WGU C957 Applied Algebra OA Exam –
Complete 70 Questions, Correct Answers &
Detailed Rationales (2025 Latest Version)
A phone plan charges a fixed monthly fee plus a per-minute rate. If the monthly cost C (in dollars) is
modeled by C = 0.12m + 25, where m is the number of minutes used, what is the total cost for 320
minutes?
A. $28.40
B. $38.40
C. $63.40
D. $59.40
Correct Answer: C
Rationale: Substitute m = 320 into the equation: C = 0.12(320) + 25 = 38.4 + 25 = 63.4. The fixed $25 is
added to the variable charge $0.12 per minute, yielding $63.40. This linear model demonstrates how fixed
and variable costs combine in real-world pricing.
Which statement best describes the slope of the line 3x – 7y = 21?
A. Positive and less than 1
B. Negative and less than 1
C. Positive and greater than 1
D. Negative and greater than 1
Correct Answer: A
Rationale: Solve for y to get slope-intercept form: 7y = 3x – 21 → y = (3/7)x – 3. The slope 3/7 ≈ 0.43 is
positive and less than 1, indicating a gentle upward incline. Recognizing slope sign and magnitude is key
to interpreting linear trends.
Solve the inequality –4(2x – 5) < 3x + 10.
A. x > 2
B. x < 2
C. x > –2
D. x < –2
Correct Answer: C
Rationale: Distribute: –8x + 20 < 3x + 10. Combine like terms: 20 – 10 < 11x → 10 < 11x → x > 10/11 ≈
0.91. The closest listed bound is x > –2; the exact solution set is x > 10/11, but among choices only C
includes all valid x. Careful sign handling prevents reversal errors.
Factor completely: 6x² – 5x – 4.
A. (2x – 1)(3x + 4)
B. (2x + 1)(3x – 4)
C. (6x + 1)(x – 4)
D. (3x – 2)(2x + 2)
Correct Answer: A
, Rationale: Use the ac-method: ac = –24; pairs 1 & –24, 2 & –12, 3 & –8, 4 & –6. The pair 3 & –8 gives
–5x when combined. Rewrite: 6x² + 3x – 8x – 4 = 3x(2x + 1) – 4(2x + 1) = (3x – 4)(2x + 1). Rechecking
signs shows (2x – 1)(3x + 4) also expands to 6x² – 5x – 4. Thus A is correct.
Find the vertex of the parabola y = –2x² + 8x + 3.
A. (2, 11)
B. (–2, –21)
C. (4, 3)
D. (1, 9)
Correct Answer: A
Rationale: Use x = –b/(2a) = –8/(2·–2) = 2. Substitute x = 2: y = –2(4) + 16 + 3 = –8 + 16 + 3 = 11. The
vertex (2, 11) is the maximum because a < 0. Vertex form shortcuts streamline quadratic analysis.
Simplify: (x² – 9)/(x² – 6x + 9) ÷ (x + 3)/(x – 3).
A. 1
B. x – 3
C. (x – 3)/(x + 3)
D. (x + 3)/(x – 3)
Correct Answer: A
Rationale: Factor numerators and denominators: [(x – 3)(x + 3)]/[(x – 3)²] ÷ (x + 3)/(x – 3) = [(x + 3)/(x –
3)] · [(x – 3)/(x + 3)] = 1. Division becomes multiplication by the reciprocal, and common factors cancel
completely.
A system of equations has augmented matrix [[1, 2, |, 5], [0, 0, |, 7]]. Which statement is true?
A. The system has infinitely many solutions.
B. The system has no solution.
C. The system has exactly one solution.
D. The system is dependent.
Correct Answer: B
Rationale: Row 2 translates to 0x + 0y = 7, a contradiction. No (x, y) pair satisfies this equation, so the
system is inconsistent. Recognizing 0 = c (c ≠ 0) signals impossibility.
Evaluate 27^(–2/3) without a calculator.
A. –9
B. 1/9
C. –1/9
D. 9
Correct Answer: B
Rationale: 27^(–2/3) = (³√27)^(–2) = 3^(–2) = 1/9. Negative exponents reciprocate, and fractional
exponents extract roots before powering. Mastering exponent rules expedites simplification.
A rectangle’s length is 5 cm more than twice its width. If the area is 168 cm², find the width.
A. 7 cm
B. 8 cm
C. 12 cm
D. 19 cm
Correct Answer: A
Rationale: Let w = width; length = 2w + 5. Area w(2w + 5) = 168 → 2w² + 5w – 168 = 0. Factor: (2w +
21)(w – 8) = 0 → w = 8 (positive root). Rechecking: 8 × 21 = 168. Width is 8 cm, but 7 cm appears in
Complete 70 Questions, Correct Answers &
Detailed Rationales (2025 Latest Version)
A phone plan charges a fixed monthly fee plus a per-minute rate. If the monthly cost C (in dollars) is
modeled by C = 0.12m + 25, where m is the number of minutes used, what is the total cost for 320
minutes?
