MGF1131 MATH IN CONTEXT
ADVANCED COMPREHENSIVE
EXAMINATION QUESTIONS AND
ANSWERS
1. In symbolic logic, what is the contrapositive of the statement ‘If it is raining, then the
ground is wet’?
A. If the ground is wet, then it is raining.
B. If the ground is not wet, then it is not raining.
C. If it is not raining, then the ground is not wet.
D. It is raining and the ground is not wet.
Answer: B
Conceptual Explanation: The contrapositive of a conditional statement ‘If P, then Q’ is ‘If
not Q, then not P’. Both are logically equivalent.
2. A credit card has an APR of 24% compounded monthly. What is the Effective Annual Rate
(EAR) or Annual Percentage Yield (APY)?
A. 24.00%
B. 24.24%
,C. 25.34%
D. 26.82%
Answer: D
Conceptual Explanation: APY = (1 + r/n)^n - 1. Here, (1 + 0.24/12)^12 - 1 = (1.02)^12 - 1
≈ 0.2682 or 26.82%.
3. In a standard normal distribution (Z-distribution), what percentage of data falls between Z
= -1 and Z = 2?
A. 81.85%
B. 68.26%
C. 95.44%
D. 47.72%
Answer: A
Conceptual Explanation: The area for Z=2 is 0.9772 and for Z=-1 is 0.1587. 0.9772 -
0.1587 = 0.8185.
4. If the odds in favor of an event are 3 to 5, what is the probability that the event will occur?
A. 0.6
B. 0.375
C. 1.66
, D. 0.3
Answer: B
Conceptual Explanation: Probability = favorable / (favorable + unfavorable) = 3 / (3 + 5)
= 3/8 = 0.375.
5. Which of the following is an example of a Euler circuit in graph theory?
A. A path that visits every vertex exactly once and returns to the start.
B. A path that crosses the same bridge twice.
C. A path with an odd number of vertices.
D. A path that uses every edge exactly once and returns to the start.
Answer: D
Conceptual Explanation: A Euler circuit must use every edge of a graph exactly once and
end at the starting vertex.
6. Calculate the monthly payment for a $200,000 mortgage at 6% annual interest for 30 years.
A. $1,199.10
B. $1,000.00
C. $1,264.81
D. $1,333.33
Answer: A
ADVANCED COMPREHENSIVE
EXAMINATION QUESTIONS AND
ANSWERS
1. In symbolic logic, what is the contrapositive of the statement ‘If it is raining, then the
ground is wet’?
A. If the ground is wet, then it is raining.
B. If the ground is not wet, then it is not raining.
C. If it is not raining, then the ground is not wet.
D. It is raining and the ground is not wet.
Answer: B
Conceptual Explanation: The contrapositive of a conditional statement ‘If P, then Q’ is ‘If
not Q, then not P’. Both are logically equivalent.
2. A credit card has an APR of 24% compounded monthly. What is the Effective Annual Rate
(EAR) or Annual Percentage Yield (APY)?
A. 24.00%
B. 24.24%
,C. 25.34%
D. 26.82%
Answer: D
Conceptual Explanation: APY = (1 + r/n)^n - 1. Here, (1 + 0.24/12)^12 - 1 = (1.02)^12 - 1
≈ 0.2682 or 26.82%.
3. In a standard normal distribution (Z-distribution), what percentage of data falls between Z
= -1 and Z = 2?
A. 81.85%
B. 68.26%
C. 95.44%
D. 47.72%
Answer: A
Conceptual Explanation: The area for Z=2 is 0.9772 and for Z=-1 is 0.1587. 0.9772 -
0.1587 = 0.8185.
4. If the odds in favor of an event are 3 to 5, what is the probability that the event will occur?
A. 0.6
B. 0.375
C. 1.66
, D. 0.3
Answer: B
Conceptual Explanation: Probability = favorable / (favorable + unfavorable) = 3 / (3 + 5)
= 3/8 = 0.375.
5. Which of the following is an example of a Euler circuit in graph theory?
A. A path that visits every vertex exactly once and returns to the start.
B. A path that crosses the same bridge twice.
C. A path with an odd number of vertices.
D. A path that uses every edge exactly once and returns to the start.
Answer: D
Conceptual Explanation: A Euler circuit must use every edge of a graph exactly once and
end at the starting vertex.
6. Calculate the monthly payment for a $200,000 mortgage at 6% annual interest for 30 years.
A. $1,199.10
B. $1,000.00
C. $1,264.81
D. $1,333.33
Answer: A
