Math 1 Skills

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  • Algebra Foundations
    • Real Number System
      • Comparing Real Numbers
        • Order positive decimals
        • Order positive fractions
        • Condensed: Order positive decimals & fractions
        • Order decimals & fractions
        • Order positive rational numbers, no radicals, no exponents
        • Order rational numbers, no radicals, no exponents
        • Order real numbers, no exponents
        • Order real numbers, exponents are positive
        • Order real numbers
        • Comparing expressions on given interval
      • Application of Comparing Real Numbers
        • Order real numbers, positive exponents, percents are whole, including real-world context
        • Order real numbers, positive exponents, percents are whole, including real-world context
        • Given table, order rational numbers, real-world context
        • Given set or list, order rational numbers, real-world context
      • Classifying Real Numbers
        • Determine relationships between subsets of real numbers
        • Determine relationships between subsets of rational numbers
        • Determine result of adding & multiplying rational & irrational numbers
    • Algebraic Properties
      • Identify properties used in numerical expressions
      • Identify properties used in numerical & algebraic expressions
      • Identify properties used to solve linear equations
      • Identify steps to solve linear equations
      • Identify equivalent algebraic expressions, including real-world context
      • Evaluate & identify equivalent numerical expressions, including real-world context
    • Scientific Notation
      • Operations with Scientific Notation
        • Add numbers in scientific notation
        • Subtract numbers in scientific notation, real-world context
        • Multiply numbers in scientific notation 
        • Divide numbers in scientific notation 
        • Condensed: Add, subtract, multiply, & divide numbers in scientific notation
      • Application of Scientific Notation
        • Convert number from standard form to scientific notation, real-world context
        • Convert numbers between standard form & scientific notation, real-world context
        • Add numbers in scientific notation, real-world context
        • Subtract numbers in scientific notation, real-world context
        • Multiply numbers in scientific notation, real-world context
        • Divide numbers in scientific notation, real-world context
        • Compare magnitude of numbers in scientific notation, real-world context
    • Expressions & Operations
      • Evaluating Expressions
        • Evaluate expressions for specified value, one variable, two terms
        • Evaluate expressions for specified values, two variables, two terms
        • Evaluate expressions for specified values, two variables, two terms, one term with three factors
        • Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
        • Evaluate expressions for specified value, one variable, two terms, multiple operations, including powers of absolute values
        • Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
        • Evaluate expressions for specified values, two variables, quotient of expressions
        • Identify values that solve inequalities, expression on left side
        • Identify values that solve inequalities, expression on right side
      • Simplifying Expressions
        • Simplify algebraic expressions, one variable, distribute once & combine like terms
        • Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
        • Simplify algebraic expressions, one variable, distribute once & product of two factors
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
        • Simplify algebraic expressions, one variable, distribute once, fraction multiplier
        • Simplify algebraic expressions, one variable, distribute once, decimal multiplier
        • Simplify algebraic expressions, one variable, distribute once, including rationals
        • Simplify algebraic expressions, one variable, distribute twice
        • Simplify algebraic expressions, two variables, integer coefficients
        • Simplify algebraic expressions, two variables, distribute twice
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
        • Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
        • Identify equivalent expressions involving distribution, two or more terms
        • Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
        • Identify equivalent expressions involving distribution
    • Inferential Reasonings Word Problems
      • Identify appropriate steps to solve problem, real-world context
      • Determine reasonable estimates, linear relationships, real-world context
      • Determine reasonable estimates, multi-step, real-world context
  • Equations
    • Two-Step Equations
      • Solve ax ± b = c
      • Solve two-step linear equations, fractional answers
      • Solve two-step linear equations, fractional coefficients
      • Solve two-step linear equations, decimal coefficients
      • Condensed: Solve x/a ± b = c
      • Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
      • Condensed: Solve one- or two-step linear equations, fractional coefficients
      • Condensed: Solve two-step linear equations
      • Solve two-step linear equations, algebra tiles
      • Determine if given value is solution to two-step linear equations
      • Determine two-step linear equations, real-world context
      • Given two-step linear equation, identify real-world situation represented by equation
      • Solve problems that can be represented by two-step equations, real-world context
    • Multi-Step Equations
      • Solve linear equations, sum or difference on one side
      • Solve linear equations, product on one side
      • Solve linear equations, like terms on both sides
      • Solve linear equations, distributive property on one side, up to two terms on other side
      • Solve three-step linear equations involving distribution of decimal multiplier
      • Solve three-step linear equations involving distribution, fractional multiplier cancels if distributed
      • Solve three-step linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
      • Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
      • Solve linear equations, term minus distributive property on one side
      • Solve linear equations, distributive property & additional term on one side
      • Condensed: Solve linear equations involving distributive property on one side
      • Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
      • Solve (ax ± b)/c = d
    • Equations with Variables on Both Sides
      • Solve linear equations, variables on both sides
      • Solve linear equations, distributive property on both sides, integers
      • Solve multi-step linear equations
      • Solve linear equations, distributive property on both sides, additional term on one side
      • Solve linear equations, distributive property & additional term on one side & binomial on other side
      • Solve linear equations, binomials on both sides, decimals
      • Solve linear equations, variables as numerators on both sides
      • Solve linear equations, binomials on both sides, fractions
      • Solve linear equations, distributive property on both sides, rationals
      • Condensed: Solve linear equations, variables on both sides or like terms
      • Condensed: Solve linear equations, variables on both sides, rationals
      • Determine equations with variables on both sides, real-world context
      • Determine & solve linear equations with variables on both sides, real-world context
      • Given equation with variables on both sides, identify real-world situation represented by equation
    • Absolute Value Equations
      • Solve linear absolute value equations
      • Solve linear absolute value equations, extra constant or coefficient
      • Condensed: Solve linear absolute value equations, including extra constant or coefficient
      • Create linear absolute value equations, real-world context
      • Solve linear absolute value equations, variable on both sides
    • Solving for Specified Variable
      • Given linear equation of form ay = bx, solve for y
      • Given linear equation of form ay = bx + c, solve for y
      • Given linear equation in standard form, solve for y
      • Given linear equation of form a + by = cx, solve for y
      • Solve literal equation for variable
      • Solve literal equation for variable, variable may appear twice, linear terms
      • Solve for specific variable in mathematical formula
      • Solve for specific variable in scientific formula
      • Given linear equation with two terms on each side, solve for specified variable
      • Given linear equation with three terms on one side, solve for specified variable
      • Condensed: Given linear equation in various forms, solve for specified variable
  • Inequalities
    • One-Variable Inequalities
      • Basic One-Variable Inequalities
        • Graph inequalities on number line
        • Determine graph from inequality or inequality from graph
        • Given graph, determine inequality
        • Solve & graph one-step inequalities, whole number coefficients
        • Solve & graph one-step inequalities, integer coefficients
        • Solve & graph one-step inequalities, including fractional coefficients
        • Solve & graph one-step inequalities, including negative & fractional coefficients
        • Solve & graph two-step inequalities
        • Solve multi-step inequalities, including variables on both sides
        • Solve multi-step inequalities using distributive property
        • Solve & graph inequalities, variables on both sides, including distributive property
        • Condensed: Solve & graph inequalities
        • Determine equivalence of inequalities & solution set
      • Application of One-Variable Inequalities
        • Determine inequalities with variables on both sides, real-world context
        • Given inequality with variable on both sides, identify real-world problem modeled by inequality
        • Identify one-step inequalities that model real-world problems or interpret inequality components
        • Determine one-step inequalities, including real-world context
        • Determine one-step inequalities, rational numbers, including real-world context
