MAT 101 FINAL EXAM | COLLEGE ALGEBRA -
STRAIGHTERLINE | 100% CORRECT ACTUAL
QUESTIONS AND ANSWERS
1. Solve for x: 6x - 8 = 4x + 12
A. 8
B. 10
C. 12
D. 14
Correct Answer: B
Rationale: Subtract 4x from both sides: 2x - 8 = 12. Add 8: 2x = 20. Divide by 2: x = 10 .
2. Solve for x: 3(x + 2) = 5x - 8
A. 5
B. 7
C. 9
D. 11
Correct Answer: B
Rationale: Distribute: 3x + 6 = 5x - 8. Subtract 3x: 6 = 2x - 8. Add 8: 14 = 2x. Divide by
2: x = 7 .
3. Solve the inequality: 2x - 5 < 9
A. x < 7
B. x > 7
C. x < 14
D. x > 14
Correct Answer: A
Rationale: Add 5: 2x < 14. Divide by 2: x < 7 .
4. Solve the inequality: -3x + 7 ≤ 22
A. x ≤ -5
B. x ≥ -5
,C. x ≤ 5
D. x ≥ 5
Correct Answer: B
Rationale: Subtract 7: -3x ≤ 15. Divide by -3 (reverse inequality sign): x ≥ -5 .
5. Solve for x: (x + 3)/4 = (x - 1)/2
A. 5
B. 6
C. 7
D. 8
Correct Answer: A
Rationale: Cross-multiply: 2(x + 3) = 4(x - 1). Distribute: 2x + 6 = 4x - 4. Simplify: 10 =
2x. x = 5 .
6. Solve for x: 2.5x - 3 = 7
A. 2
B. 3
C. 4
D. 5
Correct Answer: C
Rationale: Add 3: 2.5x = 10. Divide by 2.5: x = 4 .
7. Solve for x: 7x - 3 = 2(3x + 4) - 5
A. 4
B. 5
C. 6
D. 7
Correct Answer: C
Rationale: Distribute: 7x - 3 = 6x + 8 - 5. Simplify: 7x - 3 = 6x + 3. Subtract 6x: x - 3 = 3.
x = 6.
8. What is the slope of the line passing through points (2, 3) and (5, 9)?
A. 1
B. 2
,C. 3
D. 4
Correct Answer: B
Rationale: m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2 .
9. What is the slope of the line: 4x - 2y = 8
A. 1
B. 2
C. -2
D. 4
Correct Answer: B
Rationale: Rewrite in slope-intercept form: -2y = -4x + 8 → y = 2x - 4. Slope = 2 .
10. The sum of two consecutive integers is 45. Find the larger integer.
A. 21
B. 22
C. 23
D. 24
Correct Answer: C
Rationale: Let x be the smaller integer, x+1 the larger. Equation: x + (x+1) = 45 → 2x + 1
= 45 → 2x = 44 → x = 22. Larger = 23 .
11. A car rental company charges $30 per day plus $0.15 per mile. If a customer
pays $75 for a 3-day rental, how many miles were driven?
A. 100
B. 200
C. 300
D. 400
Correct Answer: C
Rationale: Total = 30(3) + 0.15m = 75 → 90 + 0.15m = 75 → 0.15m = 75 - 90 → 0.15m
= 45 → m = 300.
12. Solve for x: 4x - 7 = 2x + 15
A. 9
B. 10
, C. 11
D. 12
Correct Answer: C
Rationale: Subtract 2x: 2x - 7 = 15. Add 7: 2x = 22. x = 11.
13. What is the y-intercept of the line y = -3x + 6?
A. (0, -3)
B. (0, 3)
C. (0, 6)
D. (0, -6)
Correct Answer: C
Rationale: In y = mx + b, b is the y-intercept. y = -3x + 6 has y-intercept (0, 6).
14. Find the equation of the line with slope 4 passing through (1, 3).
A. y = 4x - 1
B. y = 4x + 1
C. y = 4x - 3
D. y = 4x + 3
Correct Answer: A
Rationale: Use point-slope form: y - 3 = 4(x - 1) → y - 3 = 4x - 4 → y = 4x - 1.
15. Solve for x: 5x + 2 = 3x - 10
A. -4
B. -6
C. 4
D. 6
Correct Answer: B
Rationale: Subtract 3x: 2x + 2 = -10. Subtract 2: 2x = -12. x = -6.
