The breadth of material listed on the syllabus for this test is extensive, and many of the topics are tremendously complex in themselves. Fortunately not all of the topics listed are actually tested, and the kinds of questions that are asked on the exam are generally more reasonable and straightforward than the ones present in the recommended readings.
As I found out through personal experience, you do not need to spend money at all in purchasing study materials for this exam. Virtually everything you need can already be found online. The most crucial study aid is the list of sample questions from past exams, generously provided by the Society of Actuaries. Along with these questions, you will also find a list of step-by-step solutions which will enable you to check your work. For successful performance on the test, it is essential to be able to successfully solve these problems on your own and to know why you obtained the solutions you did. The problems on the exam are remarkably similar to the ones in the sample questions, so you should do well on your exam if you can solve the problems from prior tests.
In the course of my own studying, I made the mistake of purchasing Michael A. Bean’s Probability: The Science of Uncertainty: a book which does an extremely poor job at explaining the mathematical concepts required for the actuarial exam, because it already presupposes the reader’s expert knowledge of such concepts. Too often, crucial explanations and proofs are omitted from this book, to be left as “exercises to the reader”– quite a challenge for a reader who simply seeks a basic grasp of the subject!
Furthermore, the exercises in Bean’s book are not conducive to learning the essentials of the probability concepts discussed; these problems are instead so convoluted and laden with unnecessary complications as to baffle even the expert mathematician. Exam P itself is much more reasonable than that; the problems often require some thinking and multiple steps, but you will not be required to pull brilliant, esoteric insights out of thin air, as Bean’s exercises require you to do. To add to the trouble, Bean does not provide answers in the back of the book for most of his problems — thus disabling you from checking your work.
The best textbook by far for actuarial students preparing to take Exam P is Marcel B. Finan’s A Probability Course for the Actuaries, which you can download for free in pdf format. It starts with the very basics of set theory and probability and gradually works its way toward the most advanced concepts to be tested. Every section focuses on a different key idea and builds on the previous topics; there are also instructive detailed proofs, examples, and practice problems to guide you along the way. This book is available to the public and has an immense wealth of excellent resources. In preparing for the exam, I did some work for Dr. Finan in making the answer keys to the exercises in this book, which I made available in 2008.
With focus, determination, and discipline, you can do well on Exam P and achieve entry into the fascinating and lucrative world of actuarial science. And with these excellent free study materials, all you will need to invest into your education is the $225 exam fee, your time, and your effort.