Re: half of a page and half page?
Number 2 is the only likely one but I want to check that you know it doesn't mean the same as "I have just finished [doing] half the test paper". The test paper might be ten pages long. Statement number 2 means that you have only completed half of page one (I am assuming that people would logically start at page one, but it is possible that for some reason you have only completed half of page three, or seven, or ten, and have not started any of the other pages.)
Originally Posted by Ju
Sentence three, by using "... the page of the test paper" does suggest that the test paper is only one page long. I just can't imagine why anyone would word it so convolutedly. "I have just finished half the one-page test paper" would make much more sense.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.