IFoA_CAA_M0 Module 0 - Entry Exam Questions and Answers

Determine which of the options is equal to log(3) - 2log(x+1).

A)

B)

C)

D)

Let A = 

Let B = 

Calculate   

1/5 of actuarial students like skiing.

2/5of actuarial students like snowboarding.

1/3  of actuarial students like skiing and snowboarding.

Calculate the proportion of actuarial students that like skiing or snowboarding.

A)

B)

C)

D)

Consider the function:

Calculate the partial derivative .

A)

B)

C)

D)

An individual purchases a share in a company at a price of £45. Six months later he sells the share for £39.

Calculate the percentage change in the value of the share over the six month period, correct to one decimal place.

v = f(x, y, z) is a real valued function of 3 variables.

Express the partial derivative of v with respect to z in standard mathematical notation.

A)

B)

C)

D)

Calculate

An insurance company sells policies where, for each policy, the policyholder pays the first £50 of the cost of any claim. A claim reported to the insurance company takes some unknown value £x.

Identify which of the mathematical expressions below represents the cost in £ to the insurance company of the claim.

For -3.14 ≤ x ≤ +3.14, the graph of the function, sin x, is show below.

Identify the range of this defined function.

In a small island nation, local sea vessels are identified using "a letter and 4 digits" classification system. The "letter" can be any of the 26 letters in the English alphabet, A to Z,  while the "digit" can be any number from 0 to 9. E.g: Z9835.

Calculate the probability of a sea vessel having an identification ending in "007".

Determine which of the statements is true about the root(s) of the following equation:

Solve the following equation for x:

12x +10 = 3x - 8

Identify which of the following statements are true.

I. Skewness measures how peaked a set of data is.

II. Skewness is a measure of asymmetry of the distribution of the data about its mean.

III. For a symmetrically distributed data, the mean equals the median but not necessarily the mode.

IV. The value of a measure of skewness can be positive, zero or negative.

Calculate the second order derivative of y with respect to x, where:

y = 3x2 + ex

Assuming the position of the first quartile of an appropriately ordered dataset is given by 

and the position of the third quartile of an appropriately ordered dataset is given by

Calculate the range and interquartile range of the above dataset.

Identify the condition that fully describes the existence of independence between two events A and B.