Online Exam: College

Actuaries in the U.S., Canada and other parts of the world earn professional credentials by passing a series of examinations. This Online Exam is designed to give you an idea of the types of questions you might encounter on the preliminary actuarial examinations administered by the Casualty Actuarial Society and Society of Actuaries. Please be sure to review the Actuarial Exams section of the Web Site, where you can access complete sample actuarial exams.

Answer the five multiple choice questions below, then click submit to see your results. If you are a high school student, please take our High School version of the Online Exam.

Evaluate the following integral given that A is the region bounded by x = 0, y = 0, and x + y = 1.

× e^-(x+2y) dx dy
A

	A. 3(1-e^-2)/8
	B. 3(1-e^-1)/8
	C. (1-e^-1)²/2
	D. (1-e^-1)²
	E. None of the above

An insurance company issues policies to two groups of insured A and B. For a certain type of coverage, the number of claims per year for each group follows the Poisson distribution

For group A, = 1, and for group B, = 1.5.

If in calendar year 2003, 2/5 of this company's policyholders are of group A, what is the probability that the combined number of claims from both groups is no more that two.

	A. 0.627
	B. 0.857
	C. 0.544
	D. 0.287
	E. 0.879

An insurance company has 150,000 to spend on the development and promotion of a new insurance policy for renters. If x is spent on the development and y is spent on the promotion, policies will be sold.

Calculate the maximum sales, in thousands, the company can attain.

	A. 398
	B. 435
	C. 453
	D. 473
	E. 487

In calendar year 2003, the medical claim costs per employee of a company is estimated to have the following probability density function:

f(x) = k × e^{- x / 2} x > 0

where k is a constant that you need to calculate, and x is in units of $1000.

What is the probability that costs per employee in 2003 will exceed $6000.

	A. 0.993
	B. 0.954
	C. 0.199
	D. 0.801
	E. 0.503

Which of the following statements is true?

	A. The vertex of the parabola described by f(x) = 2(x-5)² - 1 is at (5,1).
	B. The graph of f(x) = -2(x+4)² - 8 has one y-intercept and two x-intercepts.
	C. The maximum value of the quadratic function f(x) = - x² + x + 1 is 1.
	D. No quadratic function has a range of
	E. None of the above.