WGU C957 Applied Algebra OA Actual Exam
2026/2027 | Complete Questions & Detailed
Rationales | Pass Guaranteed - A+ Graded
TABLE OF CONTENTS
Section 1 | Linear Equations and Inequalities | Q1 – Q10
Section 2 | Systems of Equations and Matrices | Q11 – Q20
Section 3 | Quadratic and Polynomial Functions | Q21 – Q30
Section 4 | Exponential and Logarithmic Functions | Q31 – Q40
Section 5 | Real-World Applications and Data Modeling | Q41 – Q50
Instructions: Choose the single best answer. Pass: 80% in 90 minutes.
══════════════════════════════════════
SECTION 1: LINEAR EQUATIONS AND INEQUALITIES Q1 – Q10
══════════════════════════════════════
Question 1 of 50
A homeowner hires a plumber to repair a burst pipe in the basement. The plumber
charges a flat $75 service fee plus $45 per hour of labor. The homeowner has set aside
exactly $300 for this repair and needs to know the maximum number of full hours the
plumber can work without exceeding the budget.
A. 4 hours
B. 5 hours ✓ CORRECT
C. 6 hours
D. 7 hours
Correct Answer: B
Rationale: Setting up the inequality 75 + 45h ≤ 300 and solving yields h ≤ 5, so five hours
is the maximum whole number of hours within budget. Option A is incorrect because
four hours would cost only $255 and leaves money unused, failing to maximize the
,allocated budget. This type of linear model is common in service-industry pricing where
a flat rate combines with variable hourly labor.
Question 2 of 50
A fitness coach tracks a client's progress on a treadmill. At the two-week check-in, the
client is running at 5 miles per hour; by the six-week check-in, the speed has increased
to 13 miles per hour. The coach wants to model the weekly rate of improvement as a
linear relationship.
A. 1 mile per hour per week
B. 1.5 miles per hour per week
C. 3 miles per hour per week
D. 2 miles per hour per week ✓ CORRECT
Correct Answer: D
Rationale: The slope formula gives (13 − 5) ÷ (6 − 2) = 2, representing a gain of 2 miles
per hour each week. Option C is incorrect because it divides only the change in speed by
the initial week count rather than the interval between measurements. Linear
rate-of-change calculations help trainers set realistic milestone goals without
overloading clients.
Question 3 of 50
A bakery manager uses a pricing formula to determine the cost of custom cakes. After
simplifying the expression 3(x − 4) + 2 to set it equal to 2x + 5, where x represents the
number of cake layers, she needs to find the exact number of layers where both pricing
methods yield the same total cost.
A. 15 layers ✓ CORRECT
B. 12 layers
C. 9 layers
D. 7 layers
, Correct Answer: A
Rationale: Distributing and collecting like terms produces 3x − 10 = 2x + 5, which
simplifies to x = 15. Option B is incorrect because substituting 12 into the original
equation yields 26 on the left and 29 on the right, showing the expressions are not
equal. Solving linear equations with distribution is essential when comparing two
vendor pricing structures.
Question 4 of 50
A meteorologist models the temperature range in a greenhouse overnight with the
compound inequality −3 < 2x + 1 ≤ 7, where x represents hours after midnight. She
needs to express the valid time interval in standard inequality notation.
A. −2 ≤ x < 3
B. −2 < x ≤ 3 ✓ CORRECT
C. −1 < x ≤ 4
D. −3 < x ≤ 6
Correct Answer: B
Rationale: Subtracting 1 from all three parts produces −4 < 2x ≤ 6, and dividing by 2
yields −2 < x ≤ 3. Option A is incorrect because it reverses the strict and non-strict
inequality symbols, which would misrepresent whether the endpoints are included.
Compound inequalities are common in climate control where equipment must stay
within operating thresholds.
Question 5 of 50
A civil engineer is designing a ramp and knows the surface rises according to a linear
model passing through the point (3, −2) on her coordinate grid with a slope of 4. She
needs to predict the elevation y when the horizontal distance x reaches 5 meters.
