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Algebra 2 Skills

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  • Algebra Foundations
    • Real Number System & Properties
      • Determine relationships between subsets of real numbers
      • Determine relationships between subsets of rational numbers
      • Determine result of adding & multiplying rational & irrational numbers
      • Order real numbers, no exponents
      • Order real numbers, positive exponents, percents are whole, including real-world context
      • Order real numbers, positive exponents, percents are whole, including real-world context
      • Order irrational numbers
      • Comparing expressions on given interval
      • Compare irrational numbers
      • Condensed: Compare & order irrational numbers
    • Expressions & Operations
      • Evaluating Expressions
        • Evaluate expressions for specified value, one variable, two terms
        • 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, two terms
        • Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
        • Evaluate expressions for specified values, two variables, two terms, one term with three factors
        • 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, One Variable
        • Simplify algebraic expressions, one variable, distribute once, fraction multiplier
        • Simplify algebraic expressions, one variable, distribute once, decimal multiplier
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
        • Simplify algebraic expressions, one variable, distribute once, including rationals
        • Simplify algebraic expressions, one variable, distribute once & combine like terms
        • Simplify algebraic expressions, one variable, distribute once & product of two factors
        • Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
        • Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
        • Simplify algebraic expressions, one variable, distribute twice
        • 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
      • Simplifying Expressions, Two Variable
        • Simplify algebraic expressions, two variables, positive integer coefficients
        • Simplify algebraic expressions, two variables, distribute twice
      • Identifying Equivalent Expressions
        • Identify equivalent expressions involving distribution
        • Identify equivalent expressions involving distribution, two or more terms
        • Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
    • Equations
      • Solving Equations
        • Determine number of solutions in linear equations, distribute at most one time
        • Determine number of solutions in linear equations, distribute up to two times
        • Condensed: Determine number of solutions in linear equations
        • Condensed: Solve linear equations, variables on both sides or like terms
        • Solve linear equations, distributive property & additional term on one side
        • Solve linear equations, term minus distributive property on one side
        • Solve linear equations, distributive property & additional term on one side & binomial on other side
        • Solve linear equations, including no solution & infinitely many solutions
        • Condensed: Solve linear equations involving distributive property on one side
        • Solve linear equations, distributive property on both sides, rationals
        • Solve linear equations, distributive property on both sides, additional term on one side
      • 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 of form a + by = cx, solve for y
        • Given linear equation in standard form, solve for y
        • 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
        • 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
      • Application of Equations
        • Solve problems that can be represented by two-step equations, real-world context
        • Determine equations or identify real-world situations represented by one-step or two-step equations 
        • Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
        • 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
      • Literal Equations
        • Solve literal equation for variable
        • Solve literal equation for variable, variable may appear twice, linear terms
        • Determine how change to one variable affects another variable
    • Inequalities
      • Solving Inequalities Algebraically
        • Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
        • Given linear inequality & x-value, determine y-value
        • Solve linear programming problems, real-world context
        • Given description, determine linear inequality in standard form, graph, & determine specific solutions, real-world context
        • Given description, determine linear inequalities in standard form, including tables, real-world context
        • Given description, determine linear inequalities in standard form & specific solutions, real-world context
        • Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
      • Solving Inequalities Graphically
        • 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
        • Given linear inequality, identify correct graph, slope-intercept form
        • Given linear inequality, determine graph, slope-intercept form
        • Condensed: Determine equivalent linear inequalities & graphical solutions
        • Given description & table, graph linear inequality, real-world context
        • Graph linear inequalities, various forms
        • Condensed: Graph linear equations or inequalities
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
      • Solving Inequalities, Given Graph
        • Given linear inequality graph, determine solutions & non-solutions
        • Given graph, determine linear inequality
        • Determine equivalent systems of linear inequalities & graphical solutions
        • Condensed: Determine points that are solutions to linear equations or inequalities
      • Writing Inequalities
        • Given graph, identify linear inequality, slope-intercept form
        • Given graph, determine inequalities in standard form, real-world context
      • Compound Inequalities
        • Solve compound inequalities, "and" solutions, multiple choice
        • Solve & graph compound inequalities, "and" solutions
        • Solve & graph compound inequalities, "and" solutions, including real-world context
        • Solve & graph compound inequalities, "or" solutions
        • Condensed: Solve & graph compound inequalities
        • Given description, determine compound inequality, graph, & possible solutions
        • Given description, determine graph of inequality
    • Systems of Equations
      • Solving Systems of Equations, Graphing
        • Given system of linear equations, determine point of intersection, slope-intercept form
        • Given system of linear equations, graph & determine point of intersection, slope-intercept form
        • 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 equations in slope-intercept form
        • Given graph of system of linear equations, determine solution, rays on graph to establish pattern
      • Solving Systems of Equations, Substitution
        • 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
        • Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
        • Solve systems of linear equations, infinite possibilities or no solution
        • Condensed: Given system of linear equations, determine solution, substitution bias
        • 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: Solve or determine system of equations, likely to have same variable isolated
        • 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
      • Solving Systems of Equations, Elimination
        • Given system of linear equations in standard form, determine point of intersection, integer coordinates
        • Solve systems of linear equations, multiply at most one equation
        • Solve systems of linear equations, multiply one or both equations
        • Determine systems of linear equations & solutions, elimination bias, real-world context
        • Condensed: Solve or determine system of equations, both equations in standard form
      • Solving Systems of Equations, Mixed Methods
        • Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
        • Determine system of two equations, one linear & one quadratic
        • Condensed: Determine systems of linear equations & solutions
        • Solve systems of two equations, algebraic, one linear & one quadratic
        • Solve systems of two equations, graphical, one linear & one quadratic
        • Condensed: Solve systems of two equations, one linear & one quadratic
      • Determining Solution to System of Equations
        • Given system of linear equations, identify solution or x- or y-value of solution
        • Given system of linear equations, identify x- or y-value of solution
        • Given system of linear equations, identify solution
        • Given tables, determine system of linear equations
        • Determine reasonableness of solutions to systems of linear & quadratic equations
      • Application of Determining Solution to System of Equations
        • Given table representing system of linear equations, determine solution, real-world context
        • Given system of linear equations & description, identify solution, real-world context
        • Condensed: Given system of linear equations, identify solution, including real-world context
        • Determine systems of linear equations & solutions, real-world context
