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Math 2 Skills

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  • Algebra Foundations
    • Classifying Rational & Irrational Numbers
      • Classify numbers as rational or irrational
      • Classify rational numbers by definitions
      • Classify rational numbers using graphic organizers
      • Classify rational numbers, including graphic organizers
      • Determine result of adding & multiplying rational & irrational numbers
    • Ordering & Comparing Irrational Numbers
      • Estimate irrational values
      • Estimate irrational values, including negatives
      • Estimate irrational values, multiple terms or factors
      • Estimate irrational values, including cube roots & number line representations
      • Order irrational numbers
      • Compare irrational numbers
      • Condensed: Compare & order irrational numbers
  • Rational Exponents & Radicals
    • Rational Exponents
      • Convert from radical to rational exponent, single value in radicand
      • Convert from radical to rational exponent, algebraic term in radicand
      • Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
      • Simplify radical expression raised to power that is multiple of index
      • Condensed: Convert from radical to rational exponent
      • Simplify rational exponent expressions using power rule, with coefficients
      • Condensed: Simplify rational exponents using product & power rules
      • Condensed: Evaluate rational exponent expressions
      • Convert from rational exponent to radical, single value base
      • Convert from rational exponent to radical, algebraic base
      • Condensed: Convert from rational exponent to radical
    • Properties of Exponents
      • Simplify rational exponent expressions using power rule, no coefficients
      • 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
      • Simplify rational exponent expressions using quotient rule, no coefficients
      • Simplify rational exponent expressions using quotient rule, with coefficients
      • Create equivalent exponential expressions using exponent properties
    • Evaluating Expressions
      • Evaluate rational exponent expressions, positive exponents
      • Evaluate rational exponent expressions, negative exponents
    • Solving Exponential Expressions
      • Solve equations involving rational exponents, one- or two-step
      • Solve equations involving rational exponents, multi-step
      • Condensed: Solve equations involving rational exponents
      • Solve simple exponential equations
      • Solve exponential equations, common bases given
      • Solve exponential equations, one base reduces to common base
      • Solve exponential equations, both bases reduce to common base
      • Solve exponential equations, no logs required
      • Solve exponential equations, two different bases, no common base possible
      • Solve exponential equations, one variable & one base
    • Radicals
      • Simplify radical expressions, perfect powers
      • Add & subtract radical expressions, one or two variables, simplified radicals
      • Add & subtract radical expressions, one or two variables, radicals to simplify
      • Condensed: Add & subtract radical expressions
      • Multiply radical expressions, numbers & variables
  • Complex Numbers
    • Simplifying Complex Numbers
      • Simplify powers of i
      • Express square roots of negatives using i
      • Simplify imaginary numbers
    • Operations with Complex Numbers
      • Add & subtract complex numbers
      • Add or subtract square roots of negative numbers
      • Multiply complex numbers
      • Multiply square roots of negative numbers
      • Divide complex number by constant
      • Divide complex numbers
      • Condensed: Add, subtract, & multiply square roots of negative numbers
      • Condensed: Multiply & divide complex numbers
      • Condensed: Add, subtract, multiply, & divide complex numbers
      • Square complex numbers
    • Quadratic Equations with Complex Solutions
      • Calculate discriminant, then determine number of real or complex solutions
      • Solve using quadratic formula, complex solutions
      • Factor sum of squares using complex factors
      • Determine complex solutions by factoring sum of squares
      • Determine number of complex & real roots of quadratic functions
      • Solve quadratic equations using square root method, complex solutions
      • Solve quadratic equations, complete the square, integers, a = 1, complex solutions
      • Condensed: Solve quadratic equations, complex solutions
      • Solve quadratic equations, complete the square, integers, a > 1, complex solutions
      • Condensed: Solve quadratic equations, complete the square, integers, 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
      • Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
  • Expressions
    • Interpreting & Identifying Parts of an Expression
      • Identify terms of expressions
      • Classify polynomials by degree
      • Determine degree of polynomials
      • Classify polynomials by degree & number of terms
      • Identify leading coefficient of polynomials
      • Determine degree, leading coefficient, & type of polynomial
      • Condensed: Classify polynomials & identify components of polynomials
      • Determine degree of polynomials, including two variables
      • Identify leading coefficient of polynomials, including two variables
      • Identify polynomial as monomial, binomial, or trinomial, including two variables
      • Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables
    • Rewriting Equivalent Expressions
      • Simplify algebraic expressions, one variable, distribute once & product of two factors
      • Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
      • Simplify algebraic expressions, one variable, distribute once, including rationals
      • Simplify algebraic expressions, one variable, distribute twice
      • Simplify algebraic expressions, two variables, distribute twice
  • Equations & Inequalities
    • Creating & Solving Equations in One Variable
      • Two-Step Equations
        • Solve two-step linear equations, decimal coefficients
        • Solve two-step linear equations, fractional coefficients
        • Solve two-step linear equations, fractional answers
        • 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 
        • Condensed: Solve one- or two-step linear equations, including fractional answers
        • Condensed: Solve one- or two-step linear equations, fractional coefficients
        • Condensed: Solve two-step linear equations
      • Three-Step Equations
        • Solve three-step linear equations involving distribution of decimal multiplier
        • Solve three-step linear equations involving distribution, fractional multiplier cancels if distributed
        • Solve three-step linear equations involving distribution, fractional multiplier doesn't cancel if distributed
        • Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
      • Multi-Step Equations
        • Solve linear equations, distributive property on one side
        • Solve multi-step linear equations
      • Equations with Variables on Both Sides
        • Solve linear equations, binomials on both sides, decimals
        • Solve linear equations, binomials on both sides, fractions
        • Solve linear equations, variables as numerators on both sides
        • Solve linear equations, distributive property on both sides, integers
        • Solve linear equations, distributive property on both sides, rationals
        • Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
        • Solve linear equations, distributive property on both sides, additional term on one side
        • Solve linear equations, including no solution & infinitely many solutions
        • Condensed: Solve linear equations, variables on both sides, rationals