SECTION 2: FUNCTIONS AND GRAPHING (Questions 16-35)
16. If f(x) = 2x² - 3x + 1, find f(2).
A. 3
B. 5
STRAIGHTERLINE | 100% CORRECT ACTUAL
QUESTIONS AND ANSWERS
1. Solve for x: 6x - 8 = 4x + 12
A. 8
B. 10
C. 12
D. 14
Correct Answer: B
Rationale: Subtract 4x from both sides: 2x - 8 = 12. Add 8: 2x = 20. Divide by 2: x = 10 .
2. Solve for x: 3(x + 2) = 5x - 8
A. 5
B. 7
C. 9
D. 11
Correct Answer: B
Rationale: Distribute: 3x + 6 = 5x - 8. Subtract 3x: 6 = 2x - 8. Add 8: 14 = 2x. Divide by
2: x = 7 .
3. Solve the inequality: 2x - 5 < 9
A. x < 7
B. x > 7
C. x < 14
D. x > 14
Correct Answer: A
Rationale: Add 5: 2x < 14. Divide by 2: x < 7 .
4. Solve the inequality: -3x + 7 ≤ 22
A. x ≤ -5
B. x ≥ -5
,C. x ≤ 5
D. x ≥ 5
Correct Answer: B
Rationale: Subtract 7: -3x ≤ 15. Divide by -3 (reverse inequality sign): x ≥ -5 .
5. Solve for x: (x + 3)/4 = (x - 1)/2
A. 5
B. 6
C. 7
D. 8
Correct Answer: A
Rationale: Cross-multiply: 2(x + 3) = 4(x - 1). Distribute: 2x + 6 = 4x - 4. Simplify: 10 =
2x. x = 5 .
6. Solve for x: 2.5x - 3 = 7
A. 2
B. 3
C. 4
D. 5
Correct Answer: C
Rationale: Add 3: 2.5x = 10. Divide by 2.5: x = 4 .
7. Solve for x: 7x - 3 = 2(3x + 4) - 5
A. 4
B. 5
C. 6
D. 7
Correct Answer: C
Rationale: Distribute: 7x - 3 = 6x + 8 - 5. Simplify: 7x - 3 = 6x + 3. Subtract 6x: x - 3 = 3.
x = 6.
8. What is the slope of the line passing through points (2, 3) and (5, 9)?
A. 1
B. 2
,C. 3
D. 4
Correct Answer: B
Rationale: m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2 .
9. What is the slope of the line: 4x - 2y = 8
A. 1
B. 2
C. -2
D. 4
Correct Answer: B
Rationale: Rewrite in slope-intercept form: -2y = -4x + 8 → y = 2x - 4. Slope = 2 .
10. The sum of two consecutive integers is 45. Find the larger integer.
A. 21
B. 22
C. 23
D. 24
Correct Answer: C
Rationale: Let x be the smaller integer, x+1 the larger. Equation: x + (x+1) = 45 → 2x + 1
= 45 → 2x = 44 → x = 22. Larger = 23 .
11. A car rental company charges $30 per day plus $0.15 per mile. If a customer
pays $75 for a 3-day rental, how many miles were driven?
A. 100
B. 200
C. 300
D. 400
Correct Answer: C
Rationale: Total = 30(3) + 0.15m = 75 → 90 + 0.15m = 75 → 0.15m = 75 - 90 → 0.15m
= 45 → m = 300.
12. Solve for x: 4x - 7 = 2x + 15
A. 9
B. 10
, C. 11
D. 12
Correct Answer: C
Rationale: Subtract 2x: 2x - 7 = 15. Add 7: 2x = 22. x = 11.
13. What is the y-intercept of the line y = -3x + 6?
A. (0, -3)
B. (0, 3)
C. (0, 6)
D. (0, -6)
Correct Answer: C
Rationale: In y = mx + b, b is the y-intercept. y = -3x + 6 has y-intercept (0, 6).
14. Find the equation of the line with slope 4 passing through (1, 3).
A. y = 4x - 1
B. y = 4x + 1
C. y = 4x - 3
D. y = 4x + 3
Correct Answer: A
Rationale: Use point-slope form: y - 3 = 4(x - 1) → y - 3 = 4x - 4 → y = 4x - 1.
15. Solve for x: 5x + 2 = 3x - 10
A. -4
B. -6
C. 4
D. 6
Correct Answer: B
Rationale: Subtract 3x: 2x + 2 = -10. Subtract 2: 2x = -12. x = -6.
SECTION 2: FUNCTIONS AND GRAPHING (Questions 16-35)
16. If f(x) = 2x² - 3x + 1, find f(2).
A. 3
B. 5
