WGU C957 Applied Algebra OA Exam – Complete
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
A car rental company charges a flat fee of $45 plus $0.25 per mile driven. Which linear equation
models the total cost C for driving x miles?
A. C = 0.25x + 45
B. C = 45x + 0.25
C. C = 0.25x – 45
D. C = 45 – 0.25x
Correct Answer: A
1. Rationale: The total cost equals the variable cost (0.25 per mile) times the number of
miles plus the fixed cost (45). This matches the slope-intercept form y = mx + b where
0.25 is the slope and 45 is the y-intercept.
Solve for x: 3(2x – 5) = 9 – 4(x + 1)
A. x = 2
B. x = 1
C. x = –1
D. x = 4
Correct Answer: A
2. Rationale: Distribute on both sides to obtain 6x – 15 = 9 – 4x – 4. Combine like terms:
6x – 15 = 5 – 4x. Add 4x to both sides and add 15 to both sides to get 10x = 20, so x = 2.
What is the slope of the line passing through (–3, 7) and (5, –1)?
A. –1
B. 1
C. –2
D. 2
Correct Answer: A
3. Rationale: Slope m = (y₂ – y₁)/(x₂ – x₁) = (–1 – 7)/(5 – (–3)) = –8/8 = –1. The negative
slope indicates the line decreases 1 unit vertically for every 1 unit of horizontal increase.
Which inequality represents all real numbers at least 8 units away from –2 on the number line?
A. |x + 2| ≥ 8
,B. |x – 2| ≥ 8
C. |x + 8| ≥ 2
D. |x – 8| ≥ –2
Correct Answer: A
4. Rationale: Distance from –2 is expressed as |x – (–2)| = |x + 2|. “At least 8 units”
translates to ≥ 8, so |x + 2| ≥ 8 is correct.
Factor completely: 6x² – 13x – 5
A. (3x + 1)(2x – 5)
B. (6x – 1)(x + 5)
C. (2x + 1)(3x – 5)
D. (6x + 5)(x – 1)
Correct Answer: A
5. Rationale: Find two numbers whose product is 6·(–5) = –30 and sum is –13. The
numbers –15 and 2 work. Rewrite: 6x² – 15x + 2x – 5, group, and factor to (3x + 1)(2x –
5).
If f(x) = 2x² – 5x + 3, what is f(–1)?
A. 10
B. 0
C. 6
D. –4
Correct Answer: A
6. Rationale: Substitute –1 for x: 2(–1)² – 5(–1) + 3 = 2(1) + 5 + 3 = 2 + 5 + 3 = 10.
Solve the quadratic equation x² – 6x + 2 = 0 using the quadratic formula.
A. x = 3 ± √7
B. x = –3 ± √7
C. x = 3 ± √11
D. x = –3 ± √11
Correct Answer: A
7. Rationale: With a = 1, b = –6, c = 2, the quadratic formula gives x = [6 ± √(36 – 8)]/2 =
[6 ± √28]/2 = [6 ± 2√7]/2 = 3 ± √7.
Simplify: (x³y⁻²)/(x⁻¹y⁴)
A. x⁴/y⁶
B. y⁶/x⁴
C. x²/y²
D. x³y²
, Correct Answer: A
8. Rationale: Subtract exponents for like bases: x³ – (–1) = x⁴ and y⁻² – 4 = –6, so the
expression becomes x⁴y⁻⁶ = x⁴/y⁶.
A rectangle’s length is 5 cm more than its width. If the area is 84 cm², find the width.
A. 7 cm
B. 8 cm
C. 9 cm
D. 12 cm
Correct Answer: A
9. Rationale: Let width = w, then length = w + 5. Area w(w + 5) = 84 → w² + 5w – 84 = 0.
Factoring gives (w + 12)(w – 7) = 0, so w = 7 cm (positive solution).
Which system has infinitely many solutions?
A. 2x – 3y = 6 and 4x – 6y = 12
B. x + y = 5 and x – y = 1
C. 3x + 2y = 7 and 6x + 4y = 10
D. y = 2x + 1 and y = –2x + 3
Correct Answer: A
10. Rationale: The second equation is exactly twice the first, so both equations describe the
same line. Every point on the line satisfies both equations, giving infinitely many
solutions.
Simplify: √(50x⁵)
A. 5x²√(2x)
B. 10x√(5x)
C. 2x²√(25x)
D. 25x²√(2x)
Correct Answer: A
11. Rationale: Factor 50x⁵ = 25·2·x⁴·x. Take square roots of perfect squares: √(25x⁴) = 5x²,
leaving √(2x) inside the radical.
Find the x-intercept of the line 4x – 3y = 24.
A. (6, 0)
B. (0, –8)
C. (8, 0)
D. (–6, 0)
Correct Answer: A
12. Rationale: Set y = 0: 4x = 24 → x = 6. The x-intercept is the point (6, 0).
70 Questions, Correct Answers & Detailed
Rationales ( Latest Version)
A car rental company charges a flat fee of $45 plus $0.25 per mile driven. Which linear equation
models the total cost C for driving x miles?
