IFoA_CAA_M0問題集、IFoA実際の試験問題

質問 1

X is a random variable with expected value E(X).
Identify which of the following is not a valid method for calculating the variance of X.

A. E( X2 ) - E(X)

B. The second moment of X minus the square of the first moment of X.

C. E( X2 ) - [ E(X) ]2

D. E[ X - E(X) ]2

正解: A

質問 2

Calculate the total area enclosed by the x-axis and the function below, between x = 1.5 and x = 2.
f(x) = 2x3

A. 5.469

B. 10.938

C. 2.734

D. 8.000

正解: A

質問 3

State what the limit of a function with input variable x represents.

A. The limit represents the smallest value that the function can take over its considered range.

B. The limit represents the value of x for which the function is incalculable.

C. The limit represents the value of the function when x=0.

D. The limit represents the behaviour of a function as x approaches a certain value.

正解: D

質問 4

Calculate the second order derivative of y with respect to x, where:
y = 3x2 + ex

A. 6x + ex-1

B. 6 + (x - 1)ex-2

C. 6x + ex

D. 6 + ex

正解: D

質問 5

Consider the function f(x) = x2-6x+20. This function has a stationary point at x = 3.
Determine the nature of this stationary point and how do we know this to be true.

A. It is a minimum stationary point because the value of the function at x = 3 is 11, which is positive.

B. It is a maximum stationary point because the value of the function at x = 3 is 11, which is positive.

C. It is a maximum stationary point because the second derivative of the function with respect to x takes the value 2, which is positive.

D. It is a minimum stationary point because the second derivative of the function with
respect to x takes the value 2, which is positive.

正解: D

質問 6

One of the two solutions to the equation is .

Determine the second solution.

A)

B)

C)

D)

A. Option A

B. Option C

C. Option B

D. Option D

正解: B

質問 7

The graph shows the frequency distribution of the age of people with a certain kind of insurance contract.

Describe the shape of the underlying data.

A. Positively skewed

B. Symmetric

C. Negatively skewed

D. Symmetric about the mean

正解: C

IFoA Module 0 - Entry - IFoA_CAA_M0 模擬練習