        • Determine & justify solutions to systems of linear equations, real-world context
        • Condensed: Determine systems of linear equations & solutions, including real-world context
        • Given graph of system of linear equations, identify specific domain value, real-world context
        • Graph systems of linear equations & determine solutions, including real-world context
      • Solving Systems of Equations, Three Equations
        • Solve systems of three linear equations using substitution
        • Solve systems of three linear equations using Gaussian elimination
        • Solve systems of three linear equations using matrices
        • Condensed: Solve systems of three linear equations
        • Determine system of three linear equations, real-world context
    • Systems of Inequalities
      • Solving Systems of Inequalities Graphically
        • Given graph, determine solution of systems of linear inequalities
        • Given linear system of inequalities graph, identify true statements
        • Graph systems of two linear inequalities, slope-intercept form
        • Condensed: Determine graphs of linear inequalities or system of linear inequalities
        • Solve systems of linear inequalities
        • Graph systems of three linear inequalities, slope-intercept form
        • Given description of system of linear inequalities, identify graph of system
      • Application of Solving Systems of Inequalities Graphically
        • Condensed: Graph system of linear inequalities & determine system of linear inequalities, including 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 description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
      • Solving Systems of Inequalities Algebraically
        • Given description, determine system of linear inequalities in standard form & solution point, real-world context
        • Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
    • Functions
      • Identifying Functions
        • Determine functions, set & table representations
        • Identify & determine functions, set & table representations
        • Determine functions, mapping representations
        • Determine functions, graphical representations
        • Given step graphs, identify functions
        • Identify functions, description representations
        • Given relation & additional point, determine functions, multiple representations
      • Identifying & Justifying Functions
        • Determine & justify functions, set representations
        • Determine & justify functions, table representations
        • Identify & determine functions, set & table representations
        • Determine & justify functions, mapping representations
        • Identify functions using equivalent mapping diagrams & sets of ordered pairs
        • Determine & justify functions, graphical representations
        • Identify & justify functions & non-functions, graphical representations
        • Identify functions, multiple representations, including justification
        • Condensed: Identify, justify, & determine functions
      • Identifying & Justifying Functions, No Domain & Range Language
        • Determine & justify functions, set representations, no domain & range language
        • Determine & justify functions, table representations, no domain & range language
        • Determine & justify functions, mapping representations, no domain & range language
        • Determine functions, multiple representations, including justification, no domain & range language
      • Function Notation
        • Given linear function, determine function value
        • Given quadratic function, determine function value
        • Condensed: Given linear or quadratic function, determine function value
        • Given graph, determine function value
        • Condensed: Given graph or linear function, determine function value
        • Interpret & solve problems involving function notation, real-world context
  • Linear Functions
    • Domain & Range of Linear Functions
      • Determine if value is in domain or range, set & table representations
      • Determine if value is in domain or range, graphical representations
      • Given graph, determine domain & range
      • Determine continuous domain & range, real-world context
      • Determine restricted domain & range of linear functions
      • Determine discrete domain & range, real-world context
      • Condensed: Determine domain & range, including real-world context
    • Graphing Linear Functions
      • 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, Integer Slope Only
        • 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 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, including horizontal & vertical, integer slope, various scales
      • Slope-Intercept Form to Graph
        • Graph linear equations, fractional slope
        • Graph linear equations, fractional slope, various scales
        • Condensed: Graph linear equations, including horizontal & vertical, various scales
        • Given description of linear equation, identify graph, fractional slope, real-world context
        • Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
        • Condensed: Identify equivalent equations, graphs, & tables
      • Vertical & Horizontal Lines to Graph
        • Given vertical linear equation, determine graph
        • Given horizontal linear equation, determine graph
    • Identifying Key Features of Linear Function
      • Identify Linear or Non-Linear Relationships
        • Identify linear & non-linear relationships, various representations
      • Determine or Plot Intercepts, Given Graph
        • 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 graph of linear equation, determine slope & intercepts
      • Determine or Plot Intercepts, Given Equation
        • Given linear equation in slope-intercept form, determine coordinates of y-intercept
        • Given linear equation in slope-intercept form, determine coordinates of x-intercept
        • Given linear equation in slope-intercept form, plot y-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 equation of horizontal or vertical line, plot y-intercept
        • Given linear equation, determine intercepts
        • Given linear equation in standard form, determine coordinates of y-intercept
        • Given linear equation, determine slope & intercepts
    • Writing Equation of Linear Function
      • Writing Equation Given Point & Slope
        • Given slope & y-intercept, determine equation
        • Given point & integer slope or rate of change, determine linear equation in slope-intercept form
        • Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
        • 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 point-slope form, integer slope, including slope-intercept form conversion
        • 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, fractional slope, including slope-intercept form conversion
        • Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
      • Writing Equation Given Various Components
        • Given points or slope & point, determine linear equation in standard form
        • Given points or slope & point, determine linear equation in point-slope or 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
        • Writing 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
        • Writing Equation Given Graph, Integer Slopes,Various Y-Intercepts
          • 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, determine equation in slope-intercept form, integer slopes, various scales
          • Given linear graph, identify equation in slope-intercept form, integer slopes, various scales
          • Given equation in slope-intercept form, identify graph, integer slopes, various scales
          • Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
        • Writing Equation Given Graph, Various Y-Intercepts
          • Given linear graph, identify equation, slope-intercept form
          • 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 graph of vertical line, determine equation
          • Given graph of horizontal line, determine equation
      • Writing Equation of Parallel or Perpendicular Line
        • Identifying Parallel, Perpendicular, or Neither
          • Given two slope-intercept form equations, identify as parallel or perpendicular
          • Given two pairs of points, determine if lines containing points are parallel or perpendicular
        • Writing Equation of Parallel or Perpendicular in Slope-Intercept Form
          • Given equation in slope-intercept form, determine slope of parallel line
          • Given equation in slope-intercept form, determine slope of perpendicular line
          • Condensed: Given equation in slope-intercept form, determine slope of parallel or perpendicular line
          • Given equation in slope-intercept form, 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 slope-intercept form, determine equation of parallel or perpendicular line through specified point
          • Condensed: Determine equations for parallel & perpendicular lines through specified points
          • Given slope & point, determine equation for parallel or perpendicular line through specified point
          • Given two points for one line, determine equation for parallel or perpendicular line through specified point
          • Given graph of line, determine equation for parallel or perpendicular line through specified point
        • Writing Equation of Parallel or Perpendicular in Various Forms
          • Given equation in various forms, determine slope of parallel line
