either "proved" or "proven").

Answer

"A" is correct. This is very advanced English, and you will have to learn these structures. You can't just second guess your way through an advanced grammar test.

Answer

This one is difficult.
With her efforts to build team spirit proved fruitless = With her efforts to build a team having been proved fruitless =  Once her efforts to build team spirit were proved fruitless.

I would have stated it the second way.  You can see that the phrasing in the question is confusing.  You see that construct "with +  +  +  " in written English, but almost never spoken.

Answer

Look again: 'A' can't be the right answer.
Maybe you're reading the answers to another exercise?