MAT 101 FINAL EXAM|COLLEGE
ALGEBRA|ACTUAL QUESTIONS AND
ANSWERS 100% CORRECT|2025
UPDATE|STRAIGHTERLINE.
### QUESTIONS 1-10: REAL NUMBERS & ORDER OF OPERATIONS
**Question 1**
Simplify: \( 8 + 6 \times 3 - 4 \div 2 \)
A) 24
B) 22
C) 20
D) 18
**Answer: A) 24**
**Rationale:** Following PEMDAS: multiplication and division first (left
to right): \(6 \times 3 = 18\), \(4 \div 2 = 2\). Then addition and
subtraction: \(8 + 18 - 2 = 24\).
,---
**Question 2**
Evaluate: \( 3^4 - 2^5 \)
A) 49
B) 17
C) 81
D) 1
**Answer: A) 49**
**Rationale:** \(3^4 = 81\), \(2^5 = 32\). \(81 - 32 = 49\).
---
**Question 3**
Simplify: \( \frac{3}{4} + \frac{5}{6} \)
A) \( \frac{8}{10} \)
B) \( \frac{19}{12} \)
C) \( \frac{4}{5} \)
D) \( \frac{15}{24} \)
,**Answer: B) \( \frac{19}{12} \)**
**Rationale:** Find common denominator (12): \( \frac{3}{4} =
\frac{9}{12} \), \( \frac{5}{6} = \frac{10}{12} \). Sum: \( \frac{9}{12} +
\frac{10}{12} = \frac{19}{12} \).
---
**Question 4**
Which property is illustrated by: \( 3(4 + 5) = 3(4) + 3(5) \)
A) Commutative Property
B) Associative Property
C) Distributive Property
D) Identity Property
**Answer: C) Distributive Property**
**Rationale:** The distributive property states \(a(b + c) = ab + ac\).
This is exactly what is shown.
---
**Question 5**
, Simplify: \( \sqrt{72} \)
A) \( 6\sqrt{2} \)
B) \( 8\sqrt{3} \)
C) \( 2\sqrt{18} \)
D) \( 12\sqrt{6} \)
**Answer: A) \( 6\sqrt{2} \)**
**Rationale:** \(72 = 36 \times 2\), so \( \sqrt{72} = \sqrt{36} \times
\sqrt{2} = 6\sqrt{2} \).
---
**Question 6**
Evaluate: \( |-8| - |3| \)
A) 11
B) -11
C) 5
D) -5
**Answer: C) 5**
ALGEBRA|ACTUAL QUESTIONS AND
ANSWERS 100% CORRECT|2025
UPDATE|STRAIGHTERLINE.
### QUESTIONS 1-10: REAL NUMBERS & ORDER OF OPERATIONS
**Question 1**
Simplify: \( 8 + 6 \times 3 - 4 \div 2 \)
A) 24
B) 22
C) 20
D) 18
**Answer: A) 24**
**Rationale:** Following PEMDAS: multiplication and division first (left
to right): \(6 \times 3 = 18\), \(4 \div 2 = 2\). Then addition and
subtraction: \(8 + 18 - 2 = 24\).
,---
**Question 2**
Evaluate: \( 3^4 - 2^5 \)
A) 49
B) 17
C) 81
D) 1
**Answer: A) 49**
**Rationale:** \(3^4 = 81\), \(2^5 = 32\). \(81 - 32 = 49\).
---
**Question 3**
Simplify: \( \frac{3}{4} + \frac{5}{6} \)
A) \( \frac{8}{10} \)
B) \( \frac{19}{12} \)
C) \( \frac{4}{5} \)
D) \( \frac{15}{24} \)
,**Answer: B) \( \frac{19}{12} \)**
**Rationale:** Find common denominator (12): \( \frac{3}{4} =
\frac{9}{12} \), \( \frac{5}{6} = \frac{10}{12} \). Sum: \( \frac{9}{12} +
\frac{10}{12} = \frac{19}{12} \).
---
**Question 4**
Which property is illustrated by: \( 3(4 + 5) = 3(4) + 3(5) \)
A) Commutative Property
B) Associative Property
C) Distributive Property
D) Identity Property
**Answer: C) Distributive Property**
**Rationale:** The distributive property states \(a(b + c) = ab + ac\).
This is exactly what is shown.
---
**Question 5**
, Simplify: \( \sqrt{72} \)
A) \( 6\sqrt{2} \)
B) \( 8\sqrt{3} \)
C) \( 2\sqrt{18} \)
D) \( 12\sqrt{6} \)
**Answer: A) \( 6\sqrt{2} \)**
**Rationale:** \(72 = 36 \times 2\), so \( \sqrt{72} = \sqrt{36} \times
\sqrt{2} = 6\sqrt{2} \).
---
**Question 6**
Evaluate: \( |-8| - |3| \)
A) 11
B) -11
C) 5
D) -5
**Answer: C) 5**
