WGU QTT2 Tasks 1–3 – Finite Mathematics – (Passed Task).
.
Each question includes:
Answer (letter)
Rationale explaining the mathematical reasoning and WGU rubric expectations
TASK 1: Real Number Systems & Venn Diagrams
Topic 1.1: Classifying Real Numbers (Questions 1-20)
Question 1
Which of the following best describes the set of rational numbers?
A) Numbers that can be expressed as a ratio of two integers where the
denominator is not zero
B) All numbers that cannot be expressed as a fraction
C) Only positive whole numbers
D) Numbers that terminate but do not repeat
,Answer: A
Rationale: Rational numbers are defined as numbers that can be written as a/b
where a and b are integers and b ≠ 0. This includes terminating decimals,
repeating decimals, and integers. This definition is foundational for Task 1's
number classification requirements .
Question 2
Which number is irrational?
A) 0.75
B) √16
C) π (pi)
D) -5
Answer: C
Rationale: An irrational number cannot be expressed as a ratio of two integers. Pi
(π) is a classic example—its decimal representation never terminates or repeats.
√16 = 4 (rational), 0.75 = 3/4 (rational), and -5 = -5/1 (rational). Task 1 requires
distinguishing between rational and irrational numbers in the real number system
.
,Question 3
The number 0 belongs to which of the following sets?
A) Natural numbers only
B) Whole numbers and integers
C) Irrational numbers only
D) Natural numbers and whole numbers
Answer: B
Rationale: Zero is a whole number and an integer, but it is NOT a natural number
(natural numbers typically start at 1). Zero is rational (0/1), not irrational.
Understanding proper classification is essential for Task 1 Venn diagram
construction .
Question 4
Which statement about the real number system is TRUE?
A) All integers are natural numbers
B) All rational numbers are integers
, C) All whole numbers are integers
D) All irrational numbers are rational
Answer: C
Rationale: Whole numbers {0,1,2,3,...} are a subset of integers {...,-2,-1,0,1,2,...}.
Not all integers are natural numbers (negative numbers are integers but not
natural numbers). Rational numbers include fractions, not just integers. Irrational
and rational numbers are disjoint sets .
Question 5
Classify the number -7/3:
A) Natural number
B) Whole number
C) Integer
D) Rational number
Answer: D
Rationale: -7/3 is a rational number because it is expressed as a ratio of two
integers. It is NOT an integer (integers are whole numbers without fractions). It is
.
Each question includes:
Answer (letter)
Rationale explaining the mathematical reasoning and WGU rubric expectations
TASK 1: Real Number Systems & Venn Diagrams
Topic 1.1: Classifying Real Numbers (Questions 1-20)
Question 1
Which of the following best describes the set of rational numbers?
A) Numbers that can be expressed as a ratio of two integers where the
denominator is not zero
B) All numbers that cannot be expressed as a fraction
C) Only positive whole numbers
D) Numbers that terminate but do not repeat
,Answer: A
Rationale: Rational numbers are defined as numbers that can be written as a/b
where a and b are integers and b ≠ 0. This includes terminating decimals,
repeating decimals, and integers. This definition is foundational for Task 1's
number classification requirements .
Question 2
Which number is irrational?
A) 0.75
B) √16
C) π (pi)
D) -5
Answer: C
Rationale: An irrational number cannot be expressed as a ratio of two integers. Pi
(π) is a classic example—its decimal representation never terminates or repeats.
√16 = 4 (rational), 0.75 = 3/4 (rational), and -5 = -5/1 (rational). Task 1 requires
distinguishing between rational and irrational numbers in the real number system
.
,Question 3
The number 0 belongs to which of the following sets?
A) Natural numbers only
B) Whole numbers and integers
C) Irrational numbers only
D) Natural numbers and whole numbers
Answer: B
Rationale: Zero is a whole number and an integer, but it is NOT a natural number
(natural numbers typically start at 1). Zero is rational (0/1), not irrational.
Understanding proper classification is essential for Task 1 Venn diagram
construction .
Question 4
Which statement about the real number system is TRUE?
A) All integers are natural numbers
B) All rational numbers are integers
, C) All whole numbers are integers
D) All irrational numbers are rational
Answer: C
Rationale: Whole numbers {0,1,2,3,...} are a subset of integers {...,-2,-1,0,1,2,...}.
Not all integers are natural numbers (negative numbers are integers but not
natural numbers). Rational numbers include fractions, not just integers. Irrational
and rational numbers are disjoint sets .
Question 5
Classify the number -7/3:
A) Natural number
B) Whole number
C) Integer
D) Rational number
Answer: D
Rationale: -7/3 is a rational number because it is expressed as a ratio of two
integers. It is NOT an integer (integers are whole numbers without fractions). It is