          • Given equation in various forms, determine slope of perpendicular line
          • Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
          • 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
          • Given equation in various forms, determine equation of parallel line through specified point
          • Given equation in various forms, determine equation of perpendicular line through specified point
          • Given equation in various forms, determine equation of parallel or perpendicular line through specified point
          • Identify equation that is parallel or perpendicular to line through two given points
    • Transformations of Linear Functions
      • Identify & graph reflections of linear functions
      • Identify & graph vertical & horizontal shifts of linear functions
      • Identify & graph vertical & horizontal stretches & compressions of linear functions
      • Identify descriptions of graphs of linear parent functions & transformed functions
      • Graph linear functions using all transformations
      • Condensed: Graph linear functions & identify transformations
      • Given description of transformation, determine linear function
      • Given table, identify transformations of linear functions
      • Describe parameter changes to linear parent functions
      • Compare linear functions represented differently
    • Application of Linear Functions, Given Slope-Intercept or Two Points
      • 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
      • Given slope & intercept, interpret linear relationship & determine slope-intercept equation, 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
      • Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
    • Application of Linear Functions
      • Given linear word problem, identify graph
      • Form 6 – Given linear graph, interpret linear relationship & determine slope-intercept equation
      • Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
      • Determine graph or information from graph, real-world context
      • Given linear equation, interpret slope & y-intercept, real-world context
      • Determine effects of parameter changes in linear relationships, real-world context
    • Linear Regression
      • 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
  • Exponents
    • 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
    • Simplify Negative Exponents
      • Express negative power using positive exponent
      • Express negative power using positive exponent, coefficient other than one
    • Power Rule of Exponents
      • Power Rule, One Variable
        • Apply power rule, one variable, positive 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
        • Simplify single variable powers, negative base or coefficient
      • Power Rule, Multiple Variables
        • Apply power rule, including multiple variables, positive exponents
        • Apply power rule, including multiple variables & 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, coefficient of negative one in power, including multiple variables & negative exponents
        • Apply power rule, negative base or coefficient, multiple variables, including negative exponents
        • Apply power rule, multiple variables, coefficients other than one, including negative exponents
        • Simplify powers, fractional algebraic base, including negative exponents
    • Product Rule of Exponents
      • Product Rule, One Variable
        • Apply product rule of exponents, one variable, positive exponents
        • Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
        • Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
        • Apply product rule of exponents, one variable, positive exponents, coefficients other than one
      • Product Rule, Multiple Variables
        • Apply product rule of exponents, two variables, three to four factors, positive 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, positive exponents
        • 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 of exponents, positive exponents
        • Apply product rule, multiple variables, coefficients other than one, including negative exponents
        • Apply product rule of exponents, negative exponents
    • Quotient Rule of Exponents
      • Quotient Rule, One Variable
        • 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, one variable, at least one negative exponent
      • Quotient Rule, Multiple Variables
        • 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
        • Apply quotient rule of exponents, positive exponents
        • 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
        • 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
    • Power & Product Rules of Exponents
      • Apply power rule of exponents, positive exponents
    • Product & Quotient Rules of Exponents
      • Multiply Two Fractions
        • Apply product & quotient rules of exponents, multiply two fractions, one or two 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, multiply two fractions, multiple variables, positive exponents
        • 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 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
      • Divide Two Fractions
        • 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, one or two 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 product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
      • Multiply & Divide Two Fractions
        • Apply product & quotient rules of exponents, negative exponents
        • Apply product & quotient rules of exponents, negative exponents, coefficients other than one
      • Apply product & quotient rules of exponents, multiply two fractions, one or two 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, multiply two fractions, multiple variables, positive exponents
      • 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 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 product & quotient rules of exponents, divide two fractions, one or two variables, at least one non-positive exponent
      • 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, negative exponents, coefficients other than one
      • Apply product & quotient rules of exponents, negative exponents
      • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
      • Apply product & quotient rules of exponents, one or two variables, positive exponents
    • Power, Product, & Quotient Rule of Exponents Mixed
      • Exponents Mixed, One Variable
        • Apply power & product rules of exponents, one variable, positive exponents
        • Apply product & power rules of exponents, one variable, coefficient of negative one
        • Apply product, quotient, & power rules of exponents, one variable
      • Exponents Mixed, Positive Exponents
        • Apply product & quotient rules of exponents, one or two variables, positive exponents
        • Apply power & product rules of exponents, multiple variables, positive exponents
        • Apply power & product rules of exponents, fraction with numerator of one, positive exponents
        • Apply power, product, & quotient rules of exponents, positive exponents
        • Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
        • Apply power, product, & quotient rules of exponents, divide fractions, positive exponents
      • Exponents Mixed, Including Negative Exponents
        • Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
        • Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
        • Apply power, product, & quotient rules of exponents, including negative exponents
        • Apply power rule of exponents, negative exponents
        • Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
        • Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
        • Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
        • Apply product rule of exponents, coefficients other than one
        • Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents
        • Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents
        • 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
    • Rational Exponents
      • Power Rule
        • Evaluate rational exponent expressions, positive exponents
        • Evaluate rational exponent expressions, negative exponents
        • Condensed: Evaluate rational exponent expressions
        • Simplify rational exponent expressions using power rule, no coefficients
        • Simplify rational exponent expressions using power rule, with coefficients
      • Product Rule
        • Simplify rational exponent expressions using product rule, no coefficients
        • Simplify rational exponent expressions using product rule, coefficients not with base
        • Simplify rational exponent expressions using product rule, coefficients with base
      • Quotient Rule
        • Simplify rational exponent expressions using quotient rule, no coefficients
        • Simplify rational exponent expressions using quotient rule, with coefficients
      • Exponent Rules Mixed
        • Evaluate numerical expressions with rational exponents
        • Simplify numerical expressions with rational exponents
        • Condensed: Simplify rational exponents using product & power rules
      • Convert Rational Exponents & Radicals
        • Convert from rational exponent to radical, single value base
        • Convert from rational exponent to radical, algebraic base
        • Condensed: Convert from rational exponent to radical
  • Polynomials
    • Classifying Polynomials
      • Identify terms of expressions
