NT003 Arizona Essential
Academic Skills Subtest III:
Mathematics
,QUESTIONS
Question 1
Assign the first, second, and third focus areas to “Solve problems involving the
conversion of units within and between standard and metric measurement
systems and calculate derived measurements”; “Solve word problems involving
integers, fractions, decimals, percentages, ratios, and proportions”; and
“Identify and extend arithmetic and geometric patterns and sequences”,
respectively. Which sequence is correct?
A. Understand Measurement Principles and Geometry Concepts → Understand Number
Properties and Number Operations → Understand Fundamental Principles of Algebra
B. Understand Measurement Principles and Geometry Concepts → Understand Fundamental
Principles of Algebra → Understand Number Properties and Number Operations
C. Understand Fundamental Principles of Algebra → Understand Number Properties and Number
Operations → Understand Measurement Principles and Geometry Concepts
D. Understand Number Properties and Number Operations → Understand Measurement
Principles and Geometry Concepts → Understand Fundamental Principles of Algebra
Correct Answer: A
Full Explanation: Understand Measurement Principles and Geometry Concepts: Solve problems
involving the conversion of units within and between standard and metric measurement systems
and calculate derived measurements. Understand Number Properties and Number Operations:
Solve word problems involving integers, fractions, decimals, percentages, ratios, and proportions.
Understand Fundamental Principles of Algebra: Identify and extend arithmetic and geometric
patterns and sequences. B: Positions 2, 3 do not preserve the corresponding task-to-focus
relationships. C: Positions 1, 3 do not preserve the corresponding task-to-focus relationships. D:
Positions 1, 2 do not preserve the corresponding task-to-focus relationships.
2
,QUESTIONS
Question 2
“Understand Probability and Statistics” has been confused with the task “Solve
real-world problems involving basic measurement (e.g., length, perimeter,
area) and geometric concepts, including the Pythagorean theorem and surface
area and volume of rectangular solids”. Which description should replace that
task?
A. Compute and interpret the mean, median, and mode of a set of data
B. Solve linear algebraic equations and inequalities in one variable
C. Analyze and identify fundamental types and properties of two- and three-dimensional figures,
including triangles, quadrilaterals, and circles
D. Solve real-world problems involving basic measurement (e.g., length, perimeter, area) and
geometric concepts, including the Pythagorean theorem and surface area and volume of
rectangular solids
Correct Answer: A
Full Explanation: Understand Probability and Statistics: Compute and interpret the mean,
median, and mode of a set of data. Understand Measurement Principles and Geometry Concepts:
Solve real-world problems involving basic measurement (e.g., length, perimeter, area) and
geometric concepts, including the Pythagorean theorem and surface area and volume of
rectangular solids. B: This describes “Understand Fundamental Principles of Algebra”, rather than
the requested focus. C: This describes “Understand Measurement Principles and Geometry
Concepts”, rather than the requested focus. D: This describes “Understand Measurement
Principles and Geometry Concepts”, rather than the requested focus.
3
, QUESTIONS
Question 3
A comparison covers “Understand Measurement Principles and Geometry
Concepts”, “Understand Number Properties and Number Operations”,
“Understand Problem Solving, Reasoning, and Mathematical Communication”,
“Understand Probability and Statistics”. Which association preserves the
correct relationship? Pay particular attention to the role of “Solve problems
involving scale, lines, line segments, and angles”.
A. Understand Measurement Principles and Geometry Concepts — Use algorithms (i.e., a set of
instructions) to perform a given calculation or solve a problem
B. Understand Measurement Principles and Geometry Concepts — Apply addition, subtraction,
multiplication, and division to solve multidigit computations with positive and negative
integers, fractions, decimals, and percentages
C. Understand Measurement Principles and Geometry Concepts — Solve problems involving
scale, lines, line segments, and angles
D. Understand Measurement Principles and Geometry Concepts — Demonstrate knowledge of
the concepts of range, standard deviation, and spread
Correct Answer: C
Full Explanation: Understand Measurement Principles and Geometry Concepts: Solve problems
involving scale, lines, line segments, and angles. A: This option instead describes the following
different focus: Understand Problem Solving, Reasoning, and Mathematical Communication: Use
algorithms (i.e., a set of instructions) to perform a given calculation or solve a problem. B: This
option instead describes the following different focus: Understand Number Properties and Number
Operations: Apply addition, subtraction, multiplication, and division to solve multidigit
computations with positive and negative integers, fractions, decimals, and percentages. D: This
option instead describes the following different focus: Understand Probability and Statistics:
Demonstrate knowledge of the concepts of range, standard deviation, and spread.
Question 4
The activity “Solve linear algebraic equations and inequalities in one variable”
is attributed to “Understand Problem Solving, Reasoning, and Mathematical
Communication”. Which label corrects that attribution?
A. Understand Number Properties and Number Operations
B. Understand Fundamental Principles of Algebra
C. Understand Probability and Statistics
D. Understand Problem Solving, Reasoning, and Mathematical Communication
Correct Answer: B
Full Explanation: Understand Fundamental Principles of Algebra: Solve linear algebraic equations
and inequalities in one variable. A: That focus concerns “Demonstrate knowledge of the relative
magnitude of numbers”, not the activity being assigned. C: That focus concerns “Calculate and
evaluate the probability of a specific event and/or outcome”, not the activity being assigned. D:
That focus concerns “Estimate the solution to a given problem”, not the activity being assigned.
