COMPUTER SCIENCE
WGU C960 – Discrete Mathematics II Objective Assessment
Review — 2026/2027
Complete Blueprint Coverage
A+
A+ 5 100%
QUESTIONS VERIFIED EXAM DOMAINS COVERED RATIONALES INCLUDED
CATEGORIES
Algorithms & Complexity
Number Theory & Cryptography
Recursion, Induction & Recurrences
Counting & Combinatorics
Discrete Probability & Modeling Computation
STUVIAACTUALEXAM
, ALGORITHMS & COMPLEXITY
Q1.
A software engineer analyzes a nested loop algorithm where the outer loop runs n times and the inner loop runs from 1 to i for
each outer iteration i. The engineer needs the tightest asymptotic bound on the number of basic operations. Which expression
correctly describes the complexity?
A. O(n)
B. O(n log n)
C. O(n²)
D. O(2■)
Correct Answer: A
Rationale:
The total number of iterations is the sum 1+2+...+n = n(n+1)/2, which is Θ(n²). Therefore the tightest common big-O bound among the choices is O(n²).
Q2.
An algorithm performs a constant-time operation, then recursively solves two subproblems of size n/2, and finally combines the
results in linear time. Using the Master Theorem, what is the asymptotic running time?
A. Θ(n)
B. Θ(n log n)
C. Θ(n²)
D. Θ(log n)
Correct Answer: D
Rationale:
This is the classic divide-and-conquer form T(n) = 2T(n/2) + Θ(n). By the Master Theorem (case 2) the solution is Θ(n log n).
Q3.
A developer claims that an algorithm whose worst-case running time is 5n² + 100n + 20 is O(n³). Another developer claims it is
also Ω(n). Which statement about these claims is accurate?
A. Only the first claim is true
B. Only the second claim is true
C. Both claims are true
D. Neither claim is true
Correct Answer: A
Rationale:
Big-O is an upper bound; any quadratic function is also O(n³). Big-Omega is a lower bound; a quadratic is certainly Ω(n). Both asymptotic statements
hold.
, ALGORITHMS & COMPLEXITY
Q4.
Binary search is performed on a sorted array of 1 048 576 elements. In the worst case, how many comparisons are required
(approximately)?
A. 20
B. 1 048 576
C. 2²■
D. 40
Correct Answer: C
Rationale:
Binary search has worst-case complexity Θ(log■ n). log■(1 048 576) = 20, so approximately 20 comparisons are needed.
Q5.
An algorithm is observed to take roughly four times as long when the input size is doubled, for large inputs. Which complexity
class best matches this empirical behavior?
A. O(n)
B. O(n log n)
C. O(n²)
D. O(2■)
Correct Answer: A
Rationale:
If time grows by a factor of four when n doubles, the dominant term is quadratic: (2n)² = 4n². This matches O(n²).
Q6.
Consider the pseudocode: for i ← 1 to n do for j ← 1 to n do if A[i] = B[j] then return true. What is the best-case running time of
this algorithm?
A. Θ(1)
B. Θ(n)
C. Θ(n²)
D. Θ(n log n)
Correct Answer: B
Rationale:
In the best case the very first pair matches and the algorithm returns immediately, performing only a constant amount of work.
WGU C960 – Discrete Mathematics II Objective Assessment
Review — 2026/2027
Complete Blueprint Coverage
A+
A+ 5 100%
QUESTIONS VERIFIED EXAM DOMAINS COVERED RATIONALES INCLUDED
CATEGORIES
Algorithms & Complexity
Number Theory & Cryptography
Recursion, Induction & Recurrences
Counting & Combinatorics
Discrete Probability & Modeling Computation
STUVIAACTUALEXAM
, ALGORITHMS & COMPLEXITY
Q1.
A software engineer analyzes a nested loop algorithm where the outer loop runs n times and the inner loop runs from 1 to i for
each outer iteration i. The engineer needs the tightest asymptotic bound on the number of basic operations. Which expression
correctly describes the complexity?
A. O(n)
B. O(n log n)
C. O(n²)
D. O(2■)
Correct Answer: A
Rationale:
The total number of iterations is the sum 1+2+...+n = n(n+1)/2, which is Θ(n²). Therefore the tightest common big-O bound among the choices is O(n²).
Q2.
An algorithm performs a constant-time operation, then recursively solves two subproblems of size n/2, and finally combines the
results in linear time. Using the Master Theorem, what is the asymptotic running time?
A. Θ(n)
B. Θ(n log n)
C. Θ(n²)
D. Θ(log n)
Correct Answer: D
Rationale:
This is the classic divide-and-conquer form T(n) = 2T(n/2) + Θ(n). By the Master Theorem (case 2) the solution is Θ(n log n).
Q3.
A developer claims that an algorithm whose worst-case running time is 5n² + 100n + 20 is O(n³). Another developer claims it is
also Ω(n). Which statement about these claims is accurate?
A. Only the first claim is true
B. Only the second claim is true
C. Both claims are true
D. Neither claim is true
Correct Answer: A
Rationale:
Big-O is an upper bound; any quadratic function is also O(n³). Big-Omega is a lower bound; a quadratic is certainly Ω(n). Both asymptotic statements
hold.
, ALGORITHMS & COMPLEXITY
Q4.
Binary search is performed on a sorted array of 1 048 576 elements. In the worst case, how many comparisons are required
(approximately)?
A. 20
B. 1 048 576
C. 2²■
D. 40
Correct Answer: C
Rationale:
Binary search has worst-case complexity Θ(log■ n). log■(1 048 576) = 20, so approximately 20 comparisons are needed.
Q5.
An algorithm is observed to take roughly four times as long when the input size is doubled, for large inputs. Which complexity
class best matches this empirical behavior?
A. O(n)
B. O(n log n)
C. O(n²)
D. O(2■)
Correct Answer: A
Rationale:
If time grows by a factor of four when n doubles, the dominant term is quadratic: (2n)² = 4n². This matches O(n²).
Q6.
Consider the pseudocode: for i ← 1 to n do for j ← 1 to n do if A[i] = B[j] then return true. What is the best-case running time of
this algorithm?
A. Θ(1)
B. Θ(n)
C. Θ(n²)
D. Θ(n log n)
Correct Answer: B
Rationale:
In the best case the very first pair matches and the algorithm returns immediately, performing only a constant amount of work.
