TEXES CORE 4 8 MATHEMATICS
PRACTICE TEST ITEMS ANSWERS
NUMERACY AND PROBLEM SOLVING
SKILLS ANALYSIS 2026
EXAM OVERVIEW
Detail Information
Test Code 807 (Subtest of 211)
Number of Questions 42 scored questions
Time Limit 1 hour and 5 minutes
Format Computer-administered test (CAT)
Approximate Weight 21% of Core Subjects 4-8 exam
Passing Score 240 (scaled)
The Mathematics subtest assesses knowledge across Mathematics Standards I–VIII,
organized into competencies covering Number Concepts, Patterns and Algebra,
Geometry and Measurement, Probability and Statistics, Mathematical Processes,
Mathematical Perspectives, Mathematical Learning and Instruction, and Mathematical
Assessment .
SECTION 1: NUMBER CONCEPTS (Competency 001)
,Question 1: Which of the following right triangles has a hypotenuse with a length
that is an irrational number?
A. A right triangle with leg lengths of 4 and 3
B. A right triangle with leg lengths of 12 and 5
C. A right triangle with leg lengths of 24 and 7
D. A right triangle with leg lengths of 25 and 9
Answer: D
Rationale: The length of the hypotenuse is given by the Pythagorean theorem: 𝑐 =
√𝑎2 + 𝑏 2 . Option D gives √252 + 92 = √625 + 81 = √706, which is irrational. The other
options yield rational results: 5, 13, and 25 respectively .
Skill: Distinguishing between rational and irrational numbers.
Question 2: Which of the following is an irrational number?
A. 5/8
B. √2
C. 0.75
D. −4
Answer: B
Rationale: √2 is irrational because it cannot be expressed as a simplified fraction, and
its decimal expansion is non-terminating and non-repeating .
Skill: Identifying irrational numbers.
,Question 3: Which set contains only natural numbers?
A. {0, 1, 2, 3}
B. {−1, 0, 1}
C. {1/2, 2, 3}
D. {π, 2, 4}
Answer: A
Rationale: Natural numbers are positive integers starting from 1 (some definitions
include 0). The set {0, 1, 2, 3} contains only natural numbers .
Skill: Understanding number systems and classifications.
Question 4: Which of the following correctly represents 0.00056 in scientific
notation?
A. 5.6 × 10^−4
B. 5.6 × 10^−3
C. 56 × 10^−5
D. 0.56 × 10^−3
Answer: A
Rationale: To write 0.00056 in scientific notation, move the decimal four places to the
right: 5.6 × 10^−4 .
Skill: Scientific notation and place value.
, Question 5: Convert 0.875 to a fraction in simplest form.
A. 7/8
B. 13/16
C. 5/6
D. 3/4
Answer: A
Rationale: 0.875 = 875/1000 = 7/8 after dividing numerator and denominator by 125 .
Skill: Converting decimals to fractions.
Question 6: What is the absolute value of –12 + 5?
A. –7
B. 7
C. –17
D. 17
Answer: B
Rationale: –12 + 5 = –7; the absolute value of –7 is 7 .
Skill: Evaluating absolute value expressions.
Question 7: Which property justifies the step: 3 × (4 + 5) = 3 × 4 + 3 × 5?
A. Commutative
B. Associative
PRACTICE TEST ITEMS ANSWERS
NUMERACY AND PROBLEM SOLVING
SKILLS ANALYSIS 2026
EXAM OVERVIEW
Detail Information
Test Code 807 (Subtest of 211)
Number of Questions 42 scored questions
Time Limit 1 hour and 5 minutes
Format Computer-administered test (CAT)
Approximate Weight 21% of Core Subjects 4-8 exam
Passing Score 240 (scaled)
The Mathematics subtest assesses knowledge across Mathematics Standards I–VIII,
organized into competencies covering Number Concepts, Patterns and Algebra,
Geometry and Measurement, Probability and Statistics, Mathematical Processes,
Mathematical Perspectives, Mathematical Learning and Instruction, and Mathematical
Assessment .
SECTION 1: NUMBER CONCEPTS (Competency 001)
,Question 1: Which of the following right triangles has a hypotenuse with a length
that is an irrational number?
A. A right triangle with leg lengths of 4 and 3
B. A right triangle with leg lengths of 12 and 5
C. A right triangle with leg lengths of 24 and 7
D. A right triangle with leg lengths of 25 and 9
Answer: D
Rationale: The length of the hypotenuse is given by the Pythagorean theorem: 𝑐 =
√𝑎2 + 𝑏 2 . Option D gives √252 + 92 = √625 + 81 = √706, which is irrational. The other
options yield rational results: 5, 13, and 25 respectively .
Skill: Distinguishing between rational and irrational numbers.
Question 2: Which of the following is an irrational number?
A. 5/8
B. √2
C. 0.75
D. −4
Answer: B
Rationale: √2 is irrational because it cannot be expressed as a simplified fraction, and
its decimal expansion is non-terminating and non-repeating .
Skill: Identifying irrational numbers.
,Question 3: Which set contains only natural numbers?
A. {0, 1, 2, 3}
B. {−1, 0, 1}
C. {1/2, 2, 3}
D. {π, 2, 4}
Answer: A
Rationale: Natural numbers are positive integers starting from 1 (some definitions
include 0). The set {0, 1, 2, 3} contains only natural numbers .
Skill: Understanding number systems and classifications.
Question 4: Which of the following correctly represents 0.00056 in scientific
notation?
A. 5.6 × 10^−4
B. 5.6 × 10^−3
C. 56 × 10^−5
D. 0.56 × 10^−3
Answer: A
Rationale: To write 0.00056 in scientific notation, move the decimal four places to the
right: 5.6 × 10^−4 .
Skill: Scientific notation and place value.
, Question 5: Convert 0.875 to a fraction in simplest form.
A. 7/8
B. 13/16
C. 5/6
D. 3/4
Answer: A
Rationale: 0.875 = 875/1000 = 7/8 after dividing numerator and denominator by 125 .
Skill: Converting decimals to fractions.
Question 6: What is the absolute value of –12 + 5?
A. –7
B. 7
C. –17
D. 17
Answer: B
Rationale: –12 + 5 = –7; the absolute value of –7 is 7 .
Skill: Evaluating absolute value expressions.
Question 7: Which property justifies the step: 3 × (4 + 5) = 3 × 4 + 3 × 5?
A. Commutative
B. Associative