        • Determine equations with variables on both sides, real-world context
        • Determine & solve linear equations with variables on both sides, real-world context
        • Given equation with variables on both sides, identify real-world situation represented by equation
      • Determining Number of Solutions
        • 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
    • Creating & Solving Inequalities in One Variable
      • Basic One-Variable Inequalities
        • Solve & graph two-step inequalities, integers
        • Solve & graph two-step inequalities, decimals
        • Solve & graph two-step inequalities, fractions
        • Solve two-step inequalities, integers
        • Solve two-step inequalities, decimals
        • Solve two-step inequalities, fractions
        • Determine if given value is solution to two-step inequality
        • Condensed: Solve two-step inequalities
        • Condensed: Solve & graph two-step inequalities
      • Application of One-Variable Inequalities
        • Determine inequalities with variables on both sides, real-world context
        • Determine & solve two-step inequalities, less than, real-world context
        • Determine & solve two-step inequalities, greater than, real-world context
        • Given two-step inequality, identify real-world problem modeled by inequality
        • Determine two-step inequalities, rational numbers, including real-world context
        • Given inequality with variable on both sides, identify real-world problem modeled by inequality
    • Creating & Solving Equations & Inequalities in Two or More Variables
      • Direct & Inverse Variation
        • Solve word problems involving joint variation
        • Solve word problems involving combined variation
        • Given point & "y varies directly with x & inversely with z", determine equation
        • Given point, "y varies jointly with x & z", & another value, determine equation
        • Solve word problems involving direct variation 
        • Condensed: Determine direct, inverse, joint, or combined variation equations
      • Graphing Linear Inequalities
        • Given linear inequality, identify correct graph, slope-intercept form
        • 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 graph, identify linear inequality, slope-intercept form
        • Graph systems of three linear inequalities, slope-intercept form
        • Given linear inequality, determine graph, slope-intercept form
        • Graph linear inequalities, various forms
        • Given description & table, graph linear inequality, real-world context
      • Writing & Solving Inequalities
        • Given linear inequality, determine solutions & non-solutions, slope-intercept form
        • Given linear inequality graph, determine solutions & non-solutions
        • Given graph, determine linear inequality
        • Given linear inequality & x-value, determine y-value
        • Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
        • Given graph, determine inequalities in standard form, real-world context
        • Solve linear programming problems, 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
        • Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
        • Condensed: Determine equivalent linear inequalities & graphical solutions
        • Determine rational inequalities, real-world context
    • Solving for Specified Variable
      • 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 for specific variable in mathematical formula
      • Solve for specific variable in scientific formula
    • Solving Systems of Equations
      • Solving Systems of Two Linear Equations
        • Condensed: Given system of linear equations, determine point of intersection, integer coordinates
        • Condensed: Given system of linear equations, determine solution, substitution bias
        • Condensed: Given system of linear equations, identify solution, including real-world context
        • Condensed: Determine systems of linear equations & solutions
        • Condensed: Determine systems of linear equations & solutions, including real-world context
        • Condensed: Given system of linear equations or description, graph system, including real-world context
        • Condensed: Solve or determine system of equations, likely to have same variable isolated
        • Condensed: Solve or determine system of equations, both equations in standard form
        • Determine & justify solutions to systems of linear equations, real-world context
        • Graph systems of linear equations & determine solutions, including real-world context
      • Solving Systems of Three Linear Equations
        • Solve systems of three linear equations using Gaussian elimination
        • Solve systems of three linear equations using substitution
        • Determine system of three linear equations, real-world context
        • Condensed: Solve systems of three linear equations
        • Solve systems of three linear equations using matrices
      • Solving Systems of Linear & Quadratic Equations
        • Identify ordered pair solutions to systems of two equations, one linear & one quadratic
        • Solve systems of two equations, algebraic, one linear & one quadratic
        • Determine system of two equations, one linear & one quadratic
        • Determine reasonableness of solutions to systems of linear & quadratic equations
        • Solve systems of two equations, graphical, one linear & one quadratic
        • Condensed: Solve systems of two equations, one linear & one quadratic
    • Solving Systems of Inequalities
      • Basic System of Inequalities
        • Solve systems of linear inequalities
        • Given graph, determine solution of systems of linear inequalities
        • Determine equivalent systems of linear inequalities & graphical solutions
        • Graph systems of two linear inequalities, slope-intercept form
        • Graph systems of three linear inequalities, slope-intercept form
        • Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
        • Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
        • Given linear system of inequalities graph, identify true statements
        • Given description of system of linear inequalities, identify graph of system
        • Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
      • Application of Systems of Inequalities
        • 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, determine system of linear inequalities in standard form & solution point, real-world context
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
        • Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
  • Functions
    • Domain & Range of Functions
      • Determining Domain & Range of Functions
        • Determine if value is in domain or range, set & table representations
        • Determine restricted domain & range of linear functions
        • Given graph, determine domain & range
        • Determine if value is in domain or range, graphical representations
        • Determine restricted domain & range of quadratic functions
        • Determine asymptotic domain restrictions of rational functions
        • Determine domain & range of rational functions using inequalities, interval notation & set notation
        • Determine domain & range of various functions using various notations
      • Application of Domain & Range of Functions
        • Determine continuous domain & range, real-world context
        • Determine discrete domain & range, real-world context
        • Condensed: Determine domain & range, including real-world context
    • Determining & Justifying Functions
      • 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, mapping representations, no domain & range language
      • Determine functions, multiple representations, including justification, no domain & range language
    • Inverse Functions
      • Determine inverse of linear function
      • Determine inverse of various functions
