Students often ask me whether the final exam for my course will be 'cumulative', testing material covered both before and after the midterm. The alternative is that the final only tests material taught after the midterm.
I understand that some professors do give non-cumulative final exams, but I find it hard to think of a situation where this would be appropriate. In my courses, we build ideas onto other ideas. I select a particular order of topics (e.g. genetics then evolution then ecology) for precisely that reason. By first studying genetics, we develop the genetic underpinnings needed to understand evolution, and by understanding evolution we can better appreciate issues relevant to ecology. The exam questions I like best are the ones that ask students to pull together concepts taught in different parts of the course.
Telling students that material covered before the midterm won't be needed for the final is tantamount to telling them to forget that material - it's not even valuable enough to remember for another 6 weeks, much less beyond the final exam.