Algebra 2 Skills
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Algebra Foundations
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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
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Expressions & Operations
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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
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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
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Simplifying Expressions, Two Variable
- Simplify algebraic expressions, two variables, positive integer coefficients
- Simplify algebraic expressions, two variables, distribute twice
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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
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Equations
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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
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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
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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
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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
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Inequalities
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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
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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
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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
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Writing Inequalities
- Given graph, identify linear inequality, slope-intercept form
- Given graph, determine inequalities in standard form, real-world context
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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
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Systems of Equations
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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
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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
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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
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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
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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
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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
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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
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Systems of Inequalities
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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
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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
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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
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Functions
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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
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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
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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
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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
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Linear Functions
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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
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Graphing Linear Functions
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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
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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
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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
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Vertical & Horizontal Lines to Graph
- Given vertical linear equation, determine graph
- Given horizontal linear equation, determine graph
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Identifying Key Features of Linear Function
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Identify Linear or Non-Linear Relationships
- Identify linear & non-linear relationships, various representations
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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
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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
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Writing Equation of Linear Function
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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
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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
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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
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Writing Equation Given Graph
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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
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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
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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
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Writing Equation of Parallel or Perpendicular Line
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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
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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
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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
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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
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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
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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
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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
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Exponents
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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
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Simplify Negative Exponents
- Express negative power using positive exponent
- Express negative power using positive exponent, coefficient other than one
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Power Rule of Exponents
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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
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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
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Product Rule of Exponents
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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
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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
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Quotient Rule of Exponents
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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
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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
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Power & Product Rules of Exponents
- Apply power rule of exponents, positive exponents
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Product & Quotient Rules of Exponents
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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
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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
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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
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Power, Product, & Quotient Rule of Exponents Mixed
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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
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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
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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
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Application of Exponents
- Determine algebraic expressions for perimeter & area of rectangles
- Given algebraic expressions for area & side of rectangles, determine expression for missing side
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Rational Exponents
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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
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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
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Quotient Rule
- Simplify rational exponent expressions using quotient rule, no coefficients
- Simplify rational exponent expressions using quotient rule, with coefficients
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Exponent Rules Mixed
- Evaluate numerical expressions with rational exponents
- Simplify numerical expressions with rational exponents
- Condensed: Simplify rational exponents using product & power rules
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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
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Polynomials
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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
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Interpreting Polynomials
- Interpret terms or factors in expressions, including real-world context
- Identify & apply polynomial identities
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Operations with Polynomials
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Addition & Subtraction of Polynomials
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Addition 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
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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
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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
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Multiplication of Polynomials
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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
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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
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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
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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
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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
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Factoring Polynomials
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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
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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
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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
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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
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Factor GCF & Remaining Quadratic
- Factor GCF & remaining quadratic expression, a = 1, one variable
- Factor GCF & remaining quadratic expression, a ≥ 1, one variable
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Factor Common Binomial
- Factor common binomial
- Factor binomial & its opposite
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Factor by Grouping
- Factor cubic polynomial by grouping, one variable
- Factor cubic polynomial by grouping & difference of two squares, one variable
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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
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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
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Determine Number of Roots
- Determine maximum number of roots for polynomial function
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Interpreting Graphs of Polynomials
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Intercepts & Multiplicities
- Determine x- & y-intercepts of cubic functions
- Determine x-intercepts/zeros & y-intercepts of polynomial functions
- Determine zeros of polynomials & their multiplicities
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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
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Determine Attributes
- Given table, determine attributes of polynomial function
- Given cubic equation, identify descriptions of transformations
- Condensed: Determine graphical attributes of polynomial functions
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Determine Graph or Equation
- Given zeros, determine graph of polynomial function
- Given equation, graph polynomial function
- Given graph, determine equation of polynomial function
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Determine Points of Intersection of Two Functions
- Determine points of intersection of two polynomial functions
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Function Operations, Inverses, & Solutions
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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
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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
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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
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Complex Numbers
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Simplify Complex Numbers
- Express square roots of negatives using i
- Simplify imaginary numbers
- Simplify powers of i
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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
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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
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Quadratic Functions
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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
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Graphing 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
- Graph quadratic equations
- Given equation, graph quadratic function
- Condensed: Graph quadratic functions using any transformation
- Given table, determine attributes of quadratic function, real-world context
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Identifying Key Features of Quadratic Functions
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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
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Intercepts of Quadratic Functions
- 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
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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
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Transformations of Quadratic Functions
- 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
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Writing Equations of Quadratic Functions
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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
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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
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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
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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
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Solving Quadratic Equations
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Solving Quadratic Equations, Zeros
- Apply zero product property to solve factored quadratic equations
- Identify zeros of factored quadratics
- Determine relationship between zeros & linear factors of quadratic functions
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Solving Quadratic Equations, GCF
- 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
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Solving Quadratic Equations, Factoring
- 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
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Solving Quadratic Equations, Graphing
- Given graph of quadratic function, determine roots/zeros
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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
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Solving Quadratic Equations, Quadratic Formula
- 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
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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
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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
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Application of Solving Quadratic Equations
- Determine or use quadratic equations, real-world context
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Solving Quadratic Inequalities
- Solve quadratic inequalities, “and” solutions
- Solve quadratic inequalities, “or” solutions
- Condensed: Solve quadratic inequalities
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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
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Absolute Value Functions
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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
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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
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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
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Writing Equation of Absolute Value Functions
- Given graph, determine absolute value equation
- Given description of transformation, determine absolute value equation
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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
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Cubic Functions
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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
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Rational Expressions & Functions
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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
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Operations with Rational Expressions
- Multiply rational expressions
- Divide rational expressions
- Condensed: Multiply & divide rational expressions
- Add rational expressions
- Subtract rational expressions
- Condensed: Add & subtract rational expressions
- Condensed: Add, subtract, multiply, & divide rational expressions
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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
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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
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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
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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
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Radical Expressions & Functions
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Simplifying Radical Expressions
- 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
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Operations with Radicals
- Add & subtract radical expressions, one or two variables, simplified radicals
- Add & subtract radical expressions, one or two variables, radicals to simplify
- Condensed: Add & subtract radical expressions
- Multiply radical expressions, numbers & variables
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Convert Radicals & Rationals
- Convert from radical to rational exponent, single value in radicand
- Convert from radical to rational exponent, algebraic term in radicand
- Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
- Condensed: Convert from radical to rational exponent
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Solving Radical Equations
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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
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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
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Square Root & Cube Root Mixed
- Compare perfect square & cube roots
- Condensed: Evaluate & compare perfect square & cube roots
- Condensed: Solve square root & cube root equations
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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
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Transformations of Radical 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
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Graphing Radical Functions
- 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
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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
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Logarithms
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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
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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
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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
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Exponential & Logarithmic Functions
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Exponential Functions
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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
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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
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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
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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
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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
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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
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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
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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
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Logarithmic Functions
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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
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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
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Writing Equations of Logarithmic Functions
- Given graph, determine equation of log function
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Exponential & Logarithmic Equations
- Given log equation, determine exponential equation
- Given exponential equation, determine log equation
- Condensed: Convert between exponential & log equations
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Direct & Inverse Variation
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Direct & Inverse Variation
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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
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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
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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
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Sequences
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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
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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
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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
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Finite Geometric Series
- Determine sum of finite geometric series
- Determine sum of finite geometric series, real-world context
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Data Analysis
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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
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Probability
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Addition Rule
- 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
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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
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Conditional Probability
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
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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
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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
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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
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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
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Normal Distributions
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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
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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
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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
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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
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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
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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
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Trigonometry
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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
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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
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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
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