4
Academic Skills Subtest III:
Mathematics
,QUESTIONS
Question 1
Assign the first, second, and third focus areas to “Solve problems involving the
conversion of units within and between standard and metric measurement
systems and calculate derived measurements”; “Solve word problems involving
integers, fractions, decimals, percentages, ratios, and proportions”; and
“Identify and extend arithmetic and geometric patterns and sequences”,
respectively. Which sequence is correct?
A. Understand Measurement Principles and Geometry Concepts → Understand Number
Properties and Number Operations → Understand Fundamental Principles of Algebra
B. Understand Measurement Principles and Geometry Concepts → Understand Fundamental
Principles of Algebra → Understand Number Properties and Number Operations
C. Understand Fundamental Principles of Algebra → Understand Number Properties and Number
Operations → Understand Measurement Principles and Geometry Concepts
D. Understand Number Properties and Number Operations → Understand Measurement
Principles and Geometry Concepts → Understand Fundamental Principles of Algebra
Correct Answer: A
Full Explanation: Understand Measurement Principles and Geometry Concepts: Solve problems
involving the conversion of units within and between standard and metric measurement systems
and calculate derived measurements. Understand Number Properties and Number Operations:
Solve word problems involving integers, fractions, decimals, percentages, ratios, and proportions.
Understand Fundamental Principles of Algebra: Identify and extend arithmetic and geometric
patterns and sequences. B: Positions 2, 3 do not preserve the corresponding task-to-focus
relationships. C: Positions 1, 3 do not preserve the corresponding task-to-focus relationships. D:
Positions 1, 2 do not preserve the corresponding task-to-focus relationships.
2
,QUESTIONS
Question 2
“Understand Probability and Statistics” has been confused with the task “Solve
real-world problems involving basic measurement (e.g., length, perimeter,
area) and geometric concepts, including the Pythagorean theorem and surface
area and volume of rectangular solids”. Which description should replace that
task?
A. Compute and interpret the mean, median, and mode of a set of data
B. Solve linear algebraic equations and inequalities in one variable
C. Analyze and identify fundamental types and properties of two- and three-dimensional figures,
including triangles, quadrilaterals, and circles
D. Solve real-world problems involving basic measurement (e.g., length, perimeter, area) and
geometric concepts, including the Pythagorean theorem and surface area and volume of
rectangular solids
Correct Answer: A
Full Explanation: Understand Probability and Statistics: Compute and interpret the mean,
median, and mode of a set of data. Understand Measurement Principles and Geometry Concepts:
Solve real-world problems involving basic measurement (e.g., length, perimeter, area) and
geometric concepts, including the Pythagorean theorem and surface area and volume of
rectangular solids. B: This describes “Understand Fundamental Principles of Algebra”, rather than
the requested focus. C: This describes “Understand Measurement Principles and Geometry
Concepts”, rather than the requested focus. D: This describes “Understand Measurement
Principles and Geometry Concepts”, rather than the requested focus.
3
, QUESTIONS
Question 3
A comparison covers “Understand Measurement Principles and Geometry
Concepts”, “Understand Number Properties and Number Operations”,
“Understand Problem Solving, Reasoning, and Mathematical Communication”,
“Understand Probability and Statistics”. Which association preserves the
correct relationship? Pay particular attention to the role of “Solve problems
involving scale, lines, line segments, and angles”.
A. Understand Measurement Principles and Geometry Concepts — Use algorithms (i.e., a set of
instructions) to perform a given calculation or solve a problem
B. Understand Measurement Principles and Geometry Concepts — Apply addition, subtraction,
multiplication, and division to solve multidigit computations with positive and negative
integers, fractions, decimals, and percentages
C. Understand Measurement Principles and Geometry Concepts — Solve problems involving
scale, lines, line segments, and angles
D. Understand Measurement Principles and Geometry Concepts — Demonstrate knowledge of
the concepts of range, standard deviation, and spread
Correct Answer: C
Full Explanation: Understand Measurement Principles and Geometry Concepts: Solve problems
involving scale, lines, line segments, and angles. A: This option instead describes the following
different focus: Understand Problem Solving, Reasoning, and Mathematical Communication: Use
algorithms (i.e., a set of instructions) to perform a given calculation or solve a problem. B: This
option instead describes the following different focus: Understand Number Properties and Number
Operations: Apply addition, subtraction, multiplication, and division to solve multidigit
computations with positive and negative integers, fractions, decimals, and percentages. D: This
option instead describes the following different focus: Understand Probability and Statistics:
Demonstrate knowledge of the concepts of range, standard deviation, and spread.
Question 4
The activity “Solve linear algebraic equations and inequalities in one variable”
is attributed to “Understand Problem Solving, Reasoning, and Mathematical
Communication”. Which label corrects that attribution?
A. Understand Number Properties and Number Operations
B. Understand Fundamental Principles of Algebra
C. Understand Probability and Statistics
D. Understand Problem Solving, Reasoning, and Mathematical Communication
Correct Answer: B
Full Explanation: Understand Fundamental Principles of Algebra: Solve linear algebraic equations
and inequalities in one variable. A: That focus concerns “Demonstrate knowledge of the relative
magnitude of numbers”, not the activity being assigned. C: That focus concerns “Calculate and
evaluate the probability of a specific event and/or outcome”, not the activity being assigned. D:
That focus concerns “Estimate the solution to a given problem”, not the activity being assigned.
4
