To be fair to the OP, (I've been watching this thread to see how it develops, feel free to split this off to a new 'person-independent' thread) the design of tests is highly non-trivial because of the central question: "what does this particular test measure?"
Clearly, different tests measure different things- for example, a multiple choice, closed-notes exam measures different skills as compared to a free-response, open-note exam.
Personally, I struggle with creating exams for the intro sequence- colleagues call my questions "context-rich questions", and they are open-book/open-note. Here's an example question: " I saw a 10g acorn fall from about 10 m up, hit the sidewalk and bounce back up to 2 m. How much mechanical energy was lost, and where did it go?" My primary goal here, as with all my exam questions, is to measure the student's ability solve problems by first identifying the essential concept(s) and ignoring irrelevant details, and then apply the appropriate equations. Correct computation is worth a minority of points.
In my experience, only 20% of the class gets anything approaching the correct answer to the above question. The most common error (> 50%) stems from trying to apply kinematics of collisions rather than conservation of energy. The next most common error is the use of inconsistent units- [mgh = (10)(9.8)(2)J]. It doesn't matter if I work a similar problem in class prior to the exam. More generally, nearly all my students seem incapable of "ignoring irrelevant details".
For the past 6 years I have been teaching the intro physics sequence, I have documented a near-exact zero correlation between homework scores and my exam scores, indicating that homework problems (these are from the book, I don't generate homework questions) are not helpful preparation for my exam questions. More concerning is what I wrote above: working out similar problems in class also apparently does not prepare students for the exam. So I continue to struggle with helping students learn how to solve problems.
One alternative approach is to simply use 'canned' exams that more closely match homework problems- for example, state problems in such a way that there are no irrelevant details. That's fine, but those exams measure different things than my exams.