WGU C957 Applied Algebra Objective
Assessment (OA) Mastery Guide: A
Comprehensive -Question Practice
Exam with Detailed Step-by-Step
Rationales, Formulas, and Problem-
Solving Strategies for First-Attempt
Success
Section 1: Linear Equations and Functions (Questions 1-40)
1. What is the slope of the line passing through the points (2, 3) and
(5, 9)?
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Rationale: Slope (m) = (y2 - y1) / (x2 - x1) = (9 - 3) / (5 - 2) = = 2.
2. What is the y-intercept of the line y = 4x - 7?
A) 4
B) -7
C) 7
,D) -4
Answer: B) -7
Rationale: The equation is in slope-intercept form (y = mx + b). The y-
intercept (b) is -7.
3. What is the x-intercept of the line 3x + 2y = 12?
A) 3
B) 2
C) 4
D) 6
Answer: C) 4
Rationale: To find the x-intercept, set y = 0 and solve for x: 3x + 2(0) = 12 -
> 3x = 12 -> x = 4.
4. What is the slope of a line perpendicular to a line with a slope of
2/3?
A) 2/3
B) -2/3
C) 3/2
D) -3/2
Answer: D) -3/2
Rationale: Perpendicular slopes are negative reciprocals. The negative
reciprocal of 2/3 is -3/2.
5. What is the slope of a line parallel to a line with a slope of -5?
A) 5
B) -5
C) 1/5
D) -1/5
Answer: B) -5
Rationale: Parallel lines have the exact same slope.
,6. Write the equation of a line with a slope of -2 and a y-intercept of 5.
A) y = -2x + 5
B) y = 2x - 5
C) y = 5x - 2
D) y = -2x - 5
Answer: A) y = -2x + 5
Rationale: Plug m = -2 and b = 5 into the slope-intercept form, y = mx +
b.
7. A cell phone plan costs a flat fee of $30 per month plus $0.10 per
text. What is the total cost (C) for sending 't' texts in a month?
A) C = 30t + 0.10
B) C = 0.10t + 30
C) C = 30.10t
D) C = 30t + 10
Answer: B) C = 0.10t + 30
Rationale: The total cost is the variable cost ($0.10 per text times the
number of texts) plus the fixed cost ($30).
8. The cost to rent a car is $50 per day plus $0.25 per mile driven. If the
total cost was $150 and the car was rented for 2 days, how many miles
were driven?
A) 100
B) 200
C) 400
D) 50
Answer: B) 200
Rationale: Total Cost = 50(days) + 0.25(miles). 150 = 50(2) + 0.25m -> 150
= 100 + 0.25m -> 50 = 0.25m -> m = 200.
9. What is the domain of the function f(x) = 3x - 4?
A) x > 4
, B) x < 4
C) All Real Numbers
D) x ≥ 4
Answer: C) All Real Numbers
Rationale: This is a linear function, which is defined for all real numbers.
10. What is the range of the function f(x) = x² + 2?
A) y > 2
B) y ≥ 2
C) y < 2
D) All Real Numbers
Answer: B) y ≥ 2
Rationale: The vertex of the parabola is at (0, 2). The parabola opens
upwards, so the y-values are all greater than or equal to 2.
11. Find the slope of the line 2y = -6x + 8.
A) -3
B) 3
C) -6
D) 4
Answer: A) -3
Rationale: Divide both sides by 2 to get y = -3x + 4. The coefficient of x is
the slope, m = -3.
12. Which of the following is a function?
A) {(1,2), (1,3), (2,4)}
B) {(2,3), (3,4), (5,6)}
C) {(2,3), (3,3), (2,4)}
D) {(1,2), (2,2), (1,4)}
Answer: B) {(2,3), (3,4), (5,6)}
Rationale: A function has a unique output (y-value) for each input (x-
value). In B, every x is different.
Assessment (OA) Mastery Guide: A
Comprehensive -Question Practice
Exam with Detailed Step-by-Step
Rationales, Formulas, and Problem-
Solving Strategies for First-Attempt
Success
Section 1: Linear Equations and Functions (Questions 1-40)
1. What is the slope of the line passing through the points (2, 3) and
(5, 9)?
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Rationale: Slope (m) = (y2 - y1) / (x2 - x1) = (9 - 3) / (5 - 2) = = 2.
2. What is the y-intercept of the line y = 4x - 7?
A) 4
B) -7
C) 7
,D) -4
Answer: B) -7
Rationale: The equation is in slope-intercept form (y = mx + b). The y-
intercept (b) is -7.
3. What is the x-intercept of the line 3x + 2y = 12?
A) 3
B) 2
C) 4
D) 6
Answer: C) 4
Rationale: To find the x-intercept, set y = 0 and solve for x: 3x + 2(0) = 12 -
> 3x = 12 -> x = 4.
4. What is the slope of a line perpendicular to a line with a slope of
2/3?
A) 2/3
B) -2/3
C) 3/2
D) -3/2
Answer: D) -3/2
Rationale: Perpendicular slopes are negative reciprocals. The negative
reciprocal of 2/3 is -3/2.
5. What is the slope of a line parallel to a line with a slope of -5?
A) 5
B) -5
C) 1/5
D) -1/5
Answer: B) -5
Rationale: Parallel lines have the exact same slope.
,6. Write the equation of a line with a slope of -2 and a y-intercept of 5.
A) y = -2x + 5
B) y = 2x - 5
C) y = 5x - 2
D) y = -2x - 5
Answer: A) y = -2x + 5
Rationale: Plug m = -2 and b = 5 into the slope-intercept form, y = mx +
b.
7. A cell phone plan costs a flat fee of $30 per month plus $0.10 per
text. What is the total cost (C) for sending 't' texts in a month?
A) C = 30t + 0.10
B) C = 0.10t + 30
C) C = 30.10t
D) C = 30t + 10
Answer: B) C = 0.10t + 30
Rationale: The total cost is the variable cost ($0.10 per text times the
number of texts) plus the fixed cost ($30).
8. The cost to rent a car is $50 per day plus $0.25 per mile driven. If the
total cost was $150 and the car was rented for 2 days, how many miles
were driven?
A) 100
B) 200
C) 400
D) 50
Answer: B) 200
Rationale: Total Cost = 50(days) + 0.25(miles). 150 = 50(2) + 0.25m -> 150
= 100 + 0.25m -> 50 = 0.25m -> m = 200.
9. What is the domain of the function f(x) = 3x - 4?
A) x > 4
, B) x < 4
C) All Real Numbers
D) x ≥ 4
Answer: C) All Real Numbers
Rationale: This is a linear function, which is defined for all real numbers.
10. What is the range of the function f(x) = x² + 2?
A) y > 2
B) y ≥ 2
C) y < 2
D) All Real Numbers
Answer: B) y ≥ 2
Rationale: The vertex of the parabola is at (0, 2). The parabola opens
upwards, so the y-values are all greater than or equal to 2.
11. Find the slope of the line 2y = -6x + 8.
A) -3
B) 3
C) -6
D) 4
Answer: A) -3
Rationale: Divide both sides by 2 to get y = -3x + 4. The coefficient of x is
the slope, m = -3.
12. Which of the following is a function?
A) {(1,2), (1,3), (2,4)}
B) {(2,3), (3,4), (5,6)}
C) {(2,3), (3,3), (2,4)}
D) {(1,2), (2,2), (1,4)}
Answer: B) {(2,3), (3,4), (5,6)}
Rationale: A function has a unique output (y-value) for each input (x-
value). In B, every x is different.
