MGF1131 MATHEMATICS IN CONTEXT
COMPREHENSIVE ASSESSMENT
QUESTIONS AND ANSWERS
1. Consider the statement: ‘If it is raining, then the ground is wet.’ Which of the following is
the contrapositive?
A. If the ground is not wet, then it is not raining.
B. If it is not raining, then the ground is not wet.
C. If the ground is wet, then it is raining.
D. The ground is wet and it is not raining.
Answer: A
Conceptual Explanation: The contrapositive of an implication p -> q is ~q -> ~p. In this
case, ‘If not wet, then not raining’.
2. Given a set A with a cardinality of 6, how many proper subsets does set A have?
A. 63
B. 64
C. 32
,D. 12
Answer: A
Conceptual Explanation: The number of subsets is 2^n, and the number of proper subsets
is 2^n - 1. Since 2^6 = 64, the answer is 63.
3. An investment offers a nominal interest rate of 6% compounded monthly. What is the
effective annual yield (APY)?
A. 6.00%
B. 6.12%
C. 6.25%
D. 6.17%
Answer: D
Conceptual Explanation: APY = (1 + r/n)^n - 1. Here, (1 + 0.06/12)^12 - 1 = (1.005)^12 -
1 ≈ 0.06167 or 6.17%.
4. In a normal distribution, approximately what percentage of data falls within two standard
deviations of the mean?
A. 95%
B. 68%
C. 99.7%
D. 50%
, Answer: A
Conceptual Explanation: According to the Empirical Rule (68-95-99.7 rule), 95% of data
in a normal distribution falls within two standard deviations.
5. Which of the following describes an Euler circuit in graph theory?
A. A circuit that visits every edge exactly once and returns to the start.
B. A circuit that visits every vertex exactly once.
C. A path that visits every edge exactly once.
D. A path that visits every vertex exactly once.
Answer: A
Conceptual Explanation: An Euler circuit must cover every edge of a graph exactly once
and start and end at the same vertex.
6. Using the Borda Count method for 4 candidates, how many points are awarded to a first-
place vote?
A. 4 points
B. 3 points
C. 1 point
D. 0 points
Answer: A
COMPREHENSIVE ASSESSMENT
QUESTIONS AND ANSWERS
1. Consider the statement: ‘If it is raining, then the ground is wet.’ Which of the following is
the contrapositive?
A. If the ground is not wet, then it is not raining.
B. If it is not raining, then the ground is not wet.
C. If the ground is wet, then it is raining.
D. The ground is wet and it is not raining.
Answer: A
Conceptual Explanation: The contrapositive of an implication p -> q is ~q -> ~p. In this
case, ‘If not wet, then not raining’.
2. Given a set A with a cardinality of 6, how many proper subsets does set A have?
A. 63
B. 64
C. 32
,D. 12
Answer: A
Conceptual Explanation: The number of subsets is 2^n, and the number of proper subsets
is 2^n - 1. Since 2^6 = 64, the answer is 63.
3. An investment offers a nominal interest rate of 6% compounded monthly. What is the
effective annual yield (APY)?
A. 6.00%
B. 6.12%
C. 6.25%
D. 6.17%
Answer: D
Conceptual Explanation: APY = (1 + r/n)^n - 1. Here, (1 + 0.06/12)^12 - 1 = (1.005)^12 -
1 ≈ 0.06167 or 6.17%.
4. In a normal distribution, approximately what percentage of data falls within two standard
deviations of the mean?
A. 95%
B. 68%
C. 99.7%
D. 50%
, Answer: A
Conceptual Explanation: According to the Empirical Rule (68-95-99.7 rule), 95% of data
in a normal distribution falls within two standard deviations.
5. Which of the following describes an Euler circuit in graph theory?
A. A circuit that visits every edge exactly once and returns to the start.
B. A circuit that visits every vertex exactly once.
C. A path that visits every edge exactly once.
D. A path that visits every vertex exactly once.
Answer: A
Conceptual Explanation: An Euler circuit must cover every edge of a graph exactly once
and start and end at the same vertex.
6. Using the Borda Count method for 4 candidates, how many points are awarded to a first-
place vote?
A. 4 points
B. 3 points
C. 1 point
D. 0 points
Answer: A