      • Determine if functions are inverses using composition
      • Determine domain & range of inverse functions
      • Graph function and its inverse
      • Condensed: Given function, determine equation, graph, & domain & range of inverse
      • Determine inverse of quadratic & square root functions
      • Determine inverse of cubic & cube root functions
      • Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions
    • Composition of Functions
      • Determine if functions are inverses using composition
      • Evaluate compositions of functions
    • Comparing Properties of Two Functions
      • Compare rates of changes represented differently
      • Determine whether given table represents linear or exponential function
      • Determine whether given table represents linear, exponential, or quadratic function
      • Compare linear functions represented differently
      • Calculate average rate of change of function from table
      • Calculate average rate of change of function, real-world context
      • Calculate average rate of change of function from graph
      • Condensed: Calculate average rate of change of function
      • Calculate average rate of change of a function from an equation
      • Determine whether given graph represents linear, exponential, or quadratic function
      • Condensed: Determine what function given table or graph represents
    • Interpreting Functions Given Context
      • Determining Function Value
        • Given set or table, determine function value
        • Given graph, determine function value
        • Given linear function, determine function value
        • Given quadratic function, determine function value
        • Condensed: Given graph or linear function, determine function value
        • Condensed: Given linear or quadratic function, determine function value
      • Identifying Functions, Mixed Representations
        • Determine function definition, fill in the blank
        • Determine & justify functions, set representations
        • Determine & justify functions, table representations
        • Identify & determine functions, set & table representations
        • Determine functions, set & table representations
        • Determine functions, mapping representations
        • Determine & justify functions, mapping representations
        • Identify functions using equivalent mapping diagrams & sets of ordered pairs
        • Identify functions, multiple representations, including justification
        • Given relation & additional point, determine functions, multiple representations
        • Condensed: Identify, justify, & determine functions
        • Identify functions, description representations
      • Identifying Functions, Graphical Representations
        • Determine functions, graphical representations
        • Identify & justify functions & non-functions, graphical representations
        • Determine & justify functions, graphical representations
        • Given step graphs, identify functions
    • Building Functions to Model Relationships
      • 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)(#)
    • Graph Mixed Functions
      • Given various functions, identify graph
      • Given graph, identify various functions
  • Absolute Value Functions
    • Absolute Value Equations
      • Solve linear absolute value equations
      • Solve linear absolute value equations, extra constant or coefficient
      • Condensed: Solve linear absolute value equations, including extra constant or coefficient
      • Create linear absolute value equations, real-world context
      • Solve linear absolute value equations, variable on both sides
    • Absolute Value Inequalities
      • 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 inequalities, including extra constant or coefficient
      • Condensed: Solve & graph linear absolute value inequalities, including setup
      • Condensed: Solve & graph linear absolute value inequalities
      • Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
      • Given linear absolute value inequality, determine compound inequality
      • Create linear absolute value inequalities, real-world context
    • Graphing Absolute Value Functions
      • Graph absolute value functions using vertex & intercepts
      • Given absolute value equation, identify description of transformation
      • Graph absolute value functions using all transformations
      • Condensed: Graph absolute value functions using any transformation
    • Transformations of Absolute Value Functions
      • Identify & graph vertical & horizontal shifts of absolute value functions
      • Identify & graph reflections of absolute value functions
      • Identify & graph vertical & horizontal stretches & compressions of absolute value functions
      • Graph absolute value functions using all transformations
      • Given absolute value equation, identify description of transformation
      • Condensed: Graph absolute value functions using any transformation
      • Compare absolute value functions represented differently
    • Key Features of Absolute Value Functions
      • Determine x- & y-intercepts of absolute value functions
      • Determine minimum & maximum of absolute value functions
      • Determine points of intersection of absolute value functions
      • Condensed: Determine graphical attributes of absolute value functions
    • Writing Equation of Absolute Value Functions
      • Given description of transformation, determine absolute value equation
      • Given graph, determine absolute value equation
  • Piecewise Functions
    • Given graph of piece-wise function, determine equation
    • Graph piece-wise functions
  • Quadratic Equations & Inequalities
    • Solving Quadratic Equations
      • Solving Quadratics, Factoring
        • Apply zero product property to solve factored quadratic equations
        • Identify zeros of factored quadratics
        • Determine relationship between zeros & linear factors of quadratic functions
        • Solve quadratic equations using factoring, a = 1, b ≠ 0, |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 = 1, b ≠ 0, c ≤ 40, terms on both sides
        • Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
        • Solve quadratic equations using factoring, |a| ≤ 10, |c| ≤ 40, terms on both sides
        • Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
        • Solve quadratic equations using factoring, perfect square trinomial
        • Solve quadratic equations using factoring, difference of squares
      • Solving Quadratics, Square Root Method
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
        • Solve quadratic equations using square root method, a(cx ± h)^2 + k = #
        • Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
        • Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
        • Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
        • Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
        • Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
        • Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
      • Solving Quadratics, Quadratic Formula
        • Given quadratic equation in standard form, determine discriminant
        • Given quadratic equation in standard form, determine number of solutions
        • Given proportion, solve resulting quadratic equation, b = 0
        • Given proportion, solve resulting quadratic equation, b ≠ 0
        • 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 quadratic equation in standard form, determine exact solutions
        • Given quadratic equation in standard form, determine exact solutions, combine like terms first
      • Solving Quadratics, Completing the Square
        • Solve quadratic equations, complete the square, a = 1, real solutions
        • Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
        • Solve quadratic equations, perfect square trinomial
