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Mathematics
- Standard Area - CC.2.2: Algebraic Concepts
- Grade Level - CC.2.2.HS: GRADE High School
Use the concept and notation of functions to interpret and apply them in terms of their context.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.2.1:
Functions
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Eligible Content - A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
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Eligible Content - A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.
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Eligible Content - A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
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Eligible Content - A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.
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Eligible Content - A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).
- Assessment Anchor - A1.2.2:
Coordinate Geometry
- Assessment Anchor - A1.2.2:
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Eligible Content - A1.2.2.1.1 Identify, describe and/or use constant rates of change.
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Eligible Content - A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
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Eligible Content - A1.2.2.1.3
Write or identify a linear equation when given
- the graph of the line
- 2 points on the line, or
- the slope and a point on a line,
(Linear equation may be in point-slope, standard and/or slope-intercept form).
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Eligible Content - A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.
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Eligible Content - A1.2.2.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot.
- Assessment Anchor - A2.2.1:
Patterns, Relations, and Functions
- Assessment Anchor - A2.2.1:
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Eligible Content - A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
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Eligible Content - A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
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Eligible Content - A2.2.1.1.3 Determine the domain, range or inverse of a relation.
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Eligible Content - A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
- Assessment Anchor - G.2.2:
Measurements of Two-Dimensional Shapes and Figures
- Assessment Anchor - G.2.2:
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Eligible Content - G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles.
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Eligible Content - G.2.2.1.2 Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles.
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Eligible Content - G.2.2.2.1 Estimate area, perimeter or circumference of an irregular figure.
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Eligible Content - G.2.2.2.2 Find the measurement of a missing length given the perimeter, circumference, or area.
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Eligible Content - G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.
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Eligible Content - G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure.
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Eligible Content - G.2.2.2.5 Find the area of a sector of a circle.
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Eligible Content - G.2.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area. (e.g., How does changing the length of the radius of a circle affect the circumference of the circle?).
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Eligible Content - G.2.2.4.1 Use area models to find probabilities.Standard - CC.2.2.HS.C.2
Graph and analyze functions and use their properties to make connections between the different representations.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.2.1:
Functions
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Eligible Content - A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
-
Eligible Content - A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.
-
Eligible Content - A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
-
Eligible Content - A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.
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Eligible Content - A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).
- Assessment Anchor - A1.2.2:
Coordinate Geometry
- Assessment Anchor - A1.2.2:
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Eligible Content - A1.2.2.1.1 Identify, describe and/or use constant rates of change.
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Eligible Content - A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
-
Eligible Content - A1.2.2.1.3
Write or identify a linear equation when given
- the graph of the line
- 2 points on the line, or
- the slope and a point on a line,
(Linear equation may be in point-slope, standard and/or slope-intercept form).
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Eligible Content - A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.
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Eligible Content - A1.2.2.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot.
- Assessment Anchor - A2.2.1:
Patterns, Relations, and Functions
- Assessment Anchor - A2.2.1:
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Eligible Content - A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
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Eligible Content - A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
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Eligible Content - A2.2.1.1.3 Determine the domain, range or inverse of a relation.
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Eligible Content - A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
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Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
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Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
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Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.C.3
Write functions or sequences that model relationships between two quantities.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.2:
Linear Equations
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Eligible Content - A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).
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Eligible Content - A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
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Eligible Content - A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).
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Eligible Content - A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
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Eligible Content - A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
- Assessment Anchor - A1.2.1:
Functions
- Assessment Anchor - A1.2.1:
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Eligible Content - A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
-
Eligible Content - A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.
-
Eligible Content - A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
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Eligible Content - A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.
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Eligible Content - A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).
- Assessment Anchor - A1.2.2:
Coordinate Geometry
- Assessment Anchor - A1.2.2:
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Eligible Content - A1.2.2.1.1 Identify, describe and/or use constant rates of change.
