NT203 Arizona Middle
Grades Mathematics
,QUESTIONS
Question 1
A note about “Solving problems involving ratios, unit rates, proportions,
direct/inverse variation, and percents (including percent increase/decrease,
markups, and discounts)” is labeled “Compound and Conditional Probability”.
Which replacement label more directly identifies its focus?
A. Concepts of Calculus
B. Compound and Conditional Probability
C. Proportional Reasoning
D. Operations with Real Numbers
Correct Answer: C
Full Explanation: Proportional Reasoning: Solving problems involving ratios, unit rates,
proportions, direct/inverse variation, and percents (including percent increase/decrease, markups,
and discounts). A: That focus concerns “Basic introductory concepts of calculus, including limits,
average and instantaneous rates of change, graphical behavior of functions, and intuitive
understanding of the area under a curve”, not the activity being assigned. B: That focus concerns
“Determining probabilities of independent and dependent compound events, mutually exclusive
events, and conditional probability”, not the activity being assigned. D: That focus concerns
“Performing and solving multi-step problems involving integers, decimals, and fractions”, not the
activity being assigned.
Question 2
When differentiating “Error and Precision” and “Estimation”, which concern is
associated with “Error and Precision”?
A. Recognizing, describing, and extending arithmetic, geometric, and recursive patterns and
number sequences
B. Writing and translating between slope-intercept form, point-slope form, and standard form of
linear equations
C. Techniques for estimating quantities, numerical results, and the reasonableness of
calculations
D. Concepts of precision, accuracy, significant digits, and measurement error in scientific and
practical contexts
Correct Answer: D
Full Explanation: Error and Precision: Concepts of precision, accuracy, significant digits, and
measurement error in scientific and practical contexts. Estimation: Techniques for estimating
quantities, numerical results, and the reasonableness of calculations. A: This describes “Patterns
and Sequences”, rather than the requested focus. B: This describes “Forms of Linear Equations”,
rather than the requested focus. C: This describes “Estimation”, rather than the requested focus.
2
,QUESTIONS
Question 3
Assign a technical focus to “Systems of Equations” first and “Nonlinear
Systems” second. Which pairing is appropriate?
A. First: Solving systems of linear equations and inequalities using graphical, substitution, and
elimination methods; second: Solving systems involving linear and nonlinear equations
B. First: Solving systems involving linear and nonlinear equations; second: Solving systems
involving linear and nonlinear equations
C. First: Solving systems involving linear and nonlinear equations; second: Solving systems of
linear equations and inequalities using graphical, substitution, and elimination methods
D. First: Solving systems of linear equations and inequalities using graphical, substitution, and
elimination methods; second: Solving systems of linear equations and inequalities using
graphical, substitution, and elimination methods
Correct Answer: A
Full Explanation: Systems of Equations: Solving systems of linear equations and inequalities
using graphical, substitution, and elimination methods. Nonlinear Systems: Solving systems
involving linear and nonlinear equations. B: Repeating the second assignment does not address
the first requirement. C: The two roles are reversed: the first assignment belongs with the second
focus, and vice versa. D: Repeating the first assignment leaves the second requirement without its
own matching focus.
3
, QUESTIONS
Question 4
A comparison covers “Calculating and interpreting measures of central
tendency (mean, median, mode) and measures of dispersion”,
“Transformational Geometry”, “Computational Algorithms”, “Data
Distributions and Inference”. Which association preserves the correct
relationship? Pay particular attention to the role of “Analyzing data
distributions, identifying outliers and skewness, recognizing
correlations/trends in scatter plots, and making informal statistical inferences”.
A. Data Distributions and Inference — Analyzing and performing transformations on the
coordinate plane, including translations, reflections, rotations, dilations, and glide reflections
B. Data Distributions and Inference — range, interquartile range, variance, standard deviation
C. Data Distributions and Inference — Analyzing data distributions, identifying outliers and
skewness, recognizing correlations/trends in scatter plots, and making informal statistical
inferences
D. Data Distributions and Inference — Conventional and alternative algorithms for addition,
subtraction, multiplication, and division
Correct Answer: C
Full Explanation: Data Distributions and Inference: Analyzing data distributions, identifying
outliers and skewness, recognizing correlations/trends in scatter plots, and making informal
statistical inferences. A: This option instead describes the following different focus:
Transformational Geometry: Analyzing and performing transformations on the coordinate plane,
including translations, reflections, rotations, dilations, and glide reflections. B: This option instead
describes the following different focus: Calculating and interpreting measures of central tendency
(mean, median, mode) and measures of dispersion: range, interquartile range, variance, standard
deviation. D: This option instead describes the following different focus: Computational Algorithms:
Conventional and alternative algorithms for addition, subtraction, multiplication, and division.