      • Identify polynomial as monomial, binomial, or trinomial
      • Classify polynomials by degree & number of terms
      • Condensed: Classify polynomials & identify components of polynomials
      • Determine degree, leading coefficient, & type of polynomial
      • Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables
    • Interpreting Polynomials
      • Interpret terms or factors in expressions, including real-world context
      • Identify & apply polynomial identities
    • Operations with Polynomials
      • Addition & Subtraction of Polynomials
        • Addition of Polynomials
          • Add binomials & trinomials, degrees zero to two
          • Add binomials & trinomials, degrees zero to three
          • Given polynomial & sum of polynomials, determine missing polynomial
          • Determine sums of polynomials or missing polynomial addends
        • Subtraction of Polynomials
          • Subtract binomials & trinomials, degrees zero to two
          • Subtract binomials & trinomials, degrees zero to three
          • Given polynomial & difference of polynomials, determine missing polynomial
          • Determine differences of polynomials or missing polynomial subtrahends
        • Addition & Subtraction of Polynomials
          • Condensed: Add or subtract binomials & trinomials
          • Condensed: Determine sums or differences of polynomials or missing polynomial operands
          • Add & subtract polynomials to determine expressions for perimeter of various shapes
          • Determine missing value to make polynomial statement true, addition & subtraction
          • Add & subtract binomials & trinomials, two variables
      • Multiplication of Polynomials
        • Multiplication of Polynomials, One Variable
          • Multiply monomial times binomial or trinomial, mixed degrees
          • Multiply binomial times binomial, both degree one
          • Square linear binomial
          • Multiply binomial times binomial, mixed degrees
          • Condensed: Multiply binomial times binomial
          • Multiply linear binomial times quadratic trinomial
          • Multiply binomial times trinomial, mixed degrees
          • Simplify monomial minus product of monomial & binomial or trinomial
          • Given monomial & binomial or trinomial, multiply or identify missing value
          • Determine missing value to make polynomial statement true, multiplication
          • Multiply polynomials to determine expressions for areas of rectangles & triangles
        • Multiplication of Polynomials, Two Variables
          • Multiply monomial times binomial or trinomial, two variables
          • Multiply binomial times binomial, two variables
          • Multiply binomial times trinomial, two variables
          • Condensed: Multiply monomials, binomials, & trinomials, two variables
        • Binomial Theorem
          • Apply binomial theorem to expand (x ± y)^3
          • Apply binomial theorem to expand (x ± y)^n, n ≥ 4
          • Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
        • Multiply monomial times binomial or trinomial, mixed degrees
        • Multiply monomial times binomial or trinomial, two variables
        • Multiply binomial times binomial, both degree one
        • Square linear binomial
        • Multiply binomial times binomial, mixed degrees
        • Multiply linear binomial times quadratic trinomial
        • Multiply binomial times trinomial, mixed degrees
        • Condensed: Multiply binomial times binomial
        • Given monomial & binomial or trinomial, multiply or identify missing value
        • Apply binomial theorem to expand (x ± y)^3
        • Multiply polynomials to determine expressions for areas of rectangles & triangles
        • Determine missing value to make polynomial statement true, multiplication
        • Apply binomial theorem to expand (x ± y)^n, n ≥ 4
        • Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
        • Simplify monomial minus product of monomial & binomial or trinomial
        • Multiply binomial times binomial, two variables
        • Multiply binomial times trinomial, two variables
        • Condensed: Multiply monomials, binomials, & trinomials, two variables
      • Division of Polynomials
        • Divide polynomials, degree one or two by degree one or two
        • Divide polynomials, degree three or four by degree one
        • Divide polynomials, degree three or four by degree two
        • Divide polynomials, divisor supports synthetic division
        • Condensed: Divide polynomials, degree three or four by degree one or two
        • Condensed: Divide polynomials
        • Divide quadratic trinomial by linear binomial, word problem context
        • Apply remainder theorem
      • Mixed Operations of Polynomials
        • Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
        • Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
        • Determine missing operation to make polynomial statement true
        • Condensed: Determine missing value to make polynomial statement true
    • Factoring Polynomials
      • Factoring Trinomials, a=1
        • Factor quadratic trinomials, a = 1, b > 0, c > 0
        • Factor quadratic trinomials, a = 1
        • Factor quadratic trinomials, a = 1, terms scrambled
        • Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
        • Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < |c| ≤ 10
        • Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
      • Factoring Trinomials, a>1
        • Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
        • Factor quadratic trinomials, 1 < |a| ≤ 10, 0 < |c| ≤ 30
        • Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
        • Factor quadratic trinomials, 1 < |a| ≤ 30, 0 < |c| ≤ 40
        • Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
      • Factor Perfect Square Trinomials
        • Factor perfect square trinomials, degree two, one variable
        • Factor perfect square trinomials, degree two, two variables
        • Condensed: Factor perfect square trinomials, degree two
        • Factor perfect square trinomials, fraction coefficients
      • Factoring Difference of Squares
        • Factor difference of two squares, degree two, one variable
        • Factor difference of two squares, degree two, one variable, terms scrambled
        • Factor difference of two squares, degree two, one variable, coefficient one
        • Condensed: Factor difference of two squares, degree two
        • Factor difference of two squares, two variables
        • Factor difference of two squares, one or two variables
      • Factor GCF & Remaining Quadratic
        • Factor GCF & remaining quadratic expression, a = 1, one variable
        • Factor GCF & remaining quadratic expression, a ≥ 1, one variable
      • Factor Common Binomial
        • Factor common binomial
        • Factor binomial & its opposite
      • Factor by Grouping
        • Factor cubic polynomial by grouping, one variable
        • Factor cubic polynomial by grouping & difference of two squares, one variable
      • Factor Sum & Difference of Cubes
        • Factor sum & difference of two cubes, degree three, one variable
        • Factor sum & difference of two cubes, degree six, one variable
        • Factor sum & difference of two cubes, degree three, two variables
        • Condensed: Factor sum & difference of two cubes, degree three
        • Factor sum & difference of two cubes, degree six, two variables
        • Condensed: Factor sum & difference of two cubes, degree six
      • Identify Factors
        • Identify factors of polynomials
        • Determine linear factors of polynomials, degree three
        • Determine linear factors of polynomials, degree four
        • Determine quadratic factors of polynomials, degree four
        • Condensed: Determine linear factors of polynomials, degree three or four
      • Determine Number of Roots
        • Determine maximum number of roots for polynomial function
    • Interpreting Graphs of Polynomials
      • Intercepts & Multiplicities
        • Determine x- & y-intercepts of cubic functions
        • Determine x-intercepts/zeros & y-intercepts of polynomial functions
        • Determine zeros of polynomials & their multiplicities
      • Extrema, Increase & Decrease, End Behavior, & Symmetry
        • Determine minimum & maximum of polynomial functions
        • Determine intervals of increase & decrease of polynomial functions
        • Determine end behavior of polynomial functions
        • Determine symmetry of various functions
      • Determine Attributes
        • Given table, determine attributes of polynomial function
        • Given cubic equation, identify descriptions of transformations
        • Condensed: Determine graphical attributes of polynomial functions
      • Determine Graph or Equation
        • Given zeros, determine graph of polynomial function
        • Given equation, graph polynomial function
        • Given graph, determine equation of polynomial function
      • Determine Points of Intersection of Two Functions
        • Determine points of intersection of two polynomial functions
  • Function Operations, Inverses, & Solutions
    • Operations with Functions
      • Add functions, (f + g)(x)
      • Subtract functions, (f – g)(x)
      • Multiply functions, (f * g)(x)
      • Divide functions, (f / g)(x)
      • Condensed: Add, subtract, multiply, & 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)(#)
      • Evaluate compositions of functions
    • Inverse Functions
      • Determine inverse of linear function
