MATH 110 FINAL EXAM QUESTIONS AND
CORRECT EXPLANATIONS 2026/2027
GRADED A+
,Section 1: Contemporary/Liberal Arts Mathematics
(Based on UT Knoxville and Hobart & William Smith finals)
1. Lincoln owes $3000 on his credit card, which charges 18% annual interest. He
stops charging and wants to pay off the balance in 3 years with monthly
payments. Using the loan payment formula, his monthly payment would be
closest to:
, A. $85.50
B. $108.50
C. $125.75
D. $150.00
Correct Answer: B
*Rationale: Using the loan payment formula PMT = P × (r/n) / [1 - (1 + r/n)^(-nY)],
with P = $3000, r = 0.18, n = 12, Y = 3, the monthly payment is approximately
$108.50. This demonstrates the time value of money concept.*
2. A ten-sided die (digits 0-9) is rolled infinitely. At some point, would you expect
to see your 10-digit phone number as a consecutive string of digits?
A. Yes, with probability 1 (almost surely)
B. No, because phone numbers are too long
C. Only if the die is fair
D. Yes, but only if you roll exactly 10^10 times
Correct Answer: A
Rationale: The digits of a fair die form a normal number. Any finite string of digits
appears with probability 1 in an infinite random sequence. This is a consequence
of the infinite monkey theorem.
3. Which two sets have the same cardinality (size)?
A. {1, 2, 3, 4, ...} and {2, 4, 6, 8, ...}
B. {1, 2, 3, 4, ...} and {..., -3, -2, -1, 0, 1, 2, 3, ...}
C. The set of natural numbers and the set of rational numbers
D. All of the above
Correct Answer: D
*Rationale: All three pairs are countably infinite and can be placed in one-to-one
correspondence with the natural numbers. Even integers can be mapped by n →
CORRECT EXPLANATIONS 2026/2027
GRADED A+
,Section 1: Contemporary/Liberal Arts Mathematics
(Based on UT Knoxville and Hobart & William Smith finals)
1. Lincoln owes $3000 on his credit card, which charges 18% annual interest. He
stops charging and wants to pay off the balance in 3 years with monthly
payments. Using the loan payment formula, his monthly payment would be
closest to:
, A. $85.50
B. $108.50
C. $125.75
D. $150.00
Correct Answer: B
*Rationale: Using the loan payment formula PMT = P × (r/n) / [1 - (1 + r/n)^(-nY)],
with P = $3000, r = 0.18, n = 12, Y = 3, the monthly payment is approximately
$108.50. This demonstrates the time value of money concept.*
2. A ten-sided die (digits 0-9) is rolled infinitely. At some point, would you expect
to see your 10-digit phone number as a consecutive string of digits?
A. Yes, with probability 1 (almost surely)
B. No, because phone numbers are too long
C. Only if the die is fair
D. Yes, but only if you roll exactly 10^10 times
Correct Answer: A
Rationale: The digits of a fair die form a normal number. Any finite string of digits
appears with probability 1 in an infinite random sequence. This is a consequence
of the infinite monkey theorem.
3. Which two sets have the same cardinality (size)?
A. {1, 2, 3, 4, ...} and {2, 4, 6, 8, ...}
B. {1, 2, 3, 4, ...} and {..., -3, -2, -1, 0, 1, 2, 3, ...}
C. The set of natural numbers and the set of rational numbers
D. All of the above
Correct Answer: D
*Rationale: All three pairs are countably infinite and can be placed in one-to-one
correspondence with the natural numbers. Even integers can be mapped by n →