        • Given one-step inequality, identify real-world problem modeled by inequality
        • Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
        • Determine & solve two-step inequalities, greater than, real-world context
        • Determine & solve two-step inequalities, less than, real-world context
        • Determine two-step inequalities, rational numbers, including real-world context
        • Given two-step inequality, identify real-world problem modeled by inequality
    • Linear Inequalities
      • Basic Linear Inequalities
        • Graph linear inequalities, slope-intercept form, only oblique lines
        • Graph linear inequalities, vertical & horizontal lines
        • Graph linear inequalities, slope-intercept form, including vertical & horizontal lines
        • Graph linear inequalities, various forms
        • Given linear inequality, identify correct graph, slope-intercept form
        • Given linear inequality, determine graph, slope-intercept form
        • Given linear inequality, determine solutions & non-solutions, slope-intercept form
        • Given linear inequality graph, determine solutions & non-solutions
        • Given linear inequality & x-value, determine y-value
        • Given graph, identify linear inequality, slope-intercept form
        • Given graph, determine linear inequality
        • Condensed: Determine equivalent linear inequalities & graphical solutions
        • Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
      • Application of Linear Inequalities
        • Given description, determine linear inequalities in standard form & specific solutions, real-world context
        • Given description, determine linear inequalities in standard form, including tables, real-world context
        • Given description, determine linear inequality in standard form, graph, & determine specific solutions, real-world context
        • Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
        • Given description & table, graph linear inequality, real-world context
        • Given graph, determine inequalities in standard form, real-world context
        • Solve linear programming problems, real-world context
    • Compound Inequalities
      • Solve & graph compound inequalities, “and” solutions
      • Solve & graph compound inequalities, “and” solutions, including real-world context
      • Solve & graph compound inequalities, “or” solutions
      • Solve compound inequalities, “and” solutions, multiple choice
      • Condensed: Solve & graph compound inequalities
      • Given description, determine graph of inequality
      • Given description, determine compound inequality, graph, & possible solutions
      • Interpret meaning of inequality, real-world context
    • Absolute Value Inequalities
      • Given linear absolute value inequality, determine compound inequality
      • Solve & graph linear absolute value inequalities, “and” solutions, including setup
      • Solve & graph linear absolute value inequalities, “and” solutions
      • Solve & graph linear absolute value inequalities, “or” solutions, including setup
      • Solve & graph linear absolute value inequalities, “or” solutions
      • Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
      • Solve & graph linear absolute value inequalities, including setup
      • Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
      • Condensed: Solve & graph linear absolute value inequalities, including setup
      • Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
      • Solve & graph linear absolute value inequalities, including extra constant or coefficient
      • Condensed: Solve & graph linear absolute value inequalities
      • Create linear absolute value inequalities, real-world context
  • Functions
    • Independent & Dependent Variables
      • Given table, identify dependent or independent variable
      • Given table or graph, identify dependent or independent variable
      • Given equation, identify dependent or independent variable
      • Given description, identify dependent or independent variable
    • Identifying Functions
      • Determine function definition, fill in the blank
      • Determine & justify functions, mapping representations, no domain & range language
      • Determine functions, mapping representations
      • Identify & determine functions, set & table representations
      • Determine functions, set & table representations
      • Determine functions, graphical representations
      • Given relation & additional point, determine functions, multiple representations
      • Determine functions, multiple representations, including justification, no domain & range language
      • Identify functions, description representations
    • Identifying & Justifying Functions
      • Determine & justify functions, mapping representations
      • Determine & justify functions, set representations
      • Determine & justify functions, set representations, no domain & range language
      • Determine & justify functions, table representations
      • Determine & justify functions, table representations, no domain & range language
      • Determine & justify functions, graphical representations
      • Determine functions, mapping representations, no domain & range language
      • Identify & justify functions & non-functions, graphical representations
      • Identify functions using equivalent mapping diagrams & sets of ordered pairs
      • Identify functions, multiple representations, including justification
      • Condensed: Identify, justify, & determine functions
    • Domain & Range of Functions
      • Determine if value is in domain or range, set & table representations
      • Determine if value is in domain or range, graphical representations
      • Determine restricted domain & range of linear functions
      • Determine discrete domain & range, real-world context
      • Determine continuous domain & range, real-world context
      • Given graph, determine domain & range
      • Condensed: Determine domain & range, including real-world context
      • Determine asymptotic domain restrictions of rational functions
    • Function Notation
      • Given set or table, determine function value
      • Given graph, determine function value
      • Given linear function, determine function value
      • Given quadratic function, determine function value
      • Condensed: Given graph or linear function, determine function value
      • Condensed: Given linear or quadratic function, determine function value
      • Interpret & solve problems involving function notation, real-world context
    • Inverse Functions
      • Determine inverse of linear function
      • Determine if functions are inverses using composition
      • Determine inverse of various functions
      • Graph function and its inverse
      • Determine domain & range of inverse functions
      • Condensed: Given function, determine equation, graph, & domain & range of inverse
    • Operations with Functions
      • Add functions, (f + g)(x)
      • Subtract functions, (f – g)(x)
      • Multiply functions, (f * g)(x)
      • Divide functions, (f / g)(x)
      • Add function values, (f + g)(#)
      • Subtract function values, (f – g)(#)
      • Multiply function values, (f * g)(#)
      • Divide function values, (f / g)(#)
      • Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)
      • Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
      • Evaluate compositions of functions
  • Linear Concepts
    • Determining Solution of a Linear Equation
      • Given graph of linear equation, identify point on line
      • Given linear equation in slope-intercept form, determine if point is on line
      • Given linear equation in standard form, determine if point is on line
      • Given linear equation in slope-intercept form, identify point on line
      • Given linear equation in standard form, identify point on line
      • Given horizontal or vertical linear equation, determine if point is on line
      • Given horizontal or vertical linear equation, identify point on line
      • Condensed: Given linear equation in slope-intercept form & graph, identify point on line
      • Given linear equation in slope-intercept form & value of one variable, determine value of other variable
      • Given linear equation in slope-intercept form & y-value, determine x-value, fractional coefficients or constants
    • Slope of Line
      • Find & Use Slope
        • Given equation in slope-intercept form, determine next value in table, Δx = 1
        • Given equation in slope-intercept form, determine next value in table
        • Given equation in slope-intercept form, determine values in table
        • Given table of linear equation, determine rate of change & specific value
        • Given table, determine rate of change & specific value, function notation
        • Given table, determine rate of change & specific value, function notation, integer rate of change
        • Given linear graph, determine slope & y-intercept, integer slope
        • Given table of linear function, determine slope & y-intercept
      • Compare Slopes
        • Identify linear table with most extreme rate of change
        • Identify linear graph with most extreme rate of change
        • Given description, compare rates of change, real-world context
        • Compare rates of changes represented differently
        • Condensed: Compare rates of change
      • Identify Slope Category
        • Given linear graph, identify type of slope
        • Given linear equation, identify type of slope
        • Identify linear graph with specific type of slope
        • Given table of linear equation, identify type of slope
        • Given graph of horizontal or vertical line, determine rate of change
        • Condensed: Identify type of slope
      • Find Slope
        • Given equation in slope-intercept form, determine rate of change, integer solution
        • Given equation in slope-intercept form, determine rate of change
        • Given linear equation in standard form, determine rate of change
        • Given equation of horizontal or vertical line, determine rate of change
        • Given equation in point-slope form, identify slope
        • Given two points with integer coordinates, determine rate of change
        • Given two points, determine rate of change, integer solution, including undefined
