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MODULE-0 Real Exam Questions

Entry exam of the Certified Actuarial Analyst qualification

58 questions available · Page 1 of 6

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Question 1 Single choice

Identify which of the following statements is correct.

  1. A

    x in(n)

  2. B

    In(x)+ in(n)

  3. C

    n in (x)

  4. D

    In (nx)

Show answer and explanation

Correct answer: C

Question 2 Single choice

Identify the necessary and sufficient condition under which the quadratic equation ax2+ 2a2x + a3= 0
hasone repeated real root.

  1. A

    a>0

  2. B

    a0

  3. C

    a = 0

  4. D

    a<0

Show answer and explanation

Correct answer: A

Question 3 Single choice

Identify which of the following statements about statistical measures for a set of data is false.

  1. A

    The sample variance is always smaller than or equal to the largest value.

  2. B

    The sample variance is always greater than or equal to zero.

  3. C

    The range can be greater than the largest value.

  4. D

    The range is always greater than or equal to zero.

Show answer and explanation

Correct answer: C

Question 4 Single choice

Determine

  1. A

    Option A

  2. B

    Option B

  3. C

    Option C

  4. D

    Option D

Show answer and explanation

Correct answer: C

Question 5 Single choice

The particular solution of the second-order difference equation

Determine the values of(A, B).

  1. A

    (-2,5)

  2. B

    (5,-2)

  3. C

    (-2, 3)

  4. D

    (-3, 2)

Show answer and explanation

Correct answer: B

Question 6 Single choice

Consider the function f(x)x2 6x=20. This functions has a stationary point at x=3.

Determine the nature of this stationary point and how we know this to be true.

  1. A

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

  2. B

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

  3. C

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

  4. D

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

Show answer and explanation

Correct answer: C

Question 7 Single choice

Determine which of the following function is equal to (2+ x)3

  1. A

    8 + 4x + 2X2+ x3

  2. B

    8 + 12x + 2X2+ x3

  3. C

    1+ 3x + 3X2+ x3

  4. D

    6+ 3x + 3X2+ x3

Show answer and explanation

Correct answer: B

Question 8 Single choice

Consider the following definite integral:

Determine for which combination of a and b the integral converges.

  1. A

    Option A

  2. B

    Option B

  3. C

    Option C

  4. D

    Option D

Show answer and explanation

Correct answer: D

Question 9 Single choice

A set of 17 observed values is being studied.

Identify which of the following statements is/are true.

I The median must be equalto one of the observed values.

II. The mean could be different from all of the observed values.

Ill If the observations are positively skewed, then the mean is less than the median

IV. More than one mode is not possible.

  1. A

    II and IV only

  2. B

    I and II only

  3. C

    III only

  4. D

    I only

Show answer and explanation

Correct answer: D

Question 10 Single choice

Calculate the scalar product of the vectors A and B. where A = (5,10, 2) and B - (2. 3, 3).

  1. A

    118

  2. B

    46

  3. C

    136

  4. D

    (10,30,6)

Show answer and explanation

Correct answer: D