 ## Algebra 2 Skills

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• Algebra Foundations
• Real Number System & Properties
• Determine relationships between subsets of real numbers
• Determine relationships between subsets of rational numbers
• Determine result of adding & multiplying rational & irrational numbers
• Order real numbers, no exponents
• Order real numbers, positive exponents, percents are whole, including real-world context
• Order real numbers, positive exponents, percents are whole, including real-world context
• Order irrational numbers
• Comparing expressions on given interval
• Compare irrational numbers
• Condensed: Compare & order irrational numbers
• Expressions & Operations
• Evaluating Expressions
• Evaluate expressions for specified value, one variable, two terms
• Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
• Evaluate expressions for specified value, one variable, two terms, multiple operations, including powers of absolute values
• Evaluate expressions for specified values, two variables, two terms
• Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
• Evaluate expressions for specified values, two variables, two terms, one term with three factors
• Evaluate expressions for specified values, two variables, quotient of expressions
• Identify values that solve inequalities, expression on left side
• Identify values that solve inequalities, expression on right side
• Simplifying Expressions, One Variable
• Simplify algebraic expressions, one variable, distribute once, fraction multiplier
• Simplify algebraic expressions, one variable, distribute once, decimal multiplier
• Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
• Simplify algebraic expressions, one variable, distribute once, including rationals
• Simplify algebraic expressions, one variable, distribute once & combine like terms
• Simplify algebraic expressions, one variable, distribute once & product of two factors
• Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
• Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
• Simplify algebraic expressions, one variable, distribute twice
• Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
• Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
• Simplifying Expressions, Two Variable
• Simplify algebraic expressions, two variables, positive integer coefficients
• Simplify algebraic expressions, two variables, distribute twice
• Identifying Equivalent Expressions
• Identify equivalent expressions involving distribution
• Identify equivalent expressions involving distribution, two or more terms
• Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
• Equations
• Solving Equations
• 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
• Condensed: Solve linear equations, variables on both sides or like terms
• Solve linear equations, distributive property & additional term on one side
• Solve linear equations, term minus distributive property on one side
• Solve linear equations, distributive property & additional term on one side & binomial on other side
• Solve linear equations, including no solution & infinitely many solutions
• Condensed: Solve linear equations involving distributive property on one side
• Solve linear equations, distributive property on both sides, rationals
• Solve linear equations, distributive property on both sides, additional term on one side
• Solving for Specified Variable
• Given linear equation of form ay = bx, solve for y
• Given linear equation of form ay = bx + c, solve for y
• Given linear equation of form a + by = cx, solve for y
• Given linear equation in standard form, solve for y
• 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 literal equation for variable
• Solve literal equation for variable, variable may appear twice, linear terms
• Solve for specific variable in mathematical formula
• Solve for specific variable in scientific formula
• Application of Equations
• 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
• Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
• 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
• Literal Equations
• Solve literal equation for variable
• Solve literal equation for variable, variable may appear twice, linear terms
• Determine how change to one variable affects another variable
• Inequalities
• Solving Inequalities Algebraically
• Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
• Given linear inequality & x-value, determine y-value
• Solve linear programming problems, real-world context
• Given description, determine linear inequality in standard form, graph, & determine specific solutions, 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
• Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
• Solving Inequalities Graphically
• 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
• Condensed: Determine equivalent linear inequalities & graphical solutions
• Given description & table, graph linear inequality, real-world context
• Graph linear inequalities, various forms
• Condensed: Graph linear equations or inequalities
• Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
• Solving Inequalities, Given Graph
• Given linear inequality graph, determine solutions & non-solutions
• Given graph, determine linear inequality
• Determine equivalent systems of linear inequalities & graphical solutions
• Condensed: Determine points that are solutions to linear equations or inequalities
• Writing Inequalities
• Given graph, identify linear inequality, slope-intercept form
• Given graph, determine inequalities in standard form, real-world context
• Compound Inequalities
• Solve compound inequalities, “and” solutions, multiple choice
• Solve & graph compound inequalities, “and” solutions
• Solve & graph compound inequalities, “and” solutions, including real-world context
• Solve & graph compound inequalities, “or” solutions
• Condensed: Solve & graph compound inequalities
• Given description, determine compound inequality, graph, & possible solutions
• Given description, determine graph of inequality
• Systems of Equations
• Solving Systems of Equations, Graphing
• Given system of linear equations, determine point of intersection, slope-intercept form
• Given system of linear equations, graph & determine point of intersection, slope-intercept form
• Given system of linear equations, graph system, including tables
• Given description of system of linear equations, graph & determine equations or tables
• Given graph of system of linear equations, determine equations in slope-intercept form
• Given graph of system of linear equations, determine solution, rays on graph to establish pattern
• Solving Systems of Equations, Substitution
• Given system of linear equations with same isolated variable, determine point of intersection, integer coordinates
• Given system of linear equations, determine point of intersection, integer coordinates, one horizontal or vertical & one slope-intercept form
• Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
• Solve systems of linear equations, infinite possibilities or no solution
• Condensed: Given system of linear equations, determine solution, substitution bias
• Determine solutions of linear equations, substitution bias, including given system, real-world context
• Determine systems of linear equations & solutions, substitution bias, real-world context
• Condensed: Solve or determine system of equations, likely to have same variable isolated
• Solve, interpret, or determine systems of linear equations, slope-intercept form, real-word context
• Solve, interpret, or determine systems of linear equations, standard form, real-word context
• Solving Systems of Equations, Elimination
• Given system of linear equations in standard form, determine point of intersection, integer coordinates
• Solve systems of linear equations, multiply at most one equation
• Solve systems of linear equations, multiply one or both equations
• Determine systems of linear equations & solutions, elimination bias, real-world context
• Condensed: Solve or determine system of equations, both equations in standard form
• Solving Systems of Equations, Mixed Methods
• Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
• Determine system of two equations, one linear & one quadratic
• Condensed: Determine systems of linear equations & solutions
• Solve systems of two equations, algebraic, one linear & one quadratic
• Solve systems of two equations, graphical, one linear & one quadratic
• Condensed: Solve systems of two equations, one linear & one quadratic
• Determining Solution to System of Equations
• Given system of linear equations, identify solution or x- or y-value of solution
• Given system of linear equations, identify x- or y-value of solution
• Given system of linear equations, identify solution
• Given tables, determine system of linear equations
• Determine reasonableness of solutions to systems of linear & quadratic equations