        • Given two points, determine rate of change, one coordinate is fraction
        • Given two points, determine rate of change, two coordinates are fractions
        • Given table of linear equation, determine rate of change
        • Given linear graph, determine rate of change, integer solution
        • Given linear graph, determine rate of change
        • Given linear graph, determine rate of change, various scales
        • Given linear graph, determine slope & y-intercept
        • Given graph of piece-wise function, determine rate of change over specific interval
      • Application of Slope
        • Given graph or table of linear function, determine slope or y-intercept, real-world context
        • Given right triangle, use legs to determine slope, real-world context
        • Given graph of similar right triangles, identify equivalent slopes
    • Writing Equation of Line
      • Writing Equation Given Point & Slope
        • Given slope & y-intercept, determine equation
        • Given point & integer slope, determine linear equation in point-slope form, including slope-intercept form conversion
        • Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
        • Given point & integer slope or rate of change, determine linear equation in slope-intercept form
        • Given point & fractional slope, determine linear equation in slope-intercept form, integer y-intercept
        • Given point & fractional slope, determine linear equation in slope-intercept form, fractional y-intercept
      • Writing Equation Given Two Points
        • Given two points, determine linear equation in slope-intercept form, integer slope
        • Given two points, determine linear equation in standard form, integer slope, including slope-intercept form conversion
        • Given two points, determine linear equation in point-slope form, integer slope, including slope-intercept form conversion
        • Given two points, determine linear equation in slope-intercept form, fractional slope
        • Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
        • Given two points, determine linear equation in point-slope form, fractional slope, including slope-intercept form conversion
        • Given linear table, determine slope, y-intercept, & equation
        • Given two points, determine linear equation, undefined slope
        • Given two points, determine linear equation, zero slope
      • Writing Equation Given Various Components
        • Given points or slope & point, determine linear equation in point-slope or standard form
        • Given points or slope & point, determine linear equation in standard form
        • Given points or slope & point, determine linear equation in various forms
        • Condensed: Given two points, determine linear equation in slope-intercept form, including horizontal & vertical lines
      • Writing Equation Given Graph
        • Write Equation Given Graph Through Origin
          • Given linear graph through origin with points shown on line, determine equation in slope-intercept form, integer slopes
          • Given linear graph through origin, determine equation in slope-intercept form, integer slope, 1 ≤ |m| ≤ 3
          • Given linear graph through origin, determine equation in slope-intercept form, integer slope
        • Write Equation Given Graph with Various Y-Intercepts
          • Given linear graph, determine equation in slope-intercept form, m = 1
          • Given linear graph, determine equation in slope-intercept form, m = 1, various scales
          • Given linear graph, determine equation in slope-intercept form, m = ±1, various scales
          • Given linear graph, determine equation in slope-intercept form, integer slopes
          • Given linear graph, identify equation in slope-intercept form, integer slopes, various scales
          • Given linear graph, determine equation in slope-intercept form, fractional slopes
          • Given linear graph, determine equation in point-slope form
          • Given linear graph, determine equation in standard form
          • Given linear graph, identify equation, various forms
          • Identify equivalent linear graphs & equations in slope-intercept form
          • Identify equivalent linear graphs & equations in slope-intercept form, various scales
          • Given linear graph, determine equation in slope-intercept form, integer slopes, various scales
          • Given equation in slope-intercept form, identify graph, integer slopes, various scales
          • Given linear graph, identify equation, slope-intercept form
          • Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
    • Intercepts
      • Given linear graph, plot y-intercept
      • Given linear graph, plot x-intercept
      • Given linear graph, determine coordinates of y-intercept
      • Given linear graph, determine coordinates of x-intercept
      • Given linear graph, locate intercept or determine coordinates, various scales
      • Given linear equation in slope-intercept form, determine coordinates of y-intercept
      • Given linear equation in standard form, determine coordinates of y-intercept
      • Given linear equation in slope-intercept form, determine coordinates of x-intercept
      • Given equation of horizontal or vertical line, determine coordinates of y-intercept
      • Given equation of horizontal or vertical line, determine coordinates of x-intercept
      • Given linear equation, determine intercepts
      • Given linear equation in slope-intercept form, plot y-intercept
      • Given equation of horizontal or vertical line, plot y-intercept
    • Equations, Tables, & Graphs
      • Equation to Table
        • Given linear equation, fill missing value in table, m = 1
        • Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
        • Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
        • Given linear equation, fill missing value in table, integer slope, b = 0
        • Given linear equation, fill missing value in table, integer slope, b = 0, Δx ≥ 5
        • Given linear equation & table, determine another point, integer slope, b = 0
        • Given linear equation, fill missing value in table, integer slope
        • Given linear equation & table, determine another point, m = 1
        • Given linear equation & one x-value, determine y-value in table
        • Given linear equation, determine table values
        • Given linear equation & two x-values, determine y-values in table
        • Given linear equation, fill table, m = 1
        • Given linear equation, fill table, integer slope, b = 0
        • Given linear equation, fill table, integer slope
        • Given horizontal or vertical linear equation, fill table
        • Given description & linear equation, fill table & determine solution, real-world context
      • Equation to Graph
        • Standard Form to Graph
          • Given linear equation in standard form, graph
          • Given linear equation in standard form, graph, scrambled variable terms
          • Determine linear equation in standard form & graph, real-world context
          • Condensed: Determine linear equation in standard form & graph, including real-world context
        • Slope-Intercept Form to Graph
          • Graph linear equations, m = 1
          • Graph linear equations, m = 1, various scales
          • Given equation in slope-intercept form, graph line, m = ±1, various scales
          • Graph proportional linear equation
          • Graph linear equations, integer slope not including one & negative one, b = 0
          • Graph linear equations, integer slope not including one & negative one
          • Graph linear equations, integer slope, various scales
          • Graph linear equations, fractional slope, various scales
          • Graph linear equations, including horizontal & vertical, integer slope, various scales
          • Graph linear equations, fractional slope
          • Given description of linear equation, identify graph, fractional slope, real-world context
          • Condensed: Graph linear equations, including horizontal & vertical, various scales
          • Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
      • Basic Graphing
        • Given table, graph proportional linear equation
        • Given point & integer slope, graph line
        • Given point & slope, graph line
      • Graph to Table
        • Given linear graph, determine table value, m = 1, table point off graph
        • Given linear graph, determine table value, table point off graph
        • Given linear graph with points shown on line, determine table value
        • Given linear graph through origin with points shown on line, determine table value, table point off graph
        • Given linear graph through origin with points shown on line, determine table values, one table point off graph
        • Given linear graph through origin, determine table value
        • Given linear graph through origin, determine table value, table point off graph
        • Given linear graph through origin, determine table values, one table point off graph
      • Table to Equation
        • Given table representing horizontal linear equation, determine equation
        • Given table representing vertical linear equation, determine equation
        • Given table, determine linear equation, m = 1
        • Given table, determine linear equation, integer slope, b = 0
        • Given table, determine linear equation, integer slope
        • Given table, identify linear equation in slope-intercept form, rational constants & coefficients
        • Given description, determine linear equation, fill table, & determine solution, real-world context
    • Identifying Key Features of Linear Functions
      • Given table of linear equation, determine slope & intercepts
      • Given graph of linear equation, determine slope & intercepts
      • Given linear equation, determine slope & intercepts
      • Given positive point & whole number slope, determine y-intercept, equation, & specific value
      • Given point & integer slope, determine y-intercept, equation, & specific value
      • Given linear graph, determine equation in slope-intercept form & specific value, various scales
      • Given equation in slope-intercept form, identify slope & y-intercept
      • Given linear equation in standard form, solve for y
      • Given linear equation in standard form, determine slope