A. C = 0.25x + 45
B. C = 45x + 0.25
C. C = 0.25x – 45
D. C = 45 – 0.25x
Correct Answer: A
1. Rationale: The total cost equals the variable cost (0.25 per mile) times the number of
miles plus the fixed cost (45). This matches the slope-intercept form y = mx + b where
0.25 is the slope and 45 is the y-intercept.
Solve for x: 3(2x – 5) = 9 – 4(x + 1)
A. x = 2
B. x = 1
C. x = –1
D. x = 4
Correct Answer: A
2. Rationale: Distribute on both sides to obtain 6x – 15 = 9 – 4x – 4. Combine like terms:
6x – 15 = 5 – 4x. Add 4x to both sides and add 15 to both sides to get 10x = 20, so x = 2.
What is the slope of the line passing through (–3, 7) and (5, –1)?
A. –1
B. 1
C. –2
D. 2
Correct Answer: A
3. Rationale: Slope m = (y₂ – y₁)/(x₂ – x₁) = (–1 – 7)/(5 – (–3)) = –8/8 = –1. The negative
slope indicates the line decreases 1 unit vertically for every 1 unit of horizontal increase.
Which inequality represents all real numbers at least 8 units away from –2 on the number line?
A. |x + 2| ≥ 8
,B. |x – 2| ≥ 8
C. |x + 8| ≥ 2
D. |x – 8| ≥ –2
Correct Answer: A
4. Rationale: Distance from –2 is expressed as |x – (–2)| = |x + 2|. “At least 8 units”
translates to ≥ 8, so |x + 2| ≥ 8 is correct.
Factor completely: 6x² – 13x – 5
A. (3x + 1)(2x – 5)
B. (6x – 1)(x + 5)
C. (2x + 1)(3x – 5)
D. (6x + 5)(x – 1)
Correct Answer: A
5. Rationale: Find two numbers whose product is 6·(–5) = –30 and sum is –13. The
numbers –15 and 2 work. Rewrite: 6x² – 15x + 2x – 5, group, and factor to (3x + 1)(2x –
5).
If f(x) = 2x² – 5x + 3, what is f(–1)?
A. 10
B. 0
C. 6
D. –4
Correct Answer: A
6. Rationale: Substitute –1 for x: 2(–1)² – 5(–1) + 3 = 2(1) + 5 + 3 = 2 + 5 + 3 = 10.
Solve the quadratic equation x² – 6x + 2 = 0 using the quadratic formula.
A. x = 3 ± √7
B. x = –3 ± √7
C. x = 3 ± √11
D. x = –3 ± √11
Correct Answer: A
7. Rationale: With a = 1, b = –6, c = 2, the quadratic formula gives x = [6 ± √(36 – 8)]/2 =
[6 ± √28]/2 = [6 ± 2√7]/2 = 3 ± √7.
Simplify: (x³y⁻²)/(x⁻¹y⁴)
A. x⁴/y⁶
B. y⁶/x⁴
C. x²/y²
D. x³y²
, Correct Answer: A
8. Rationale: Subtract exponents for like bases: x³ – (–1) = x⁴ and y⁻² – 4 = –6, so the
expression becomes x⁴y⁻⁶ = x⁴/y⁶.
A rectangle’s length is 5 cm more than its width. If the area is 84 cm², find the width.
A. 7 cm
B. 8 cm
C. 9 cm
D. 12 cm
Correct Answer: A
9. Rationale: Let width = w, then length = w + 5. Area w(w + 5) = 84 → w² + 5w – 84 = 0.
Factoring gives (w + 12)(w – 7) = 0, so w = 7 cm (positive solution).
Which system has infinitely many solutions?
A. 2x – 3y = 6 and 4x – 6y = 12
B. x + y = 5 and x – y = 1
C. 3x + 2y = 7 and 6x + 4y = 10
D. y = 2x + 1 and y = –2x + 3
Correct Answer: A
10. Rationale: The second equation is exactly twice the first, so both equations describe the
same line. Every point on the line satisfies both equations, giving infinitely many
solutions.
Simplify: √(50x⁵)
A. 5x²√(2x)
B. 10x√(5x)
C. 2x²√(25x)
D. 25x²√(2x)
Correct Answer: A
11. Rationale: Factor 50x⁵ = 25·2·x⁴·x. Take square roots of perfect squares: √(25x⁴) = 5x²,
leaving √(2x) inside the radical.
Find the x-intercept of the line 4x – 3y = 24.
A. (6, 0)
B. (0, –8)
C. (8, 0)
D. (–6, 0)
Correct Answer: A
12. Rationale: Set y = 0: 4x = 24 → x = 6. The x-intercept is the point (6, 0).
