Calculus is one of those subjects that is nice to learn about, but it’s hard to see how we’d actually use it in real life. You may have heard that aspiring actuaries should have some background in calculus. Or maybe you’re writing Exam P and are wondering if you’re actually going to need to use all this calculus at work.

Well, thankfully, the answer is no! Actuaries don’t use calculus at work.

But, you will use calculus quite a bit on the earlier actuarial exams. Here’s how:

Exam P

Of all the actuarial exams, Exam P is the one with the most calculus on it. Since Exam P is a course about probability, you’ll learn about probability density functions on the exam.

A probability density function is simply a formula to calculate the probability that a random variable is equal to a certain value.

But integration (ie a subtopic within calculus) comes in when you need to determine the probability that the random variable is less than a given value, or more than a given value. You’ll also use integration for finding expected values too.

Another popular application of integration on Exam P is finding the area under a curve.

You’ll also need to know how to differentiate (ie another subtopic within calculus). Quite often you’ll need to turn a cumulative distribution function into a probability density function. You do that by differentiating.

Exam FM

The calculus required for Exam FM is not as complex as that needed for Exam P.

For FM, you’ll just need to know how to integrate once you start calculating present values of streams of continuous payments and/or cash flows with interest that is paid continuously.

Fortunately the functions that you have to integrate on Exam FM are easier and more repetitive than Exam P. That’s why most people find this exam to be the easier of the two.

Other preliminary exams

Calculus is also used on some of the other preliminary exams too. Primarily you’ll just be building off of the topics that you already learned on Exam P and FM though, so it won’t be that difficult to learn.

Once you get to FSA or FCAS level exams, you can forget calculus! You won’t need it for exams or for your job.

Where to get help learning calculus

There are several places that you can go to review calculus for free. I wrote this post about it a while ago. You should check that out!

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