      • Condensed: Given linear equation in standard form, solve for y or determine slope
      • Condensed: Given linear equation in various forms, determine slope or convert to slope-intercept form
    • Vertical & Horizontal Lines
      • Given vertical linear equation, determine graph
      • Given horizontal linear equation, determine graph
      • Given graph of vertical line, determine equation
      • Given graph of horizontal line, determine equation
      • Condensed: Given graph of horizontal or vertical line, determine equation
    • Perpendicular, Parallel, or Neither
      • Identify Parallel or Perpendicular Lines
        • Given equation in slope-intercept form, determine slope of parallel line
        • Given equation in various forms, determine slope of parallel line
        • Given equation in slope-intercept form, determine slope of perpendicular line
        • Given equation in various forms, determine slope of perpendicular line
        • Condensed: Given equation in slope-intercept form, determine slope of parallel or perpendicular line
        • Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
        • Identify equation that is parallel or perpendicular to line through two given points
        • Given two slope-intercept form equations, identify as parallel or perpendicular
        • Given two equations in standard form, identify as parallel or perpendicular
        • Given two pairs of points, determine if lines containing points are parallel or perpendicular
      • Write Equations of Parallel or Perpendicular Lines
        • Given equation in slope-intercept form, determine equation of parallel line through specified point
        • Given equation in various forms, determine equation of parallel line through specified point
        • Given equation in slope-intercept form, determine equation of perpendicular line through specified point
        • Given equation in various forms, determine equation of perpendicular line through specified point
        • Given equation in slope-intercept form, determine equation of parallel or perpendicular line through specified point
        • Given equation in various forms, determine equation of parallel or perpendicular line through specified point
        • Determine equation of line through specified point parallel or perpendicular to x-axis
        • Determine equation of line through specified point parallel or perpendicular to y-axis
        • Condensed: Determine equation of line through specified point parallel or perpendicular to x- or y-axis
    • Linear Word Problems
      • Identifying Key Features Given Verbal Description
        • Form 1 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope, only input to output questions
        • Form 2 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope
        • Form 3 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
        • Form 4 – Given point & slope, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
        • Form 5 – Given two points, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
        • Form 6 – Given linear graph, interpret linear relationship & determine slope-intercept equation
        • Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
        • Given slope & intercept, interpret linear relationship & determine slope-intercept equation, including negative slope
        • Given description of linear relationship, determine slope, y-intercept, & equation, real-world context
        • Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
        • Determine linear equation in standard form & graph, real-world context
      • Choosing Correct Model Given Verbal Description
        • Identify equivalent representations of linear relationship, including real-world context
        • Given linear word problem, identify graph
        • Given description of linear equation, identify graph, integer slope, real-world context
        • Given description or table, determine linear graph, real-world context
        • Given description of linear relationship, identify graph, table, or equation, real-world context
        • Given linear equation, interpret slope & y-intercept, real-world context
    • Transformations of Linear Functions
      • Identify & graph vertical & horizontal shifts of linear functions
      • Identify & graph vertical & horizontal stretches & compressions of linear functions
      • Identify & graph reflections of linear functions
      • Given description of transformation, determine linear function
      • Graph linear functions using all transformations
      • Describe parameter changes to linear parent functions
      • Identify descriptions of graphs of linear parent functions & transformed functions
      • Given table, identify transformations of linear functions
      • Condensed: Graph linear functions & identify transformations
    • Absolute Value Functions
      • Determine x- & y-intercepts of absolute value functions
      • Identify & graph vertical & horizontal stretches & compressions of absolute value functions
      • Determine minimum & maximum of absolute value functions
      • Determine points of intersection of absolute value functions
      • Identify & graph vertical & horizontal shifts of absolute value functions
      • Identify & graph reflections of absolute value functions
      • Graph absolute value functions using all transformations
      • Given absolute value equation, identify description of transformation
      • Condensed: Graph absolute value functions using any transformation
      • Graph absolute value functions using vertex & intercepts
      • Condensed: Determine graphical attributes of absolute value functions
      • Compare absolute value functions represented differently
  • Systems
    • Systems of Equations
      • Determining Solutions to Systems of Equations
        • Given system of linear equations, identify x- or y-value of solution
        • Given system of linear equations & description, identify solution, real-world context
        • Given system of linear equations, identify solution
        • Given graph of system of linear equations, identify specific domain value, real-world context
        • Determine systems of linear equations & solutions, real-world context
        • Determine & justify solutions to systems of linear equations, real-world context
        • Given system of linear equations, identify solution or x- or y-value of solution
        • Given table representing system of linear equations, determine solution, real-world context
        • Given tables, determine system of linear equations
        • Graph systems of linear equations & determine solutions, including real-world context
        • Condensed: Given system of linear equations, identify solution, including real-world context
        • Condensed: Determine systems of linear equations & solutions, including real-world context
      • Solving Systems of Equations, Graphing
        • Given system of linear equations, graph system, including tables
        • Given description of system of linear equations, graph & determine equations or tables
        • Given graph of system of linear equations, determine solution, rays on graph to establish pattern
        • Given graph of system of linear equations, determine equations in slope-intercept form
        • Determine & verify graphical solutions to systems of linear equations, slope-intercept form
        • Condensed: Given system of linear equations or description, graph system, including real-world context
        • Given system of linear equations, graph & determine point of intersection, slope-intercept form
        • Given system of linear equations, determine point of intersection, slope-intercept form
      • Solving Systems of Equations, Substitution
        • Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
        • Given system of linear equations with same isolated variable, determine point of intersection, integer coordinates
        • Given system of linear equations, determine point of intersection, integer coordinates, one horizontal or vertical & one slope-intercept form
        • Solve, interpret, or determine systems of linear equations, slope-intercept form, real-word context
        • Solve, interpret, or determine systems of linear equations, standard form, real-word context
        • Solve systems of linear equations, infinite possibilities or no solution
        • Determine solutions of linear equations, substitution bias, including given system, real-world context
        • Determine systems of linear equations & solutions, substitution bias, real-world context
        • Condensed: Given system of linear equations, determine solution, substitution bias
        • Condensed: Solve or determine system of equations, likely to have same variable isolated
      • Solving Systems of Equations, Elimination
        • Given system of linear equations in standard form, determine point of intersection, integer coordinates
        • Determine systems of linear equations & solutions, elimination bias, real-world context
        • Condensed: Solve or determine system of equations, both equations in standard form
        • Solve systems of linear equations, multiply at most one equation
        • Solve systems of linear equations, multiply one or both equations
      • Solving Systems of Equations, Mixed Methods
        • Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
        • Condensed: Determine systems of linear equations & solutions
    • Systems of Inequalities
      • Basic Systems of Inequalities
        • Graph systems of two linear inequalities, slope-intercept form
        • Determine equivalent systems of linear inequalities & graphical solutions
        • Graph systems of three linear inequalities, slope-intercept form
        • Given graph, determine solution of systems of linear inequalities
        • Solve systems of linear inequalities
      • Application of Systems of Inequalities
        • Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
        • Given description, determine system of linear inequalities in standard form & solution point, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
        • Given description, determine system of linear inequalities in standard form & identify graph, real-world context
        • Given description, determine system of linear inequalities in standard form & graph, real-world context
