WGU C957 APPLIED ALGEBRA OBJECTIVE ASSESSMENT EXAM – QUESTIONS
AND ANSWERS | VERIFIED AND WELL DETAILED ANSWERS | PLUS RATIONALES
| DOWNLOAD AND PASS | LATEST EXAM UPDATE 2026/2027
Core Domains
• Linear Equations and Inequalities
• Systems of Equations
• Quadratic and Polynomial Functions
• Exponential and Logarithmic Functions
• Rational Expressions and Equations
• Financial Mathematics and Applications
• Data Analysis and Modeling
• Problem-Solving and Decision-Making Strategies
Introduction
This comprehensive assessment is designed to evaluate your mastery of
fundamental algebraic concepts and their practical application in professional and
real-world scenarios. The exam measures your ability to interpret mathematical
models, solve complex equations, and make data-driven decisions. Each question is
crafted to assess both theoretical understanding and applied knowledge, bridging
the gap between abstract algebra and tangible problem-solving. The multiple-
choice format, combined with scenario-based questions, challenges you to think
critically and apply mathematical reasoning. This assessment emphasizes real-
world application, ensuring you are prepared to leverage algebraic principles for
effective decision-making in various professional contexts.
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SECTION ONE: QUESTIONS 1-50
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Question 1
,What is the solution to the equation 3x + 7 = 28?
A. x = 7
B. x = 5
C. x = 9
D. x = 21
🟢 Correct Answer: A. x = 7
🔴 Explanation: Subtract 7 from both sides to get 3x = 21, then divide by 3 to get
x = 7.
Question 2
Which of the following represents the slope-intercept form of a linear equation?
A. y = mx + b
B. y = ax^2 + bx + c
C. ax + by = c
D. y - y1 = m(x - x1)
🟢 Correct Answer: A. y = mx + b
🔴 Explanation: The slope-intercept form is y = mx + b, where m is the slope and
b is the y-intercept. Option B is quadratic, C is standard form, and D is point-slope
form.
Question 3
What is the y-intercept of the line represented by the equation 2x - 3y = 12?
A. (0, 4)
B. (0, -4)
C. (0, 6)
D. (6, 0)
,🟢 Correct Answer: B. (0, -4)
🔴 Explanation: Set x = 0 to find the y-intercept. Then -3y = 12, so y = -4. The
point is (0, -4).
Question 4
Solve the following system of equations:
2x + y = 10
x-y=2
A. x = 4, y = 2
B. x = 2, y = 4
C. x = 6, y = -2
D. x = 3, y = 4
🟢 Correct Answer: A. x = 4, y = 2
🔴 Explanation: Add the equations to eliminate y: (2x + y) + (x - y) = 10 + 2,
which simplifies to 3x = 12, so x = 4. Substitute x = 4 into x - y = 2, giving 4 - y =
2, so y = 2.
Question 5
Which of the following is the correct factorization of the quadratic expression x^2
- 5x + 6?
A. (x - 2)(x - 3)
B. (x + 2)(x + 3)
C. (x - 1)(x - 6)
D. (x + 1)(x + 6)
🟢 Correct Answer: A. (x - 2)(x - 3)
, 🔴 Explanation: The expression factors into two binomials whose constants
multiply to 6 and sum to -5. The constants -2 and -3 satisfy this: (-2)(-3)=6 and
(-2)+(-3)=-5.
Question 6
A car rental company charges a flat fee of $30 plus $0.15 per mile driven. What is
the total cost, C, as a function of miles driven, m?
A. C(m) = 30m + 0.15
B. C(m) = 0.15m + 30
C. C(m) = 30 - 0.15m
D. C(m) = 30m - 0.15
🟢 Correct Answer: B. C(m) = 0.15m + 30
🔴 Explanation: The cost is the sum of the flat fee, which is constant, and the
variable cost of $0.15 per mile. This is represented by C(m) = 0.15m + 30.
Question 7
What is the slope of a line that is perpendicular to the line y = 3x - 2?
A. 3
B. -3
C. 1/3
D. -1/3
🟢 Correct Answer: D. -1/3
🔴 Explanation: The slope of the given line is 3. A perpendicular line has a slope
that is the negative reciprocal. The negative reciprocal of 3 is -1/3.
Question 8
If f(x) = 2x^2 - 3x + 1, what is f(2)?