• Application of Determining Solution to System of Equations
• Given table representing system of linear equations, determine solution, real-world context
• Given system of linear equations & description, identify solution, real-world context
• Condensed: Given system of linear equations, identify solution, including real-world context
• Determine systems of linear equations & solutions, real-world context
• Determine & justify solutions to systems of linear equations, real-world context
• Condensed: Determine systems of linear equations & solutions, including real-world context
• Given graph of system of linear equations, identify specific domain value, real-world context
• Graph systems of linear equations & determine solutions, including real-world context
• Solving Systems of Equations, Three Equations
• Solve systems of three linear equations using substitution
• Solve systems of three linear equations using Gaussian elimination
• Solve systems of three linear equations using matrices
• Condensed: Solve systems of three linear equations
• Determine system of three linear equations, real-world context
• Systems of Inequalities
• Solving Systems of Inequalities Graphically
• Given graph, determine solution of systems of linear inequalities
• Given linear system of inequalities graph, identify true statements
• Graph systems of two linear inequalities, slope-intercept form
• Condensed: Determine graphs of linear inequalities or system of linear inequalities
• Solve systems of linear inequalities
• Graph systems of three linear inequalities, slope-intercept form
• Given description of system of linear inequalities, identify graph of system
• Application of Solving Systems of Inequalities Graphically
• Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
• 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 & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
• Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
• Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
• Solving Systems of Inequalities Algebraically
• Given description, determine system of linear inequalities in standard form & solution point, 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 & determine solution points, real-world context
• Functions
• Identifying Functions
• Determine functions, set & table representations
• Identify & determine functions, set & table representations
• Determine functions, mapping representations
• Determine functions, graphical representations
• Given step graphs, identify functions
• Identify functions, description representations
• Given relation & additional point, determine functions, multiple representations
• Identifying & Justifying Functions
• Determine & justify functions, set representations
• Determine & justify functions, table representations
• Identify & determine functions, set & table representations
• Determine & justify functions, mapping representations
• Identify functions using equivalent mapping diagrams & sets of ordered pairs
• Determine & justify functions, graphical representations
• Identify & justify functions & non-functions, graphical representations
• Identify functions, multiple representations, including justification
• Condensed: Identify, justify, & determine functions
• Identifying & Justifying Functions, No Domain & Range Language
• 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, multiple representations, including justification, no domain & range language
• Function Notation
• Given linear function, determine function value
• Given quadratic function, determine function value
• Condensed: Given linear or quadratic function, determine function value
• Given graph, determine function value
• Condensed: Given graph or linear function, determine function value
• Interpret & solve problems involving function notation, real-world context
• Linear Functions
• Domain & Range of Linear Functions
• Determine if value is in domain or range, set & table representations
• Determine if value is in domain or range, graphical representations
• Given graph, determine domain & range
• Determine continuous domain & range, real-world context
• Determine restricted domain & range of linear functions
• Determine discrete domain & range, real-world context
• Condensed: Determine domain & range, including real-world context
• Graphing Linear Functions
• Standard Form to Graph
• Given linear equation in standard form, graph
• Given linear equation in standard form, graph, scrambled variable terms
• Determine linear equation in standard form & graph, real-world context
• Condensed: Determine linear equation in standard form & graph, including real-world context
• Slope-Intercept Form to Graph, Integer Slope Only
• Graph linear equations, m = 1
• Graph linear equations, m = 1, various scales
• Given equation in slope-intercept form, graph line, m = ±1, various scales
• Graph linear equations, integer slope not including one & negative one, b = 0
• Graph linear equations, integer slope not including one & negative one
• Graph linear equations, integer slope, various scales
• Graph linear equations, including horizontal & vertical, integer slope, various scales
• Slope-Intercept Form to Graph
• Graph linear equations, fractional slope
• Graph linear equations, fractional slope, various scales
• Condensed: Graph linear equations, including horizontal & vertical, various scales
• Given description of linear equation, identify graph, fractional slope, real-world context
• Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
• Condensed: Identify equivalent equations, graphs, & tables
• Vertical & Horizontal Lines to Graph
• Given vertical linear equation, determine graph
• Given horizontal linear equation, determine graph
• Identifying Key Features of Linear Function
• Identify Linear or Non-Linear Relationships
• Identify linear & non-linear relationships, various representations
• Determine or Plot Intercepts, Given Graph
• Given linear graph, determine coordinates of y-intercept
• Given linear graph, determine coordinates of x-intercept
• Given linear graph, locate intercept or determine coordinates, various scales
• Given graph of linear equation, determine slope & intercepts
• Determine or Plot Intercepts, Given Equation
• Given linear equation in slope-intercept form, determine coordinates of y-intercept
• Given linear equation in slope-intercept form, determine coordinates of x-intercept
• Given linear equation in slope-intercept form, plot y-intercept
• Given equation of horizontal or vertical line, determine coordinates of y-intercept
• Given equation of horizontal or vertical line, determine coordinates of x-intercept
• Given equation of horizontal or vertical line, plot y-intercept
• Given linear equation, determine intercepts
• Given linear equation in standard form, determine coordinates of y-intercept
• Given linear equation, determine slope & intercepts
• Writing Equation of Linear Function
• Writing Equation Given Point & Slope
• Given slope & y-intercept, determine equation
• Given point & integer slope or rate of change, determine linear equation in slope-intercept form
• Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
• Given point & fractional slope, determine linear equation in slope-intercept form, integer y-intercept
• Given point & fractional slope, determine linear equation in slope-intercept form, fractional y-intercept
• Writing Equation Given Two Points
• Given two points, determine linear equation in point-slope form, integer slope, including slope-intercept form conversion
• Given two points, determine linear equation in slope-intercept form, integer slope
• Given two points, determine linear equation in standard form, integer slope, including slope-intercept form conversion
• Given two points, determine linear equation in point-slope form, fractional slope, including slope-intercept form conversion
• Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
• Writing Equation Given Various Components
• Given points or slope & point, determine linear equation in standard form
• Given points or slope & point, determine linear equation in point-slope or standard form
• Given points or slope & point, determine linear equation in various forms
• Condensed: Given two points, determine linear equation in slope-intercept form, including horizontal & vertical lines
• Writing Equation Given Graph
• Writing Equation Given Graph Through Origin
• Given linear graph through origin with points shown on line, determine equation in slope-intercept form, integer slopes
• Given linear graph through origin, determine equation in slope-intercept form, integer slope, 1 ≤ |m| ≤ 3
• Given linear graph through origin, determine equation in slope-intercept form, integer slope
• Writing Equation Given Graph, Integer Slopes,Various Y-Intercepts
• Given linear graph, determine equation in slope-intercept form, m = 1, various scales
• Given linear graph, determine equation in slope-intercept form, m = ±1, various scales
