Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Practice Questions

SOA Exam FAM bridges short-term and long-term actuarial mathematics. Practice 1,040 questions covering severity and frequency models, credibility, mortality, premium calculation, and option pricing.

1023 Questions
10 Topics
48 Lessons
3 Difficulty Levels
2026 Syllabus
100% Free

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Sample Questions

Question 1 Easy
Which expression equals P(Ax)P(A_x)?
Solution
P=(1−da¨x)/a¨x=1/a¨x−dP=(1-d\ddot{a}_x)/\ddot{a}_x=1/\ddot{a}_x-d.

(A) adds dd. (C) reverses subtraction. (D) is too small. (E) is too large.

The answer is (B).
Question 2 Medium
Which of the following statements about TVaR is FALSE?
Solution
TVaR0=E[X]\text{TVaR}_0 = E[X], while VaR0\text{VaR}_0 is the minimum possible value (often 0 for loss distributions). Since E[X]E[X] generally does not equal the minimum, (E) is FALSE.

(A) True: TVaR satisfies subadditivity. (B) True: TVaR ≥\ge VaR always. (C) True for continuous distributions. (D) True: TVaR satisfies all four coherence axioms.
Question 3 Hard
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Solution
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Sample Lesson

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Parametric Survival Models, Life Tables, and Their Relationships

Mortality Models · 12 min read

Problem Preview: A population follows Gompertz's law with \( B = 0.0003 \) and \( c = 1.07 \). You need \( {}_{10}p_{50} \). Half the candidates write the integral of \( Bc^{50+s} \) as \( Bc^{50} \cdot 10 \) — treating the exponential as constant. The correct integral is \( Bc^{50}(c^{10}-1)/\ln c \), giving 0.8813 instead of 0.9133.

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Topics

Short-Term Insurance and Reinsurance Coverages

62 questions

Severity, Frequency, and Aggregate Models

148 questions

Parametric Estimation

54 questions

Introduction to Credibility

40 questions

Pricing and Reserving for Short-Term Insurance Coverages

117 questions

Option Pricing Fundamentals

53 questions

Long-Term Insurance Coverages and Retirement Financial Security Programs

46 questions

Mortality Models

133 questions

Present Value Random Variables for Long-Term Insurance Coverages

162 questions

Premium and Policy Value Calculation for Long-Term Insurance Coverages

208 questions
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