A. 4 meters
B. 6 meters ✓ CORRECT
2026/2027 | Complete Questions & Detailed
Rationales | Pass Guaranteed - A+ Graded
TABLE OF CONTENTS
Section 1 | Linear Equations and Inequalities | Q1 – Q10
Section 2 | Systems of Equations and Matrices | Q11 – Q20
Section 3 | Quadratic and Polynomial Functions | Q21 – Q30
Section 4 | Exponential and Logarithmic Functions | Q31 – Q40
Section 5 | Real-World Applications and Data Modeling | Q41 – Q50
Instructions: Choose the single best answer. Pass: 80% in 90 minutes.
══════════════════════════════════════
SECTION 1: LINEAR EQUATIONS AND INEQUALITIES Q1 – Q10
══════════════════════════════════════
Question 1 of 50
A homeowner hires a plumber to repair a burst pipe in the basement. The plumber
charges a flat $75 service fee plus $45 per hour of labor. The homeowner has set aside
exactly $300 for this repair and needs to know the maximum number of full hours the
plumber can work without exceeding the budget.
A. 4 hours
B. 5 hours ✓ CORRECT
C. 6 hours
D. 7 hours
Correct Answer: B
Rationale: Setting up the inequality 75 + 45h ≤ 300 and solving yields h ≤ 5, so five hours
is the maximum whole number of hours within budget. Option A is incorrect because
four hours would cost only $255 and leaves money unused, failing to maximize the
,allocated budget. This type of linear model is common in service-industry pricing where
a flat rate combines with variable hourly labor.
Question 2 of 50
A fitness coach tracks a client's progress on a treadmill. At the two-week check-in, the
client is running at 5 miles per hour; by the six-week check-in, the speed has increased
to 13 miles per hour. The coach wants to model the weekly rate of improvement as a
linear relationship.
A. 1 mile per hour per week
B. 1.5 miles per hour per week
C. 3 miles per hour per week
D. 2 miles per hour per week ✓ CORRECT
Correct Answer: D
Rationale: The slope formula gives (13 − 5) ÷ (6 − 2) = 2, representing a gain of 2 miles
per hour each week. Option C is incorrect because it divides only the change in speed by
the initial week count rather than the interval between measurements. Linear
rate-of-change calculations help trainers set realistic milestone goals without
overloading clients.
Question 3 of 50
A bakery manager uses a pricing formula to determine the cost of custom cakes. After
simplifying the expression 3(x − 4) + 2 to set it equal to 2x + 5, where x represents the
number of cake layers, she needs to find the exact number of layers where both pricing
methods yield the same total cost.
A. 15 layers ✓ CORRECT
B. 12 layers
C. 9 layers
D. 7 layers
, Correct Answer: A
Rationale: Distributing and collecting like terms produces 3x − 10 = 2x + 5, which
simplifies to x = 15. Option B is incorrect because substituting 12 into the original
equation yields 26 on the left and 29 on the right, showing the expressions are not
equal. Solving linear equations with distribution is essential when comparing two
vendor pricing structures.
Question 4 of 50
A meteorologist models the temperature range in a greenhouse overnight with the
compound inequality −3 < 2x + 1 ≤ 7, where x represents hours after midnight. She
needs to express the valid time interval in standard inequality notation.
A. −2 ≤ x < 3
B. −2 < x ≤ 3 ✓ CORRECT
C. −1 < x ≤ 4
D. −3 < x ≤ 6
Correct Answer: B
Rationale: Subtracting 1 from all three parts produces −4 < 2x ≤ 6, and dividing by 2
yields −2 < x ≤ 3. Option A is incorrect because it reverses the strict and non-strict
inequality symbols, which would misrepresent whether the endpoints are included.
Compound inequalities are common in climate control where equipment must stay
within operating thresholds.
Question 5 of 50
A civil engineer is designing a ramp and knows the surface rises according to a linear
model passing through the point (3, −2) on her coordinate grid with a slope of 4. She
needs to predict the elevation y when the horizontal distance x reaches 5 meters.
A. 4 meters
B. 6 meters ✓ CORRECT
