WGU C960 — Discrete Mathematics II OA Prep Question Bank
WGU C960
Discrete Mathematics II
Objective Assessment Exam Prep Question Bank
Latest 2026/2027 Edition
100 Original Practice Questions with Worked Solutions
A Comprehensive Independent Exam Preparation Resource
Covering: Algorithms & Big-O Analysis | Number Theory & Cryptography | Recursion & Induction
Counting Techniques | Discrete Probability | Models of Computation
Independent Study Guide • Not affiliated with or endorsed by WGU
Page 1 of 31
, WGU C960 — Discrete Mathematics II OA Prep Question Bank
Course Overview
WGU C960 – Discrete Mathematics II is an undergraduate Computer Science course that builds the mathematical
foundation used throughout algorithm design, cryptography, and theoretical computer science. The course
emphasizes rigorous reasoning about searching and sorting algorithms, algorithmic efficiency using Big-O,
Big-Omega, and Big-Theta notation, number theory and modular arithmetic as the basis for RSA cryptography,
recursion and recurrence relations, mathematical induction and proof techniques, combinatorics and counting
methods, discrete probability, and formal models of computation such as finite state machines.
The Objective Assessment (OA) for C960 evaluates a student's ability to apply these concepts to concrete problems:
tracing algorithms by hand, computing modular inverses and RSA keys, constructing and evaluating proofs by
induction, solving counting and probability problems, and analyzing the time complexity of iterative and recursive
algorithms.
This guide provides 100 original practice questions, written independently to mirror the competencies assessed by
the OA. Every question includes a complete, step-by-step worked solution so that the reasoning — not just the final
answer — becomes part of your study process.
Study Tips for the Objective Assessment
1. Work problems by hand before checking the worked solution. The OA is timed, and computational fluency
with GCDs, modular exponentiation, and combinatorial formulas comes only from repetition.
2. Memorize the core Big-O growth hierarchy: O(1) < O(log n) < O(n) < O(n log n) < O(n^2) < O(2^n) < O(n!).
Being able to instantly rank these speeds up both algorithm analysis and recurrence-solving questions.
3. Practice the Euclidean Algorithm and Extended Euclidean Algorithm until they are automatic — they
underlie GCD computation, modular inverses, and RSA key generation, all of which appear repeatedly on the
OA.
4. For RSA problems, always work through the four steps in order: compute n = p·q, compute φ(n) =
(p−1)(q−1), find e with gcd(e, φ(n)) = 1, and find d as the modular inverse of e mod φ(n).
5. When proving statements by induction, explicitly write out the base case, state the inductive hypothesis in
full, and show every algebraic step connecting P(k) to P(k+1) — partial credit thinking does not transfer to
multiple-choice recognition, so practice writing the complete argument.
6. For counting problems, first decide whether order matters (permutation) or does not matter (combination),
and whether outcomes are mutually exclusive (rule of sum) or independent stages (rule of product) before
choosing a formula.
7. Draw a probability tree or a Venn diagram for any conditional probability or inclusion-exclusion problem —
visualizing the sample space prevents the most common counting errors.
8. Trace recursive functions on paper with a call stack diagram, especially for problems like Fibonacci, factorial,
and Towers of Hanoi, so that recurrence relations feel concrete rather than abstract.
9. Review the Master Theorem cases (f(n) smaller than, equal to, or larger than n^(log_b a)) since many
recurrence questions can be solved in seconds once the three cases are memorized.
10. Time yourself on practice sets. The OA rewards both accuracy and speed, so simulate exam conditions
during your final review pass through this question bank.
Page 2 of 31
, WGU C960 — Discrete Mathematics II OA Prep Question Bank
Practice Questions
Question 1
Which of the following best describes the worst-case time complexity of linear search on an unsorted array of n
elements?
A. O(1)
B. O(log n)
C. O(n)
D. O(n log n)
Correct Answer: C
Worked Solution:
Linear search must, in the worst case, examine every element before concluding a target is absent (or is the last
element checked). This gives a worst-case running time proportional to n, so the complexity is O(n).
Question 2
In Big-O notation, which statement correctly describes the relationship f(n) = O(g(n))?
A. f(n) grows strictly faster than g(n) for all n
B. There exist positive constants c and n0 such that f(n) ≤ c·g(n) for all n ≥ n0
C. f(n) and g(n) are equal for all n
D. g(n) is always larger than f(n) for small values of n only
Correct Answer: B
Worked Solution:
Big-O provides an asymptotic upper bound. f(n) = O(g(n)) means that beyond some threshold n0, f(n) never exceeds
a constant multiple c of g(n). This captures long-run growth behavior, not exact equality or behavior at small n.
Question 3
Which of the following is the correct definition of a prime number?
