MAT 101 FINAL EXAM | COLLEGE
ALGEBRA | ACTUAL QUESTIONS AND
ANSWERS 100% CORRECT | 2025
UPDATE | STRAIGHTERLINE
This comprehensive guide contains verified questions and answers
for the MAT 101 College Algebra Final Exam at Straighterline, based
on 2025 exam materials. All answers include detailed rationales for
effective exam preparation .
Section 1: Solving Equations and Inequalities
Question 1: Solve the equation: 3(x – 4) = 2(x + 5)
Correct Answer: x = 22
Rationale: 3x – 12 = 2x + 10 → 3x – 2x = 10 + 12 → x = 22 .
Question 2: Solve the inequality: 2x + 3 > 11
Correct Answer: x > 4
Rationale: 2x + 3 > 11 → 2x > 8 → x > 4 .
Question 3: Solve the absolute value equation: |2x – 5| = 9
Correct Answer: x = 7 or x = –2
,Rationale: 2x – 5 = 9 → 2x = 14 → x = 7; 2x – 5 = –9 → 2x = –4 → x =
–2 .
Question 4: Solve the compound inequality: –4 ≤ 2x + 2 ≤ 10
Correct Answer: –3 ≤ x ≤ 4
Rationale: Subtract 2: –6 ≤ 2x ≤ 8 → Divide by 2: –3 ≤ x ≤ 4 .
Question 5: Solve the quadratic equation: x² – 5x + 6 = 0
Correct Answer: x = 2 or x = 3
Rationale: (x – 2)(x – 3) = 0 → x = 2, x = 3 .
Question 6: Solve by completing the square: x² + 6x – 7 = 0
Correct Answer: x = 1 or x = –7
Rationale: x² + 6x = 7 → x² + 6x + 9 = 7 + 9 → (x + 3)² = 16 → x + 3 = ±4
→ x = 1, x = –7 .
Question 7: Use the quadratic formula to solve: 2x² – 4x – 5 = 0
Correct Answer: x = (4 ± √(16 + 40)) / (4) = (4 ± √56) / 4 = (4 ± 2√14) /
4 = 1 ± (√14)/2
Rationale: x = [–b ± √(b² – 4ac)] / (2a) = [4 ± √(16 + 40)] / (4) = [4 ±
√56] / 4 .
, Question 8: Solve the equation: √(x + 5) = x – 1
Correct Answer: x = 4
Rationale: Square both sides: x + 5 = x² – 2x + 1 → 0 = x² – 3x – 4 → 0
= (x – 4)(x + 1) → x = 4, x = –1 (extraneous) . Check x = 4: √9 = 3 = 4 –
1✓.
Section 2: Functions and Their Graphs
Question 9: If f(x) = 2x² – 3x + 4, find f(–2)
Correct Answer: f(–2) = 2(4) – 3(–2) + 4 = 8 + 6 + 4 = 18
Rationale: Substitute x = –2 into the function: 2(4) – 3(–2) + 4 = 8 + 6
+ 4 = 18 .
Question 10: Find the domain of f(x) = √(x – 5)
Correct Answer: [5, ∞)
Rationale: The expression inside the square root must be ≥ 0: x – 5 ≥ 0
→x≥5.
Question 11: Find the domain of f(x) = (x + 2) / (x² – 9)
Correct Answer: All real numbers except x = 3 and x = –3
Rationale: Denominator cannot be zero: x² – 9 ≠ 0 → x ≠ 3, x ≠ –3 .
ALGEBRA | ACTUAL QUESTIONS AND
ANSWERS 100% CORRECT | 2025
UPDATE | STRAIGHTERLINE
This comprehensive guide contains verified questions and answers
for the MAT 101 College Algebra Final Exam at Straighterline, based
on 2025 exam materials. All answers include detailed rationales for
effective exam preparation .
Section 1: Solving Equations and Inequalities
Question 1: Solve the equation: 3(x – 4) = 2(x + 5)
Correct Answer: x = 22
Rationale: 3x – 12 = 2x + 10 → 3x – 2x = 10 + 12 → x = 22 .
Question 2: Solve the inequality: 2x + 3 > 11
Correct Answer: x > 4
Rationale: 2x + 3 > 11 → 2x > 8 → x > 4 .
Question 3: Solve the absolute value equation: |2x – 5| = 9
Correct Answer: x = 7 or x = –2
,Rationale: 2x – 5 = 9 → 2x = 14 → x = 7; 2x – 5 = –9 → 2x = –4 → x =
–2 .
Question 4: Solve the compound inequality: –4 ≤ 2x + 2 ≤ 10
Correct Answer: –3 ≤ x ≤ 4
Rationale: Subtract 2: –6 ≤ 2x ≤ 8 → Divide by 2: –3 ≤ x ≤ 4 .
Question 5: Solve the quadratic equation: x² – 5x + 6 = 0
Correct Answer: x = 2 or x = 3
Rationale: (x – 2)(x – 3) = 0 → x = 2, x = 3 .
Question 6: Solve by completing the square: x² + 6x – 7 = 0
Correct Answer: x = 1 or x = –7
Rationale: x² + 6x = 7 → x² + 6x + 9 = 7 + 9 → (x + 3)² = 16 → x + 3 = ±4
→ x = 1, x = –7 .
Question 7: Use the quadratic formula to solve: 2x² – 4x – 5 = 0
Correct Answer: x = (4 ± √(16 + 40)) / (4) = (4 ± √56) / 4 = (4 ± 2√14) /
4 = 1 ± (√14)/2
Rationale: x = [–b ± √(b² – 4ac)] / (2a) = [4 ± √(16 + 40)] / (4) = [4 ±
√56] / 4 .
, Question 8: Solve the equation: √(x + 5) = x – 1
Correct Answer: x = 4
Rationale: Square both sides: x + 5 = x² – 2x + 1 → 0 = x² – 3x – 4 → 0
= (x – 4)(x + 1) → x = 4, x = –1 (extraneous) . Check x = 4: √9 = 3 = 4 –
1✓.
Section 2: Functions and Their Graphs
Question 9: If f(x) = 2x² – 3x + 4, find f(–2)
Correct Answer: f(–2) = 2(4) – 3(–2) + 4 = 8 + 6 + 4 = 18
Rationale: Substitute x = –2 into the function: 2(4) – 3(–2) + 4 = 8 + 6
+ 4 = 18 .
Question 10: Find the domain of f(x) = √(x – 5)
Correct Answer: [5, ∞)
Rationale: The expression inside the square root must be ≥ 0: x – 5 ≥ 0
→x≥5.
Question 11: Find the domain of f(x) = (x + 2) / (x² – 9)
Correct Answer: All real numbers except x = 3 and x = –3
Rationale: Denominator cannot be zero: x² – 9 ≠ 0 → x ≠ 3, x ≠ –3 .
