1st question is Linear Algebra

2nd question is Calc 2+Differential Equations

3rd question is probability/stats

an analysis class would probably help as well

I guess it's pretty feasible to take all of those in a year, especially if mathematics is your area of study. This wasn't the case in engineering in my experience. In any case, this wouldn't be so bad with a 4 year degree. Not really any harder than other PhD candidacy exams I've looked at