        • Condensed: Solve quadratic equations, complete the square, real solutions
        • Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
        • Determine constant required to complete the square, a ≥ 1, including fractions
        • Solve quadratic equations, complete the square, a > 1, real solutions
        • Solve quadratic equations, complete the square, integers, a > 1, real solutions
        • Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
        • Condensed: Solve quadratic equations, complete the square, integers, including complex solutions
        • Solve quadratic equations, complete the square, integers, a = 1, real solutions
        • Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
        • Condensed: Solve quadratic equations, complete the square, integers, real solutions
    • Solving Quadratic Inequalities
      • Solve quadratic inequalities, "and" solutions
      • Solve quadratic inequalities, "or" solutions
      • Condensed: Solve quadratic inequalities
  • Quadratic Functions
    • Writing Equations of Quadratic Functions
      • Standard Form
        • Given graph of quadratic function, determine equation
        • Given integer solutions of quadratic equation, determine function in standard form
        • Given zeros of quadratic function, determine quadratic equation with integer coefficients
        • Given rational solutions of quadratic equation, determine function in standard form
        • Given graph of quadratic function, determine equation in standard form
        • Given vertex & point, determine quadratic equation, standard form
        • Given three points in plane, determine quadratic equation
        • Given quadratic equation in vertex form, determine standard form of equation
      • Vertex Form
        • Given vertex & point, determine quadratic equation, vertex form
        • Given quadratic equation in standard form, determine vertex form of equation
        • Given graph of quadratic function, determine equation
        • Given description of transformation, determine quadratic function
        • Given graphical attributes, determine equation of parabola
    • Graphing Quadratic Functions
      • Given quadratic equation, determine graph, b = 0
      • Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
      • 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: Given quadratic equation, determine attributes & graph
    • Transformations of Quadratic Functions
      • Identify & graph vertical & horizontal shifts of quadratic functions
      • Identify & graph reflections of quadratic functions
      • Identify & graph vertical & horizontal stretches & compressions of quadratic functions
      • Given quadratic equation, identify description of transformation
      • Identify descriptions of graphs of quadratic parent functions & transformed functions
      • Graph quadratic functions using all transformations
      • Condensed: Graph quadratic functions using any transformation
      • Compare quadratic functions represented differently
    • Key Features of Quadratic Functions
      • Determining 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
      • Determining Intercepts of Quadratic Functions
        • Determine x-intercept(s) of quadratic functions
        • Determine zero(s) of quadratic functions
        • Determine y-intercept of quadratic functions
        • Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
        • Determine x-intercepts/zeros & y-intercepts of quadratic functions, vertex form
        • Given graph or table of quadratic function, determine x- & y- intercepts
      • Determining Vertex, Axis of Symmetry, & 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 intervals of increase & decrease of quadratic functions
        • Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
        • Determine end behavior of quadratic functions
      • Determining 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 quadratic equation, vertex, & point, graph function & determine attributes
        • Given graph of quadratic function, determine attributes
        • Describe parameter changes to quadratic parent functions
        • Given table, determine attributes of quadratic function, real-world context
        • Condensed: Determine graphical attributes of quadratic functions
        • Condensed: Given graph, equation, or table, determine attributes of quadratic function
        • Determine intervals where quadratic function is positive or negative
    • Modeling with Quadratic Functions
      • Modeling by First Writing Quadratic Function
        • 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 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
      • Modeling by Solving Without Writing Function
        • Determine effects of parameter changes in quadratic relationships, real-world context
        • Given height of dropped object, determine position function & specific time
        • Condensed: Given initial height & velocity of object in vertical motion, determine position function, maximum height, or time to maximum height
        • Condensed: Given initial height & velocity of object in vertical motion, determine position function & specific times
        • Condensed: Given initial height & velocity of object in vertical motion, determine position graph, position function, & specific times
  • Polynomial Expressions
    • Interpreting Polynomials
      • Interpret terms or factors in expressions, including real-world context
    • Adding & Subtracting Polynomials
      • Add binomials & trinomials, degrees zero to two
      • Subtract binomials & trinomials, degrees zero to two
      • Add binomials & trinomials, degrees zero to three
      • Subtract binomials & trinomials, degrees zero to three
      • Condensed: Add or subtract binomials & trinomials
      • Determine sums of polynomials or missing polynomial addends
      • Determine differences of polynomials or missing polynomial subtrahends
      • Condensed: Determine sums or differences of polynomials or missing polynomial operands
      • Add & subtract polynomials to determine expressions for perimeter of various shapes
      • Given polynomial & sum of polynomials, determine missing polynomial
      • Given polynomial & difference of polynomials, determine missing polynomial
      • Determine missing value to make polynomial statement true, addition & subtraction
      • Add & subtract binomials & trinomials, two variables
    • Multiplying Polynomials
      • Multiplying Polynomials Basic
        • Multiply monomial times binomial or trinomial, mixed degrees
        • Multiply monomial times binomial or trinomial, two variables
        • Condensed: Multiply binomial times binomial
        • Multiply binomial times trinomial, mixed degrees
        • Multiply linear binomial times quadratic trinomial
        • Apply binomial theorem to expand (x ± y)^3
        • Multiply monomial times binomial or trinomial, degrees zero to two
        • Multiply binomial times binomial, both degree one
        • Multiply binomial times binomial, mixed degrees
        • Square linear binomial
        • 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
      • Application of Multiplying Polynomials
        • 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
      • Given monomial & binomial or trinomial, multiply or identify missing value
      • Multiply monomial times binomial or trinomial, mixed degrees
      • Multiply monomial times binomial or trinomial, two variables
      • Condensed: Multiply binomial times binomial
      • Determine missing value to make polynomial statement true, multiplication
      • Multiply binomial times trinomial, mixed degrees
      • Multiply linear binomial times quadratic trinomial
      • Apply binomial theorem to expand (x ± y)^3
      • Multiply polynomials to determine expressions for areas of rectangles & triangles