• Given linear graph, determine equation in slope-intercept form, integer slopes
• Given linear graph, determine equation in slope-intercept form, integer slopes, various scales
• Given linear graph, identify equation in slope-intercept form, integer slopes, various scales
• Given equation in slope-intercept form, identify graph, integer slopes, various scales
• Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
• Writing Equation Given Graph, Various Y-Intercepts
• Given linear graph, identify equation, slope-intercept form
• Given linear graph, determine equation in slope-intercept form, fractional slopes
• Given linear graph, determine equation in point-slope form
• Given linear graph, determine equation in standard form
• Given linear graph, identify equation, various forms
• Identify equivalent linear graphs & equations in slope-intercept form
• Identify equivalent linear graphs & equations in slope-intercept form, various scales
• Given graph of vertical line, determine equation
• Given graph of horizontal line, determine equation
• Writing Equation of Parallel or Perpendicular Line
• Identifying Parallel, Perpendicular, or Neither
• Given two slope-intercept form equations, identify as parallel or perpendicular
• Given two pairs of points, determine if lines containing points are parallel or perpendicular
• Writing Equation of Parallel or Perpendicular in Slope-Intercept Form
• Given equation in slope-intercept form, determine slope of parallel line
• Given equation in slope-intercept form, determine slope of perpendicular line
• Condensed: Given equation in slope-intercept form, determine slope of parallel or perpendicular line
• Given equation in slope-intercept form, determine equation of parallel line through specified point
• Given equation in slope-intercept form, determine equation of perpendicular line through specified point
• Given equation in slope-intercept form, determine equation of parallel or perpendicular line through specified point
• Condensed: Determine equations for parallel & perpendicular lines through specified points
• Given slope & point, determine equation for parallel or perpendicular line through specified point
• Given two points for one line, determine equation for parallel or perpendicular line through specified point
• Given graph of line, determine equation for parallel or perpendicular line through specified point
• Writing Equation of Parallel or Perpendicular in Various Forms
• Given equation in various forms, determine slope of parallel line
• Given equation in various forms, determine slope of perpendicular line
• Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
• Determine equation of line through specified point parallel or perpendicular to x-axis
• Determine equation of line through specified point parallel or perpendicular to y-axis
• Condensed: Determine equation of line through specified point parallel or perpendicular to x- or y-axis
• Given equation in various forms, determine equation of parallel line through specified point
• Given equation in various forms, determine equation of perpendicular line through specified point
• Given equation in various forms, determine equation of parallel or perpendicular line through specified point
• Identify equation that is parallel or perpendicular to line through two given points
• Transformations of Linear Functions
• Identify & graph reflections of linear functions
• Identify & graph vertical & horizontal shifts of linear functions
• Identify & graph vertical & horizontal stretches & compressions of linear functions
• Identify descriptions of graphs of linear parent functions & transformed functions
• Graph linear functions using all transformations
• Condensed: Graph linear functions & identify transformations
• Given description of transformation, determine linear function
• Given table, identify transformations of linear functions
• Describe parameter changes to linear parent functions
• Compare linear functions represented differently
• Application of Linear Functions, Given Slope-Intercept or Two Points
• Form 1 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope, only input to output questions
• Form 2 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope
• Form 3 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
• Given slope & intercept, interpret linear relationship & determine slope-intercept equation, including negative slope
• Form 4 – Given point & slope, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
• Form 5 – Given two points, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
• Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
• Application of Linear Functions
• Given linear word problem, identify graph
• Form 6 – Given linear graph, interpret linear relationship & determine slope-intercept equation
• Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
• Determine graph or information from graph, real-world context
• Given linear equation, interpret slope & y-intercept, real-world context
• Determine effects of parameter changes in linear relationships, real-world context
• Linear Regression
• Sketch line of best fit & determine equation, graph scales of one
• Sketch line of best fit & determine equation, various graph scales
• Sketch line of best fit & determine equation, real-world context
• Sketch line of best fit
• Sketch line of best fit & determine predicted value
• Condensed: Sketch line of best fit & determine equation
• Determine residuals
• Exponents
• Numerical Exponential Expressions
• Evaluate powers, whole number base, non-positive exponent
• Evaluate powers, integer base, non-positive exponent, including negative coefficients
• Evaluate powers, fractional base, positive exponent
• Evaluate powers, fractional base, negative exponent
• Evaluate powers, positive fractional base, including non-positive exponents
• Evaluate powers, fractional bases
• Condensed: Evaluate powers with negative exponents
• Simplify Negative Exponents
• Express negative power using positive exponent
• Express negative power using positive exponent, coefficient other than one
• Power Rule of Exponents
• Power Rule, One Variable
• Apply power rule, one variable, positive exponents
• Apply power rule, one variable, at least one negative exponent
• Apply power rule, one variable, including non-positive exponents
• Apply power rule, one variable, coefficient of negative one, at least one negative exponent
• Simplify single variable powers, negative base or coefficient
• Power Rule, Multiple Variables
• Apply power rule, including multiple variables, positive exponents
• Apply power rule, including multiple variables & negative exponents
• Apply power rule, including multiple variables & negative exponents
• Apply power rule, coefficient of negative one, multiple variables, including negative exponents
• Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
• Apply power rule, negative base or coefficient, multiple variables, including negative exponents
• Apply power rule, multiple variables, coefficients other than one, including negative exponents
• Simplify powers, fractional algebraic base, including negative exponents
• Product Rule of Exponents
• Product Rule, One Variable
• Apply product rule of exponents, one variable, positive exponents
• Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
• Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
• Apply product rule of exponents, one variable, positive exponents, coefficients other than one
• Product Rule, Multiple Variables
• Apply product rule of exponents, two variables, three to four factors, positive exponents
• Apply product rule of exponents, two variables, three to four factors, at least one negative exponent
• Apply product rule of exponents, two variables, three to four factors, one variable cancels
• Apply product rule of exponents, two variables, four to six factors, positive exponents
• Apply product rule of exponents, two variables, four to six factors, at least one negative exponent
• Apply product rule of exponents, two variables, four to six factors, at least one variable cancels
• Apply product rule of exponents, positive exponents
• Apply product rule, multiple variables, coefficients other than one, including negative exponents
• Apply product rule of exponents, negative exponents
• Quotient Rule of Exponents
• Quotient Rule, One Variable
• Apply quotient rule of exponents, one variable, positive exponents, greater exponent in numerator
• Apply quotient rule of exponents, one variable, positive exponents, greater exponent in denominator
• Apply quotient rule of exponents, one variable, at least one negative exponent
• Quotient Rule, Multiple Variables
• Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents
• Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, positive exponents
• Apply quotient rule of exponents, positive exponents
• Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, at least one negative exponent
• Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, at least one negative exponent
• Apply quotient rule of exponents, negative exponents
• Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, including negative exponents, coefficients other than one
• Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents, coefficients other than one
• Power & Product Rules of Exponents
• Apply power rule of exponents, positive exponents
• Product & Quotient Rules of Exponents
• Multiply Two Fractions
• Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
• Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
• Divide Two Fractions
• Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
• Multiply & Divide Two Fractions
• Apply product & quotient rules of exponents, negative exponents
• Apply product & quotient rules of exponents, negative exponents, coefficients other than one
• Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
• Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
• Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, negative exponents, coefficients other than one
• Apply product & quotient rules of exponents, negative exponents
• Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
• Apply product & quotient rules of exponents, one or two variables, positive exponents
• Power, Product, & Quotient Rule of Exponents Mixed
• Exponents Mixed, One Variable
• Apply power & product rules of exponents, one variable, positive exponents
• Apply product & power rules of exponents, one variable, coefficient of negative one
• Apply product, quotient, & power rules of exponents, one variable
• Exponents Mixed, Positive Exponents
• Apply product & quotient rules of exponents, one or two variables, positive exponents
• Apply power & product rules of exponents, multiple variables, positive exponents
• Apply power & product rules of exponents, fraction with numerator of one, positive exponents
• Apply power, product, & quotient rules of exponents, positive exponents
• Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
• Apply power, product, & quotient rules of exponents, divide fractions, positive exponents
• Exponents Mixed, Including Negative Exponents
• Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
• Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
• Apply power, product, & quotient rules of exponents, including negative exponents
• Apply power rule of exponents, negative exponents
• Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
• Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
• Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
• Apply product rule of exponents, coefficients other than one
• Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents
• Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents
• Apply product, quotient, & power rules of exponents, multiple variables
• Application of Exponents
• Determine algebraic expressions for perimeter & area of rectangles
• Given algebraic expressions for area & side of rectangles, determine expression for missing side
• Rational Exponents
• Power Rule
• Evaluate rational exponent expressions, positive exponents
• Evaluate rational exponent expressions, negative exponents
• Condensed: Evaluate rational exponent expressions
• Simplify rational exponent expressions using power rule, no coefficients
• Simplify rational exponent expressions using power rule, with coefficients
• Product Rule
• 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
• Quotient Rule
• Simplify rational exponent expressions using quotient rule, no coefficients
• Simplify rational exponent expressions using quotient rule, with coefficients
• Exponent Rules Mixed
• Evaluate numerical expressions with rational exponents
• Simplify numerical expressions with rational exponents
• Condensed: Simplify rational exponents using product & power rules
• Convert Rational Exponents & Radicals
• Convert from rational exponent to radical, single value base
• Convert from rational exponent to radical, algebraic base
• Condensed: Convert from rational exponent to radical
• Polynomials
• Classifying Polynomials
• Identify terms of expressions
• Identify polynomial as monomial, binomial, or trinomial
• Classify polynomials by degree & number of terms
• Condensed: Classify polynomials & identify components of polynomials
• Determine degree, leading coefficient, & type of polynomial
• 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
• Operations with Polynomials
• Addition & Subtraction of Polynomials
• Add binomials & trinomials, degrees zero to two
• Add binomials & trinomials, degrees zero to three
• Given polynomial & sum of polynomials, determine missing polynomial
• Determine sums of polynomials or missing polynomial addends
• Subtraction of Polynomials
• Subtract binomials & trinomials, degrees zero to two
• Subtract binomials & trinomials, degrees zero to three
• Given polynomial & difference of polynomials, determine missing polynomial
• Determine differences of polynomials or missing polynomial subtrahends
• Addition & Subtraction of Polynomials
• Condensed: Add or subtract binomials & trinomials
• Condensed: Determine sums or differences of polynomials or missing polynomial operands
• Add & subtract polynomials to determine expressions for perimeter of various shapes
• Determine missing value to make polynomial statement true, addition & subtraction
• Add & subtract binomials & trinomials, two variables
• Multiplication of Polynomials
• Multiplication of Polynomials, One Variable
• Multiply monomial times binomial or trinomial, mixed degrees
• Multiply binomial times binomial, both degree one
• Square linear binomial
• Multiply binomial times binomial, mixed degrees
• Condensed: Multiply binomial times binomial
• Multiply linear binomial times quadratic trinomial
• Multiply binomial times trinomial, mixed degrees
• Simplify monomial minus product of monomial & binomial or trinomial
• 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
• Multiplication of Polynomials, Two Variables
• Multiply monomial times binomial or trinomial, two variables
• Multiply binomial times binomial, two variables
• Multiply binomial times trinomial, two variables
• Condensed: Multiply monomials, binomials, & trinomials, two variables
• Binomial Theorem
• Apply binomial theorem to expand (x ± y)^3
• Apply binomial theorem to expand (x ± y)^n, n ≥ 4
• Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
• Multiply monomial times binomial or trinomial, mixed degrees
• Multiply monomial times binomial or trinomial, two variables
• Multiply binomial times binomial, both degree one
• Square linear binomial
• Multiply binomial times binomial, mixed degrees
• Multiply linear binomial times quadratic trinomial
• Multiply binomial times trinomial, mixed degrees
• Condensed: Multiply binomial times binomial
• Given monomial & binomial or trinomial, multiply or identify missing value
• Apply binomial theorem to expand (x ± y)^3
• Multiply polynomials to determine expressions for areas of rectangles & triangles
• Determine missing value to make polynomial statement true, multiplication
• Apply binomial theorem to expand (x ± y)^n, n ≥ 4
• Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
• 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
• Division of 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
• Condensed: Divide polynomials
• Divide quadratic trinomial by linear binomial, word problem context
• 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
• Factoring Trinomials, a=1
• Factor quadratic trinomials, a = 1, b > 0, c > 0
• Factor quadratic trinomials, a = 1
• Factor quadratic trinomials, a = 1, terms scrambled
• Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
• Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < |c| ≤ 10
• Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
• Factoring Trinomials, a>1
• Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
• Factor quadratic trinomials, 1 < |a| ≤ 10, 0 < |c| ≤ 30
• Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
• Factor quadratic trinomials, 1 < |a| ≤ 30, 0 < |c| ≤ 40
• Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
• Factor Perfect Square Trinomials
• Factor perfect square trinomials, degree two, one variable
• Factor perfect square trinomials, degree two, two variables
• Condensed: Factor perfect square trinomials, degree two
• Factor perfect square trinomials, fraction coefficients
• Factoring Difference of Squares
• Factor difference of two squares, degree two, one variable
• Factor difference of two squares, degree two, one variable, terms scrambled
• Factor difference of two squares, degree two, one variable, coefficient one
• Condensed: Factor difference of two squares, degree two
• Factor difference of two squares, two variables
• Factor difference of two squares, one or two variables
• Factor GCF & Remaining Quadratic
• Factor GCF & remaining quadratic expression, a = 1, one variable
