Applied Algebra With Verified Questions
And Answers For Year 2026/2027
**Q1. A car rental company charges a flat fee of $45 plus $0.25 per mile driven.
Which linear equation represents the total cost (C) for driving (m) miles?**
A) C = 45m + 0.25
B) C = 0.25m + 45
C) C = 45m - 0.25
D) C = 0.25(45 + m)
**Answer:** B) C = 0.25m + 45
**Rationale:** The cost per mile ($0.25) is the variable rate multiplied by miles
(m), and the flat fee ($45) is the y-intercept. This follows slope-intercept form y
= mx + b.
---
**Q2. What is the slope of the line passing through the points (-2, 5) and (4, -
7)?**
A) -2
B) 2
C) -1/2
D) 1/2
,**Answer:** A) -2
**Rationale:** Slope (m) = (y2 - y1)/(x2 - x1) = (-7 - 5)/(4 - (-2)) = (-12)/(6) = -2.
---
**Q3. A plumber charges a $75 service call fee plus $55 per hour. If the total
bill was $295, how many hours (h) did the plumber work?**
A) 3 hours
B) 4 hours
C) 5 hours
D) 6 hours
**Answer:** B) 4 hours
**Rationale:** 295 = 55h + 75 → 220 = 55h → h = 4.
---
**Q4. What is the y-intercept of the function f(x) = 3x - 12?**
A) (0, -12)
B) (0, 3)
C) (-12, 0)
D) (3, 0)
,**Answer:** A) (0, -12)
**Rationale:** The y-intercept occurs when x=0. f(0) = 3(0) - 12 = -12, giving
point (0, -12).
---
**Q5. A company's profit P (in dollars) from selling x units is modeled by P(x) =
-2x^2 + 400x - 5000. What is the maximum profit?**
A) $10,000
B) $15,000
C) $20,000
D) $25,000
**Answer:** B) $15,000
**Rationale:** The quadratic has a negative leading coefficient, so maximum
occurs at the vertex. x = -b/(2a) = -400/(2(-2)) = 100. P(100) = -2(10000) +
40000 - 5000 = 15000.
---
**Q6. A linear cost function has a fixed cost of $1200 and a variable cost of $35
per item. What is the total cost for 80 items?**
A) $2,800
B) $4,000
, C) $3,200
D) $4,800
**Answer:** B) $4,000
**Rationale:** C(x) = Fixed Cost + (Variable Cost)x = 1200 + 35x. For x = 80:
1200 + 35(80) = 1200 + 2800 = 4000.
---
**Q7. Which best describes the graph of f(x) = 4x + 7?**
A) A horizontal line
B) A line with slope of 7
C) A line with slope of 4 and y-intercept 7
D) A parabola opening upwards
**Answer:** C) A line with slope of 4 and y-intercept 7
**Rationale:** In slope-intercept form y = mx + b, m=4 and b=7.
---
**Q8. What is the x-intercept of the linear equation 2x + 3y = 18?**
A) (9, 0)
B) (0, 6)
And Answers For Year 2026/2027
**Q1. A car rental company charges a flat fee of $45 plus $0.25 per mile driven.
Which linear equation represents the total cost (C) for driving (m) miles?**
A) C = 45m + 0.25
B) C = 0.25m + 45
C) C = 45m - 0.25
D) C = 0.25(45 + m)
**Answer:** B) C = 0.25m + 45
**Rationale:** The cost per mile ($0.25) is the variable rate multiplied by miles
(m), and the flat fee ($45) is the y-intercept. This follows slope-intercept form y
= mx + b.
---
**Q2. What is the slope of the line passing through the points (-2, 5) and (4, -
7)?**
A) -2
B) 2
C) -1/2
D) 1/2
,**Answer:** A) -2
**Rationale:** Slope (m) = (y2 - y1)/(x2 - x1) = (-7 - 5)/(4 - (-2)) = (-12)/(6) = -2.
---
**Q3. A plumber charges a $75 service call fee plus $55 per hour. If the total
bill was $295, how many hours (h) did the plumber work?**
A) 3 hours
B) 4 hours
C) 5 hours
D) 6 hours
**Answer:** B) 4 hours
**Rationale:** 295 = 55h + 75 → 220 = 55h → h = 4.
---
**Q4. What is the y-intercept of the function f(x) = 3x - 12?**
A) (0, -12)
B) (0, 3)
C) (-12, 0)
D) (3, 0)
,**Answer:** A) (0, -12)
**Rationale:** The y-intercept occurs when x=0. f(0) = 3(0) - 12 = -12, giving
point (0, -12).
---
**Q5. A company's profit P (in dollars) from selling x units is modeled by P(x) =
-2x^2 + 400x - 5000. What is the maximum profit?**
A) $10,000
B) $15,000
C) $20,000
D) $25,000
**Answer:** B) $15,000
**Rationale:** The quadratic has a negative leading coefficient, so maximum
occurs at the vertex. x = -b/(2a) = -400/(2(-2)) = 100. P(100) = -2(10000) +
40000 - 5000 = 15000.
---
**Q6. A linear cost function has a fixed cost of $1200 and a variable cost of $35
per item. What is the total cost for 80 items?**
A) $2,800
B) $4,000
, C) $3,200
D) $4,800
**Answer:** B) $4,000
**Rationale:** C(x) = Fixed Cost + (Variable Cost)x = 1200 + 35x. For x = 80:
1200 + 35(80) = 1200 + 2800 = 4000.
---
**Q7. Which best describes the graph of f(x) = 4x + 7?**
A) A horizontal line
B) A line with slope of 7
C) A line with slope of 4 and y-intercept 7
D) A parabola opening upwards
**Answer:** C) A line with slope of 4 and y-intercept 7
**Rationale:** In slope-intercept form y = mx + b, m=4 and b=7.
---
**Q8. What is the x-intercept of the linear equation 2x + 3y = 18?**
A) (9, 0)
B) (0, 6)
