Module 0 iFoA (Questions + Answers)

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Question 1
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.
A. I and II
B. II and IV
C. I and III
D. II, III and IV


Answer : B

Question 2
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.
A. x - 50
B. x
C. max(x, 50)
D. max(x - 50, 0)


Answer : D

Question 3
When differentiating the product of two factors, u and v, the Product Rule can be used.
State the Product Rule.
A)



B)


C)


D)


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


Answer : D

Question 4
Define the standard deviation of a finite data set.
A. The standard deviation is the sum of the difference between each data point and its expected value.
B. The standard deviation is the product of the difference between each data point and its expected value.
C. The standard deviation is the square root of the product of the squared difference between each data point and its expected value.
D. The standard deviation is the square root of the average of the squared difference between each data point and its expected value.


Answer : D

Question 5
A recurrence relation is given by: Un = 2Un - 1 + 3
If U0 = 0, calculate U2 =
A. 3
B. 9
C. 13
D. 21


Answer : B


Question 6


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.


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


Answer : B

Question 7
A geometric series is given by -



Identify the values of x for which the series converges.
A. -1 x 1
B. -1 < x < 1
C. -5 < x < 5
D. -5 x 5


Answer : B

Question 8
Determine which of the following is the Maclaurin expansion (up to the second order term) of: e2x
A)



B)


C)


D)


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


Answer : D

Question 9
Determine which of the options is equal to log(3) - 2log(x+1).
A)



B)


C)


D)


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


Answer : D

Question 10
The stem and leaf chart below shows the ages of all the pensioners in a small village.



Identify which of the following is not true.
A. There are 13 pensioners in the village.
B. The most common age is 63.
C. The oldest pensioner is 89.
D. There is a pensioner aged 70.


Answer : C

Question 11
The first term of an arithmetic sequence is 12 and the ninth term is 68.
Calculate the sum of the first 18 terms.
A. 1,165
B. 1,287
C. 1,350
D. 1,413


Answer : B

Question 12
A coin is tossed 7 times.
Calculate the number of possible combinations that gives 4 heads and 3 tails.
A. 35
B. 42
C. 210
D. 840


Answer : A

Question 13
Identify which of the following best describes the nature of a stationary point.
A. It is where the tangent of the graph of the function is horizontal.
B. It is the point where the maximum value of the function is found.
C. It is the point where the minimum value of the function is found.
D. It is the point where values of the function start to become more stable.


Answer : A

Question 14
A boy is asked to estimate the height of his sister. He estimates that she is 1.60 metres tall.
He then measures his sister and finds that her true height is 1.40 metres.
Identify the absolute error of his estimate of her height.
A. -0.2 metres
B. 0.2 metres
C. 12.5%
D. 0.125


Answer : B

Question 15
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[ X - E(X) ]2
B. The second moment of X minus the square of the first moment of X.
C. E( X2 ) - [ E(X) ]2
D. E( X2 ) - E(X)


Answer : D


Question 16
Calculate the total area enclosed by the x-axis and the function below, between x = 1.5 and x = 2. f(x) = 2x3
A. 2.734
B. 5.469
C. 8.000
D. 10.938


Answer : B

Question 17
Calculate the determinant of the product of the matrices given below:



A. -0.00227
B. -60
C. -78
D. -440


Answer : D

Question 18
A function f(x) is known for two values:
f(2) = 8 and f(5) = 14.
Using linear interpolation estimate f(3).
A)



B)


C)


D)


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


Answer : B

Question 19
The random variable X has the following probability density function ("PDF"):



Calculate: P(x 1.5)
A. 0.164
B. 0.250
C. 0.320
D. 0.484


Answer : C

Question 20
One of the two solutions to the equation is .





Determine the second solution.


A)
B)


C)


D)


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


Answer : C


Question 21
Describe the skewness of the following data:



A. Positively skewed
B. Symmetric
C. Negatively skewed
D. Inversely skewed


Answer : A

Question 22
If -



Calculate the partial derivative
A)


B)


C)


D)


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


Answer : C

Question 23
A discrete random variable can only take the values 2,3,4 or 5. The probabilities associated with some of the outcomes are: P(X=2) = 0.2, P(X=3) = 0.3, P(X=5) = 0.1.
For a randomly drawn value of X, calculate P(X>3).
A. 0.1
B. 0.4
C. 0.5
D. 0.8


Answer : C

Question 24
Let A =





Let B =



Calculate -
A. 986
B. 1,224
C. 2,056
D. 3,286


Answer : B

Question 25
Consider the vector U = (3, -1, 5).
Calculate the magnitude of vector U to two decimal places.
A. 2.65
B. 5.92
C. 7.00
D. 9.00


Answer : B