• Factor GCF & remaining quadratic expression, a ≥ 1, one variable
• Factor Common Binomial
• Factor common binomial
• Factor binomial & its opposite
• Factor by Grouping
• Factor cubic polynomial by grouping, one variable
• Factor cubic polynomial by grouping & difference of two squares, one variable
• Factor Sum & Difference of Cubes
• 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 three, two variables
• Condensed: Factor sum & difference of two cubes, degree three
• Factor sum & difference of two cubes, degree six, two variables
• Condensed: Factor sum & difference of two cubes, degree six
• Identify Factors
• Identify factors of polynomials
• Determine linear factors of polynomials, degree three
• Determine linear factors of polynomials, degree four
• Determine quadratic factors of polynomials, degree four
• Condensed: Determine linear factors of polynomials, degree three or four
• Determine Number of Roots
• Determine maximum number of roots for polynomial function
• Interpreting Graphs of Polynomials
• Intercepts & Multiplicities
• Determine x- & y-intercepts of cubic functions
• Determine x-intercepts/zeros & y-intercepts of polynomial functions
• Determine zeros of polynomials & their multiplicities
• Extrema, Increase & Decrease, End Behavior, & Symmetry
• Determine minimum & maximum of polynomial functions
• Determine intervals of increase & decrease of polynomial functions
• Determine end behavior of polynomial functions
• Determine symmetry of various functions
• Determine Attributes
• Given table, determine attributes of polynomial function
• Given cubic equation, identify descriptions of transformations
• Condensed: Determine graphical attributes of polynomial functions
• Determine Graph or Equation
• Given zeros, determine graph of polynomial function
• Given equation, graph polynomial function
• Given graph, determine equation of polynomial function
• Determine Points of Intersection of Two Functions
• Determine points of intersection of two polynomial functions
• Function Operations, Inverses, & Solutions
• Operations with Functions
• 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)(#)
• Evaluate compositions of functions
• 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
• Determine if functions are inverses using composition
• 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
• Identifying Function, Solutions, & Points of Intersection
• Determine whether given table represents linear or exponential function
• Determine whether given table represents linear, exponential, or quadratic function
• Determine whether given graph represents linear, exponential, or quadratic function
• Condensed: Determine what function given table or graph represents
• Identify ordered pair solutions to systems of two equations, one linear & one quadratic
• Perform operations on functions represented graphically, graphical solution
• Perform operations on functions represented graphically, numerical solution
• Determine points of intersection of various functions, not absolute value or polynomial
• Condensed: Determine points of intersection of functions
• Complex Numbers
• Simplify Complex Numbers
• Express square roots of negatives using i
• Simplify imaginary numbers
• Simplify powers of i
• Operations with Complex Numbers
• Add & subtract complex numbers
• Add or subtract square roots of negative numbers
• Multiply complex numbers
• Square complex numbers
• Multiply square roots of negative numbers
• Divide complex number by constant
• Divide complex numbers
• Condensed: Multiply & divide complex numbers
• Condensed: Add, subtract, multiply, & divide complex numbers
• Condensed: Add, subtract, & multiply square roots of negative numbers
• Quadratic Equations with Complex Solutions
• Factor sum of squares using complex factors
• Calculate discriminant, then determine number of real or complex solutions
• Determine number of complex & real roots of quadratic functions
• Determine complex solutions by factoring sum of squares
• Solve quadratic equations using square root method, complex solutions
• Solve using quadratic formula, 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
• Given two complex solutions, determine quadratic equation of form x^2 + # = 0
• 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
• Determine restricted domain & range of quadratic functions
• Given quadratic equation, determine graph, b = 0
• Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
• Graph quadratic functions using all transformations
• Given quadratic equation, vertex, & point, graph function & determine attributes
• Given quadratic equation in vertex form, determine graph
• Given quadratic equation in standard form, determine graph
• Given equation, graph quadratic function
• Condensed: Graph quadratic functions using any transformation
• Given table, determine attributes of quadratic function, real-world context
• Identifying Key Features of Quadratic Functions
• Vertex, Axis of Symmetry, Increase & Decrease, & 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 axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
• Determine end behavior of quadratic functions
• Determine intervals of increase & decrease of quadratic functions
• Determine intervals where quadratic function is positive or negative
• Determine x-intercept(s) of quadratic functions
• Determine zero(s) of quadratic functions
• Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
• Determine y-intercept of quadratic functions
• Determine x-intercepts/zeros & y-intercepts of quadratic functions, vertex form
• Given graph or table of quadratic function, determine x- & y- intercepts
• Mixed Key Attributes of Quadratic Functions
• Given quadratic equation, determine attributes & graph, a = 1
• Given quadratic equation, determine attributes & graph, a = -1
• Given quadratic equation, determine attributes & graph, a ≠ ±1
• Given graph of quadratic function, determine attributes
• Condensed: Given graph, equation, or table, determine attributes of quadratic function
• Condensed: Determine graphical attributes of quadratic functions
• Condensed: Given quadratic equation, determine attributes & graph
• Identify & graph reflections of quadratic functions
• Identify & graph vertical & horizontal shifts of quadratic functions
• Identify & graph vertical & horizontal stretches & compressions of quadratic functions
• Identify descriptions of graphs of quadratic parent functions & transformed functions
• Given quadratic equation, identify description of transformation
• Given description of transformation, determine quadratic function
• Describe parameter changes to quadratic parent functions
• Determine effects of parameter changes in quadratic relationships, real-world context
• Compare quadratic functions represented differently
• Writing Equations of Quadratic Functions
• Standard & Vertex Form
• Given quadratic equation in standard form, determine vertex form of equation
• Given quadratic equation in vertex form, determine standard form of equation
• Given Vertex, Zeros, or Points
• Given vertex & point, determine quadratic equation, vertex form
• Given vertex & point, determine quadratic equation, standard form
• Given zeros of quadratic function, determine quadratic equation with integer coefficients
• Given integer solutions of quadratic equation, determine function in standard form
• Given rational solutions of quadratic equation, determine function in standard form
• Given three points in plane, determine quadratic equation
• Given Graph, Determine Equation
• Given graph of quadratic function, determine equation
• Given graph of quadratic function, determine equation
• Given graph of quadratic function, determine equation in standard form
• Focus & Directrix
• Given focus & directrix of parabola, determine equation
• Given focus & directrix of parabola, determine equation in standard form
• Given graphical attributes, determine equation of parabola
• 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 binomial equation by factoring out GCF
• Solve quadratic binomial equation by factoring out GCF, one term on each side
• Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
• Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
• Solve quadratic equations using factoring, a = 1, b ≠ 0, |c| ≤ 40, zero on one side
• Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
• Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
• Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
• Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
• Solve quadratic equations using factoring, |a| ≤ 10, b ≠ 0, |c| ≤ 40, zero on one side
• Solve quadratic equations using factoring, |a| ≤ 10, |c| ≤ 40, terms on both sides
• Solve quadratic equations using factoring, perfect square trinomial
• Solve quadratic equations, perfect square trinomial
• Solve quadratic equations using factoring, difference of squares
• Given graph of quadratic function, determine roots/zeros