      • Multiply monomial times binomial or trinomial, degrees zero to two
      • Multiply binomial times binomial, both degree one
      • Multiply binomial times binomial, mixed degrees
      • Square linear binomial
    • Dividing Polynomials
      • Divide polynomials, degree three or four by degree one
      • Divide polynomials, degree three or four by degree two
      • Divide polynomials, degree one or two by degree one or two
      • Divide polynomials, divisor supports synthetic division
      • Condensed: Divide polynomials, degree three or four by degree one or two
      • Divide quadratic trinomial by linear binomial, word problem context
      • Condensed: Divide polynomials
      • 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
      • GCF & LCM of Polynomials
        • Determine GCF in polynomials, one variable
        • Determine GCF of two monomials, two variables
        • Determine LCM of two monomials, two variables
        • Condensed: Determine GCF or LCM of two monomials, two variables
        • Determine missing component of GCF
        • Factor GCF in polynomials, one variable
        • Factor GCF in polynomials, including two variables
        • Given GCF & one monomial, identify second monomial
      • Factoring Trinomials
        • Factor quadratic trinomials, a = 1
        • Factor quadratic trinomials, a = 1, b > 0, c > 0
        • Factor quadratic trinomials, a = 1, terms scrambled
        • Factor quadratic trinomials, 1 < a ≤ 10, no GCF
        • Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
        • Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < |c| ≤ 10
        • 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
      • Factoring GCF & Remaining Trinomial
        • Factor GCF in polynomials, degree one or two, one variable
        • Factor GCF & remaining quadratic expression, a = 1, one variable
        • Factor GCF & remaining quadratic expression, a ≥ 1, one variable
      • Factoring Difference of Squares & Perfect Square Trinomials
        • Factor difference of two squares, degree two, one variable, coefficient one
        • Factor difference of two squares, degree two, one variable, terms scrambled
        • Factor difference of two squares, degree two, one variable
        • Factor difference of two squares, two variables
        • Factor perfect square trinomials, degree two, one variable
        • Factor perfect square trinomials, degree two, two variables
        • Condensed: Factor perfect square trinomials, degree two
        • Factor difference of two squares, one or two variables
        • Condensed: Factor difference of two squares, degree two
        • Factor perfect square trinomials, fraction coefficients
      • Factoring Common Binomial
        • Factor common binomial
        • Factor binomial & its opposite
      • Factoring Cubic Polynomials
        • Factor cubic polynomial by grouping, one variable
        • Factor cubic polynomial by grouping & difference of two squares, one variable
        • Factor sum & difference of two cubes, degree three, one variable
        • Condensed: Factor sum & difference of two cubes, degree three
        • Factor sum & difference of two cubes, degree three, two variables
        • Factor sum & difference of two cubes, degree six, one variable
        • Factor sum & difference of two cubes, degree six, two variables
        • Condensed: Factor sum & difference of two cubes, degree six
      • Determining Factors of Polynomials
        • Determine linear factors of polynomials, degree three
        • Determine linear factors of polynomials, degree four
        • Condensed: Determine linear factors of polynomials, degree three or four
        • Determine quadratic factors of polynomials, degree four
        • Determine maximum number of roots for polynomial function
    • Graphing Polynomials
      • Given table, determine attributes of polynomial function
      • Determine x-intercepts/zeros & y-intercepts of polynomial functions
      • Determine end behavior of polynomial functions
      • Given equation, graph polynomial function
      • Determine points of intersection of two polynomial functions
      • Determine zeros of polynomials & their multiplicities
      • Determine intervals of increase & decrease of polynomial functions
      • Given graph, determine equation of polynomial function
      • Determine minimum & maximum of polynomial functions
  • Exponential Functions & Models
    • Interpreting Exponential Models
      • Interpret values in exponential functions, real-world context
      • 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
      • Determine exponential function, real-world context
    • Solving Exponential Models
      • Given graph, identify solution to exponential equation
      • Calculate investment value, annual compounding
      • Calculate investment value, various compounding
      • Calculate depreciating asset value, annual compounding
      • Condensed: Calculate investment & depreciating asset values, annual compounding
    • Writing Exponential Functions
      • Given table, determine exponential growth function
      • Given table, determine exponential decay function
      • Given table, determine linear or exponential growth function
      • Given graph, determine equation of exponential function
    • Graphing Exponential Functions
      • Given equation, graph exponential function
      • Given exponential growth function, determine graph
      • Given exponential growth function, determine graph, includes fractional coefficients
      • Given exponential growth or decay function, determine graph, includes fractional coefficients
      • Given equation, graph exponential function, including base e
      • Compare exponential functions represented differently
    • Transformations of Exponential Functions
      • Identify & graph vertical & horizontal shifts of exponential functions
      • Identify & graph reflections 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
      • Graph exponential functions using all transformations
      • Condensed: Graph exponential functions & identify transformations
    • Key Features of Exponential Functions
      • Determining Domain & Range
        • Given equation, determine domain & range of exponential function 
        • Given verbal description & graph, determine domain & range of exponential function 
        • Determine restricted domain & range of exponential functions
        • Determine domain & range of discrete exponential functions, real-world context
      • Determining Attributes
        • Determine x-intercepts/zeros & y-intercepts of exponential functions
        • Determine y-intercept of exponential function, real-world context
        • Given exponential equation, determine asymptote
        • Given graph, determine asymptote of exponential function
        • Determine asymptote of exponential functions
        • Determine asymptote of exponential functions, real-world context
        • Determine minimum & maximum of exponential functions
        • Determine end behavior of exponential functions
        • Given table, determine attributes of exponential function
        • Condensed: Determine graphical attributes of exponential functions
  • Foundations of Geometry
    • Congruence
      • Given geometric figure, identify correct conjecture
      • Identify corresponding parts from congruence statement or determine congruence statement from figures
      • Given congruent triangles, determine values from corresponding parts
      • Given congruent sides, identify congruent angles of isosceles triangle
      • Given congruent angles, identify congruent sides of isosceles triangle
      • Determine angle measures in isosceles trapezoid, using congruent base angles
      • Identify congruent angles or determine angle measures in kites, algebraic expressions
      • Identify congruence transformations
      • Given congruent figures, identify description of transformations