        • Given linear system of inequalities graph, identify true statements
        • Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
        • Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
  • Exponents
    • Product Rule of Exponents
      • Product of Power, Only Variables
        • Express repeated variables as powers, single variable
        • Express repeated variables as powers, multiple variables
        • Express powers as repeated variables
        • Apply product rule of exponents, one variable, positive exponents
        • Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
        • Simplify single variable powers, negative base or coefficient
        • Apply product rule of exponents, two variables, three to four factors, positive exponents
        • Apply product rule of exponents, two variables, four to six factors, positive exponents
      • Product of Power, Including Coefficients
    • Quotient Rule of Exponents
      • Apply quotient rule of exponents, one variable, positive exponents, greater exponent in numerator
      • Apply quotient rule of exponents, one variable, positive exponents, greater exponent in denominator
      • Apply quotient rule of exponents, positive exponents
      • Apply product & quotient rules of exponents, one or two variables, positive exponents
      • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents
      • Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, positive exponents
    • Power Rule of Exponents
      • Apply power rule, one variable, positive exponents
      • Apply power rule, including multiple variables, positive exponents
      • Apply power & product rules of exponents, fraction with numerator of one, positive exponents
      • Apply power & product rules of exponents, one variable, positive exponents
      • Apply product & power rules of exponents, one variable, coefficient of negative one
      • Apply power & product rules of exponents, multiple variables, positive exponents
    • Negative Exponents
      • Basic Negative Exponents
        • Express negative power using positive exponent
      • Product Rule with Negative Exponents
        • Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
        • Apply product rule of exponents, negative exponents
        • Apply product rule of exponents, two variables, three to four factors, at least one negative exponent
        • Apply product rule of exponents, two variables, three to four factors, one variable cancels
        • Apply product rule of exponents, two variables, four to six factors, at least one negative exponent
        • Apply product rule of exponents, two variables, four to six factors, at least one variable cancels
        • Apply product rule, multiple variables, coefficients other than one, including negative exponents
        • Apply power rule, multiple variables, coefficients other than one, including negative exponents
      • Quotient Rule with Negative Exponents
        • Apply quotient rule of exponents, one variable, at least one negative exponent
        • Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
        • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, at least one negative exponent
        • Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, at least one negative exponent
        • Apply quotient rule of exponents, negative exponents
      • Power Rule with Negative Exponents
        • Apply power rule, one variable, at least one negative exponent
        • Apply power rule, one variable, including non-positive exponents
        • Apply power rule, one variable, coefficient of negative one, at least one negative exponent
        • Apply power rule of exponents, negative exponents
        • Apply power rule, including multiple variables & negative exponents
        • Apply power rule, coefficient of negative one, multiple variables, including negative exponents
        • Apply power rule, negative base or coefficient, multiple variables, including negative exponents
        • Apply power rule, including multiple variables & negative exponents
        • Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
        • Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
        • Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
        • Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
    • Mixed Rules of Exponents
      • Simplifying Exponential Expressions
        • Apply power rule of exponents, positive exponents
        • Simplify powers, fractional algebraic base, including negative exponents
        • Apply product rule of exponents, coefficients other than one
        • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, including negative exponents, coefficients other than one
        • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents, coefficients other than one
        • Express negative power using positive exponent, coefficient other than one
        • Apply power, product, & quotient rules of exponents, positive exponents
        • Apply power, product, & quotient rules of exponents, including negative exponents
        • Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
        • Apply product, quotient, & power rules of exponents, one variable
        • Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one non-positive exponent
      • Multiplying Exponential Expressions
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
        • Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one non-positive exponent
        • Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
        • Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents
      • Dividing Exponential Expressions
        • Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
        • Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
        • Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
        • Apply power, product, & quotient rules of exponents, divide fractions, positive exponents
        • Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents
      • MIxed Operations of Exponential Expressions
        • Apply product & quotient rules of exponents, negative exponents
        • Apply product & quotient rules of exponents, negative exponents, coefficients other than one
        • Apply product, quotient, & power rules of exponents, multiple variables
    • Application of Exponents
      • Determine algebraic expressions for perimeter & area of rectangles
      • Given algebraic expressions for area & side of rectangles, determine expression for missing side
    • Numerical Exponential Expressions
      • Evaluate powers, whole number base, non-positive exponent
      • Evaluate powers, integer base, non-positive exponent, including negative coefficients
      • Evaluate powers, fractional base, positive exponent
      • Evaluate powers, fractional base, negative exponent
      • Evaluate powers, positive fractional base, including non-positive exponents
      • Evaluate powers, fractional bases
      • Condensed: Evaluate powers with negative exponents
    • Rational Exponents
      • Evaluate numerical expressions with rational exponents
      • Simplify numerical expressions with rational exponents
      • Evaluate rational exponent expressions, positive exponents
      • Simplify rational exponent expressions using product rule, coefficients not with base
      • Evaluate rational exponent expressions, negative exponents
      • Simplify rational exponent expressions using quotient rule, with coefficients
      • Simplify rational exponent expressions using product rule, coefficients with base
      • Simplify rational exponent expressions using power rule, with coefficients
      • Condensed: Simplify rational exponents using product & power rules
      • Condensed: Evaluate rational exponent expressions
  • Radicals & Roots
    • Simplifying Radicals
      • Determine square roots of perfect squares
      • Simplify square roots
      • Simplify square roots, coefficient greater than one
      • Identify steps to simplify square roots
      • Given square root expression, evaluate for specific value
      • Condensed: Simplify square roots, including algebraic expressions
      • Evaluate perfect cube roots
      • Convert from radical to rational exponent, single value in radicand
      • Convert from radical to rational exponent, algebraic term in radicand
      • Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
      • Simplify radical expression raised to power that is multiple of index
      • Condensed: Convert from radical to rational exponent
      • Convert from rational exponent to radical, single value base
      • Convert from rational exponent to radical, algebraic base
      • Condensed: Convert from rational exponent to radical
      • Determine principal square root of perfect squares
      • Simplify radical expressions, perfect powers
      • Add & subtract radical expressions, one or two variables, simplified radicals
      • Add & subtract radical expressions, one or two variables, radicals to simplify
      • Multiply radical expressions, numbers & variables
    • Solving Radicals
      • Solve perfect square root equations
      • Condensed: Determine square roots of perfect squares
      • Solve perfect cube root equations
      • Condensed: Determine cube roots of perfect cubes
      • Condensed: Evaluate & compare perfect square & cube roots
      • Solve square root equations, square root = #
      • Solve square root equations, square root = square root
      • Solve square root equations, add & subtract from root
      • Solve square root equations, multi-step
      • Solve square root equations, divide by coefficient of root
      • Condensed: Solve square root equations, one-step & two-step
      • Solve square root equations, square root = x ± #
      • Condensed: Solve square root equations
      • Solve square root equations, square root ± square root = #
      • Identify extraneous solutions of square root equations
  • Data Analysis
    • Graphical Displays of Data
      • Dot Plots
        • Determine mean from dot plots
        • Determine median from dot plots
        • Determine mean absolute deviation from dot plots
        • Determine & compare means from two dot plots
        • Determine & compare medians from two dot plots
        • Compare mean absolute deviations from two dot plots