• Solving Quadratic Equations, Square Root Method
• Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
• Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
• Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
• Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
• Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
• Solve quadratic equations using square root method, a(cx ± h)^2 + k = #
• Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
• Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
• Given quadratic equation in standard form, determine discriminant
• Given quadratic equation in standard form, determine number of solutions
• 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 proportion, solve resulting quadratic equation, b = 0
• Given proportion, solve resulting quadratic equation, b ≠ 0
• Given quadratic equation in standard form, determine exact solutions
• Given quadratic equation in standard form, determine exact solutions, combine like terms first
• Solving Quadratic Equations, Completing the Square
• Determine constant required to complete the square, a ≥ 1, including fractions
• Solve quadratic equations, complete the square, integers, a = 1, real solutions
• Solve quadratic equations, complete the square, integers, a > 1, real solutions
• Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
• Condensed: Solve quadratic equations, complete the square, integers, real solutions
• 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, complete the square, a > 1, real solutions
• Condensed: Solve quadratic equations, complete the square, real solutions
• Solve quadratic equations, complete the square, integers, a = 1, including 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
• Solving Quadratic Equations, Determine Solutions
• Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
• Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
• Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
• Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
• Determine exact solution to quadratic equations, a = ±1, b = 0
• Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
• Application of Solving Quadratic Equations
• Determine or use quadratic equations, real-world context
• Solve quadratic inequalities, “and” solutions
• Solve quadratic inequalities, “or” solutions
• Vertical Motion Problems
• 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 height of dropped object, 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
• 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
• Absolute Value Functions
• Solving Absolute Value Equations
• Solve linear absolute value equations
• Solve linear absolute value equations, extra constant or coefficient
• Solve linear absolute value equations, variable on both sides
• Condensed: Solve linear absolute value equations, including extra constant or coefficient
• Create linear absolute value equations, real-world context
• Solving Absolute Value Inequalities
• Given linear absolute value inequality, determine compound inequality
• Solve & graph linear absolute value inequalities, “and” solutions, 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
• 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 inequality, extra coefficient or constant, including setup
• Solve & graph linear absolute value inequalities, including extra constant or coefficient
• Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
• Condensed: Solve & graph linear absolute value inequalities
• Graphing Absolute Value Functions
• Determine x- & y-intercepts of absolute value functions
• Determine minimum & maximum of absolute value functions
• Identify & graph reflections of absolute value functions
• Identify & graph vertical & horizontal shifts of absolute value functions
• Identify & graph vertical & horizontal stretches & compressions of absolute value functions
• Given absolute value equation, identify description of transformation
• Graph absolute value functions using all transformations
• Condensed: Graph absolute value functions using any transformation
• Graph absolute value functions using vertex & intercepts
• Condensed: Determine graphical attributes of absolute value functions
• Compare absolute value functions represented differently
• Determine points of intersection of absolute value functions
• Writing Equation of Absolute Value Functions
• Given graph, determine absolute value equation
• Given description of transformation, determine absolute value equation
• Piecewise & Step Functions
• Graph piece-wise functions
• Given graph of piece-wise function, determine equation
• Graph step functions
• Given graph of step function, determine equation
• Condensed: Determine graphs & equations of piece-wise & step functions
• Cubic Functions
• Graphing Cubic Functions
• Determine minimum & maximum of cubic functions
• Identify & graph reflections of cubic functions
• Identify & graph vertical & horizontal shifts of cubic functions
• Identify & graph vertical & horizontal stretches & compressions of cubic functions
• Graph cubic functions using all transformations
• Condensed: Graph cubic functions using any transformation
• Condensed: Determine graphical attributes of cubic functions
• Graph cubic functions using key points & intercepts
• Rational Expressions & Functions
• 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
• Operations with Rational Expressions
• Multiply rational expressions
• Divide rational expressions
• Condensed: Multiply & divide rational expressions
• Subtract rational expressions
• Condensed: Add & subtract rational expressions
• Condensed: Add, subtract, multiply, & divide rational expressions
• Domain of Rational Functions
• Given rational function, determine function value
• Identify value that makes rational expression undefined
• Determine values that make rational expressions undefined
• Determine asymptotic domain restrictions of rational functions
• Determine domain & range of rational functions using inequalities, interval notation & set notation
• Key Attributes of Rational Functions
• Determine x- & y-intercepts of reciprocal functions
• Determine symmetry of reciprocal functions
• Determine asymptotes of reciprocal functions
• Determine minimum & maximum of reciprocal functions
• Condensed: Determine graphical attributes of reciprocal functions
• Graphing Rational Functions
• Identify & graph reflections of reciprocal functions
• Identify & graph vertical & horizontal shifts of reciprocal functions
• Identify & graph vertical & horizontal stretches & compressions of reciprocal functions
• Given reciprocal equation, identify description of transformations
• Graph reciprocal functions using all transformations
• Graph rational functions
• Condensed: Graph reciprocal functions using any transformation
• Graph reciprocal functions using asymptotes, intercepts, & domain & range
• Compare rational functions represented differently
• Solving Rational Equations & Inequalities
• Solve equations involving rational exponents, one- or two-step
• Solve equations involving rational exponents, multi-step
• Solve rational equations, one term each side
• Solve rational equations, multiple terms on one side
• Condensed: Solve rational equations
• Condensed: Solve equations involving rational exponents
• Determine if solution to rational equation is reasonable
• Determine rational equations, real-world context
• Determine rational inequalities, real-world context
• Identify steps to simplify square roots
• Simplify square roots
• Simplify square roots, coefficient greater than one
• Given square root expression, evaluate for specific value
• Condensed: Simplify square roots, including algebraic expressions
• Evaluate perfect cube roots
• Solve perfect cube root equations
• Condensed: Determine cube roots of perfect cubes
• Compare perfect square & cube roots
• Simplify radical expression raised to power that is multiple of index
• Simplify radical expressions, perfect powers
• Multiply radical expressions, numbers & variables
• Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
• Condensed: Convert from radical to rational exponent
• Square Root
• Solve perfect square root equations
• Condensed: Determine square roots of perfect squares
• Solve square root equations, square root = #
• Solve square root equations, square root = square root
• Solve square root equations, add & subtract from root
• Solve square root equations, divide by coefficient of root
• Solve square root equations, multi-step
• Solve square root equations, square root = x ± #
• Solve square root equations, square root ± square root = #
• Condensed: Solve square root equations, one-step & two-step
• Condensed: Solve square root equations
• Identify extraneous solutions of square root equations
• Cube Root
• Solve perfect cube root equations
• Solve cube root equations, cube root = #
• Solve cube root equations, cube root = cube root
• Solve cube root equations, multi-step
