Math 3 Skills

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  • Functions
    • Combining Functions Using Arithmetic Operations
      • Add functions, (f + g)(x)
      • Subtract functions, (f – g)(x)
      • Multiply functions, (f * g)(x)
      • Divide functions, (f / g)(x)
      • Add function values, (f + g)(#)
      • Subtract function values, (f – g)(#)
      • Multiply function values, (f * g)(#)
      • Divide function values, (f / g)(#)
      • Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)
      • Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
      • Perform operations on functions represented graphically, graphical solution
      • Perform operations on functions represented graphically, numerical solution
    • Composition of Functions
      • Evaluate compositions of functions
      • Determine if functions are inverses using composition
    • Comparing Properties of Functions
      • Determine whether given table represents linear or exponential function
      • Determine whether given table represents linear, exponential, or quadratic function
      • Compare rates of changes represented differently
      • 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 a function from an equation
      • Calculate average rate of change of function from graph
      • Condensed: Calculate average rate of change of function
      • Condensed: Determine what function given table or graph represents
      • Determine whether given graph represents linear, exponential, or quadratic function
    • 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
      • 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
    • Interpreting Features of Functions Through Modeling
      • Interpret & solve problems involving function notation, real-world context
      • Determine discrete domain & range, real-world context
      • Determine graph or information from graph, real-world context
      • Determine continuous domain & range, real-world context
      • Condensed: Determine domain & range, including real-world context
    • Graph Mixed Functions
      • Given various functions, identify graph
      • Given graph, identify various functions
  • Equations & Inequalities
    • Direct & Inverse Variation
      • Solve word problems involving direct 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
      • Condensed: Determine direct, inverse, joint, or combined variation equations
    • Solving Linear Inequalities in Two or More Variables
      • Writing & Solving Inequalities
        • Given linear inequality, determine solutions & non-solutions, slope-intercept form
        • Given linear inequality graph, determine solutions & non-solutions
        • Given linear inequality & x-value, determine y-value
        • Given graph, identify linear inequality, slope-intercept form
        • Given graph, determine linear inequality
        • Given graph, determine inequalities in standard form, 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
        • Solve linear programming problems, real-world context
        • Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
      • Graphing Linear Inequalities
        • Graph linear inequalities, slope-intercept form, only oblique lines
        • Graph linear inequalities, vertical & horizontal lines
        • Graph linear inequalities, slope-intercept form, including vertical & horizontal lines
        • Given linear inequality, identify correct graph, slope-intercept form
        • Given linear inequality, determine graph, slope-intercept form
        • Given description & table, graph linear inequality, real-world context
        • Given description, determine linear inequality in standard form, graph, & determine specific solutions, real-world context
        • Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
        • Graph linear inequalities, various forms
        • Condensed: Determine equivalent linear inequalities & graphical solutions
    • Systems of Equations
      • Solving Systems of Two Linear Equations
        • Condensed: Given system of linear equations, determine solution, substitution bias
        • Condensed: Given system of linear equations, determine point of intersection, integer coordinates
        • Condensed: Solve or determine system of equations, likely to have same variable isolated
      • Solving Systems of Three Linear Equations
        • Solve systems of three linear equations using substitution
        • Condensed: Solve systems of three linear equations
        • Solve systems of three linear equations using Gaussian elimination
        • Determine system of three linear equations, real-world context
        • Solve systems of three linear equations using matrices
      • Solving Systems of One Linear & One Quadratic
        • 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
      • Application of Solving Systems of Equations
        • Determine & justify solutions to systems of linear equations, real-world context
        • Graph systems of linear equations & determine solutions, including real-world context
        • Condensed: Given system of linear equations, identify solution, including real-world context
        • Condensed: Determine systems of linear equations & solutions
        • 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, both equations in standard form
    • Systems of Inequalities
      • Solving Systems of Inequalities
        • Graph systems of two linear inequalities, slope-intercept form
