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 joint probability density function of yearly returns for two investments A and B is given below:

Calculate the covariance of returns on A and B.

	A. 0.003450
	B. 0.001747
	C. 0.001764
	D. 0.000538
	E. 0.005380

Sales, S, of a new insurance product are dependent upon the labor, L, of the sales force and the amount of advertising, A, for the product. The relationship can be modeled by

Which of the following statements is true?

	A. S increases at an increasing rate as L increases, and increases at a decreasing rate as A increases.
	B. S increases at an increasing rate as L increases, and increases at an increasing rate as A increases.
	C. S increases at a decreasing rate as L increases, and increases at a decreasing rate as A increases.
	D. S increases at a decreasing rate as L increases, and increases at an increasing rate as A increases.
	E. S increases at a constant rate as L increases, and increases at a constant rate as A increases.

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.

What is the average age to which a 90-year old man will live, given that the probability a person age x will die before age x+1 is (x - 89) / 5?

	A. 91
	B. 91.5
	C. 92
	D. 92.5
	E. 93

Given that A, B, and C are invertible matrices of correct dimensions for the stated operations and ( ' ) denote transpose, which of the following statements is not an identity?

	A. (A+B)' = A' + B'
	B. (ABC)' = C'B'A'
	C. (AB)^-1 = A^-1 B^-1
	D. (AB)^-1 = B^-1 A^-1
	E. (A')^-1 = (A^-1)'