      • Determine inverse of quadratic & square root functions
      • Determine inverse of cubic & cube root functions
      • Determine inverse of various functions
      • Determine if functions are inverses using composition
      • Graph function and its inverse
      • Determine domain & range of inverse functions
      • Condensed: Given function, determine equation, graph, & domain & range of inverse
      • Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions
    • Identifying Function, Solutions, & Points of Intersection
      • Determine whether given table represents linear or exponential function
      • Determine whether given table represents linear, exponential, or quadratic function
      • Determine whether given graph represents linear, exponential, or quadratic function
      • Condensed: Determine what function given table or graph represents
      • Identify ordered pair solutions to systems of two equations, one linear & one quadratic
      • Perform operations on functions represented graphically, graphical solution
      • Perform operations on functions represented graphically, numerical solution
      • Determine points of intersection of various functions, not absolute value or polynomial
      • Condensed: Determine points of intersection of functions
  • Complex Numbers
    • Simplify Complex Numbers
      • Express square roots of negatives using i
      • Simplify imaginary numbers
      • Simplify powers of i
    • Operations with Complex Numbers
      • Add & subtract complex numbers
      • Add or subtract square roots of negative numbers
      • Multiply complex numbers
      • Square complex numbers
      • Multiply square roots of negative numbers
      • Divide complex number by constant
      • Divide complex numbers
      • Condensed: Multiply & divide complex numbers
      • Condensed: Add, subtract, multiply, & divide complex numbers
      • Condensed: Add, subtract, & multiply square roots of negative numbers
    • Quadratic Equations with Complex Solutions
      • Factor sum of squares using complex factors
      • Calculate discriminant, then determine number of real or complex solutions
      • Determine number of complex & real roots of quadratic functions
      • Determine complex solutions by factoring sum of squares
      • Solve quadratic equations using square root method, complex solutions
      • Solve using quadratic formula, complex solutions
      • Condensed: Solve quadratic equations, complex solutions
      • Solve quadratic equations, complete the square, integers, a = 1, complex solutions
      • Solve quadratic equations, complete the square, integers, a > 1, complex solutions
      • Condensed: Solve quadratic equations, complete the square, integers, complex solutions
      • Given two complex solutions, determine quadratic equation of form x^2 + # = 0
  • Quadratic Functions
    • 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
    • Graphing Quadratic Functions
      • Given quadratic equation, determine graph, b = 0
      • Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
      • Graph quadratic functions using all transformations
      • Given quadratic equation, vertex, & point, graph function & determine attributes
      • Given quadratic equation in vertex form, determine graph
      • Given quadratic equation in standard form, determine graph
      • Graph quadratic equations
      • Given equation, graph quadratic function
      • Condensed: Graph quadratic functions using any transformation
      • Given table, determine attributes of quadratic function, real-world context
    • Identifying Key Features of Quadratic Functions
      • Vertex, Axis of Symmetry, Increase & Decrease, & Extrema of Quadratic Functions
        • Determine vertex of quadratic functions
        • 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 symmetry of quadratic functions
        • Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
        • Determine end behavior of quadratic functions
        • Determine intervals of increase & decrease of quadratic functions
        • Determine intervals where quadratic function is positive or negative
      • Intercepts of Quadratic Functions
        • Determine x-intercept(s) of quadratic functions
        • Determine zero(s) of quadratic functions
        • Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
        • 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
      • Mixed Key Attributes of Quadratic Functions
        • 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 graph, equation, or table, determine attributes of quadratic function
        • Condensed: Determine graphical attributes of quadratic functions
        • Condensed: Given quadratic equation, determine attributes & graph
    • Transformations of Quadratic Functions
      • Identify & graph reflections of quadratic functions
      • Identify & graph vertical & horizontal shifts of quadratic functions
      • Identify & graph vertical & horizontal stretches & compressions of quadratic functions
      • Identify descriptions of graphs of quadratic parent functions & transformed functions
      • Given quadratic equation, identify description of transformation
      • Given description of transformation, determine quadratic function
      • Describe parameter changes to quadratic parent functions
      • Determine effects of parameter changes in quadratic relationships, real-world context
      • Compare quadratic functions represented differently
    • Writing Equations of Quadratic Functions
      • Standard & Vertex Form
        • Given quadratic equation in standard form, determine vertex form of equation
        • Given quadratic equation in vertex form, determine standard form of equation
      • Given Vertex, Zeros, or Points
        • Given vertex & point, determine quadratic equation, vertex form
        • Given vertex & point, determine quadratic equation, standard form
        • Given zeros of quadratic function, determine quadratic equation with integer coefficients
        • Given integer solutions of quadratic equation, determine function in standard form
        • Given rational solutions of quadratic equation, determine function in standard form
        • Given three points in plane, determine quadratic equation
      • Given Graph, Determine Equation
        • Given graph of quadratic function, determine equation
        • Given graph of quadratic function, determine equation
        • Given graph of quadratic function, determine equation in standard form
      • Focus & Directrix
        • Given focus & directrix of parabola, determine equation
        • Given focus & directrix of parabola, determine equation in standard form
        • Given graphical attributes, determine equation of parabola
    • Solving Quadratic Equations
      • Solving Quadratic Equations, Zeros
        • Apply zero product property to solve factored quadratic equations
        • Identify zeros of factored quadratics
        • Determine relationship between zeros & linear factors of quadratic functions
      • Solving Quadratic Equations, GCF
        • 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
      • Solving Quadratic Equations, Factoring
        • 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, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
        • 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, |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, perfect square trinomial
        • Solve quadratic equations, perfect square trinomial
        • Solve quadratic equations using factoring, difference of squares
      • Solving Quadratic Equations, Graphing
        • Given graph of quadratic function, determine roots/zeros
      • Solving Quadratic Equations, Square Root Method
        • 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 = #
        • 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
      • Solving Quadratic Equations, 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 Quadratic Equations, Completing the Square
        • Determine constant required to complete the square, a ≥ 1, including fractions
        • Solve quadratic equations, complete the square, integers, a = 1, real solutions
        • Solve quadratic equations, complete the square, integers, a > 1, real solutions
        • Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
        • Condensed: Solve quadratic equations, complete the square, integers, real solutions
        • Solve quadratic equations, complete the square, a = 1, real solutions
        • Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
        • Solve quadratic equations, complete the square, a > 1, real solutions
        • Condensed: Solve quadratic equations, complete the square, real solutions
        • Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
        • Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
        • Condensed: Solve quadratic equations, complete the square, integers, including complex solutions
      • Solving Quadratic Equations, Determine Solutions
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
        • Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
        • Determine exact solution to quadratic equations, a = ±1, b = 0
        • Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
      • Application of Solving Quadratic Equations
        • Determine or use quadratic equations, real-world context
    • Solving Quadratic Inequalities
      • Solve quadratic inequalities, "and" solutions
      • Solve quadratic inequalities, "or" solutions