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Eligible Content - A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
-
Eligible Content - A1.2.2.1.3
Write or identify a linear equation when given
- the graph of the line
- 2 points on the line, or
- the slope and a point on a line,
(Linear equation may be in point-slope, standard and/or slope-intercept form).
-
Eligible Content - A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.
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Eligible Content - A1.2.2.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot.
- Assessment Anchor - A2.2.1:
Patterns, Relations, and Functions
- Assessment Anchor - A2.2.1:
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Eligible Content - A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
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Eligible Content - A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
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Eligible Content - A2.2.1.1.3 Determine the domain, range or inverse of a relation.
-
Eligible Content - A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
- Assessment Anchor - A2.2.2:
Applications of Functions
- Assessment Anchor - A2.2.2:
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Eligible Content - A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
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Eligible Content - A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
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Eligible Content - A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
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Eligible Content - A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
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Eligible Content - A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
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Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
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Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
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Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.C.4
Interpret the effects transformations have on functions and find the inverses of functions.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.2.1:
Functions
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Eligible Content - A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
-
Eligible Content - A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.
-
Eligible Content - A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
-
Eligible Content - A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.
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Eligible Content - A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).
- Assessment Anchor - A2.2.2:
Applications of Functions
- Assessment Anchor - A2.2.2:
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Eligible Content - A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
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Eligible Content - A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
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Eligible Content - A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
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Eligible Content - A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
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Eligible Content - A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
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Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.C.5
Construct and compare linear, quadratic and exponential models to solve problems.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.2.2:
Coordinate Geometry
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Eligible Content - A1.2.2.1.1 Identify, describe and/or use constant rates of change.
-
Eligible Content - A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
-
Eligible Content - A1.2.2.1.3
Write or identify a linear equation when given
- the graph of the line
- 2 points on the line, or
- the slope and a point on a line,
(Linear equation may be in point-slope, standard and/or slope-intercept form).
-
Eligible Content - A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.
-
Eligible Content - A1.2.2.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot.
- Assessment Anchor - A2.2.1:
Patterns, Relations, and Functions
- Assessment Anchor - A2.2.1:
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Eligible Content - A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
-
Eligible Content - A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
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Eligible Content - A2.2.1.1.3 Determine the domain, range or inverse of a relation.
-
Eligible Content - A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
- Assessment Anchor - A2.2.2:
Applications of Functions
- Assessment Anchor - A2.2.2:
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Eligible Content - A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
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Eligible Content - A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
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Eligible Content - A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
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Eligible Content - A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
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Eligible Content - A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
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Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.C.6
Interpret functions in terms of the situation they model.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.2.1:
Functions
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Eligible Content - A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
-
Eligible Content - A1.2.1.1.2 Determine if a relation is a function given a set of points or a graph.
-
Eligible Content - A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
-
Eligible Content - A1.2.1.2.1 Create, interpret and/or use the equation, graph or table of a linear function.
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Eligible Content - A1.2.1.2.2 Translate from one representation of a linear function to another (graph, table and equation).
- Assessment Anchor - A1.2.2:
Coordinate Geometry
- Assessment Anchor - A1.2.2:
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Eligible Content - A1.2.2.1.1 Identify, describe and/or use constant rates of change.
-
Eligible Content - A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems.
-
Eligible Content - A1.2.2.1.3
Write or identify a linear equation when given
- the graph of the line
- 2 points on the line, or
- the slope and a point on a line,
(Linear equation may be in point-slope, standard and/or slope-intercept form).
-
Eligible Content - A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.
-
Eligible Content - A1.2.2.2.1 Draw, find and/or write an equation for a line of best fit for a scatter plot.
- Assessment Anchor - A2.2.1:
Patterns, Relations, and Functions
- Assessment Anchor - A2.2.1:
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Eligible Content - A2.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
-
Eligible Content - A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
-
Eligible Content - A2.2.1.1.3 Determine the domain, range or inverse of a relation.
