## Math 3 Skills

VIEW ALL SKILLS

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