I need to review math before studying actuarial material. In what detail do I need to review calculus and pre-calculus? Should I obtain textbooks and try to understand the material or go to websites like Khan Academy and just be able to apply it towards exercises?
I had a couple years between calculus and studying for my first exam, I used Khan academy to refresh the things I couldn’t remember, but I also looked back at my notes (because I was/am? a hoarder with bookcases of class notes). There’s also lots of actuarial videos out there besides Khan academy.
In terms of review, probably nothing. Delve into the material and figure out what you’re missing as you go through it.
Calculus used to be it’s own exam IIRC, and then the SOA got rid of it years ago. So now Exam P is pretty much exclusively probability. The most I think you’ll need in the way of calculus for the entry level exams would be doing maybe a double integration and derivatives and if you’ve seen that material before, IMO no need for a specific review until you’re doing questions and have difficulty. I doubt you’d even need to know integration by parts.
For each exam, SOA publishes specific learning goals with a pretty decent breakdown and gives a list of texts that can be used for the material.
Here’s their outline of goals and texts for Exam P.
Notice how there are three ‘learning outcomes’ all centered around probability. And the textbooks are all centered on probability as well (not calculus).
Therefore where you should start is pick up one of the texts mentioned at the bottom of that PDF (or an earlier version, or frankly any introductory university level text on probability). Map each of the “Learning Outcomes” to the text to make sure everything is covered. Then start going through each learning outcome. Once you’ve read and understood the material, start grinding exam problems.
It’s been nearly 10 years since P/FM for me, but there was integration by parts in the materials then (and I finally learned the tabular method to deal with it). Haven’t used it since.
I think that there’s a difference between in the material, and testable. I can’t imagine the SOA would test integration by parts on an exam - it’d be a complete distraction from what they’re trying to test and a waste of time.
I put my money where my mouth is. Graduated my bmath and I maintained that a) I don’t know how to do integration by parts (long forgotten, never relearned) and b) I cannot find the inverse of a matrix bigger than 2X2. Oh yeah, profs were blah blah blah about these things in class, but never tested them. Not even once (outside of the class where those things were taught as part of the syllabus).
Calculus (and certainly pre-calculus) are very important and you should never forget. Even if it’s not tested directly, it will be tested indirectly. Good working grasp of calculus means you will be able to understand more and won’t have to memorize quite as much. You’ll be better off for many exams to come.
All modern humans that don’t have a medical excuse should be able to (if they put in adequate effort, get adequate instruction, etc) do basic calculus. It’s what separates us from other mammals.