-
Eligible Content - A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
- Assessment Anchor - A2.2.2:
Applications of Functions
- Assessment Anchor - A2.2.2:
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Eligible Content - A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
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Eligible Content - A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
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Eligible Content - A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
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Eligible Content - A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
-
Eligible Content - A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
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Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.C.7
Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.
Standard - CC.2.2.HS.C.8Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs.
Standard - CC.2.2.HS.C.9Prove the Pythagorean identity and use it to calculate trigonometric ratios.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - G.1.3:
Congruence, Similarity, and Proofs
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Eligible Content - G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids.
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Eligible Content - G.1.3.1.2 Identify and/or use proportional relationships in similar figures.
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Eligible Content - G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).
- Assessment Anchor - G.2.1:
Coordinate Geometry and Right Triangles
- Assessment Anchor - G.2.1:
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Eligible Content - G.2.1.1.1 Use the Pythagorean Theorem or trigonometric ratios to write and/or solve problems involving right triangles.
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Eligible Content - G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles.
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Eligible Content - G.2.1.2.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane.
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Eligible Content - G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
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Eligible Content - G.2.1.2.3 Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.Standard - CC.2.2.HS.D.1
Interpret the structure of expressions to represent a quantity in terms of its context.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.1:
Operations with Real Numbers and Expressions
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
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Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
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Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
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Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
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Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
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Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
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Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
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Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
- Assessment Anchor - A2.1.2:
Non-Linear Expressions
- Assessment Anchor - A2.1.2:
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Eligible Content - A2.1.2.1.1 Use exponential expressions to represent rational numbers.
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Eligible Content - A2.1.2.1.2 Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
-
Eligible Content - A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (limit to rational exponents).
-
Eligible Content - A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
-
Eligible Content - A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
-
Eligible Content - A2.1.2.2.2 Simplify rational algebraic expressions.Standard - CC.2.2.HS.D.2
Write expressions in equivalent forms to solve problems.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.1:
Operations with Real Numbers and Expressions
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
-
Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
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Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
-
Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
-
Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
-
Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
-
Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
-
Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
- Assessment Anchor - A2.1.2:
Non-Linear Expressions
- Assessment Anchor - A2.1.2:
-
Eligible Content - A2.1.2.1.1 Use exponential expressions to represent rational numbers.
-
Eligible Content - A2.1.2.1.2 Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
-
Eligible Content - A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (limit to rational exponents).
-
Eligible Content - A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
-
Eligible Content - A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
-
Eligible Content - A2.1.2.2.2 Simplify rational algebraic expressions.Standard - CC.2.2.HS.D.3
Extend the knowledge of arithmetic operations and apply to polynomials.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.1:
Operations with Real Numbers and Expressions
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
-
Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
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Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
-
Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
-
Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
-
Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
-
Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
-
Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
- Assessment Anchor - A2.1.2:
Non-Linear Expressions
- Assessment Anchor - A2.1.2:
-
Eligible Content - A2.1.2.1.1 Use exponential expressions to represent rational numbers.
-
Eligible Content - A2.1.2.1.2 Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
-
Eligible Content - A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (limit to rational exponents).
-
Eligible Content - A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
-
Eligible Content - A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
-
Eligible Content - A2.1.2.2.2 Simplify rational algebraic expressions.Standard - CC.2.2.HS.D.4
Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A2.1.2:
Non-Linear Expressions
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Eligible Content - A2.1.2.1.1 Use exponential expressions to represent rational numbers.
-
Eligible Content - A2.1.2.1.2 Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
-
Eligible Content - A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (limit to rational exponents).
