# Module 0 - Entry Exam v6.0 (IFoA-CAA-M0)

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Total 64 questions

Determine and describe the extreme values of f(x,y) = -x2 - xy - 3y2

• A. (0,1) and a saddle point
• B. (0,0) and a minimum
• C. (0,0) and a maximum
• D. (0.5,-1) and a maximum

Determine which of the following statements are not true.

I. In a histogram the height of each rectangle equals the frequency of the interval
II. A box-plot chart is constructed to show the following values: Mean, Median, Upper

Quartile, Minimum and Maximum -
III. The set of data 2,2,5,7,8,8,9,10,11,12,14,16, 20 can be represented by the following frequency table:

• A. II
• B. I and III
• C. II and III
• D. All of them

Determine the coefficient of x3 in the binomial expansion of (2 + x)5.

• A. 10
• B. 40
• C. 64
• D. 80

Calculate the sum of the following non-terminating progression:
2/10, 2/40, 2/160, 2/640,...

• A. 0.174
• B. 0.266
• C. 0.267
• D. 0.406

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

• A. P(A|B) = P(A)/P(B) and P(B|A) = P(B)/P(A)
• B. P(A|B) = P(A) - P(B) and P(B|A) = P(B) - P(A)
• C. P(A|B) = P(A) and P(B|A) = P(B)
• D. P(A|B) = P(A) + P(B) and P(B|A) = P(B) + P(A)

Solve the following equation for x:
12x +10 = 3x - 8

• A. x = -9/2
• B. x = -2
• C. x = 2
• D. x = 9/2

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

Identify the range of this defined function.

• A. [-1,1]
• B. [0,1]
• C. (-1,1)
• D. (-1,1]

A cat rescue centre keeps a record of how many kittens are born in each litter over a year.
The bar chart summarises the figures.
Consider the mean, mode and median of the number of kittens per litter.
Determine which one of the statements is true.

• A. {exhibit 3729}
• B. The mean is greater than the mode.
• C. The mode and median are the same.
• D. The median is less than the mean.The median equals 4.5.

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 second derivative of the function with respect to x takes the value 2, which is positive.
• B. It is a maximum stationary point because the second derivative of the function with respect to x takes the value 2, which is positive.
• C. It is a maximum stationary point because the value of the function at x = 3 is 11, which is positive.
• D. It is a minimum stationary point because the value of the function at x = 3 is 11, which is positive.

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.

• A. -15.4%
• B. -13.3%
• C. 13.3%
• D. 86.7%

Calculate the indefinite integral:

A)

B)

C)

D)

• A. Option A
• B. Option B
• C. Option C
• D. Option D

The variable s can take values between 2 and 6.
Identify which of the inequalities shown can be satisfied by at least one value of s.

• A. s + 5 < 6
• B. s + 9 < 6
• C. s - 6 > 2
• D. s - 2 > 2

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)

• A. Option A
• B. Option B
• C. Option C
• D. Option D

The particular solution of the second-order difference equation yn+2 - 6yn+1 + 8yn = 0 n 2 subject to the initial conditions y0 = 3 and y1 = 2 may be written in the form yn = A(2n) + B(4n) n 0.
Determine the values of (A, B).

• A. (-2, 5)
• B. (-2, 3)
• C. (-3, 2)
• D. (5, -2)

Identify which of the following involves weak inequality.
A)

B)

C)

D)

• A. Option A
• B. Option B
• C. Option C
• D. Option D