4
Grades Mathematics
,QUESTIONS
Question 1
A note about “Solving problems involving ratios, unit rates, proportions,
direct/inverse variation, and percents (including percent increase/decrease,
markups, and discounts)” is labeled “Compound and Conditional Probability”.
Which replacement label more directly identifies its focus?
A. Concepts of Calculus
B. Compound and Conditional Probability
C. Proportional Reasoning
D. Operations with Real Numbers
Correct Answer: C
Full Explanation: Proportional Reasoning: Solving problems involving ratios, unit rates,
proportions, direct/inverse variation, and percents (including percent increase/decrease, markups,
and discounts). A: That focus concerns “Basic introductory concepts of calculus, including limits,
average and instantaneous rates of change, graphical behavior of functions, and intuitive
understanding of the area under a curve”, not the activity being assigned. B: That focus concerns
“Determining probabilities of independent and dependent compound events, mutually exclusive
events, and conditional probability”, not the activity being assigned. D: That focus concerns
“Performing and solving multi-step problems involving integers, decimals, and fractions”, not the
activity being assigned.
Question 2
When differentiating “Error and Precision” and “Estimation”, which concern is
associated with “Error and Precision”?
A. Recognizing, describing, and extending arithmetic, geometric, and recursive patterns and
number sequences
B. Writing and translating between slope-intercept form, point-slope form, and standard form of
linear equations
C. Techniques for estimating quantities, numerical results, and the reasonableness of
calculations
D. Concepts of precision, accuracy, significant digits, and measurement error in scientific and
practical contexts
Correct Answer: D
Full Explanation: Error and Precision: Concepts of precision, accuracy, significant digits, and
measurement error in scientific and practical contexts. Estimation: Techniques for estimating
quantities, numerical results, and the reasonableness of calculations. A: This describes “Patterns
and Sequences”, rather than the requested focus. B: This describes “Forms of Linear Equations”,
rather than the requested focus. C: This describes “Estimation”, rather than the requested focus.
2
,QUESTIONS
Question 3
Assign a technical focus to “Systems of Equations” first and “Nonlinear
Systems” second. Which pairing is appropriate?
A. First: Solving systems of linear equations and inequalities using graphical, substitution, and
elimination methods; second: Solving systems involving linear and nonlinear equations
B. First: Solving systems involving linear and nonlinear equations; second: Solving systems
involving linear and nonlinear equations
C. First: Solving systems involving linear and nonlinear equations; second: Solving systems of
linear equations and inequalities using graphical, substitution, and elimination methods
D. First: Solving systems of linear equations and inequalities using graphical, substitution, and
elimination methods; second: Solving systems of linear equations and inequalities using
graphical, substitution, and elimination methods
Correct Answer: A
Full Explanation: Systems of Equations: Solving systems of linear equations and inequalities
using graphical, substitution, and elimination methods. Nonlinear Systems: Solving systems
involving linear and nonlinear equations. B: Repeating the second assignment does not address
the first requirement. C: The two roles are reversed: the first assignment belongs with the second
focus, and vice versa. D: Repeating the first assignment leaves the second requirement without its
own matching focus.
3
, QUESTIONS
Question 4
A comparison covers “Calculating and interpreting measures of central
tendency (mean, median, mode) and measures of dispersion”,
“Transformational Geometry”, “Computational Algorithms”, “Data
Distributions and Inference”. Which association preserves the correct
relationship? Pay particular attention to the role of “Analyzing data
distributions, identifying outliers and skewness, recognizing
correlations/trends in scatter plots, and making informal statistical inferences”.
A. Data Distributions and Inference — Analyzing and performing transformations on the
coordinate plane, including translations, reflections, rotations, dilations, and glide reflections
B. Data Distributions and Inference — range, interquartile range, variance, standard deviation
C. Data Distributions and Inference — Analyzing data distributions, identifying outliers and
skewness, recognizing correlations/trends in scatter plots, and making informal statistical
inferences
D. Data Distributions and Inference — Conventional and alternative algorithms for addition,
subtraction, multiplication, and division
Correct Answer: C
Full Explanation: Data Distributions and Inference: Analyzing data distributions, identifying
outliers and skewness, recognizing correlations/trends in scatter plots, and making informal
statistical inferences. A: This option instead describes the following different focus:
Transformational Geometry: Analyzing and performing transformations on the coordinate plane,
including translations, reflections, rotations, dilations, and glide reflections. B: This option instead
describes the following different focus: Calculating and interpreting measures of central tendency
(mean, median, mode) and measures of dispersion: range, interquartile range, variance, standard
deviation. D: This option instead describes the following different focus: Computational Algorithms:
Conventional and alternative algorithms for addition, subtraction, multiplication, and division.
4