        • Given graph, determine solution of systems of linear inequalities
        • Solve systems of linear inequalities
        • Determine equivalent systems of linear inequalities & graphical solutions
        • Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
        • Given linear system of inequalities graph, identify true statements
        • Given description of system of linear inequalities, identify graph of system
        • Graph systems of three linear inequalities, slope-intercept form
      • Application of Solving 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
        • Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
        • Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, 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
  • 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
      • 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 end behavior of quadratic functions
        • 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
    • Solving Quadratic Functions
      • Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
      • Solve quadratic equations, complete the square, a = 1, real solutions
      • Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
      • 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, real solutions
      • Condensed: Solve quadratic equations, complete the square, integers, real solutions
  • 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
      • Absolute Value Inequalities with Setup
        • Solve & graph linear absolute value inequalities, “and” solutions, including setup
        • Solve & graph linear absolute value inequality, extra coefficient or constant, 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
      • Absolute Value Inequalities without Setup
        • Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
        • Solve & graph linear absolute value inequalities, including extra constant or coefficient
        • Solve & graph linear absolute value inequalities, “and” solutions
        • Solve & graph linear absolute value inequalities, “or” solutions
        • Given linear absolute value inequality, determine compound inequality
        • Create linear absolute value inequalities, real-world context
        • Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
        • Condensed: Solve & graph linear absolute value inequalities
    • 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 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
  • Piecewise Functions
    • Given graph of piece-wise function, determine equation
    • Graph piece-wise functions
    • Graph step functions
    • Given graph of step function, determine equation
    • Condensed: Determine graphs & equations of piece-wise & step functions
  • Complex Numbers
    • Quadratic Equations with Complex Solutions
      • Solve quadratic equations using square root method, complex solutions
      • Determine number of complex & real roots of quadratic functions
      • Given two complex solutions, determine quadratic equation of form x^2 + # = 0
      • Determine complex solutions by factoring sum of squares
      • Factor sum of squares using complex factors
      • Solve using quadratic formula, complex solutions
      • Calculate discriminant, then determine number of real or complex solutions
      • Condensed: Solve quadratic equations, complete the square, 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, including 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
    • Operations with Complex Numbers
      • Square complex numbers
  • Radical Functions
    • Solving Radical Equations
      • Solving Square Root Equations
        • Solve square root equations, square root = square root
        • Solve square root equations, square root = #
        • Solve square root equations, add & subtract from root
        • Solve square root equations, divide by coefficient of root
        • Solve square root equations, square root = x ± #
        • Solve square root equations, square root ± square root = #
        • Solve square root equations, multi-step
        • Condensed: Solve square root equations, one-step & two-step
        • Condensed: Solve square root equations
        • Identify extraneous solutions of square root equations
      • Solving Cube Root Equations
        • Solve cube root equations, cube root = #
        • Solve cube root equations, cube root = cube root
        • Solve cube root equations, cube root = variable
        • Solve cube root equations, multi-step
        • Condensed: Solve cube root equations, one-step & two-step
        • Condensed: Solve square root & cube root equations
    • Graphing Square Root Functions
      • Determine x- and y-intercepts of square root functions
      • Identify & graph vertical & horizontal shifts of square root functions
      • Identify & graph reflections of square root functions
      • Identify & graph vertical & horizontal stretches & compressions of square root functions
      • Determine minimum & maximum of square root functions
      • Given square root equation, identify description of transformations
      • Condensed: Determine graphical attributes of square root functions
      • Graph square root functions using key point & intercepts
      • Graph square root functions using all transformations
      • Condensed: Graph square root functions using any transformation
      • Compare radical functions represented differently
    • Graphing Cube Root Functions
      • Determine x- & y-intercepts of cube root functions
