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.

The volume V and surface area S of a spherical balloon with radius r are given by
and S= .
The volume of the balloon increases at a rate of 60 cm³ / min when the balloon's diameter is 6 cm.

How fast is the surface area of the balloon changing when the balloon's diameter is 6 cm?

	A.20 cm2/min
	B. 40 cm2/min
	C. 80 cm2/min
	D. 113 cm2/min
	E. 120 cm2/min

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

Let be a sequence of real numbers.

For which of the following does the infinite series converge?

	A.
	B.
	C.
	D.
	E.

Eliminate the parameter t: x = 1 - 4 cos t, y = -5 + 6 sin t

	A. (x-1)² / 16 + (y+5)² / 36 = 1
	B. (x-1)² / 4 + (y+5)² / 6 = 1
	C. (x+1)² / 4 + (y-5)² / 6 = 1
	D. (x+1)² / 16 + (y-5)² / 36 = 1
	E. None of the above

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