      • Determine missing steps in proofs involving angles
      • Determine missing steps in proofs involving segments
      • Determine missing steps in proofs involving parallel lines
    • Similarity
      • Triangle Similarity
        • Determine segment lengths in triangles with angle bisectors
        • Determine segment lengths using triangle proportionality theorem
        • Determine angles of similar triangles using AA similarity
        • Determine sides of similar triangles using AA similarity
        • Determine similarity of triangles using AA similarity
        • Determine angles of similar triangles using AA similarity, algebraic expressions
        • Determine parts using similar triangles, including real-world context
        • Determine similar triangles using SAS similarity
        • Determine similar triangles using SSS similarity
        • Condensed: Determine similar triangles using SAS or SSS similarity
        • Determine missing steps in proofs involving similar triangles
        • Determine missing steps in proofs involving similar triangles, paragraph form
        • Given right triangle with altitude from right angle, identify similar triangles 
      • Similar Figures
        • Identify similar polygons
        • Given similar figures, identify proportion of side lengths
        • Given similar figures, identify proportion of side lengths, image orientations differ
        • Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
        • Identify corresponding parts of similar figures
        • Determine dimensions in similar figures, whole number dimensions
        • Determine dimensions in similar figures
        • Determine dimensions using similar figures & indirect measurements
        • Given similar figures, identify description of transformations
        • Given three parallel lines with two transversals, determine lengths
        • Determine edge, surface area, or volume of similar solids
    • Scale Factor
      • Scale Factor Determine Dimension, Perimeter or Area
        • Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
        • Determine scale factor or perimeter of dilated figures
        • Determine scale factor or area of dilated figures
        • Determine variable scale factor or variable measurement of dilated figures
        • Given similar squares, determine area & side length
        • Given similar rectangles, determine perimeter
        • Given similar triangles, determine perimeter
        • Given similar triangles, determine area
        • Given similar cones, determine surface area
        • Given scale factor, determine dimension
        • Condensed: Determine or apply scale factor between circles
        • Given similar squares, determine perimeter & side length
        • Given similar rectangles, determine area
        • Given similar cones, determine volume
        • Given similar pyramids, determine surface area
        • Given similar prisms, determine surface area
        • Given similar spheres, determine volume
        • Given similar pyramids, determine volume
        • Given similar prisms, determine volume
        • Given similar cylinders, determine volume
        • Given similar cylinders, determine surface area
        • Condensed: Given similar 2D figures, determine area or perimeter
        • Given similar spheres, determine surface area
        • Condensed: Given similar 3D figures, determine surface area or volume
      • Scale Factor Determine Coordinates
        • Condensed: Given scale factor, determine coordinates of image
        • Given scale factor, determine coordinates of image, pre-image not centered at origin
        • Given scale factor, determine coordinates of image, pre-image centered at origin
      • Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
      • Determine scale factor or perimeter of dilated figures
      • Determine scale factor or area of dilated figures
      • Determine variable scale factor or variable measurement of dilated figures
      • Given similar squares, determine area & side length
      • Given similar rectangles, determine perimeter
      • Given similar triangles, determine perimeter
      • Given similar triangles, determine area
      • Given similar cones, determine surface area
      • Given scale factor, determine coordinates of image, pre-image centered at origin
      • Given scale factor, determine dimension
      • Given scale factor, determine coordinates of image, pre-image not centered at origin
      • Condensed: Given scale factor, determine coordinates of image
      • Condensed: Determine or apply scale factor between circles
    • Two- & Three-Dimensional Objects
      • Two-Dimensional Objects
        • Classify quadrilaterals shapes based on attributes
        • Classify polygons using graphic organizers
        • Classify polygons using graphic organizers, including types of triangles
        • Classify polygons based on number of sides or relationship to other shapes
        • Classify polygons based on angles & parallel or perpendicular lines
        • Classify 2D figures
      • Three-Dimensional Objects
        • Classify 3D figures
        • Identify 3D figures & their bases
        • Determine cross sections of prisms
        • Determine cross sections of pyramids
        • Determine cross sections of cylinders
        • Determine cross sections of 3D figures
        • Condensed: Determine cross sections of cylinders, pyramids, & cones
        • Determine 2D orthographic representation of 3D blocks
        • Determine 3D figures from rotations of 2D figures
    • Circumference & Area of a Circle
      • Identify approximate formulas for circumference & area of circles
      • Determine circumference of circle, exact answers, multiple choice, including real-world context
      • Given radius or diameter, determine circumference
      • Given circumference of circle, determine radius or diameter
      • Estimate diameter or circumference & identify equations using π
      • Given radius or diameter, determine area
      • Determine area of circle, exact answers, including real-world context
      • Given area of circle, determine radius or diameter
      • Given radius or diameter, determine area or circumference
      • Condensed: Given area or circumference of circle, determine radius or diameter
      • Condensed: Determine area or circumference of circle
      • Determine areas of semicircles & quarter circles
    • Volume
      • Cylinder Volume
        • Determine volume of cylinders
        • Given volume, determine dimension of cylinder
        • Given base area & height, determine volume of cylinder
      • Pyramid Volume
        • Determine volume of pyramids
        • Given volume, determine dimension of pyramid
      • Cone Volume
        • Determine volume of cones
        • Given volume, determine dimension of cone
      • Sphere Volume
        • Determine volume of spheres
        • Determine volume or radius of spheres
        • Given volume, determine radius, diameter, or surface area of sphere
      • Mixed Figure Volume
        • Determine volume of composite figures, cylinders & cones
        • Determine volume of cylinders, cones, & spheres, including real-world context
        • Identify relationship between volume of cone & cylinder with same base & height
    • Surface Area
      • Determine surface area of pyramids
    • Triangle Relationships
      • Perpendicular & Angle Bisectors
        • Given perpendicular bisector in triangle, determine segment lengths 
        • Given angle bisector in triangle, determine angles 
        • Given perpendicular bisector in triangle, determine segment lengths, algebraic expressions
        • Given angle bisector in triangle, determine angles, algebraic expressions
        • Condensed: Given perpendicular or angle bisector in triangle, determine segment lengths or angles, including algebraic expressions