      • Identify & graph vertical & horizontal shifts of cube root functions
      • Identify & graph reflections of cube root functions
      • Identify & graph vertical & horizontal stretches & compressions of cube root functions
      • Determine minimum & maximum of cube root functions
      • Condensed: Determine graphical attributes of cube root functions
      • Graph cube root functions using key points & intercepts
      • Graph cube root functions using all transformations
      • Given cube root equation, identify descriptions of transformations
      • Condensed: Graph cube root functions using any transformation
  • Polynomial Expressions & Functions
    • Basic Polynomials
      • Determine degree of polynomials
      • Identify leading coefficient of polynomials
      • Classify polynomials by degree
      • Identify polynomial as monomial, binomial, or trinomial
      • Classify polynomials by degree & number of terms
      • Determine degree, leading coefficient, & type of polynomial
      • 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: Classify polynomials & identify components of polynomials
      • 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
    • Writing Polynomials in Standard Form
      • Identify terms of expressions
      • Determine standard form of polynomial, no like terms
      • Determine standard form of polynomial, like terms
      • Determine standard form of polynomial, no like terms, including two variables
      • Determine standard form of polynomial, like terms, including two variables
    • 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
      • Add & subtract polynomials to determine expressions for perimeter of various shapes
      • Determine sums of polynomials or missing polynomial addends
      • Given polynomial & difference of polynomials, determine missing polynomial
      • Determine differences of polynomials or missing polynomial subtrahends
      • Given monomial & binomial or trinomial, multiply or identify missing value
      • Condensed: Determine sums or differences of polynomials or missing polynomial operands
      • 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, degrees zero to two
        • Multiply binomial times binomial, both degree one
        • Square linear binomial
        • Condensed: Multiply binomial times binomial
        • Simplify monomial minus product of monomial & binomial or trinomial
      • Multiplying Polynomials, Advanced
        • Multiply monomial times binomial or trinomial, mixed degrees
        • Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
        • Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
        • Multiply binomial times binomial, mixed degrees
        • Multiply binomial times trinomial, mixed degrees
        • Multiply linear binomial times quadratic trinomial
        • Given monomial & binomial or trinomial, multiply or identify missing value
        • Multiply monomial times binomial or trinomial, two variables
        • Apply binomial theorem to expand (x ± y)^3
        • Determine missing value to make polynomial statement true, multiplication
        • Multiply polynomials to determine expressions for areas of rectangles & triangles
        • Condensed: Determine missing value to make polynomial statement true
        • Apply binomial theorem to expand (x ± y)^n, n ≥ 4
        • Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
        • Multiply binomial times binomial, two variables
        • Multiply binomial times trinomial, two variables
        • Condensed: Multiply monomials, binomials, & trinomials, two variables
    • Dividing 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
      • Divide quadratic trinomial by linear binomial, word problem context
      • Identify factors of polynomials
      • Condensed: Divide polynomials
      • Apply remainder theorem
      • Determine missing operation to make polynomial statement true
    • Factoring Expressions with One Variable
      • Factoring GCF
        • Determine GCF in polynomials, one variable
        • Factor GCF in polynomials, one variable
        • Factor GCF & remaining quadratic expression, a = 1, one variable
        • Factor GCF in polynomials, degree one or two, one variable
        • Factor GCF & remaining quadratic expression, a ≥ 1, one variable
      • Factoring Quadratic Trinomials
        • 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
        • 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
        • Factor quadratic trinomials, 1 < a ≤ 10, no GCF
        • Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
      • Factoring by Grouping
        • Factor cubic polynomial by grouping, one variable
        • Factor cubic polynomial by grouping & difference of two squares, one variable
        • Factor common binomial
        • Factor binomial & its opposite
      • Factoring Special Polynomials
        • Factor perfect square trinomials, degree two, one variable
        • Condensed: Factor perfect square trinomials, degree two
        • 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 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 six, two variables
        • Condensed: Factor sum & difference of two cubes, degree six
      • 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
    • Factoring Expressions with Multiple Variables
      • Condensed: Determine GCF or LCM of two monomials, two variables
      • Factor perfect square trinomials, degree two, two variables