        • Compare characteristics of side-by-side dot plots
        • Solve one-step problems from dot plots, real-world context
        • Solve multi-step problems from dot plots, real-world context
        • Given data, identify dot plot
        • Given data represented in various ways, identify dot plot
      • Histograms
        • Solve problems involving interpretation of histograms
        • Given various representations of data, determine histogram
      • Bar Graphs
        • Determine or interpret percentage bar graphs
      • Box Plots
        • Solve problems involving interpretation of box plots
        • Solve problems involving five-number summary
        • Determine five-number summary
        • Given boxplot, determine values from five-number summary
        • Solve problems involving interpretation of stacked box plots, real-world context
        • Condensed: Determine five-number summary, including box plots
      • Frequency Tables
        • Interpret two-way frequency tables, marginal distribution 
        • Interpret two-way frequency tables, conditional distribution 
        • Interpret two-way frequency tables, joint distribution 
        • Given two-way frequency tables, identify associations
        • Determine two-way frequency tables
        • Condensed: Interpret two-way frequency tables
        • Determine specified probabilities in two-way frequency tables
    • Measures of Center & Spread
      • Calculating Measures of Center & Spread
        • Determine mean, median, mode, & range
        • Identify definition of mean, median, mode, or range
        • Determine mean, median, mode, or range
        • Given various representations of data, identify mean, median, mode, & range
        • Determine mean, median, mode, or range from various graphs
        • Given mean, median, mode, or range, determine missing value in data set
        • Given mean, median, or range, determine missing or additional value in data set
        • Given additional value in data set, determine change in mean, median, mode, or range
        • Condensed: Determine mean, median, mode, or range, including graphs
        • Determine interquartile range of data
      • Interpreting Measures of Center & Spread
        • Identify measures of center based on data distribution
        • Identify measures of variability based on data distribution
        • Identify & interpret measures of center
        • Identify & interpret measures of variability
        • Determine or interpret shapes & features of graphs
        • Determine or interpret measures of center & spread from graphs
        • Given various representations of data, identify outlier
    • Linear Modeling
      • Scatterplots
        • Identify positive & negative correlations in scatter plots
        • Identify linear & nonlinear associations in scatter plots
        • Identify scatterplots with clustered data
        • Identify outliers in scatter plots
        • Given data, determine scatter plot
        • Condensed: Interpret scatter plots
        • Sketch line of best fit & determine equation, graph scales of one
        • Sketch line of best fit & determine equation, various graph scales
        • Sketch line of best fit & determine equation, real-world context
        • Sketch line of best fit
        • Sketch line of best fit & determine predicted value
        • Condensed: Sketch line of best fit & determine equation
        • Determine residuals
      • Regression
        • Determine linear regression equations, calculator expected
        • Determine quadratic regression equations, calculator expected
        • Determine exponential regression equations, calculator expected
        • Condensed: Determine linear, quadratic, or exponential equations, calculator expected
        • Given regression equation, determine predicted value
        • Given table, identify as linear, quadratic, or exponential
      • Correlation
        • Identify correlation & causation
        • Identify association & causation
        • Given table, determine & interpret correlation coefficient
  • Quadratic Functions
    • Solving Quadratic Functions
      • Solving Quadratics, Factoring
        • Apply zero product property to solve factored quadratic equations
        • Identify zeros of factored quadratics
        • Determine relationship between zeros & linear factors of quadratic functions
        • Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
        • Solve quadratic equations using factoring, a = 1, b ≠ 0, |c| ≤ 40, zero on one side
        • Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
        • Solve quadratic equations using factoring, difference of squares
        • Solve quadratic equations using factoring, perfect square trinomial
        • Solve quadratic binomial equation by factoring out GCF
        • Solve quadratic binomial equation by factoring out GCF, one term on each side
        • Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
        • Solve quadratic equations using factoring, |a| ≤ 10, b ≠ 0, |c| ≤ 40, zero on one side
        • Solve quadratic equations using factoring, |a| ≤ 10, |c| ≤ 40, terms on both sides
        • Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
        • Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
        • Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
        • Factor perfect square trinomials, degree two, one variable
        • Factor perfect square trinomials, degree two, two variables
      • Solving Quadratics, Given Graph
        • Given graph of quadratic function, determine roots/zeros
      • Solving Quadratic Functions, Square Root Method
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
        • Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
        • Determine exact solution to quadratic equations, a = ±1, b = 0
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
        • Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
        • Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
        • Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
        • Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
        • Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, a(cx ± h)^2 + k = #
      • Solving Quadratics, Quadratic Formula
        • Given quadratic equation in standard form, determine discriminant
        • Given quadratic equation in standard form, determine number of solutions
        • Given quadratic equation in standard form, determine solutions rounded to nearest hundredth
        • Given quadratic equation, determine solutions rounded to nearest hundredth, constant on one side
        • Given quadratic equation, determine solutions rounded to nearest hundredth, combine like terms first
        • Given quadratic equation in standard form, determine attributes & solutions rounded to nearest hundredth
        • Given proportion, solve resulting quadratic equation, b = 0
        • Given proportion, solve resulting quadratic equation, b ≠ 0
        • Given quadratic equation in standard form, determine exact solutions
        • Given quadratic equation in standard form, determine exact solutions, combine like terms first
      • Solving Quadratics, Completing the Square
        • Solve quadratic equations, complete the square, a = 1, real solutions
        • Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
        • Condensed: Solve quadratic equations, complete the square, real solutions
        • Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
        • Determine constant required to complete the square, a ≥ 1, including fractions
        • Solve quadratic equations, perfect square trinomial
        • Solve quadratic equations, complete the square, integers, a > 1, real solutions
        • Solve quadratic equations, complete the square, integers, a = 1, real solutions
        • Condensed: Solve quadratic equations, complete the square, integers, real solutions
      • Application of Solving Quadratics
        • Determine or use quadratic equations, real-world context
    • Writing Equations of Quadratic Functions
      • Given vertex & point, determine quadratic equation, vertex form
      • Given vertex & point, determine quadratic equation, standard form
      • Given graph of quadratic function, determine equation in standard form
      • Given graph of quadratic function, determine equation
      • Given quadratic equation in standard form, determine vertex form of equation
      • Given integer solutions of quadratic equation, determine function in standard form
      • Given zeros of quadratic function, determine quadratic equation with integer coefficients
      • Given rational solutions of quadratic equation, determine function in standard form
      • Given graphical attributes, determine equation of parabola
    • Domain & Range of Quadratic Functions
      • Given graph of quadratic function, determine domain & range
      • Given equation of quadratic function, determine domain & range
      • Given description of domain & range of quadratic function, choose graph
      • Condensed: Determine domain & range of quadratic function
      • Determine restricted domain & range of quadratic functions
    • Identifying Key Features of Quadratic Functions
      • Identifying Vertex, Axis of Symmetry, & Extrema of Quadratics
        • Determine minimum & maximum of quadratic functions
        • Given graph of quadratic function, determine minimum or maximum value
        • Given quadratic equation, determine minimum or maximum value
        • Determine vertex of quadratic functions
        • Determine symmetry of quadratic functions
        • Problem to be Retired (try 1127324): Determine axis of symmetry of quadratic functions
        • Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
        • Determine intervals of increase & decrease of quadratic functions
        • Determine end behavior of quadratic functions
      • Identifying Intercepts of Quadratics
        • Determine zero(s) of quadratic functions
        • Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
        • Determine x-intercept(s) of quadratic functions
        • Determine y-intercept of quadratic functions
        • Determine x-intercepts/zeros & y-intercepts of quadratic functions, vertex form
        • Given graph or table of quadratic function, determine x- & y- intercepts
      • Identifying Mixed Key Attributes of Quadratics