      • Median & Midsegment Theorem
        • Given median of triangle, determine variable or length of bisected side, algebraic expressions
        • Apply triangle midsegment theorem to determine segment lengths
        • Apply triangle midsegment theorem to determine perimeter
        • Apply triangle midsegment theorem to determine segment lengths, algebraic expressions
      • Centroid & Hinge Theorem
        • Apply centroid theorem
        • Determine coordinates of centroid of triangles
        • Apply hinge theorem
      • Triangle Theorems
        • Apply triangle theorems or determine missing steps in proofs
        • Apply triangle inequality theorem to determine side lengths
        • Determine missing steps in proofs involving triangles
        • Determine missing steps in proofs involving isosceles triangles
    • Proving Geometric Theorems Using Coordinates
      • Identify or determine parallelograms in coordinate plane
      • Identify congruent angles or determine angle measures in kites, algebraic expressions
      • Determine angle measures in isosceles trapezoid, using congruent base angles
  • Circles & Conic Sections
    • Circle Basics
      • Identify components of circles
      • Apply arc addition postulate to determine arc measures
      • Apply arc addition postulate to determine arc measures, including algebraic expressions
      • Determine relationship between congruent arcs & congruent central angles
    • Similarity Ratios
      • Given two circles, determine scale factor or missing dimension
      • Given two circles, determine scale factor of area or missing area
    • Arc Length & Area of Sector
      • Given arc measure & radius, determine arc length
      • Given arc length & radius, determine central angle
      • Given chord & radius, determine length
      • Given two chords of circle, determine length
      • Given arc length & central angle, determine circumference
      • Condensed: Determine circumferences, arc lengths, & central angles
      • Determine area of sector
    • Properties of Inscribed Angles, Radii, & Chords
      • Given central angle or arc measure, determine inscribed angle
      • Given inscribed angle, determine central angle & arc measure
      • Given inscribed angle formed by chord & tangent, determine angle or arc measure
      • Given intersecting chords, determine angle or arc measure
      • Given two diameters, radius, & two angles, determine angle or arc measure
      • Condensed: Determine inscribed angles, central angles, & arc measures
      • Determine relationship between congruent chords & congruent central angles
      • Determine relationship between congruent chords & congruent arcs
    • Inscribed & Circumscribed Figures
      • Determine angles of quadrilateral inscribed in circle, including algebraic expressions
      • Given inscribed isosceles triangle, determine base angle
      • Given isosceles triangle in circle, determine angle or arc measure
      • Given isosceles triangle in circle, determine angle measure at vertex of triangle
      • Given inscribed isosceles triangle or isosceles triangle in circle, determine angle or arc measure
      • Given inscribed isosceles triangle, determine measure of arc intercepted by base of triangle
      • Given inscribed right triangle, determine inscribed angle or arc measure 
      • Given inscribed right triangle & tangent, determine angle or arc measure
      • Condensed: Given inscribed right triangle, determine angle or arc measure
    • Properties of Secants & Tangents
      • Given Secants & Tangents Determine Angles
        • Given two tangents to circle, determine angle
        • Given secant & tangent to circle, determine angle
        • Given two secants intersecting outside circle, determine angle
        • Given two secants intersecting inside circle, determine angle
        • Given one chord & one secant of circle, determine angle
        • Given tangent & secant intersecting at point of tangency, determine angles
        • Given tangent & other segments, determine angle
        • Condensed: Given secants, tangents, & chords, determine angles
        • Given chord, secant, & tangent on same circle, determine angles & arcs
      • Given Secants & Tangents Determine Lengths
        • Given secant & tangent to circle, determine length
        • Given two secants of circle, determine length, including algebraic expressions
        • Given tangents to circles, determine lengths, algebraic expressions
        • Given secants, tangents, & chords, determine length
        • Given tangent & other segments or circle inscribed in polygon, determine lengths
    • Area of Circular Segments
      • Given radius & arc measure of 60°, 90°, or 120°, determine area of circular segment
      • Given chord length & arc measure of 60°, 90°, or 120°, determine area of circular segment
      • Given radius & arc measure, determine area of circular segment
      • Determine areas of circular segments
      • Given chord length & arc measure, determine area of circular segment
    • Equations of Circles
      • Given equation of circle, identify center & radius
      • Given center & radius, determine equation of circle
      • Given graph, determine equation of circle
      • Given equation of circle in standard form, identify graph
      • Given equation of circle, determine area
      • Given equation of circle in general form, determine standard form 
      • Condensed: Determine circle equations, centers, radii, & areas
      • Complete the square & graph, circle equations
    • Equations of Parabolas
      • Given vertex & point, determine quadratic equation, vertex form
      • Given vertex & point, determine quadratic equation, standard form
      • Given focus & directrix of parabola, determine equation
      • Given focus & directrix of parabola, determine equation in standard form
    • Equations of Circles & Parabolas
      • Condensed: Complete the square & graph, circle & parabola equations
  • Trigonometry
    • Pythagorean Theorem Calculations & Proofs
      • Determine Pythagorean triples
      • Given triangle with algebraic expressions, apply Pythagorean theorem to determine side
      • Classify triangles using Pythagorean inequality theorem
      • Apply Pythagorean theorem to find length in kite
      • Given ratio of sides & one dimension, apply Pythagorean theorem to determine specified dimension, real-world context
    • Trigonometric Ratios
      • Given special right triangle, determine trig function value, sin, cos, & tan
      • Given special right triangle, determine trig function value, cot, sec, & csc
      • Given right triangle, determine trig ratio, sin, cos, & tan
      • Given right triangle, determine angle, real-world context
      • Condensed: Given right triangle, determine sides or angles, real-world context
      • Given right triangle, determine trig ratio, cot, sec, & csc
      • Condensed: Given right triangle, determine trig ratio
      • Given sine, cosine, or tangent & quadrant, determine trig function values
      • Determine missing steps in proofs of Pythagorean identities
      • Given right triangle, determine missing side & trig ratio, sin, cos, & tan
      • Given right triangle, determine missing side & trig ratio, cot, sec, & csc
      • Identify definitions of trig functions
      • Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
      • Condensed: Given right triangle, determine missing side & trig ratio
    • Special Right Triangles
      • 45-45-90 Triangles
        • Given 45-45-90 triangle, determine hypotenuse
        • Given 45-45-90 triangle, determine leg
        • Given 45-45-90 triangle, determine side
      • 30-60-90 Triangles
        • Given 30-60-90 triangle & short leg, determine long leg
        • Given 30-60-90 triangle & short leg, determine hypotenuse
        • Given 30-60-90 triangle & long leg, determine short leg
        • Given 30-60-90 triangle & long leg, determine hypotenuse
