MAT 101 FINAL EXAM 2026 – COLLEGE
ALGEBRA, STRAIGHTERLINE,
COMPREHENSIVE PRACTICE QUESTIONS
& ANSWERS
SECTION 1: REAL NUMBERS AND ALGEBRAIC EXPRESSIONS
1. Simplify the expression: 3(2x - 5) - 4(3x + 2)
A) -6x - 23
B) 6x - 23
C) -6x + 7
D) 6x + 7
Answer: A) -6x - 23
Rationale: Distribute 3 to get 6x - 15 and -4 to get -12x - 8. Combine like terms: 6x - 12x = -
6x and -15 - 8 = -23, resulting in -6x - 23.
2. Evaluate: |-8| - |3| + |-2|
,A) 13
B) 7
C) 3
D) -3
Answer: B) 7
Rationale: The absolute value of -8 is 8, of 3 is 3, and of -2 is 2. The expression becomes 8 -
3 + 2 = 7.
3. Which property is illustrated by: 5(x + y) = 5x + 5y?
A) Associative property
B) Commutative property
C) Distributive property
D) Identity property
Answer: C) Distributive property
Rationale: The distributive property states that a(b + c) = ab + ac. Here, 5 is distributed to
both x and y inside the parentheses.
4. Simplify: (2x³y²)(3x⁴y⁵)
A) 5x⁷y⁷
B) 6x⁷y⁷
C) 6x¹²y¹⁰
D) 5x¹²y¹⁰
Answer: B) 6x⁷y⁷
Rationale: Multiply coefficients: 2 × 3 = 6. Add exponents for like bases: x³ × x⁴ = x⁷, y² × y⁵ =
y⁷.
5. Simplify: (x³)^4
A) x⁷
B) x¹²
C) x⁶⁴
D) x
,Answer: B) x¹²
Rationale: When raising a power to a power, multiply exponents: (x³)^4 = x^(3×4) = x¹².
6. Simplify: √(72)
A) 6√2
B) 2√18
C) 6√3
D) 3√8
Answer: A) 6√2
Rationale: Factor 72 = 36 × 2. Since √36 = 6, we get 6√2.
7. Rationalize the denominator: 2/√5
A) 2√5/5
B) √5/2
C) 2√5
D) 5√2/2
Answer: A) 2√5/5
Rationale: Multiply numerator and denominator by √5: 2/√5 × √5/√5 = 2√5/5.
8. Simplify: (2x² + 3x - 5) + (4x² - 2x + 7)
A) 6x⁴ + x² + 2
B) 6x² + x + 2
C) 6x² + 5x + 2
D) 6x² + x + 12
Answer: B) 6x² + x + 2
Rationale: Combine like terms: 2x² + 4x² = 6x², 3x - 2x = x, -5 + 7 = 2.
9. Simplify: (3x² - 2x + 1) - (x² + 5x - 3)
, A) 2x² - 7x + 4
B) 2x² + 3x - 2
C) 2x² - 7x - 2
D) 4x² + 3x + 4
Answer: A) 2x² - 7x + 4
Rationale: Distribute the negative sign: 3x² - 2x + 1 - x² - 5x + 3. Combine like terms: 2x² - 7x
+ 4.
10. Multiply: (2x + 3)(x - 5)
A) 2x² - 7x - 15
B) 2x² + 7x - 15
C) 2x² - 10x - 15
D) 2x² - 7x + 15
Answer: A) 2x² - 7x - 15
Rationale: Use FOIL: (2x)(x) = 2x², (2x)(-5) = -10x, (3)(x) = 3x, (3)(-5) = -15. Combine: 2x² - 7x -
15.
11. Multiply: (x - 4)²
A) x² - 8x + 16
B) x² + 8x + 16
C) x² - 16
D) x² + 16
Answer: A) x² - 8x + 16
Rationale: (x - 4)² = (x - 4)(x - 4) = x² - 8x + 16 using FOIL.