        • Given quadratic equation, determine attributes & graph, a = 1
        • Given quadratic equation, determine attributes & graph, a = -1
        • Given quadratic equation, determine attributes & graph, a ≠ ±1
        • Given graph of quadratic function, determine attributes
        • Condensed: Given quadratic equation, determine attributes & graph
        • Condensed: Given graph, equation, or table, determine attributes of quadratic function
        • Determine intervals where quadratic function is positive or negative
    • Graphing Quadratic Functions
      • Given quadratic equation, determine graph, b = 0
      • Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
      • Graph quadratic equations
      • Given quadratic equation in standard form, determine graph
      • Given quadratic equation in vertex form, determine graph
      • Given equation, graph quadratic function
      • Identify & graph reflections of quadratic functions
      • Graph quadratic functions using all transformations
      • Given quadratic equation, vertex, & point, graph function & determine attributes
      • Given table, determine attributes of quadratic function, real-world context
      • Condensed: Graph quadratic functions using any transformation
      • Condensed: Determine graphical attributes of quadratic functions
    • Transformations of Quadratic Functions
      • Identify & graph vertical & horizontal shifts of quadratic functions
      • Identify & graph vertical & horizontal stretches & compressions of quadratic functions
      • Describe parameter changes to quadratic parent functions
      • Identify descriptions of graphs of quadratic parent functions & transformed functions
      • Given description of transformation, determine quadratic function
      • Given quadratic equation, identify description of transformation
      • Determine effects of parameter changes in quadratic relationships, real-world context
    • Vertical Motion Problems
      • Given initial height & velocity of object in vertical motion, determine function, table, & graph of position
      • Given initial height & velocity of object in vertical motion, determine position function & maximum height
      • Given initial height & velocity of object in vertical motion, determine position function & time to maximum height
      • Given initial height & velocity of object in vertical motion, determine position function & time to ground
      • Given height of dropped object, determine position function & specific time
      • Given initial height & velocity of object in vertical motion, determine position function & specific time
      • Given initial height & negative velocity of object in vertical motion, determine position function & specific time
      • Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
      • Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
      • Condensed: Given initial height & velocity of object in vertical motion, determine position function, maximum height, or time to maximum height
      • Condensed: Given initial height & velocity of object in vertical motion, determine position function & specific times
      • Condensed: Given initial height & velocity of object in vertical motion, determine position graph, position function, & specific times
  • Polynomial Expressions & Functions
    • Interpret terms or factors in expressions, including real-world context
    • Condensed: Classify polynomials & identify components of polynomials
    • Determine quadratic factors of polynomials, degree four
    • Determine linear factors of polynomials, degree four
    • Factor sum & difference of two cubes, degree three, one variable
    • Condensed: Determine linear factors of polynomials, degree three or four
    • Determine x-intercepts/zeros & y-intercepts of polynomial functions
    • Determine symmetry of various functions
  • Exponential & Logarithmic Functions
    • Exponential Functions
      • Evaluating Exponential Functions
        • Given exponential function, determine function value, non-negative input
        • Given exponential function, determine function value, negative input
        • Given exponential function, determine function value, rational coefficient
        • Given exponential function, determine function value, rational base
        • Given exponential function, determine function value, rational base & coefficient
      • Domain & Range of Exponential Functions
        • Given equation, determine domain & range of exponential function 
        • Given verbal description & graph, determine domain & range of exponential function 
        • Determine domain & range of discrete exponential functions, real-world context
        • Determine restricted domain & range of exponential functions
        • Determine domain & range of discrete exponential functions
      • Graphing Exponential Functions
        • Given exponential growth function, determine graph
        • Given exponential growth function, determine graph, includes fractional coefficients
        • Given exponential growth or decay function, determine graph, includes fractional coefficients
        • Given graph, identify solution to exponential equation
        • Given equation, graph exponential function, including base e
        • Graph exponential functions using all transformations
        • Given graph, determine equation of exponential function
        • Given equation, graph exponential function
      • Identifying Key Features of Exponential Functions
        • Determine minimum & maximum of exponential functions
        • Determine asymptote of exponential functions
        • Given exponential equation, determine asymptote
        • Given graph, determine asymptote of exponential function
        • Determine asymptote of exponential functions, real-world context
        • Determine y-intercept of exponential function, real-world context
        • Determine x-intercepts/zeros & y-intercepts of exponential functions
        • Determine end behavior of exponential functions
        • Condensed: Graph exponential functions & identify transformations
        • Graph exponential functions using all transformations
        • Condensed: Determine graphical attributes of exponential functions
      • Transformations of Exponential Functions
        • Identify & graph reflections of exponential functions
        • Identify & graph vertical & horizontal shifts of exponential functions
        • Identify & graph vertical & horizontal stretches & compressions of exponential functions
        • Given table, identify transformations of exponential functions
        • Given exponential equation, identify description of transformations
      • Writing Exponential Functions
        • Given table, determine linear or exponential growth function
        • Given table, determine exponential growth function
        • Given table, determine exponential decay function
        • Given graph, determine equation of exponential function
      • Solving Exponential Functions
        • Solve simple exponential equations
        • Solve exponential equations, one variable & one base
        • Solve exponential equations, both bases reduce to common base
        • Solve exponential equations, two different bases, no common base possible
        • Solve exponential equations, base e
        • Solve exponential equations, no logs required
        • Solve exponential equations, common bases given
        • Solve exponential equations, one base reduces to common base
      • Application of Exponential Functions
        • Calculate investment value, annual compounding
        • Calculate investment value, various compounding
        • Calculate depreciating asset value, annual compounding
        • Condensed: Calculate investment & depreciating asset values, annual compounding
        • Interpret values in exponential functions, real-world context
        • Given table, determine attributes of exponential function
        • Determine asymptote of exponential functions, real-world context
        • Exponential growth & decay, real-world context
        • Determine exponential function, real-world context
        • Compare exponential functions represented differently
    • Logarithmic Functions
      • Graph Logarithmic Functions
        • Given log equation, identify description of transformations
        • Identify & graph reflections of log functions
        • Identify & graph vertical & horizontal shifts of log functions
        • Given equation, graph log function
        • Graph log functions using all transformations
        • Condensed: Graph log functions & identify transformations
        • Identify & graph vertical & horizontal stretches & compressions of log functions
      • Identify Key Features of Logarithmic Functions
        • Determine x-intercepts/zeros & y-intercepts of log functions
        • Determine asymptote of log functions
        • Determine end behavior of log functions
        • Given table, determine attributes of log function
        • Determine minimum & maximum of log functions
        • Condensed: Determine graphical attributes of log functions
      • Write Equations of Logarithmic Functions
        • Given graph, determine equation of log function
    • Exponential & Logarithmic Equations
      • Given log equation, determine exponential equation
      • Given exponential equation, determine log equation
      • Condensed: Convert between exponential & log equations
  • Sequences
    • Arithmetic Sequences
      • Determine terms in arithmetic sequences
      • Given arithmetic sequence, determine common difference & next term
      • Given formula, determine specific term of arithmetic sequence
      • Determine common difference, first term, & formula of arithmetic sequences
      • Condensed: Determine formula & specific terms of arithmetic sequences
    • Geometric Sequences
      • Given formula, determine specific term of geometric sequence
      • Determine formula & specific term of geometric sequences
      • Condensed: Determine formula or specific term of geometric sequences
      • Determine function & specific term for geometric sequences, real-world context
    • Application of Sequences
      • Identify arithmetic & geometric sequences & determine common difference or common ratio
      • Given table, determine difference in terms in arithmetic sequence, real-world context
