This exam consists of questions that come from the british A-level course of further pure mathematics. The topics covered include
Series with method of differences and partial fractions
First and second order differential equations
Loci transformations in the complex plane.
I gave this activity as an hour and a half long exam, but the student that I gave it to later attended Imperial College of London, and was among the best and brightest students I have ever had, and didn't finish in time. I suggest Using this assignment as either a homework assignment, or classwork for a few lessons. I do have an answer key as well.