      • Condensed: Solve quadratic inequalities
    • 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 initial height & velocity of object in vertical motion, determine position function & specific time
      • Given height of dropped object, 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
  • Absolute Value Functions
    • Solving Absolute Value Equations
      • Solve linear absolute value equations
      • Solve linear absolute value equations, extra constant or coefficient
      • Solve linear absolute value equations, variable on both sides
      • Condensed: Solve linear absolute value equations, including extra constant or coefficient
      • Create linear absolute value equations, real-world context
    • Solving 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, "or" solutions, including setup
      • Solve & graph linear absolute value inequalities, including setup
      • Condensed: Solve & graph linear absolute value inequalities, including setup
      • Solve & graph linear absolute value inequalities, "and" solutions
      • Solve & graph linear absolute value inequalities, "or" solutions
      • Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
      • Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
      • Solve & graph linear absolute value inequalities, including extra constant or coefficient
      • Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
      • Condensed: Solve & graph linear absolute value inequalities
    • Graphing Absolute Value Functions
      • Determine x- & y-intercepts of absolute value functions
      • Determine minimum & maximum of absolute value functions
      • Identify & graph reflections of absolute value functions
      • Identify & graph vertical & horizontal shifts of absolute value functions
      • Identify & graph vertical & horizontal stretches & compressions of absolute value functions
      • Given absolute value equation, identify description of transformation
      • Graph absolute value functions using all transformations
      • 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
      • Determine points of intersection of absolute value functions
    • Writing Equation of Absolute Value Functions
      • Given graph, determine absolute value equation
      • Given description of transformation, determine absolute value equation
  • Piecewise & Step Functions
    • Graph piece-wise functions
    • Given graph of piece-wise function, determine equation
    • Graph step functions
    • Given graph of step function, determine equation
    • Condensed: Determine graphs & equations of piece-wise & step functions
  • Cubic Functions
    • Graphing Cubic Functions
      • Determine minimum & maximum of cubic functions
      • Identify & graph reflections of cubic functions
      • Identify & graph vertical & horizontal shifts of cubic functions
      • Identify & graph vertical & horizontal stretches & compressions of cubic functions
      • Graph cubic functions using all transformations
      • Condensed: Graph cubic functions using any transformation
      • Condensed: Determine graphical attributes of cubic functions
      • Graph cubic functions using key points & intercepts
  • Rational Expressions & Functions
    • Simplifying Rational Expressions
      • Simplify rational expressions by factoring GCF, one monomial & one binomial
      • Simplify rational expressions by factoring GCF, two binomials
      • Simplify rational expressions by factoring GCF, two binomials, remaining binomials cancel
      • Simplify rational expressions by factoring GCF, one trinomial or difference of squares
      • Simplify rational expressions by factoring GCF, trinomials & differences of squares
      • Simplify rational expressions by factoring GCF, remaining leading coefficient one
      • Condensed: Simplify rational expressions
      • Condensed: Simplify rational expressions, including trinomials
    • Operations with Rational Expressions
      • Multiply rational expressions
      • Divide rational expressions
      • Condensed: Multiply & divide rational expressions
      • Add rational expressions
      • Subtract rational expressions
      • Condensed: Add & subtract rational expressions
      • Condensed: Add, subtract, multiply, & divide rational expressions
    • Domain of Rational Functions
      • Given rational function, determine function value
      • Identify value that makes rational expression undefined
      • Determine values that make rational expressions undefined
      • Determine asymptotic domain restrictions of rational functions
      • Determine domain & range of rational functions using inequalities, interval notation & set notation
    • Key Attributes of Rational Functions
      • Determine x- & y-intercepts of reciprocal functions
      • Determine symmetry of reciprocal functions
      • Determine asymptotes of reciprocal functions
      • Determine minimum & maximum of reciprocal functions
      • Condensed: Determine graphical attributes of reciprocal functions
    • Graphing Rational Functions
      • Identify & graph reflections of reciprocal functions
      • Identify & graph vertical & horizontal shifts of reciprocal functions
      • Identify & graph vertical & horizontal stretches & compressions of reciprocal functions
      • Given reciprocal equation, identify description of transformations
      • Graph reciprocal functions using all transformations
      • Graph rational functions
      • Condensed: Graph reciprocal functions using any transformation
      • Graph reciprocal functions using asymptotes, intercepts, & domain & range
      • Compare rational functions represented differently
    • Solving Rational Equations & Inequalities
      • Solve equations involving rational exponents, one- or two-step
      • Solve equations involving rational exponents, multi-step
      • Solve rational equations, one term each side
      • Solve rational equations, multiple terms on one side
      • Condensed: Solve rational equations
      • Condensed: Solve equations involving rational exponents
      • Determine if solution to rational equation is reasonable
      • Determine rational equations, real-world context
      • Determine rational inequalities, real-world context
  • Radical Expressions & Functions
    • Simplifying Radical Expressions
      • Identify steps to simplify square roots
      • Simplify square roots
      • Simplify square roots, coefficient greater than one
      • Given square root expression, evaluate for specific value
      • Condensed: Simplify square roots, including algebraic expressions
      • Evaluate perfect cube roots
      • Solve perfect cube root equations
      • Condensed: Determine cube roots of perfect cubes
      • Compare perfect square & cube roots
      • Simplify radical expression raised to power that is multiple of index
      • Simplify radical expressions, perfect powers
    • Operations with Radicals
      • Add & subtract radical expressions, one or two variables, simplified radicals
      • Add & subtract radical expressions, one or two variables, radicals to simplify
      • Condensed: Add & subtract radical expressions
      • Multiply radical expressions, numbers & variables
    • Convert Radicals & Rationals
      • 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
      • Condensed: Convert from radical to rational exponent
    • Solving Radical Equations
      • Square Root
        • Solve perfect square root equations
        • Condensed: Determine square roots of perfect squares
        • 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, divide by coefficient of root
        • Solve square root equations, multi-step
        • Solve square root equations, square root = x ± #
        • Solve square root equations, square root ± square root = #
        • Condensed: Solve square root equations, one-step & two-step
        • Condensed: Solve square root equations
        • Identify extraneous solutions of square root equations
      • Cube Root
        • Solve perfect cube root equations
        • Solve cube root equations, cube root = #
        • Solve cube root equations, cube root = cube root
        • Solve cube root equations, multi-step
        • Solve cube root equations, cube root = variable
        • Condensed: Solve cube root equations, one-step & two-step
      • Square Root & Cube Root Mixed
        • Compare perfect square & cube roots
        • Condensed: Evaluate & compare perfect square & cube roots
        • Condensed: Solve square root & cube root equations
    • Key Attributes of Radical Functions
      • Determine x- and y-intercepts of square root functions
      • Determine minimum & maximum of square root functions
      • Condensed: Determine graphical attributes of square root functions
      • Determine x- & y-intercepts of cube root functions
      • Determine minimum & maximum of cube root functions
      • Condensed: Determine graphical attributes of cube root functions
    • Transformations of Radical Functions
      • Identify & graph reflections of square root functions
      • Identify & graph vertical & horizontal shifts of square root functions
      • Identify & graph vertical & horizontal stretches & compressions of square root functions
      • Given square root equation, identify description of transformations
      • Identify & graph reflections of cube root functions
      • Identify & graph vertical & horizontal shifts of cube root functions
      • Identify & graph vertical & horizontal stretches & compressions of cube root functions