        • Given 30-60-90 triangle & hypotenuse, determine short leg
        • Given 30-60-90 triangle & hypotenuse, determine long leg
        • Given 30-60-90 triangle, determine side
      • Mixed Special Right Triangles
        • Condensed: Given special right triangle, determine trig function value
        • Condensed: Given special right triangle, determine side
        • Condensed: Determine angles or sides using special right triangle relationships, real-world context
      • Given 45-45-90 triangle, determine hypotenuse
      • Given 45-45-90 triangle, determine leg
      • Given 45-45-90 triangle, determine side
      • Given 30-60-90 triangle & short leg, determine long leg
      • Given 30-60-90 triangle & short leg, determine hypotenuse
      • Given 30-60-90 triangle & long leg, determine short leg
      • Given 30-60-90 triangle & long leg, determine hypotenuse
      • Given 30-60-90 triangle & hypotenuse, determine short leg
      • Given 30-60-90 triangle & hypotenuse, determine long leg
      • Given 30-60-90 triangle, determine side
      • Condensed: Given special right triangle, determine trig function value
      • Condensed: Given special right triangle, determine side
      • Condensed: Determine angles or sides using special right triangle relationships, real-world context
    • Solving Right Triangles
      • Determining Trigonometric Values
        • Determine trig function values, degrees, calculator expected
        • Determine trig function values, radians, calculator expected
        • Condensed: Determine trig function values, calculator expected
      • Solving Sides of Right Triangles
        • Determine leg of right triangle using sine
        • Determine hypotenuse of right triangle using sine
        • Given side & angle, determine specified side using sine
        • Determine leg of right triangle using cosine
        • Determine hypotenuse of right triangle using cosine
        • Given side & angle, determine specified side using cosine
        • Given short leg of right triangle, determine long leg using tangent
        • Given long leg of right triangle, determine short leg using tangent
        • Given side & angle, determine specified side using tangent
        • Condensed: Given side & angle, determine specified side using sine, cosine, or tangent
      • Solving Angles of Right Triangles
        • Given hypotenuse & leg of right triangle, determine angle using arcsine
        • Given hypotenuse & leg of right triangle, determine angle using arccosine
        • Given legs of right triangle, determine angle using arctangent
        • Given sides of triangle, determine angle using arcsine, arccosine, or arctangent
    • Sine & Cosine of Complementary Angles
      • Determine equivalent trig cofunction values, sin & cos
      • Determine equivalent trig cofunction values, sec & csc
      • Determine equivalent trig cofunction values, tan & cot
      • Condensed: Determine equivalent trig cofunction values
      • Determine equivalent trig cofunction values from triangles
    • Modeling with Right Triangles
      • Given legs of right triangle, determine angle using arctangent, real-world context
      • Given right triangle, determine angle, real-world context
      • Determine angles using special right triangle relationships, real-world context
      • Determine sides using special right triangle relationships, real-world context
      • Given right triangle, determine side, real-world context
    • Law of Sines & Cosines
      • Determine sides & angles of triangles using law of sines, real-world context
      • Determine sides & angles of triangles using law of cosines, real-world context
      • Condensed: Determine sides & angles of triangles using law of sines or law of cosines, real-world context
      • Determine angles of triangles using law of sines
      • Condensed: Determine sides & angles of triangles using law of sines
  • Probability
    • Sample Space
      • Determine sample spaces
      • Determine size of sample spaces, compound events
      • Determine sample spaces, compound events
      • Determine sample size, various representations
      • Identify experiments & observational studies
      • Identify systematic, cluster, stratified, & simple random samples
    • Combinations & Permutations
      • Combinations
        • 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
        • Given lists, determine combinations, choose from one list, real-world context
        • Given lists, determine combinations, choose from two lists, real-world context
      • Permutations
        • Given visual model, determine permutations, specified items predetermined
        • Determine permutations using all items, real-world context
        • Determine permutations, real-world context
        • Determine permutations, one nondistinct item, real-world context
        • Determine permutations, multiple nondistinct items, real-world context
        • Determine permutation of letters in word, distinct letters
        • Determine permutation of letters in word, nondistinct letters
        • Condensed: Determine permutation of letters in word, including nondistinct letters
      • Combinations & Permutations Combined
        • Determine combinations & permutations, two questions, real-world context
        • Determine combinations & permutations, four questions, real-world context
    • Multiplication Rule
      • Determine probabilities of flipping coins & rolling die
      • Determine probabilities of flipping coins specified number of times
      • Given visual model, determine "and" probability as fraction, decimal, or percent, dependent events
      • Determine "and" probabilities, independent events, visuals provided
      • Determine "and" probabilities, independent events, two distinct sample spaces
      • Determine "and" probabilities, independent events, same sample space
      • Determine "and" probabilities, dependent events
      • Determine "and" probabilities, dependent events, multiple choice
      • Determine "and" probabilities, independent & dependent events
      • Determine "and" probabilities, independent & dependent events, including complementary events
    • Addition Rule
      • Determine "or" probabilities
      • Determine "or" probabilities as fractions 
      • Determine "or" probabilities as fractions, decimals, or percents
      • Given visual model, determine "or" probability
      • Given visual model, determine "or" probability as fraction, decimal, or percent
    • Two-Way Frequency Tables
      • Interpret two-way frequency tables, conditional distribution 
      • Interpret two-way frequency tables, joint distribution 
      • Interpret two-way frequency tables, marginal distribution 
      • Given two-way frequency tables, identify associations
      • Determine two-way frequency tables
      • Condensed: Interpret two-way frequency tables
      • Determine specified probabilities in two-way frequency tables
      • Determine conditional probabilities from two-way frequency tables
      • Determine conditional probabilities, including two-way frequency tables
    • Simulations
      • Identify simulations used to acquire simple random samples
      • Identify simulations to model probability events
    • Using Probability to Make Predictions
      • Determine predicted values, theoretical probability
      • Determine predicted values, experimental probability
      • Determine predicted values, experimental probability, compound events
      • Determine predicted values, theoretical probability, compound events
      • Determine predicted values, experimental or theoretical probability
      • Determine inferences from samples
      • Determine predicted values or compare likelihood of events
  • Rational Functions
    • Compare rational functions represented differently
  • Radical Functions
    • Compare radical functions represented differently