## Math 2 Skills

VIEW ALL SKILLS

• 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
• 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 â‰  0, |c| â‰¤ 40, zero on one side
• Solve quadratic equations using factoring, |a| â‰¤ 10, b â‰  0, |c| â‰¤ 40, zero on one side
• Solve quadratic equations using factoring, a = 1, b â‰  0, c â‰¤ 40, terms on both sides
• Solve quadratic equations using factoring, 1 â‰¤ a â‰¤ 10, b > 0, 1 â‰¤ c â‰¤ 10, terms on both sides
• Solve quadratic equations using factoring, |a| â‰¤ 10, |c| â‰¤ 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 â‰  Â±1, b = 0, integer or rounded solutions
• Solve quadratic equations using square root method, a(cx Â± h)^2 + k = #
• Condensed: Solve quadratic equations using square root method, (x Â± h)^2 = #, rational solutions
• Condensed: Determine solutions to quadratic equations, a â‰  Â±1, b = 0
• Solve quadratic equations using square root method, (x Â± h)^2 = #, rational solutions
• Solve quadratic equations using square root method, (cx Â± h)^2 = #, rational solutions
• Solve quadratic equations using square root method, (x Â± h)^2 + k = #, rational solutions
• Solve quadratic equations using square root method, a(x Â± h)^2 = #, rational solutions
• Solve quadratic equations using square root method, a(x Â± h)^2 + k = #, rational solutions
• Solve quadratic equations using square root method, a(cx Â± h)^2 + k = #, rational solutions
• 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 â‰  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 â‰¥ 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
• 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 â‰  Â±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 Â± 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 Â± 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 â‰¤ 10, no GCF
• Factor quadratic trinomials, 1 â‰¤ a â‰¤ 10, 0 < c â‰¤ 10
• Factor quadratic trinomials, 1 â‰¤ a â‰¤ 10, 0 < |c| â‰¤ 10
• Factor quadratic trinomials, 1 < a â‰¤ 10, 0 < c â‰¤ 30
• Factor quadratic trinomials, 1 < |a| â‰¤ 10, 0 < |c| â‰¤ 30
• Factor quadratic trinomials, 1 < a â‰¤ 30, 0 < c â‰¤ 40
• Factor quadratic trinomials, 1 < |a| â‰¤ 30, 0 < |c| â‰¤ 40
• Condensed: Factor quadratic trinomials, 1 â‰¤ a â‰¤ 10, 0 < c â‰¤ 10 or 0 < |c| â‰¤ 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 â‰¥ 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 Ï€
• 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 60Â°, 90Â°, or 120Â°, determine area of circular segment
• Given chord length & arc measure of 60Â°, 90Â°, or 120Â°, 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
• 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