      • Given cube root equation, identify descriptions of transformations
      • Compare radical functions represented differently
    • Graphing Radical Functions
      • Graph square root functions using key point & intercepts
      • Graph square root functions using all transformations
      • Condensed: Graph square root functions using any transformation
      • Graph cube root functions using key points & intercepts
      • Graph cube root functions using all transformations
      • Condensed: Graph cube root functions using any transformation
  • Mixed Functions
    • Calculate average rate of change of function from table
    • Calculate average rate of change of function from graph
    • Calculate average rate of change of a function from an equation
    • Calculate average rate of change of function, real-world context
    • Condensed: Calculate average rate of change of function
    • Given graph, identify various functions
    • Given various functions, identify graph
    • Condensed: Graph various functions
    • Determine domain & range of various functions using various notations
  • Logarithms
    • Evaluating Logarithmic Expressions
      • Evaluate log expressions, whole number base
      • Evaluate log expressions, fractional bases
      • Evaluate log expressions, using change of base
      • Evaluate log expressions, natural log
      • Condensed: Evaluate log expressions
    • Solving Logarithmic Equations
      • Solve log equations, log = #
      • Solve log equations, log = log
      • Solve log equations, log + log = #, same base, using product rule
      • Solve log equations, log – log = #, same base, using quotient rule
      • Condensed: Solve log equations, log = #, using product & quotient rules
      • Condensed: Solve log equations
      • Solve natural log equations, ln = #
      • Solve natural log equations, ln = ln
      • Solve natural log equations, ln + ln = #
      • Solve natural log equations, ln – ln = #
      • Condensed: Solve natural log equations
      • Determine if solution to logarithmic equation is reasonable
    • Condensing & Expanding Logarithms
      • Apply power rule to expand or condense log expressions
      • Apply product rule to expand or condense log expressions
      • Apply quotient rule to expand or condense log expressions
      • Apply product, quotient, & power rules to expand or condense log expressions
      • Condensed: Expand or condense log expressions
  • 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 
        • Determine domain & range of discrete exponential functions
        • Determine restricted domain & range of exponential functions
        • Given verbal description & graph, determine domain & range of exponential function 
        • Determine domain & range of discrete exponential functions, real-world context
      • Graphing Exponential Functions
        • Given graph, identify solution to exponential equation
        • Given exponential growth function, determine graph
        • Graph exponential functions using all transformations
        • Given exponential growth function, determine graph, includes fractional coefficients
        • Given exponential growth or decay function, determine graph, includes fractional coefficients
        • Given equation, graph exponential function
        • Given equation, graph exponential function, including base e
        • Given graph, determine equation of exponential function
        • Compare exponential functions represented differently
      • Identifying Key Features of Exponential Functions
        • Determine x-intercepts/zeros & y-intercepts of exponential functions
        • Determine y-intercept of exponential function, real-world context
        • Determine minimum & maximum of exponential functions
        • Determine asymptote of exponential functions
        • Given graph, determine asymptote of exponential function
        • Given exponential equation, determine asymptote
        • Determine asymptote of exponential functions, real-world context
        • Determine end behavior of exponential functions
        • Condensed: Determine graphical attributes of exponential functions
        • Graph exponential functions using all transformations
        • Condensed: Graph exponential functions & identify transformations
      • 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 Equations of 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 Equations
        • Solve exponential equations, no logs required
        • Solve exponential equations, common bases given
        • Solve exponential equations, both bases reduce to common base
        • Solve simple exponential equations
        • Solve exponential equations, one base reduces to common base
        • Solve exponential equations, two different bases, no common base possible
        • Solve exponential equations, one variable & one base
        • Solve exponential equations, base e
        • Create equivalent exponential expressions using exponent properties
      • Application of Exponential Functions
        • Calculate investment value, annual compounding
        • Calculate depreciating asset value, annual compounding
        • Calculate investment value, various compounding
        • Condensed: Calculate investment & depreciating asset values, annual compounding
        • Exponential growth & decay, real-world context
        • Determine exponential function, real-world context
        • Determine asymptote of exponential functions, real-world context
        • Given table, determine attributes of exponential function
        • Interpret values in exponential functions, real-world context
    • Logarithmic Functions
      • Graphing Logarithmic Functions
        • Identify & graph reflections of log functions
        • Identify & graph vertical & horizontal shifts of log functions
        • Identify & graph vertical & horizontal stretches & compressions of log functions
        • Given log equation, identify description of transformations
        • Graph log functions using all transformations
        • Given equation, graph log function
        • Condensed: Graph log functions & identify transformations
      • Identifying Key Features of Logarithmic Functions
        • Determine x-intercepts/zeros & y-intercepts of log functions
        • Determine asymptote of log functions
        • Determine minimum & maximum of log functions
        • Determine end behavior of log functions
        • Given table, determine attributes of log function
        • Condensed: Determine graphical attributes of log functions
      • Writing 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
  • Direct & Inverse Variation
    • Direct & Inverse Variation
      • Direct & Inverse Variation, Multiple Choice
        • Determine direct variation table, multiple choice
        • Determine direct variation equation, multiple choice
        • Determine inverse variation table, multiple choice
        • Determine variation equation type, multiple choice
        • Determine direct or inverse variation, multiple choice
      • Direct & Inverse Variation, Determine Equation or Missing Number
        • Given point & "y varies directly with x", determine equation
        • Given point & "y varies directly with x & inversely with z", determine equation
        • Given point, "y varies directly with x", & another value, determine missing number
        • Given point, "y varies directly with x", & another value, determine equation & missing number
        • Given point, "y varies directly with x", & another value, determine equation & missing number, rational numbers
        • Given point & "y varies inversely with x", determine equation
        • Given point, "y varies jointly with x & z", & another value, determine equation
        • Given point, "y varies inversely with x", & another value, determine equation & missing number
        • Condensed: Determine direct, inverse, joint, or combined variation equations
      • Determine direct variation table, multiple choice
      • Determine inverse variation table, multiple choice
      • Determine variation equation type, multiple choice
      • Determine direct or inverse variation, multiple choice
      • Given point & "y varies directly with x", determine equation
      • Given point & "y varies inversely with x", determine equation
      • Given point, "y varies directly with x", & another value, determine equation & missing number
      • Given point, "y varies inversely with x", & another value, determine equation & missing number
      • Determine direct variation equation, multiple choice
      • Given point, "y varies directly with x", & another value, determine equation & missing number, rational numbers
      • Given point & "y varies directly with x & inversely with z", determine equation
      • Given point, "y varies directly with x", & another value, determine missing number
      • Given point, "y varies jointly with x & z", & another value, determine equation
      • Condensed: Determine direct, inverse, joint, or combined variation equations
    • Application of Direct & Inverse Variation
      • Solve word problems involving direct variation 
      • Determine & apply inverse variation equation, real-world context
      • Solve word problems involving joint variation
      • Solve word problems involving combined variation
  • 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
    • Application of Sequences
      • Given table, determine difference in terms in arithmetic sequence, real-world context
      • Identify arithmetic & geometric sequences & determine common difference or common ratio
