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