      • Factor difference of two squares, one or two variables
      • Factor difference of two squares, two variables
      • Factor GCF in polynomials, including two variables
      • Determine GCF of two monomials, two variables
      • Determine LCM of two monomials, two variables
      • Condensed: Factor perfect square trinomials, degree two
      • Given GCF & one monomial, identify second monomial
      • Determine missing component of GCF
      • Factor sum & difference of two cubes, degree three, two variables
      • Condensed: Factor sum & difference of two cubes, degree three
    • Graphing Polynomial Functions
      • Determine points of intersection of two polynomial functions
      • Given table, determine attributes of polynomial function
      • Determine x-intercepts/zeros & y-intercepts of polynomial functions
      • Determine intervals of increase & decrease of polynomial functions
      • Determine end behavior of polynomial functions
      • Given equation, graph polynomial function
      • Given graph, determine equation of polynomial function
      • Determine zeros of polynomials & their multiplicities
      • Determine minimum & maximum of polynomial functions
      • Condensed: Determine graphical attributes of polynomial functions
      • Given zeros, determine graph of polynomial function
    • Geometric Series
      • Determine formula & specific term of geometric sequences
      • Condensed: Determine formula or specific term of geometric sequences
      • Determine function & specific term for geometric sequences, real-world context
  • Exponential & Logarithmic Expressions & Functions
    • Logarithms Introduction
      • Evaluate log expressions, whole number base
      • Evaluate log expressions, natural log
      • Evaluate log expressions, fractional bases
      • Evaluate log expressions, using change of base
      • Condensed: Evaluate log expressions
    • Converting Between Exponential & Logarithmic Equations
      • Given exponential equation, determine log equation
      • Condensed: Convert between exponential & log equations
      • Given log equation, determine exponential equation
    • Properties of 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
      • Condensed: Expand or condense log expressions
      • Apply product, quotient, & power rules to expand or condense log expressions
    • Solving Exponential Equations, Including Using Logarithms
      • Solve exponential equations, no logs required
      • Solve exponential equations, common bases given
      • Solve exponential equations, two different bases, no common base possible
      • Solve simple exponential equations
      • Solve exponential equations, base e
      • Solve exponential equations, both bases reduce to common base
      • Solve exponential equations, one base reduces to common base
      • Solve exponential equations, one variable & one base
      • Create equivalent exponential expressions using exponent properties
    • Solving Exponential Models
      • Exponential growth & decay, real-world context
      • Calculate investment value, annual compounding
      • Calculate investment value, various compounding
      • Calculate depreciating asset value, annual compounding
      • Condensed: Calculate investment & depreciating asset values, annual compounding
      • Determine exponential function, real-world context
      • Interpret values in exponential functions, real-world context
    • Solving Logarithmic Equations
      • Solve log equations, log = log
      • Solve log equations, 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
      • Determine if solution to logarithmic equation is reasonable
    • Solving Natural Logarithmic Equations
      • Solve natural log equations, ln = ln
      • Solve natural log equations, ln = #
      • Solve natural log equations, ln + ln = #
      • Solve natural log equations, ln – ln = #
      • Condensed: Solve natural log equations
    • Key Features of Exponential Functions
      • Domain & Range of Exponential Functions
        • Determine domain & range of discrete exponential functions
        • Determine domain & range of discrete exponential functions, real-world context
        • Determine restricted domain & range of exponential functions
        • Given verbal description & graph, determine domain & range of exponential function 
        • Given equation, determine domain & range of exponential function 
      • Key Attributes 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 exponential equation, determine asymptote
        • Given graph, determine asymptote of exponential function
        • Determine asymptote of exponential functions, real-world context
        • Determine end behavior of exponential functions
        • Given table, determine attributes of exponential function
        • Condensed: Determine graphical attributes of exponential functions
    • 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
    • Graphing Exponential Functions
      • Given equation, graph exponential function, including base e
      • Given graph, determine equation of exponential function
      • 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 graph, identify solution to exponential equation
      • Given table, determine exponential growth function
      • Given table, determine exponential decay function
      • Compare exponential functions represented differently
    • Key Features of Logarithmic Functions
      • Determine x-intercepts/zeros & y-intercepts of log functions