AND ANSWERS | VERIFIED AND WELL DETAILED ANSWERS | PLUS RATIONALES
| DOWNLOAD AND PASS | LATEST EXAM UPDATE 2026/2027
Core Domains
• Linear Equations and Inequalities
• Systems of Equations
• Quadratic and Polynomial Functions
• Exponential and Logarithmic Functions
• Rational Expressions and Equations
• Financial Mathematics and Applications
• Data Analysis and Modeling
• Problem-Solving and Decision-Making Strategies
Introduction
This comprehensive assessment is designed to evaluate your mastery of
fundamental algebraic concepts and their practical application in professional and
real-world scenarios. The exam measures your ability to interpret mathematical
models, solve complex equations, and make data-driven decisions. Each question is
crafted to assess both theoretical understanding and applied knowledge, bridging
the gap between abstract algebra and tangible problem-solving. The multiple-
choice format, combined with scenario-based questions, challenges you to think
critically and apply mathematical reasoning. This assessment emphasizes real-
world application, ensuring you are prepared to leverage algebraic principles for
effective decision-making in various professional contexts.
════════════════════════════════════
SECTION ONE: QUESTIONS 1-50
════════════════════════════════════
Question 1
,What is the solution to the equation 3x + 7 = 28?
A. x = 7
B. x = 5
C. x = 9
D. x = 21
🟢 Correct Answer: A. x = 7
🔴 Explanation: Subtract 7 from both sides to get 3x = 21, then divide by 3 to get
x = 7.
Question 2
Which of the following represents the slope-intercept form of a linear equation?
A. y = mx + b
B. y = ax^2 + bx + c
C. ax + by = c
D. y - y1 = m(x - x1)
🟢 Correct Answer: A. y = mx + b
🔴 Explanation: The slope-intercept form is y = mx + b, where m is the slope and
b is the y-intercept. Option B is quadratic, C is standard form, and D is point-slope
form.
Question 3
What is the y-intercept of the line represented by the equation 2x - 3y = 12?
A. (0, 4)
B. (0, -4)
C. (0, 6)
D. (6, 0)
,🟢 Correct Answer: B. (0, -4)
🔴 Explanation: Set x = 0 to find the y-intercept. Then -3y = 12, so y = -4. The
point is (0, -4).
Question 4
Solve the following system of equations:
2x + y = 10
x-y=2
A. x = 4, y = 2
B. x = 2, y = 4
C. x = 6, y = -2
D. x = 3, y = 4
🟢 Correct Answer: A. x = 4, y = 2
🔴 Explanation: Add the equations to eliminate y: (2x + y) + (x - y) = 10 + 2,
which simplifies to 3x = 12, so x = 4. Substitute x = 4 into x - y = 2, giving 4 - y =
2, so y = 2.
Question 5
Which of the following is the correct factorization of the quadratic expression x^2
- 5x + 6?
A. (x - 2)(x - 3)
B. (x + 2)(x + 3)
C. (x - 1)(x - 6)
D. (x + 1)(x + 6)
🟢 Correct Answer: A. (x - 2)(x - 3)
, 🔴 Explanation: The expression factors into two binomials whose constants
multiply to 6 and sum to -5. The constants -2 and -3 satisfy this: (-2)(-3)=6 and
(-2)+(-3)=-5.
Question 6
A car rental company charges a flat fee of $30 plus $0.15 per mile driven. What is
the total cost, C, as a function of miles driven, m?
A. C(m) = 30m + 0.15
B. C(m) = 0.15m + 30
C. C(m) = 30 - 0.15m
D. C(m) = 30m - 0.15
🟢 Correct Answer: B. C(m) = 0.15m + 30
🔴 Explanation: The cost is the sum of the flat fee, which is constant, and the
variable cost of $0.15 per mile. This is represented by C(m) = 0.15m + 30.
Question 7
What is the slope of a line that is perpendicular to the line y = 3x - 2?
A. 3
B. -3
C. 1/3
D. -1/3
🟢 Correct Answer: D. -1/3
🔴 Explanation: The slope of the given line is 3. A perpendicular line has a slope
that is the negative reciprocal. The negative reciprocal of 3 is -1/3.
Question 8
If f(x) = 2x^2 - 3x + 1, what is f(2)?
