PDF***WGU C277 – Finite Mathematics Full Real Exam | Questions & Answers with Step-by-Step Rationales | Probability, Matrices, Sequences, Series, Finance & Linear Programming (2025 Edition)

WGU C277 Finite Mathematics Full Real Exam –
Questions & Answers with Step-by-Step Rationales,
Probability, Matrices, Sequences, Series, Finance,
Linear Programming



Section 1: Linear Equations and Systems

Q1. Solve the system of equations:

2x+3y=12x−y=22x + 3y = 12 x - y = 22x+3y=12x−y=2

Answer: x = 3, y = 1
Rationale: Solve the second equation for x: x=y+2x = y + 2x=y+2. Substitute into
the first: 2(y+2)+3y=12⇒2y+4+3y=12⇒5y=8⇒y=1.62(y+2) + 3y = 12
\Rightarrow 2y+4+3y=12 \Rightarrow 5y=8 \Rightarrow
y=1.62(y+2)+3y=12⇒2y+4+3y=12⇒5y=8⇒y=1.6. Wait, recalc carefully:

Step-by-step:

1. x−y=2⇒x=y+2x - y = 2 \Rightarrow x = y + 2x−y=2⇒x=y+2
2. Substitute into 2x+3y=122x + 3y = 122x+3y=12:
2(y+2)+3y=12⇒2y+4+3y=12⇒5y+4=122(y+2)+3y=12 \Rightarrow
2y+4+3y=12 \Rightarrow 5y + 4 =
122(y+2)+3y=12⇒2y+4+3y=12⇒5y+4=12
3. 5y=8⇒y=1.65y = 8 \Rightarrow y = 1.65y=8⇒y=1.6
4. x=1.6+2=3.6x = 1.6 + 2 = 3.6x=1.6+2=3.6

✅ Correct Answer: x = 3.6, y = 1.6



Q2. Solve the system using matrix method:

{x+y+z=62x−y+z=3x+2y−z=4\begin{cases} x + y + z = 6 \\ 2x - y + z = 3 \\ x + 2y
- z = 4 \end{cases}⎩⎨⎧x+y+z=62x−y+z=3x+2y−z=4

,Answer: x = 1, y = 2, z = 3
Rationale: Using augmented matrix and row reduction:

[11162−11312−14]⇒Solve by elimination⇒x=1,y=2,z=3\begin{bmatrix} 1 & 1 &
1 & 6 \\ 2 & -1 & 1 & 3 \\ 1 & 2 & -1 & 4 \end{bmatrix} \Rightarrow \text{Solve
by elimination} \Rightarrow x=1, y=2, z=31211−1211−1634
⇒Solve by elimination⇒x=1,y=2,z=3


Section 2: Sets and Counting

Q3. In a class of 50 students, 30 study math, 25 study science, and 10 study both.
How many study neither?

Answer: 5
Rationale: Use inclusion-exclusion:
∣M∪S∣=∣M∣+∣S∣−∣M∩S∣=30+25−10=45|M \cup S| = |M| + |S| - |M \cap S| = 30+25-
10=45∣M∪S∣=∣M∣+∣S∣−∣M∩S∣=30+25−10=45
Students neither: 50−45=550-45=550−45=5



Q4. How many 3-digit numbers can be formed using digits 1,2,3,4 if repetition is
allowed?

Answer: 64
Rationale: Each of 3 positions has 4 choices: 4×4×4=644 \times 4 \times 4 =
644×4×4=64



Section 3: Probability

Q5. A die is rolled. What is the probability of getting an even number?

Answer: 1/2
Rationale: Even numbers are {2,4,6}, total outcomes = 6, so P=3/6=1/2P = 3/6 =
1/2P=3/6=1/2

, Q6. Two cards are drawn from a standard deck without replacement. Probability
both are hearts?

Answer: 13/52 × 12/51 = 1/17 ≈ 0.0588
Rationale: First card: 13 hearts/52. Second: 12/51. Multiply probabilities.



Section 4: Sequences and Series

Q7. Find the 10th term of the arithmetic sequence: 2, 5, 8, …

Answer: 29
Rationale: an=a1+(n−1)d=2+(10−1)∗3=2+27=29a_n = a_1 + (n-1)d = 2 + (10-
1)*3 = 2 + 27 = 29an=a1+(n−1)d=2+(10−1)∗3=2+27=29



Q8. Sum of first 15 terms of the sequence above:

Answer: 315
Rationale: Sn=n/2∗(a1+an)=15/2∗(2+44)=15/2∗46=345S_n = n/2 * (a_1 + a_n) =
15/2*(2+44)=15/2*46=345Sn=n/2∗(a1+an)=15/2∗(2+44)=15/2∗46=345 Wait
recalc:

Check a_15: a15=2+(15−1)∗3=2+42=44a_15 = 2 + (15-1)*3 = 2 + 42 = 44a1
5=2+(15−1)∗3=2+42=44
Then S15=15/2∗(2+44)=15/2∗46=345S_15 = 15/2 * (2+44) = 15/2*46 = 345S1
5=15/2∗(2+44)=15/2∗46=345 ✅ Correct: 345



Section 5: Matrices & Determinants

Q9. Find the determinant of:

[2314]\begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} [2134]

Answer: 5
Rationale: det = (24) - (31) = 8 - 3 = 5