A. An integer greater than 1 whose only positive divisors are 1 and itself
B. Any integer that is not divisible by 2
C. An integer with exactly three positive divisors
D. Any odd integer greater than 1
Correct Answer: A
Worked Solution:
By definition, a prime number is an integer greater than 1 whose only positive divisors are 1 and the number itself.
Options B, C, and D either mischaracterize primality or describe unrelated properties.
Question 4
What is the primary purpose of a base case in a recursive function?
A. To increase the function's time complexity
B. To stop the recursive calls and prevent infinite recursion
C. To make the function run faster on large inputs
D. To store intermediate results for later reuse
Page 3 of 31
, WGU C960 — Discrete Mathematics II OA Prep Question Bank
Correct Answer: B
Worked Solution:
A base case defines the condition under which a recursive function stops calling itself and returns a value directly.
Without a base case, the recursion would continue indefinitely, causing a stack overflow.
Question 5
Which of the following correctly states the multiplication rule (rule of product) in combinatorics?
A. If a task can be done in m ways and a second independent task can be done in n ways, the two tasks
together can be done in m + n ways
B. If a task can be done in m ways and a second independent task can be done in n ways, the two tasks
together can be done in m · n ways
C. The rule of product only applies when m = n
D. The rule of product cannot be extended beyond two tasks
Correct Answer: B
Worked Solution:
The rule of product states that when two independent tasks have m and n possible outcomes respectively, the number
of ways to perform both tasks in sequence is m · n. This differs from the rule of sum, which applies to mutually
exclusive alternatives and uses addition.
Question 6
In modular arithmetic, what does the notation a ≡ b (mod n) mean?
A. a and b leave the same remainder when divided by n
B. a is exactly equal to b
C. n divides a but not b
D. a is always greater than b
Correct Answer: A
Worked Solution:
a ≡ b (mod n) means n divides (a − b), which is equivalent to saying a and b leave the same remainder when divided
by n. This is the formal definition of congruence modulo n.
Question 7
Which statement about mathematical induction is correct?
A. Induction only proves a statement is true for a single value of n
B. Induction requires proving a base case and an inductive step where P(k) implies P(k+1)
C. Induction proves a statement is false for all n
D. Induction does not require a base case
Correct Answer: B
Worked Solution:
A standard proof by mathematical induction has two parts: establishing a base case (typically the smallest value of n
for which the statement should hold) and proving the inductive step, in which the truth of P(k) is used to establish
the truth of P(k+1).
Question 8
What is Euler's Totient Function φ(n) used to count?
Page 4 of 31
WGU C960
Discrete Mathematics II
Objective Assessment Exam Prep Question Bank
Latest 2026/2027 Edition
100 Original Practice Questions with Worked Solutions
A Comprehensive Independent Exam Preparation Resource
Covering: Algorithms & Big-O Analysis | Number Theory & Cryptography | Recursion & Induction
Counting Techniques | Discrete Probability | Models of Computation
Independent Study Guide • Not affiliated with or endorsed by WGU
Page 1 of 31
, WGU C960 — Discrete Mathematics II OA Prep Question Bank
Course Overview
WGU C960 – Discrete Mathematics II is an undergraduate Computer Science course that builds the mathematical
foundation used throughout algorithm design, cryptography, and theoretical computer science. The course
emphasizes rigorous reasoning about searching and sorting algorithms, algorithmic efficiency using Big-O,
Big-Omega, and Big-Theta notation, number theory and modular arithmetic as the basis for RSA cryptography,
recursion and recurrence relations, mathematical induction and proof techniques, combinatorics and counting
methods, discrete probability, and formal models of computation such as finite state machines.
The Objective Assessment (OA) for C960 evaluates a student's ability to apply these concepts to concrete problems:
tracing algorithms by hand, computing modular inverses and RSA keys, constructing and evaluating proofs by
induction, solving counting and probability problems, and analyzing the time complexity of iterative and recursive
algorithms.
This guide provides 100 original practice questions, written independently to mirror the competencies assessed by
the OA. Every question includes a complete, step-by-step worked solution so that the reasoning — not just the final
answer — becomes part of your study process.
Study Tips for the Objective Assessment
1. Work problems by hand before checking the worked solution. The OA is timed, and computational fluency
with GCDs, modular exponentiation, and combinatorial formulas comes only from repetition.
2. Memorize the core Big-O growth hierarchy: O(1) < O(log n) < O(n) < O(n log n) < O(n^2) < O(2^n) < O(n!).
Being able to instantly rank these speeds up both algorithm analysis and recurrence-solving questions.
3. Practice the Euclidean Algorithm and Extended Euclidean Algorithm until they are automatic — they
underlie GCD computation, modular inverses, and RSA key generation, all of which appear repeatedly on the
OA.
4. For RSA problems, always work through the four steps in order: compute n = p·q, compute φ(n) =
(p−1)(q−1), find e with gcd(e, φ(n)) = 1, and find d as the modular inverse of e mod φ(n).