• Solve cube root equations, cube root = variable
• Condensed: Solve cube root equations, one-step & two-step
• Square Root & Cube Root Mixed
• Compare perfect square & cube roots
• Condensed: Evaluate & compare perfect square & cube roots
• Condensed: Solve square root & cube root equations
• Key Attributes of Radical Functions
• Determine x- and y-intercepts of square root functions
• Determine minimum & maximum of square root functions
• Condensed: Determine graphical attributes of square root functions
• Determine x- & y-intercepts of cube root functions
• Determine minimum & maximum of cube root functions
• Condensed: Determine graphical attributes of cube root functions
• Identify & graph reflections of square root functions
• Identify & graph vertical & horizontal shifts of square root functions
• Identify & graph vertical & horizontal stretches & compressions of square root functions
• Given square root equation, identify description of transformations
• Identify & graph reflections of cube root functions
• Identify & graph vertical & horizontal shifts of cube root functions
• Identify & graph vertical & horizontal stretches & compressions of cube root functions
• Given cube root equation, identify descriptions of transformations
• Compare radical functions represented differently
• Graph square root functions using key point & intercepts
• Graph square root functions using all transformations
• Condensed: Graph square root functions using any transformation
• Graph cube root functions using key points & intercepts
• Graph cube root functions using all transformations
• Condensed: Graph cube root functions using any transformation
• Mixed Functions
• Calculate average rate of change of function from table
• Calculate average rate of change of function from graph
• Calculate average rate of change of a function from an equation
• Calculate average rate of change of function, real-world context
• Condensed: Calculate average rate of change of function
• Given graph, identify various functions
• Given various functions, identify graph
• Condensed: Graph various functions
• Determine domain & range of various functions using various notations
• Logarithms
• Evaluating Logarithmic Expressions
• Evaluate log expressions, whole number base
• Evaluate log expressions, fractional bases
• Evaluate log expressions, using change of base
• Evaluate log expressions, natural log
• Condensed: Evaluate log expressions
• Solving Logarithmic Equations
• Solve log equations, log = #
• Solve log equations, log = 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
• Solve natural log equations, ln = #
• Solve natural log equations, ln = ln
• Solve natural log equations, ln + ln = #
• Solve natural log equations, ln – ln = #
• Condensed: Solve natural log equations
• Determine if solution to logarithmic equation is reasonable
• Condensing & Expanding 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
• Apply product, quotient, & power rules to expand or condense log expressions
• Condensed: Expand or condense log expressions
• Exponential & Logarithmic Functions
• Exponential Functions
• Evaluating Exponential Functions
• 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
• Domain & Range of Exponential Functions
• Given equation, determine domain & range of exponential function
• Determine domain & range of discrete exponential functions
• Determine restricted domain & range of exponential functions
• Given verbal description & graph, determine domain & range of exponential function
• Determine domain & range of discrete exponential functions, real-world context
• Graphing Exponential Functions
• Given graph, identify solution to exponential equation
• Given exponential growth function, determine graph
• Graph exponential functions using all transformations
• 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
• Given equation, graph exponential function, including base e
• Given graph, determine equation of exponential function
• Compare exponential functions represented differently
• Identifying Key Features 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 graph, determine asymptote of exponential function
• Given exponential equation, determine asymptote
• Determine asymptote of exponential functions, real-world context
• Determine end behavior of exponential functions
• Condensed: Determine graphical attributes of exponential functions
• Graph exponential functions using all transformations
• Condensed: Graph exponential functions & identify transformations
• Transformations of Exponential Functions
• Identify & graph reflections of exponential functions
• Identify & graph vertical & horizontal shifts 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
• Writing Equations of Exponential Functions
• Given table, determine linear or exponential growth function
• Given table, determine exponential growth function
• Given table, determine exponential decay function
• Given graph, determine equation of exponential function
• Solving Exponential Equations
• Solve exponential equations, no logs required
• Solve exponential equations, common bases given
• Solve exponential equations, both bases reduce to common base
• Solve simple exponential equations
• Solve exponential equations, one base reduces to common base
• Solve exponential equations, two different bases, no common base possible
• Solve exponential equations, one variable & one base
• Solve exponential equations, base e
• Create equivalent exponential expressions using exponent properties
• Application of Exponential Functions
• Calculate investment value, annual compounding
• Calculate depreciating asset value, annual compounding
• Calculate investment value, various compounding
• Condensed: Calculate investment & depreciating asset values, annual compounding
• Exponential growth & decay, real-world context
• Determine exponential function, real-world context
• Determine asymptote of exponential functions, real-world context
• Given table, determine attributes of exponential function
• Interpret values in exponential functions, real-world context
• Logarithmic Functions
• Graphing Logarithmic Functions
• Identify & graph reflections of log functions
• Identify & graph vertical & horizontal shifts 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
• Given equation, graph log function
• Condensed: Graph log functions & identify transformations
• Identifying Key Features of Logarithmic Functions
• Determine x-intercepts/zeros & y-intercepts of log functions
• Determine asymptote of log functions
• Determine minimum & maximum of log functions
• Determine end behavior of log functions
• Given table, determine attributes of log function
• Condensed: Determine graphical attributes of log functions
• Writing Equations of Logarithmic Functions
• Given graph, determine equation of log function
• Exponential & Logarithmic Equations
• Given log equation, determine exponential equation
• Given exponential equation, determine log equation
• Condensed: Convert between exponential & log equations
• Direct & Inverse Variation
• Direct & Inverse Variation
• Direct & Inverse Variation, Multiple Choice
• Determine direct variation table, multiple choice
• Determine direct variation equation, multiple choice
• Determine inverse variation table, multiple choice
• Determine variation equation type, multiple choice
• Determine direct or inverse variation, multiple choice
• Direct & Inverse Variation, Determine Equation or Missing Number
• Given point & “y varies directly with x”, determine equation
• Given point & “y varies directly with x & inversely with z”, determine equation
• Given point, “y varies directly with x”, & another value, determine missing number
• Given point, “y varies directly with x”, & another value, determine equation & missing number
• Given point, “y varies directly with x”, & another value, determine equation & missing number, rational numbers
• Given point & “y varies inversely with x”, determine equation
• Given point, “y varies jointly with x & z”, & another value, determine equation
• Given point, “y varies inversely with x”, & another value, determine equation & missing number
• Condensed: Determine direct, inverse, joint, or combined variation equations
• Determine direct variation table, multiple choice
• Determine inverse variation table, multiple choice
• Determine variation equation type, multiple choice
• Determine direct or inverse variation, multiple choice
• Given point & “y varies directly with x”, determine equation
• Given point & “y varies inversely with x”, determine equation
• Given point, “y varies directly with x”, & another value, determine equation & missing number
• Given point, “y varies inversely with x”, & another value, determine equation & missing number
• Determine direct variation equation, multiple choice
• Given point, “y varies directly with x”, & another value, determine equation & missing number, rational numbers