      • Given formula, determine terms in arithmetic & geometric sequences
      • Condensed: Identify arithmetic & geometric sequences & determine components of sequences
      • Determine function & specific term for arithmetic & geometric sequences, real-world context
  • Foundations of Geometry
    • Vocabulary
      • Determine definitions of undefined terms of geometry, fill in the blank
      • Determine definitions of angles & shapes, fill in the blank
      • Determine definitions of conjectures, fill in the blank
      • Determine definitions of theorems, fill in the blank
      • Determine definitions of postulates, fill in the blank
      • Condensed: Determine definitions of general geometry vocabulary, fill in the blank
    • Distance & Midpoint
      • Distance
        • Determine distance between two points on number line
        • Determine fractional distance between two points on number line
        • Determine distance between points
        • Determine distance between points, horizontal or vertical
        • Determine distance between points, including coordinate plane
        • Given segment on coordinate plane, determine length
        • Determine fractional distance or fractional point dividing segment into specified ratio
        • Given coordinates for vertices of triangle, determine length of sides
        • Given coordinates, use length to determine segment congruence
      • Midpoint
        • Determine midpoint of segment on number line
        • Given endpoints, determine midpoint
        • Determine midpoint of two points on coordinate plane
        • Given midpoint & endpoint, determine other endpoint on coordinate plane
        • Condensed: Determine midpoint or endpoint of segment on coordinate plane
        • Given endpoint & point dividing segment into specified ratio, determine other endpoint on coordinate plane
        • Determine point that divides segment into specified ratio on coordinate plane
        • Condensed: Determine endpoint or point dividing segment into specified ratio on coordinate plane
      • Distance & Midpoint Combined
        • Given midpoint or distance between points, determine missing endpoint
        • Condensed: Determine distance or midpoint on number line
    • Angles
      • Classify angles from figure
      • Identify angle names
      • Identify angle pairs
      • Identify types of angles in figures
      • Estimate angle measures
      • Identify 90°, 180°, 270°, & 360° angles
      • Measure angles using protractor 
      • Measure angles using protractor, real-world context
      • Identify angles with specified measures
      • Apply angle addition postulate to determine angle measures
      • Apply angle addition postulate to determine angle measures, algebraic expressions
      • Condensed: Apply angle addition postulate to determine angle measures, including algebraic expressions
    • Properties of Triangles
      • Classifying Triangles
        • Classify triangles by sides
        • Classify triangles by angles
        • Classify triangle based on given angle measures
        • Classify triangles based on angles & sides
        • Apply triangle inequality theorem to determine range of values for unknown side
        • Apply triangle inequality theorem to determine side lengths
      • Isosceles & Equilateral Triangles
        • Given congruent sides, identify congruent angles of isosceles triangle
        • Given congruent angles, identify congruent sides of isosceles triangle
        • Solve problems involving perimeter of equilateral triangles
        • Solve problems involving perimeter of isosceles triangles
        • Given equilateral triangle & algebraic expressions for sides, solve for variable or determine side length
        • Given equilateral triangle & algebraic expression for angle, solve for variable 
        • Determine angle measure in isosceles triangle, at most one algebraic expression
        • Determine angle measure in isosceles triangle, up to two algebraic expressions
        • Condensed: Solve problems involving perimeter of equilateral & isosceles triangles
      • Triangle Angle Sum & Exterior Angles
        • Given two angle measures in triangle, determine angle measure
        • Given two angle measures in triangle, determine & justify angle measure
        • Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions
        • Apply triangle angle sum theorem to determine angles, algebraic expressions
        • Apply triangle angle sum theorem to determine angles, multiple algebraic expressions
        • Given description, apply triangle angle sum theorem to determine angles, algebraic expressions
        • Apply triangle exterior angle theorem to determine angles, including algebraic expressions
        • Condensed: Apply triangle angle sum theorem & exterior angle theorem to determine angles, including algebraic expressions
      • Perpendicular & Angle Bisectors
        • Given perpendicular bisector in triangle, determine segment lengths 
        • Given perpendicular bisector in triangle, determine segment lengths, algebraic expressions
        • Given angle bisector in triangle, determine angles 
        • Given angle bisector in triangle, determine angles, algebraic expressions
        • Determine segment lengths in triangles with angle bisectors
        • Condensed: Given perpendicular or angle bisector in triangle, determine segment lengths or angles, including algebraic expressions
    • Area & Perimeter on the Coordinate Plane
      • Determine area of polygons in coordinate plane
      • Determine area of polygons in coordinate plane, real-world context
      • Given coordinates of vertices, determine side lengths & perimeter of polygons
      • Given coordinates of vertices, determine area of triangle or rectangle
      • Determine area of composite figures on coordinate plane, no circular shapes
  • Triangle Similarity & Congruence
    • Similar Triangles
      • Identify corresponding parts of similar figures
      • Determine angles of similar triangles using AA similarity
      • Determine similarity of triangles using AA similarity
      • Determine similar triangles using SAS similarity
      • Determine similar triangles using SSS similarity
      • Determine missing steps in proofs involving similar triangles
      • Determine missing steps in proofs involving similar triangles, paragraph form
      • Determine sides of similar triangles using AA similarity
      • Determine angles of similar triangles using AA similarity, algebraic expressions
      • Determine segment lengths using triangle proportionality theorem
      • Condensed: Determine similar triangles using SAS or SSS similarity
    • Proofs
      • Determine missing steps in proofs involving SSS in triangles
      • Determine missing steps in proofs involving SAS in triangles
      • Determine missing steps in proofs involving AAS in triangles
      • Determine missing steps in proofs involving ASA in triangles
      • Determine missing steps in proofs involving triangle congruence theorems
      • Determine missing steps in proofs involving triangle congruence theorems, paragraph form
      • Determine missing steps in proofs involving corresponding parts
      • Determine missing steps in proofs involving corresponding parts, paragraph form
      • Determine missing steps in proofs involving quadrilaterals
      • Apply triangle theorems or determine missing steps in proofs
      • Determine missing steps in proofs involving quadrilaterals, paragraph form
  • Geometric Transformations
    • Translations
      • Given coordinate vertices of figure, determine translated image
      • Given figure on coordinate plane, determine translated coordinates
      • Identify rule or determine translated point on coordinate plane
    • Reflections
      • Determine coordinates of reflected points
      • Given coordinate vertices of figure, determine reflected image
      • Identify rule or reflected point on coordinate plane
      • Given figure on coordinate plane, determine reflected coordinates
    • Rotations
      • Given coordinate vertices of figure, determine rotated image
      • Given figure on coordinate plane, determine rotated coordinates
      • Identify rule or rotated point on coordinate plane
    • Dilations
      • Identify characteristics of dilations
      • Identify rule or dilated point on coordinate plane, including variable scale factors
    • Mixed Transformations
      • Transformations of Angles, Lines, & Segments
        • Identify characteristics of transformed lines
        • Identify characteristics of transformed line segments
        • Identify characteristics of transformed parallel lines
        • Identify characteristics of transformed angles
        • Identify characteristics of transformed lines, segments, & angles
      • Transformations of Figures
        • Given congruent figures, identify description of transformations
        • Given similar figures, identify description of transformations
        • Identify congruence transformations
        • Identify rule or determine transformed point on coordinate plane
        • Identify rule for transformed shape on coordinate plane
        • Composition of transformations on coordinate plane
        • Identify characteristics of transformations
        • Identify reflections & rotations on coordinate plane
        • Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates
        • Condensed: Given similar or congruent figures, identify description of transformations
        • Condensed: Identify rule or determine transformed point on coordinate plane
  • Absolute Value Functions
    • Given graph, determine absolute value equation
    • Given description of transformation, determine absolute value equation
    • Condensed: Graph absolute value functions using any transformation
    • Given absolute value equation, identify description of transformation
  • Trigonometry
    • Identify definitions of trig functions
    • Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
    • Given right triangle, determine missing side & trig ratio, sin, cos, & tan
    • Given right triangle, determine missing side & trig ratio, cot, sec, & csc
    • Condensed: Given right triangle, determine missing side & trig ratio
  • Probaility
    • Determine conditional probabilities from two-way frequency tables
    • Determine conditional probabilities, including two-way frequency tables