      • 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
    • Finite Geometric Series
      • Determine sum of finite geometric series
      • Determine sum of finite geometric series, real-world context
  • Data Analysis
    • Samples & Populations
      • Identify samples & populations
      • Identify biased samples & questions
      • Determine sample spaces
      • Identify statistical questions
      • Identify variables of interest
      • Identify statistical inferences
      • Condensed: Identify samples, populations, variables of interest, & statistical inferences
      • Identify experiments & observational studies
      • Identify systematic, cluster, stratified, & simple random samples
      • Identify simulations used to acquire simple random samples
      • Identify simulations to model probability events
      • Identify descriptive & inferential statistics
    • Probability
      • Addition Rule
        • Given visual model, determine "or" probability
        • Given visual model, determine "or" probability as fraction, decimal, or percent
        • Determine "or" probabilities as fractions 
        • Determine "or" probabilities as fractions, decimals, or percents
        • Determine "or" probabilities
        • Determine "or" probabilities
        • Determine "or" probabilities, including "and" situations
      • Multiplication Rule
        • Given visual model, determine "and" probability as fraction, decimal, or percent, dependent events
        • Determine probabilities of flipping coins & rolling die
        • Determine probabilities of flipping coins specified number of times
        • Determine "and" probabilities, independent events, visuals provided
        • Determine "and" probabilities, independent events, same sample space
        • Determine "and" probabilities, independent events, two distinct sample spaces
        • Determine "and" probabilities, dependent events, multiple choice
        • Determine "and" probabilities, dependent events
        • Determine "and" probabilities, independent & dependent events
        • Determine "and" probabilities, independent & dependent events, including complementary events
      • Conditional Probability
        • Determine conditional probabilities from two-way frequency tables
        • Determine conditional probabilities, including two-way frequency tables
    • Permutations
      • Given visual model, determine permutations, specified items predetermined
      • Determine permutation of letters in word, nondistinct letters
      • Determine permutation of letters in word, distinct letters
      • Condensed: Determine permutation of letters in word, including nondistinct letters
      • Determine permutations, one nondistinct item, real-world context
      • Determine permutations, multiple nondistinct items, real-world context
      • Determine permutations using all items, real-world context
      • Determine permutations, real-world context
    • Combinations
      • Given lists, determine combinations, choose from one list, real-world context
      • Given lists, determine combinations, choose from two lists, real-world context
      • Determine number of combinations using fundamental counting principle, real-world context
      • Determine number of combinations using fundamental counting principle, including repeated letters & digits, real-world context
      • Determine combinations, real-world context
    • Determine z-Score & Probability
      • Given mean & standard deviation, determine z-score, real-world context
      • Given z-score, determine probability
      • Given mean, determine z-score & probability, real-world context
      • Given proportion, determine z-score & probability, real-world context
      • Condensed: Given mean or proportion, determine z-score & probability, real-world context
    • Confidence Intervals
      • Determine margin of error for confidence interval
      • Given sample data, estimate population mean using confidence intervals
      • Given sample data, estimate population proportion using confidence intervals
      • Condensed: Given sample data, estimate population proportion or mean using confidence intervals
    • Normal Distributions
      • Determine Test Statistic or Hypotheses, One Mean or Proportion
        • Determine test statistics, one mean
        • Determine test statistics, one proportion
        • Condensed: Determine test statistics, one mean or proportion
        • Identify hypotheses for hypothesis test, one mean
        • Identify hypotheses for hypothesis test, one proportion
        • Condensed: Identify hypotheses for hypothesis test, one mean or proportion
      • Determine Test Statistic or Hypotheses, Two Means or Proportions
        • Determine test statistics, two means
        • Determine test statistics, two proportions
        • Condensed: Determine test statistics, two means or proportions
        • Identify hypotheses for hypothesis test, two means
        • Identify hypotheses for hypothesis test, two proportions
        • Condensed: Identify hypotheses for hypothesis test, two means or proportions
      • Steps in Hypothesis Testing, One Mean or Proportion
        • Identify & determine hypothesis test steps, one mean
        • Identify & determine hypothesis test steps, one proportion
        • Condensed: Identify & determine hypothesis test steps, one mean or proportion
        • Determine critical z-score & p-value
      • Steps in Hypothesis Testing, Two Means or Proportions
        • Identify & determine hypothesis test steps, two means
        • Identify & determine hypothesis test steps, two proportions
        • Condensed: Identify & determine hypothesis test steps, two means or proportions
      • Determine Conclusions
        • Determine conclusion from statistical summaries
        • Given critical z-score & test statistic, determine conclusion for null hypothesis
      • Identify hypotheses for hypothesis test, one mean
      • Identify hypotheses for hypothesis test, one proportion
      • Condensed: Identify hypotheses for hypothesis test, one mean or proportion
      • Identify hypotheses for hypothesis test, two means
      • Identify hypotheses for hypothesis test, two proportions
      • Condensed: Identify hypotheses for hypothesis test, two means or proportions
      • Determine test statistics, one mean
      • Determine test statistics, one proportion
      • Determine test statistics, two proportions
      • Condensed: Determine test statistics, one mean or proportion
      • Determine critical z-score & p-value
      • Given critical z-score & test statistic, determine conclusion for null hypothesis
      • Determine test statistics, two means
      • Identify & determine hypothesis test steps, two means
      • Condensed: Identify & determine hypothesis test steps, two means or proportions
      • Identify & determine hypothesis test steps, two proportions
      • Identify & determine hypothesis test steps, one proportion
    • Regression
      • Determine linear regression equations, calculator expected
      • Determine exponential regression equations, calculator expected
      • Determine quadratic regression equations, calculator expected
      • Given table, use technology to determine radical equation
      • Given regression equation, determine predicted value
  • Trigonometry
    • Graphing Trigonometric Functions
      • Given graph or equation, determine amplitude of trig function
      • Given graph or equation, determine midline of trig function
      • Given graph or equation, determine period of trig function
      • Condensed: Given graph or equation, determine characteristics of trig function
      • Determine graph of trig functions, sin, one transformation
      • Determine graph of trig functions, sin, multiple transformations
      • Determine graph of trig functions, cos, one transformation
      • Determine graph of trig functions, cos, multiple transformations
      • Determine graph of trig functions, tan & cot
      • Determine graph of trig functions, sec & csc
      • Identify trigonometric functions to model periodic data, real-world context
    • Trigonometric Ratios
      • Identify definitions of trig functions
      • Given right triangle, determine missing side & trig ratio, sin, cos, & tan
      • Given right triangle, determine missing side & trig ratio, cot, sec, & csc
      • Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
      • Condensed: Given right triangle, determine missing side & trig ratio
    • Trigonometric Identities
      • Determine missing steps in proofs of Pythagorean identities
    • Given graph or equation, determine period of trig function
    • Given graph or equation, determine midline of trig function
    • Given graph or equation, determine amplitude of trig function
    • Condensed: Given graph or equation, determine characteristics of trig function
    • Determine graph of trig functions, sin, one transformation
    • Determine graph of trig functions, sin, multiple transformations
    • Determine graph of trig functions, cos, one transformation
    • Determine graph of trig functions, cos, multiple transformations
    • Determine graph of trig functions, tan & cot
    • Determine graph of trig functions, sec & csc
    • Identify trigonometric functions to model periodic data, real-world context
    • Identify definitions of trig functions
    • Given right triangle, determine missing side & trig ratio, sin, cos, & tan
    • Given right triangle, determine missing side & trig ratio, cot, sec, & csc