MATH 110 MODULE 1: FUNDAMENTALS
OF ALGEBRA 2026/2027 UPDATE. JUST
RELEASED
1. Which of the following numbers belongs to the set of irrational numbers?
A. 0.333… (repeating)
B. sqrt(20)
C. sqrt(16)
D. -5/2
Answer: B
Conceptual Explanation: Irrational numbers cannot be expressed as a ratio of two
integers. sqrt(20) simplifies to 2*sqrt(5), which is non-repeating and non-terminating.
2. Simplify the expression: 3[4 - 2(x - 5)] + 6x.
A. 12x + 42
B. 6x + 42
C. 12x - 18
D. 42
Answer: D
,Conceptual Explanation: Distribute inside the brackets: 3[4 - 2x + 10] + 6x = 3[14 - 2x] +
6x = 42 - 6x + 6x = 42.
3. Solve for x: 4/(x-2) = 3/(x+1).
A. x = 5
B. x = -10
C. x = 10
D. x = -5
Answer: B
Conceptual Explanation: Cross-multiply: 4(x + 1) = 3(x - 2) -> 4x + 4 = 3x - 6 -> x = -10.
4. Which property of real numbers is illustrated by: a(b + c) = ab + ac?
A. Commutative Property of Addition
B. Associative Property of Multiplication
C. Distributive Property
D. Identity Property of Addition
Answer: C
Conceptual Explanation: The distributive property states that multiplying a sum by a
number is the same as multiplying each addend by the number and then adding the
products.
, 5. Find the distance between the points (-3, 5) and (2, -7).
A. 13
B. sqrt(17)
C. 7
D. 15
Answer: A
Conceptual Explanation: Using the distance formula: sqrt((2 - (-3))^2 + (-7 - 5)^2) =
sqrt(5^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13.
6. Solve the inequality: |2x - 5| > 9.
A. -2 < x < 7
B. x > 7
C. x < -2 or x > 7
D. x < -7 or x > 2
Answer: C
Conceptual Explanation: For |u| > a, u > a or u < -a. 2x - 5 > 9 -> 2x > 14 -> x > 7. 2x - 5 < -9
-> 2x < -4 -> x < -2.
7. Evaluate the expression: (8^(2/3)) * (16^(-1/4)).
A. 1
OF ALGEBRA 2026/2027 UPDATE. JUST
RELEASED
1. Which of the following numbers belongs to the set of irrational numbers?
A. 0.333… (repeating)
B. sqrt(20)
C. sqrt(16)
D. -5/2
Answer: B
Conceptual Explanation: Irrational numbers cannot be expressed as a ratio of two
integers. sqrt(20) simplifies to 2*sqrt(5), which is non-repeating and non-terminating.
2. Simplify the expression: 3[4 - 2(x - 5)] + 6x.
A. 12x + 42
B. 6x + 42
C. 12x - 18
D. 42
Answer: D
,Conceptual Explanation: Distribute inside the brackets: 3[4 - 2x + 10] + 6x = 3[14 - 2x] +
6x = 42 - 6x + 6x = 42.
3. Solve for x: 4/(x-2) = 3/(x+1).
A. x = 5
B. x = -10
C. x = 10
D. x = -5
Answer: B
Conceptual Explanation: Cross-multiply: 4(x + 1) = 3(x - 2) -> 4x + 4 = 3x - 6 -> x = -10.
4. Which property of real numbers is illustrated by: a(b + c) = ab + ac?
A. Commutative Property of Addition
B. Associative Property of Multiplication
C. Distributive Property
D. Identity Property of Addition
Answer: C
Conceptual Explanation: The distributive property states that multiplying a sum by a
number is the same as multiplying each addend by the number and then adding the
products.
, 5. Find the distance between the points (-3, 5) and (2, -7).
A. 13
B. sqrt(17)
C. 7
D. 15
Answer: A
Conceptual Explanation: Using the distance formula: sqrt((2 - (-3))^2 + (-7 - 5)^2) =
sqrt(5^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13.
6. Solve the inequality: |2x - 5| > 9.
A. -2 < x < 7
B. x > 7
C. x < -2 or x > 7
D. x < -7 or x > 2
Answer: C
Conceptual Explanation: For |u| > a, u > a or u < -a. 2x - 5 > 9 -> 2x > 14 -> x > 7. 2x - 5 < -9
-> 2x < -4 -> x < -2.
7. Evaluate the expression: (8^(2/3)) * (16^(-1/4)).
A. 1