      • Determine minimum & maximum of log functions
      • Determine asymptote of log functions
      • Determine end behavior of log functions
      • Condensed: Determine graphical attributes of log functions
      • Given table, determine attributes of log function
    • Transformations of Logarithmic Functions
      • Identify & graph vertical & horizontal shifts of log functions
      • Identify & graph reflections 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
      • Condensed: Graph log functions & identify transformations
    • Graphing Logarithmic Functions
      • Given equation, graph log function
      • Given graph, determine equation of log function
  • Rational Expressions & Functions
    • Rational Function Values
      • Identify value that makes rational expression undefined
      • Determine values that make rational expressions undefined
      • Given rational function, determine function value
    • 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
    • Solving Rational Equations
      • Solve equations involving rational exponents, one- or two-step
      • Solve equations involving rational exponents, multi-step
      • Condensed: Solve equations involving rational exponents
      • Solve rational equations, one term each side
      • Solve rational equations, multiple terms on one side
      • Condensed: Solve rational equations
    • Modeling Rational Functions
      • Determine rational equations, real-world context
      • Determine if solution to rational equation is reasonable
      • Determine rational inequalities, real-world context
    • Multiplying & Dividing Rational Expressions
      • Multiply rational expressions
      • Divide rational expressions
      • Condensed: Multiply & divide rational expressions
    • Adding & Subtracting Rational Expressions
      • Add rational expressions
      • Subtract rational expressions
      • Condensed: Add & subtract rational expressions
      • Condensed: Add, subtract, multiply, & divide rational expressions
    • Graphing Rational Functions
      • Graph rational functions
      • Compare rational functions represented differently
  • Foundations of Geometry
    • Two- & Three-Dimensional Figures
      • 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
      • Classify 3D figures
      • Determine cross sections of prisms
      • Determine cross sections of pyramids
      • Determine cross sections of cylinders
      • Determine 3D figures from rotations of 2D figures
      • Condensed: Determine cross sections of cylinders, pyramids, & cones
    • Geometric Modeling
      • Apply concepts of density based on area & volume, real-world context
      • Apply geometric methods to solve design problems, real-world context
      • Describe objects using geometric shapes, measures, & properties
    • Finite Geometric Series
      • Determine sum of finite geometric series
      • Determine sum of finite geometric series, real-world context
  • Circles & Conic Sections
    • Equations of Circles
      • Complete the square & graph, circle equations
    • Equations of Parabolas
    • Equations of Circles & Parabolas
      • Condensed: Complete the square & graph, circle & parabola equations
    • Chords, Tangents, & Secants
      • Given chord, secant, & tangent on same circle, determine angles & arcs
  • Trigonometry
    • Radians & Degrees
      • Convert radians to degrees
      • Convert degrees to radians
      • Condensed: Convert between degrees & radians
      • Determine trig function values, degrees, calculator expected
      • Determine trig function values, radians, calculator expected
      • Condensed: Determine trig function values, calculator expected
    • Solving Right Triangles
      • Determining Trig Values
        • Identify definitions of trig functions
        • 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 trig ratio, cot, sec, & csc
        • Given right triangle, determine missing side & trig ratio, sin, cos, & tan
        • Given right triangle, determine missing side & trig ratio, cot, sec, & csc
        • Condensed: Given right triangle, determine trig ratio
        • Condensed: Given special right triangle, determine trig function value
      • Solving Sides of Right Triangles
        • Given side & angle, determine specified side using tangent
        • Given side & angle, determine specified side using cosine
        • Given side & angle, determine specified side using sine
        • Given short leg of right triangle, determine long leg using tangent
        • Given long leg of right triangle, determine short leg using tangent
        • Determine hypotenuse of right triangle using cosine
        • Determine leg of right triangle using cosine
        • Determine hypotenuse of right triangle using sine
        • Determine leg of right triangle using sine
        • 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
    • Unit Circle
      • Trig Function Values, Degrees
        • Determine trig function values, unit circle, first quadrant, degrees, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, second quadrant, degrees, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, third quadrant, degrees, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, fourth quadrant, degrees, sin, cos, & tan, exact answers
        • Determine sine values, unit circle, degrees, exact answers
        • Determine cosine values, unit circle, degrees, exact answers
        • Determine tangent values, unit circle, degrees, exact answers
