I don't think this is really needed/optimal for the following rationale. In general, you are covering a few select topics and student competency varies on those topics. The bell curve will sort itself out and the general theme of someone getting 70% of the easy right and 30% of the hard right will be more common than the opposite: students getting all difficulty at easy, zero at harder.
Instead I would just think of the exam construction this way. Normal books for classes from grade school through diffyQs tend to have problems at the I/II/III levels. I is complete plug and chug. II is slightly harder, some manipulation. III can be challenging (at different levels of challenging but still not as easy).
I would just look at all the topics you covered (say 5 lessons from a MWF class, 2 weeks with test on last F). Design a 50 minute exam to cover the 5 topics. It is probable 5 II problems (one for each section) as well as a smattering of I problems, perhaps to hit subtopics in the lessons, to the extent time allows.
If you want to assign one III problem, do it at the end of the exam (on any of the topics). The purpose of that is mostly student differentiation (B versus A or +/- shades). It can be required or extra credit as you think best (if timing tight or students struggling to reach reasonable percentage of 80%/90% cuttofs, make it extra credit).
I do think it is reasonable to give different points for the II and I problems. Just do it based on rough time required. As a ballpark, 2:1, but use your judgment and keep it simple.
The III problem can probably be 3 in 3:2:1. (15, 10, 5 is easy point math for students under the gun.) Given how this drives the % cuttoffs, it is another argument for making that problem EC.
[When I say I/II/III, I mean probably very close analogs of the problems, but you can even consider to include unassigned HW problems that are right out of the book, especially if the drill materials are lengthy.]
Avoid the temptation to get cute and assign problems different in form from the homework or requiring a lot of synthesis of various skills. Test what was in the lessons! That is hard enough, usually and the students have accomplished a lot if they master that. If you can't resist the temptation to get cute, creative, and show how smart you are, then do it with the III problem at the end (and probably DO make it extra credit).
In terms of A/B/C differentiation, it will handle itself fine accross the questions. Getting 90% right of a bunch of II problems with a few Is mixed in is non trivial in a tested 50 minute environment, with no reference materials. Kid probably deserves an A for that.