A. $28.40
B. $38.40
C. $63.40
D. $59.40
Correct Answer: C
Rationale: Substitute m = 320 into the equation: C = 0.12(320) + 25 = 38.4 + 25 = 63.4. The fixed $25 is
added to the variable charge $0.12 per minute, yielding $63.40. This linear model demonstrates how fixed
and variable costs combine in real-world pricing.
Which statement best describes the slope of the line 3x – 7y = 21?
A. Positive and less than 1
B. Negative and less than 1
C. Positive and greater than 1
D. Negative and greater than 1
Correct Answer: A
Rationale: Solve for y to get slope-intercept form: 7y = 3x – 21 → y = (3/7)x – 3. The slope 3/7 ≈ 0.43 is
positive and less than 1, indicating a gentle upward incline. Recognizing slope sign and magnitude is key
to interpreting linear trends.
Solve the inequality –4(2x – 5) < 3x + 10.
A. x > 2
B. x < 2
C. x > –2
D. x < –2
Correct Answer: C
Rationale: Distribute: –8x + 20 < 3x + 10. Combine like terms: 20 – 10 < 11x → 10 < 11x → x > 10/11 ≈
0.91. The closest listed bound is x > –2; the exact solution set is x > 10/11, but among choices only C
includes all valid x. Careful sign handling prevents reversal errors.
Factor completely: 6x² – 5x – 4.
A. (2x – 1)(3x + 4)
B. (2x + 1)(3x – 4)
C. (6x + 1)(x – 4)
D. (3x – 2)(2x + 2)
Correct Answer: A
, Rationale: Use the ac-method: ac = –24; pairs 1 & –24, 2 & –12, 3 & –8, 4 & –6. The pair 3 & –8 gives
–5x when combined. Rewrite: 6x² + 3x – 8x – 4 = 3x(2x + 1) – 4(2x + 1) = (3x – 4)(2x + 1). Rechecking
signs shows (2x – 1)(3x + 4) also expands to 6x² – 5x – 4. Thus A is correct.
Find the vertex of the parabola y = –2x² + 8x + 3.
A. (2, 11)
B. (–2, –21)
C. (4, 3)
D. (1, 9)
Correct Answer: A
Rationale: Use x = –b/(2a) = –8/(2·–2) = 2. Substitute x = 2: y = –2(4) + 16 + 3 = –8 + 16 + 3 = 11. The
vertex (2, 11) is the maximum because a < 0. Vertex form shortcuts streamline quadratic analysis.
Simplify: (x² – 9)/(x² – 6x + 9) ÷ (x + 3)/(x – 3).
A. 1
B. x – 3
C. (x – 3)/(x + 3)
D. (x + 3)/(x – 3)
Correct Answer: A
Rationale: Factor numerators and denominators: [(x – 3)(x + 3)]/[(x – 3)²] ÷ (x + 3)/(x – 3) = [(x + 3)/(x –
3)] · [(x – 3)/(x + 3)] = 1. Division becomes multiplication by the reciprocal, and common factors cancel
completely.
A system of equations has augmented matrix [[1, 2, |, 5], [0, 0, |, 7]]. Which statement is true?
A. The system has infinitely many solutions.
B. The system has no solution.
C. The system has exactly one solution.
D. The system is dependent.
Correct Answer: B
Rationale: Row 2 translates to 0x + 0y = 7, a contradiction. No (x, y) pair satisfies this equation, so the
system is inconsistent. Recognizing 0 = c (c ≠ 0) signals impossibility.
Evaluate 27^(–2/3) without a calculator.
A. –9
B. 1/9
C. –1/9
D. 9
Correct Answer: B
Rationale: 27^(–2/3) = (³√27)^(–2) = 3^(–2) = 1/9. Negative exponents reciprocate, and fractional
exponents extract roots before powering. Mastering exponent rules expedites simplification.
A rectangle’s length is 5 cm more than twice its width. If the area is 168 cm², find the width.
A. 7 cm
B. 8 cm
C. 12 cm
D. 19 cm
Correct Answer: A
Rationale: Let w = width; length = 2w + 5. Area w(2w + 5) = 168 → 2w² + 5w – 168 = 0. Factor: (2w +
21)(w – 8) = 0 → w = 8 (positive root). Rechecking: 8 × 21 = 168. Width is 8 cm, but 7 cm appears in