        • Determine trig function values, unit circle, axes, degrees, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, degrees, sin, cos, & tan, exact answers
      • Trig Function Values, Radians
        • Determine trig function values, unit circle, first quadrant, radians, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, second quadrant, radians, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, third quadrant, radians, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, fourth quadrant, radians, sin, cos, & tan, exact answers
        • Determine trig function values, unit circle, axes, radians, sin, cos, & tan
        • Determine sine values, unit circle, radians, exact answers
        • Determine cosine values, unit circle, radians, exact answers
        • Determine tangent values, unit circle, radians, exact answers
        • Given arc length & radius, determine radian measure
        • Determine trig function values, unit circle, radians, sin, cos, & tan, exact answers
      • Trig Function Values, Degrees & Radians
        • Determine trig function values, unit circle, cot, csc, & sec, exact answers
        • Determine trig function values, unit circle, sin, cos, & tan, exact answers
    • Solving General Triangles Using Law of Sines & Cosines
      • Determine sides of triangles using law of sines
      • Determine sides of triangles using law of cosines
      • Determine angles of triangles using law of cosines
      • Determine sides or angles of triangles using law of cosines, multiple choice
      • Condensed: Determine sides & angles of triangles using law of 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 area of triangles using sine formula
      • Determine angles of triangles using law of sines
      • Condensed: Determine sides & angles of triangles using law of sines
    • Trigonometric Modeling
      • 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
      • Condensed: Determine angles or sides using special right triangle relationships, real-world context
      • Given legs of right triangle, determine angle using arctangent, real-world context
      • Given right triangle, determine side, real-world context
      • Condensed: Given right triangle, determine sides or angles, real-world context
    • Graphing Trigonometric Functions
      • Given graph or equation, determine amplitude of trig function
      • Given graph or equation, determine period of trig function
      • Given graph or equation, determine midline 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, cos, one transformation
      • Determine graph of trig functions, sin, multiple transformations
      • Determine graph of trig functions, cos, multiple transformations
      • Identify trigonometric functions to model periodic data, real-world context
      • Determine graph of trig functions, tan & cot
      • Determine graph of trig functions, sec & csc
  • Data Analysis & Probability
    • Conditional Probability
      • Determine conditional probabilities from two-way frequency tables
      • Determine conditional probabilities, including two-way frequency tables
    • Interpreting Categorical & Quantitative Data
      • Identify descriptive & inferential statistics
      • 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
    • Making Inferences & Justifying Conclusions
      • Determine inferences from samples
      • Determine expected value & identify conclusion
      • Identify variables of interest
      • Condensed: Identify samples, populations, variables of interest, & statistical inferences
      • Identify statistical inferences
      • Identify samples & populations
    • Using Probability to Make Decisions
      • 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 predicted values or compare likelihood of events
    • Normal Distributions
      • 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
    • Hypothesis Tests
      • Hypothesis Tests, One Mean
        • Identify hypotheses for hypothesis test, one mean
        • Determine test statistics, one mean
        • Identify & determine hypothesis test steps, one mean
      • Hypothesis Tests, Two Means
        • Identify hypotheses for hypothesis test, two means
        • Determine test statistics, two means
        • Identify & determine hypothesis test steps, two means
      • Hypothesis Tests, One Proportion
        • Determine test statistics, one proportion
        • Identify hypotheses for hypothesis test, one proportion
        • Identify & determine hypothesis test steps, one proportion
      • Hypothesis Tests, Two Proportions
        • Determine test statistics, two proportions
        • Identify hypotheses for hypothesis test, two proportions
        • Identify & determine hypothesis test steps, two proportions
      • Hypothesis Tests, Mixed
        • Determine critical z-score & p-value
        • Given critical z-score & test statistic, determine conclusion for null hypothesis
        • Condensed: Identify hypotheses for hypothesis test, one mean or proportion
        • Determine conclusion from statistical summaries
        • Condensed: Determine test statistics, one mean or proportion
        • Condensed: Identify hypotheses for hypothesis test, two means or proportions
        • Condensed: Identify & determine hypothesis test steps, one mean or proportion
        • Condensed: Determine test statistics, two means or proportions
        • Condensed: Identify & determine hypothesis test steps, two means or proportions