• Given point & “y varies directly with x & inversely with z”, determine equation
• Given point, “y varies directly with x”, & another value, determine missing number
• Given point, “y varies jointly with x & z”, & another value, determine equation
• Condensed: Determine direct, inverse, joint, or combined variation equations
• Application of Direct & Inverse Variation
• Solve word problems involving direct variation
• Determine & apply inverse variation equation, real-world context
• Solve word problems involving joint variation
• Solve word problems involving combined variation
• Sequences
• Arithmetic Sequences
• Determine terms in arithmetic sequences
• Given arithmetic sequence, determine common difference & next term
• Given formula, determine specific term of arithmetic sequence
• Determine common difference, first term, & formula of arithmetic sequences
• Condensed: Determine formula & specific terms of arithmetic sequences
• Geometric Sequences
• Given formula, determine specific term of geometric sequence
• Determine formula & specific term of geometric sequences
• Condensed: Determine formula or specific term of geometric sequences
• Application of Sequences
• Given table, determine difference in terms in arithmetic sequence, real-world context
• Identify arithmetic & geometric sequences & determine common difference or common ratio
• Given formula, determine terms in arithmetic & geometric sequences
• Condensed: Identify arithmetic & geometric sequences & determine components of sequences
• Determine function & specific term for arithmetic & geometric sequences, real-world context
• Finite Geometric Series
• Determine sum of finite geometric series
• Determine sum of finite geometric series, real-world context
• Data Analysis
• Samples & Populations
• Identify samples & populations
• Identify biased samples & questions
• Determine sample spaces
• Identify statistical questions
• Identify variables of interest
• Identify statistical inferences
• Condensed: Identify samples, populations, variables of interest, & statistical inferences
• 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
• Identify descriptive & inferential statistics
• Probability
• Given visual model, determine “or” probability
• Given visual model, determine “or” probability as fraction, decimal, or percent
• Determine “or” probabilities as fractions
• Determine “or” probabilities as fractions, decimals, or percents
• Determine “or” probabilities
• Determine “or” probabilities
• Determine “or” probabilities, including “and” situations
• Multiplication Rule
• Given visual model, determine “and” probability as fraction, decimal, or percent, dependent events
• Determine probabilities of flipping coins & rolling die
• Determine probabilities of flipping coins specified number of times
• Determine “and” probabilities, independent events, visuals provided
• Determine “and” probabilities, independent events, same sample space
• Determine “and” probabilities, independent events, two distinct sample spaces
• Determine “and” probabilities, dependent events, multiple choice
• Determine “and” probabilities, dependent events
• Determine “and” probabilities, independent & dependent events
• Determine “and” probabilities, independent & dependent events, including complementary events
• Conditional Probability
• Determine conditional probabilities from two-way frequency tables
• Determine conditional probabilities, including two-way frequency tables
• Permutations
• Given visual model, determine permutations, specified items predetermined
• Determine permutation of letters in word, nondistinct letters
• Determine permutation of letters in word, distinct letters
• Condensed: Determine permutation of letters in word, including nondistinct letters
• Determine permutations, one nondistinct item, real-world context
• Determine permutations, multiple nondistinct items, real-world context
• Determine permutations using all items, real-world context
• Determine permutations, real-world context
• Combinations
• Given lists, determine combinations, choose from one list, real-world context
• Given lists, determine combinations, choose from two lists, real-world context
• 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
• Determine z-Score & Probability
• 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
• Normal Distributions
• Determine Test Statistic or Hypotheses, One Mean or Proportion
• Determine test statistics, one mean
• Determine test statistics, one proportion
• Condensed: Determine test statistics, one mean or proportion
• Identify hypotheses for hypothesis test, one mean
• Identify hypotheses for hypothesis test, one proportion
• Condensed: Identify hypotheses for hypothesis test, one mean or proportion
• Determine Test Statistic or Hypotheses, Two Means or Proportions
• Determine test statistics, two means
• Determine test statistics, two proportions
• Condensed: Determine test statistics, two means or proportions
• Identify hypotheses for hypothesis test, two means
• Identify hypotheses for hypothesis test, two proportions
• Condensed: Identify hypotheses for hypothesis test, two means or proportions
• Steps in Hypothesis Testing, One Mean or Proportion
• Identify & determine hypothesis test steps, one mean
• Identify & determine hypothesis test steps, one proportion
• Condensed: Identify & determine hypothesis test steps, one mean or proportion
• Determine critical z-score & p-value
• Steps in Hypothesis Testing, Two Means or Proportions
• Identify & determine hypothesis test steps, two means
• Identify & determine hypothesis test steps, two proportions
• Condensed: Identify & determine hypothesis test steps, two means or proportions
• Determine Conclusions
• Determine conclusion from statistical summaries
• Given critical z-score & test statistic, determine conclusion for null hypothesis
• Identify hypotheses for hypothesis test, one mean
• Identify hypotheses for hypothesis test, one proportion
• Condensed: Identify hypotheses for hypothesis test, one mean or proportion
• Identify hypotheses for hypothesis test, two means
• Identify hypotheses for hypothesis test, two proportions
• Condensed: Identify hypotheses for hypothesis test, two means or proportions
• Determine test statistics, one mean
• Determine test statistics, one proportion
• Determine test statistics, two proportions
• Condensed: Determine test statistics, one mean or proportion
• Determine critical z-score & p-value
• Given critical z-score & test statistic, determine conclusion for null hypothesis
• Determine test statistics, two means
• Identify & determine hypothesis test steps, two means
• Condensed: Identify & determine hypothesis test steps, two means or proportions
• Identify & determine hypothesis test steps, two proportions
• Identify & determine hypothesis test steps, one proportion
• Regression
• Determine linear regression equations, calculator expected
• Determine exponential regression equations, calculator expected
• Determine quadratic regression equations, calculator expected
• Given table, use technology to determine radical equation
• Given regression equation, determine predicted value
• Trigonometry
• Graphing Trigonometric Functions
• Given graph or equation, determine amplitude of trig function
• Given graph or equation, determine midline of trig function
• Given graph or equation, determine period 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, sin, multiple transformations
• Determine graph of trig functions, cos, one transformation
• Determine graph of trig functions, cos, multiple transformations
• Determine graph of trig functions, tan & cot
• Determine graph of trig functions, sec & csc
• Identify trigonometric functions to model periodic data, real-world context
• Trigonometric Ratios
• Identify definitions of trig functions
• Given right triangle, determine missing side & trig ratio, sin, cos, & tan
• Given right triangle, determine missing side & trig ratio, cot, sec, & csc
• Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
• Condensed: Given right triangle, determine missing side & trig ratio
• Trigonometric Identities
• Determine missing steps in proofs of Pythagorean identities
• Given graph or equation, determine period of trig function
• Given graph or equation, determine midline of trig function
• Given graph or equation, determine amplitude 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, sin, multiple transformations
• Determine graph of trig functions, cos, one transformation
• Determine graph of trig functions, cos, multiple transformations
• Determine graph of trig functions, tan & cot
• Determine graph of trig functions, sec & csc
• Identify trigonometric functions to model periodic data, real-world context
• Identify definitions of trig functions
• Given right triangle, determine missing side & trig ratio, sin, cos, & tan
• Given right triangle, determine missing side & trig ratio, cot, sec, & csc