-
Eligible Content - A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
-
Eligible Content - A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
-
Eligible Content - A2.1.2.2.2 Simplify rational algebraic expressions.Standard - CC.2.2.HS.D.5
Use polynomial identities to solve problems.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.1:
Operations with Real Numbers and Expressions
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
-
Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
-
Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
-
Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
-
Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
-
Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
-
Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
-
Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
- Assessment Anchor - A2.1.2:
Non-Linear Expressions
- Assessment Anchor - A2.1.2:
-
Eligible Content - A2.1.2.1.1 Use exponential expressions to represent rational numbers.
-
Eligible Content - A2.1.2.1.2 Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers - exponents should not exceed power of 10).
-
Eligible Content - A2.1.2.1.3
Simplify/evaluate expressions involving multiplying with exponents (e.g. x6 * x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (limit to rational exponents).
-
Eligible Content - A2.1.2.1.4
Simplify or evaluate expressions involving logarithms and exponents (e.g. log28 = 3 or log42 = ½).
-
Eligible Content - A2.1.2.2.1
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
-
Eligible Content - A2.1.2.2.2 Simplify rational algebraic expressions.
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
-
Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
-
Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.D.6
Extend the knowledge of rational functions to rewrite in equivalent forms.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.1:
Operations with Real Numbers and Expressions
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
-
Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
-
Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
-
Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
-
Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
-
Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
-
Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
-
Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
-
Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
-
Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.D.7
Create and graph equations or inequalities to describe numbers or relationships.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.2:
Linear Equations
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Eligible Content - A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).
-
Eligible Content - A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
-
Eligible Content - A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).
-
Eligible Content - A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
-
Eligible Content - A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
- Assessment Anchor - A1.1.3:
Linear Inequalities
- Assessment Anchor - A1.1.3:
-
Eligible Content - A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
-
Eligible Content - A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.
-
Eligible Content - A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).
-
Eligible Content - A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities).
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Eligible Content - A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).
- Assessment Anchor - A2.2.2:
Applications of Functions
- Assessment Anchor - A2.2.2:
-
Eligible Content - A2.2.2.1.1 Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
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Eligible Content - A2.2.2.1.2 Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
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Eligible Content - A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
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Eligible Content - A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
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Eligible Content - A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
-
Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
-
Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.D.8
Apply inverse operations to solve equations or formulas for a given variable.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.2:
Linear Equations
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Eligible Content - A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).
-
Eligible Content - A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
-
Eligible Content - A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).
-
Eligible Content - A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
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Eligible Content - A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
-
Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
-
Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
-
Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
-
Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.D.9
Use reasoning to solve equations and justify the solution method.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.1:
Operations with Real Numbers and Expressions
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
-
Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
-
Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
-
Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
-
Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
-
Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
-
Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
-
Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
- Assessment Anchor - A1.1.2:
Linear Equations
- Assessment Anchor - A1.1.2:
-
Eligible Content - A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).
-
Eligible Content - A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
-
Eligible Content - A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).
-
Eligible Content - A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
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Eligible Content - A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
- Assessment Anchor - A1.1.3:
Linear Inequalities
- Assessment Anchor - A1.1.3:
-
Eligible Content - A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
-
Eligible Content - A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.
-
Eligible Content - A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).
-
Eligible Content - A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities).
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Eligible Content - A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
-
Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
-
Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
-
Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
-
Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).Standard - CC.2.2.HS.D.10
Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.
- Standard Area - CC.2.2: Algebraic Concepts
- Assessment Anchor - A1.1.2:
Linear Equations
-
Eligible Content - A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).
-
Eligible Content - A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
-
Eligible Content - A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).
-
Eligible Content - A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
-
Eligible Content - A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
- Assessment Anchor - A1.1.3:
Linear Inequalities
- Assessment Anchor - A1.1.3:
-
Eligible Content - A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
-
Eligible Content - A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.
-
Eligible Content - A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).
-
Eligible Content - A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities).
-
Eligible Content - A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).
- Assessment Anchor - A2.1.3:
Non-Linear Equations
- Assessment Anchor - A2.1.3:
-
Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
-
Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
-
Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
-
Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
-
Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
-
Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).