5. When proving statements by induction, explicitly write out the base case, state the inductive hypothesis in
full, and show every algebraic step connecting P(k) to P(k+1) — partial credit thinking does not transfer to
multiple-choice recognition, so practice writing the complete argument.
6. For counting problems, first decide whether order matters (permutation) or does not matter (combination),
and whether outcomes are mutually exclusive (rule of sum) or independent stages (rule of product) before
choosing a formula.
7. Draw a probability tree or a Venn diagram for any conditional probability or inclusion-exclusion problem —
visualizing the sample space prevents the most common counting errors.
8. Trace recursive functions on paper with a call stack diagram, especially for problems like Fibonacci, factorial,
and Towers of Hanoi, so that recurrence relations feel concrete rather than abstract.
9. Review the Master Theorem cases (f(n) smaller than, equal to, or larger than n^(log_b a)) since many
recurrence questions can be solved in seconds once the three cases are memorized.
10. Time yourself on practice sets. The OA rewards both accuracy and speed, so simulate exam conditions
during your final review pass through this question bank.
Page 2 of 31
, WGU C960 — Discrete Mathematics II OA Prep Question Bank
Practice Questions
Question 1
Which of the following best describes the worst-case time complexity of linear search on an unsorted array of n
elements?
A. O(1)
B. O(log n)
C. O(n)
D. O(n log n)
Correct Answer: C
Worked Solution:
Linear search must, in the worst case, examine every element before concluding a target is absent (or is the last
element checked). This gives a worst-case running time proportional to n, so the complexity is O(n).
Question 2
In Big-O notation, which statement correctly describes the relationship f(n) = O(g(n))?
A. f(n) grows strictly faster than g(n) for all n
B. There exist positive constants c and n0 such that f(n) ≤ c·g(n) for all n ≥ n0
C. f(n) and g(n) are equal for all n
D. g(n) is always larger than f(n) for small values of n only
Correct Answer: B
Worked Solution:
Big-O provides an asymptotic upper bound. f(n) = O(g(n)) means that beyond some threshold n0, f(n) never exceeds
a constant multiple c of g(n). This captures long-run growth behavior, not exact equality or behavior at small n.
Question 3
Which of the following is the correct definition of a prime number?
A. An integer greater than 1 whose only positive divisors are 1 and itself
B. Any integer that is not divisible by 2
C. An integer with exactly three positive divisors
D. Any odd integer greater than 1
Correct Answer: A
Worked Solution:
By definition, a prime number is an integer greater than 1 whose only positive divisors are 1 and the number itself.
Options B, C, and D either mischaracterize primality or describe unrelated properties.
Question 4
What is the primary purpose of a base case in a recursive function?
A. To increase the function's time complexity
B. To stop the recursive calls and prevent infinite recursion
C. To make the function run faster on large inputs
D. To store intermediate results for later reuse
Page 3 of 31
, WGU C960 — Discrete Mathematics II OA Prep Question Bank
Correct Answer: B
Worked Solution:
A base case defines the condition under which a recursive function stops calling itself and returns a value directly.
Without a base case, the recursion would continue indefinitely, causing a stack overflow.
Question 5
Which of the following correctly states the multiplication rule (rule of product) in combinatorics?
A. If a task can be done in m ways and a second independent task can be done in n ways, the two tasks
together can be done in m + n ways
B. If a task can be done in m ways and a second independent task can be done in n ways, the two tasks
together can be done in m · n ways
C. The rule of product only applies when m = n
D. The rule of product cannot be extended beyond two tasks
Correct Answer: B
Worked Solution:
The rule of product states that when two independent tasks have m and n possible outcomes respectively, the number
of ways to perform both tasks in sequence is m · n. This differs from the rule of sum, which applies to mutually
exclusive alternatives and uses addition.
Question 6
In modular arithmetic, what does the notation a ≡ b (mod n) mean?
A. a and b leave the same remainder when divided by n
B. a is exactly equal to b
C. n divides a but not b
D. a is always greater than b
Correct Answer: A
Worked Solution:
a ≡ b (mod n) means n divides (a − b), which is equivalent to saying a and b leave the same remainder when divided
by n. This is the formal definition of congruence modulo n.
Question 7
Which statement about mathematical induction is correct?
A. Induction only proves a statement is true for a single value of n
B. Induction requires proving a base case and an inductive step where P(k) implies P(k+1)
C. Induction proves a statement is false for all n
D. Induction does not require a base case
Correct Answer: B
Worked Solution:
A standard proof by mathematical induction has two parts: establishing a base case (typically the smallest value of n
for which the statement should hold) and proving the inductive step, in which the truth of P(k) is used to establish
the truth of P(k+1).
Question 8
What is Euler's Totient Function φ(n) used to count?
Page 4 of 31