12. Multiply: (x + 7)(x - 7)
A) x² - 49
B) x² + 49
C) x² - 14x + 49
D) x² + 14x + 49
ALGEBRA, STRAIGHTERLINE,
COMPREHENSIVE PRACTICE QUESTIONS
& ANSWERS
SECTION 1: REAL NUMBERS AND ALGEBRAIC EXPRESSIONS
1. Simplify the expression: 3(2x - 5) - 4(3x + 2)
A) -6x - 23
B) 6x - 23
C) -6x + 7
D) 6x + 7
Answer: A) -6x - 23
Rationale: Distribute 3 to get 6x - 15 and -4 to get -12x - 8. Combine like terms: 6x - 12x = -
6x and -15 - 8 = -23, resulting in -6x - 23.
2. Evaluate: |-8| - |3| + |-2|
,A) 13
B) 7
C) 3
D) -3
Answer: B) 7
Rationale: The absolute value of -8 is 8, of 3 is 3, and of -2 is 2. The expression becomes 8 -
3 + 2 = 7.
3. Which property is illustrated by: 5(x + y) = 5x + 5y?
A) Associative property
B) Commutative property
C) Distributive property
D) Identity property
Answer: C) Distributive property
Rationale: The distributive property states that a(b + c) = ab + ac. Here, 5 is distributed to
both x and y inside the parentheses.
4. Simplify: (2x³y²)(3x⁴y⁵)
A) 5x⁷y⁷
B) 6x⁷y⁷
C) 6x¹²y¹⁰
D) 5x¹²y¹⁰
Answer: B) 6x⁷y⁷
Rationale: Multiply coefficients: 2 × 3 = 6. Add exponents for like bases: x³ × x⁴ = x⁷, y² × y⁵ =
y⁷.
5. Simplify: (x³)^4
A) x⁷
B) x¹²
C) x⁶⁴
D) x
,Answer: B) x¹²
Rationale: When raising a power to a power, multiply exponents: (x³)^4 = x^(3×4) = x¹².
6. Simplify: √(72)
A) 6√2
B) 2√18
C) 6√3
D) 3√8
Answer: A) 6√2
Rationale: Factor 72 = 36 × 2. Since √36 = 6, we get 6√2.
7. Rationalize the denominator: 2/√5
A) 2√5/5
B) √5/2
C) 2√5
D) 5√2/2
Answer: A) 2√5/5
Rationale: Multiply numerator and denominator by √5: 2/√5 × √5/√5 = 2√5/5.
8. Simplify: (2x² + 3x - 5) + (4x² - 2x + 7)
A) 6x⁴ + x² + 2
B) 6x² + x + 2
C) 6x² + 5x + 2
D) 6x² + x + 12
Answer: B) 6x² + x + 2
Rationale: Combine like terms: 2x² + 4x² = 6x², 3x - 2x = x, -5 + 7 = 2.
9. Simplify: (3x² - 2x + 1) - (x² + 5x - 3)
, A) 2x² - 7x + 4
B) 2x² + 3x - 2
C) 2x² - 7x - 2
D) 4x² + 3x + 4
Answer: A) 2x² - 7x + 4
Rationale: Distribute the negative sign: 3x² - 2x + 1 - x² - 5x + 3. Combine like terms: 2x² - 7x
+ 4.
10. Multiply: (2x + 3)(x - 5)
A) 2x² - 7x - 15
B) 2x² + 7x - 15
C) 2x² - 10x - 15
D) 2x² - 7x + 15
Answer: A) 2x² - 7x - 15
Rationale: Use FOIL: (2x)(x) = 2x², (2x)(-5) = -10x, (3)(x) = 3x, (3)(-5) = -15. Combine: 2x² - 7x -
15.
11. Multiply: (x - 4)²
A) x² - 8x + 16
B) x² + 8x + 16
C) x² - 16
D) x² + 16
Answer: A) x² - 8x + 16
Rationale: (x - 4)² = (x - 4)(x - 4) = x² - 8x + 16 using FOIL.
12. Multiply: (x + 7)(x - 7)
A) x² - 49
B) x² + 49
C) x² - 14x + 49
D) x² + 14x + 49
