Math 1 Skills
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Algebra Foundations
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Real Number System
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Comparing Real Numbers
- Order positive decimals
- Order positive fractions
- Condensed: Order positive decimals & fractions
- Order decimals & fractions
- Order positive rational numbers, no radicals, no exponents
- Order rational numbers, no radicals, no exponents
- Order real numbers, no exponents
- Order real numbers, exponents are positive
- Order real numbers
- Comparing expressions on given interval
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Application of Comparing Real Numbers
- Order real numbers, positive exponents, percents are whole, including real-world context
- Order real numbers, positive exponents, percents are whole, including real-world context
- Given table, order rational numbers, real-world context
- Given set or list, order rational numbers, real-world context
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Classifying Real Numbers
- Determine relationships between subsets of real numbers
- Determine relationships between subsets of rational numbers
- Determine result of adding & multiplying rational & irrational numbers
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Algebraic Properties
- Identify properties used in numerical expressions
- Identify properties used in numerical & algebraic expressions
- Identify properties used to solve linear equations
- Identify steps to solve linear equations
- Identify equivalent algebraic expressions, including real-world context
- Evaluate & identify equivalent numerical expressions, including real-world context
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Scientific Notation
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Operations with Scientific Notation
- Add numbers in scientific notation
- Subtract numbers in scientific notation, real-world context
- Multiply numbers in scientific notation
- Divide numbers in scientific notation
- Condensed: Add, subtract, multiply, & divide numbers in scientific notation
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Application of Scientific Notation
- Convert number from standard form to scientific notation, real-world context
- Convert numbers between standard form & scientific notation, real-world context
- Add numbers in scientific notation, real-world context
- Subtract numbers in scientific notation, real-world context
- Multiply numbers in scientific notation, real-world context
- Divide numbers in scientific notation, real-world context
- Compare magnitude of numbers in scientific notation, real-world context
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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 values, two variables, two terms
- Evaluate expressions for specified values, two variables, two terms, one term with three factors
- 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, multiple operations, including absolute value & powers
- 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
- Simplify algebraic expressions, one variable, distribute once & combine like terms
- Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
- Simplify algebraic expressions, one variable, distribute once & product of two factors
- 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
- Simplify algebraic expressions, one variable, distribute once, fraction multiplier
- Simplify algebraic expressions, one variable, distribute once, decimal multiplier
- Simplify algebraic expressions, one variable, distribute once, including rationals
- Simplify algebraic expressions, one variable, distribute twice
- Simplify algebraic expressions, two variables, integer coefficients
- Simplify algebraic expressions, two variables, distribute twice
- Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
- Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
- Identify equivalent expressions involving distribution, two or more terms
- Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
- Identify equivalent expressions involving distribution
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Inferential Reasonings Word Problems
- Identify appropriate steps to solve problem, real-world context
- Determine reasonable estimates, linear relationships, real-world context
- Determine reasonable estimates, multi-step, real-world context
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Equations
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Two-Step Equations
- Solve ax ± b = c
- Solve two-step linear equations, fractional answers
- Solve two-step linear equations, fractional coefficients
- Solve two-step linear equations, decimal coefficients
- Condensed: Solve x/a ± b = c
- Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
- Condensed: Solve one- or two-step linear equations, fractional coefficients
- Condensed: Solve two-step linear equations
- Solve two-step linear equations, algebra tiles
- Determine if given value is solution to two-step linear equations
- Determine two-step linear equations, real-world context
- Given two-step linear equation, identify real-world situation represented by equation
- Solve problems that can be represented by two-step equations, real-world context
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Multi-Step Equations
- Solve linear equations, sum or difference on one side
- Solve linear equations, product on one side
- Solve linear equations, like terms on both sides
- Solve linear equations, distributive property on one side, up to two terms on other side
- Solve three-step linear equations involving distribution of decimal multiplier
- Solve three-step linear equations involving distribution, fractional multiplier cancels if distributed
- Solve three-step linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
- Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
- Solve linear equations, term minus distributive property on one side
- Solve linear equations, distributive property & additional term on one side
- Condensed: Solve linear equations involving distributive property on one side
- Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
- Solve (ax ± b)/c = d
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Equations with Variables on Both Sides
- Solve linear equations, variables on both sides
- Solve linear equations, distributive property on both sides, integers
- Solve multi-step linear equations
- Solve linear equations, distributive property on both sides, additional term on one side
- Solve linear equations, distributive property & additional term on one side & binomial on other side
- Solve linear equations, binomials on both sides, decimals
- Solve linear equations, variables as numerators on both sides
- Solve linear equations, binomials on both sides, fractions
- Solve linear equations, distributive property on both sides, rationals
- Condensed: Solve linear equations, variables on both sides or like terms
- Condensed: Solve linear equations, variables on both sides, rationals
- Determine equations with variables on both sides, real-world context
- Determine & solve linear equations with variables on both sides, real-world context
- Given equation with variables on both sides, identify real-world situation represented by equation
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Absolute Value Equations
- Solve linear absolute value equations
- Solve linear absolute value equations, extra constant or coefficient
- Condensed: Solve linear absolute value equations, including extra constant or coefficient
- Create linear absolute value equations, real-world context
- Solve linear absolute value equations, variable on both sides
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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 in standard form, solve for y
- Given linear equation of form a + by = cx, solve for y
- 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
- 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
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Inequalities
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One-Variable Inequalities
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Basic One-Variable Inequalities
- Graph inequalities on number line
- Determine graph from inequality or inequality from graph
- Given graph, determine inequality
- Solve & graph one-step inequalities, whole number coefficients
- Solve & graph one-step inequalities, integer coefficients
- Solve & graph one-step inequalities, including fractional coefficients
- Solve & graph one-step inequalities, including negative & fractional coefficients
- Solve & graph two-step inequalities
- Solve multi-step inequalities, including variables on both sides
- Solve multi-step inequalities using distributive property
- Solve & graph inequalities, variables on both sides, including distributive property
- Condensed: Solve & graph inequalities
- Determine equivalence of inequalities & solution set
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Application of One-Variable Inequalities
- Determine inequalities with variables on both sides, real-world context
- Given inequality with variable on both sides, identify real-world problem modeled by inequality
- Identify one-step inequalities that model real-world problems or interpret inequality components
- Determine one-step inequalities, including real-world context
- Determine one-step inequalities, rational numbers, including real-world context
- Given one-step inequality, identify real-world problem modeled by inequality
- Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
- Determine & solve two-step inequalities, greater than, real-world context
- Determine & solve two-step inequalities, less than, real-world context
- Determine two-step inequalities, rational numbers, including real-world context
- Given two-step inequality, identify real-world problem modeled by inequality
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Linear Inequalities
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Basic Linear Inequalities
- Graph linear inequalities, slope-intercept form, only oblique lines
- Graph linear inequalities, vertical & horizontal lines
- Graph linear inequalities, slope-intercept form, including vertical & horizontal lines
- Graph linear inequalities, various forms
- Given linear inequality, identify correct graph, slope-intercept form
- Given linear inequality, determine graph, slope-intercept form
- Given linear inequality, determine solutions & non-solutions, slope-intercept form
- Given linear inequality graph, determine solutions & non-solutions
- Given linear inequality & x-value, determine y-value
- Given graph, identify linear inequality, slope-intercept form
- Given graph, determine linear inequality
- Condensed: Determine equivalent linear inequalities & graphical solutions
- Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
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Application of Linear Inequalities
- Given description, determine linear inequalities in standard form & specific solutions, real-world context
- Given description, determine linear inequalities in standard form, including tables, real-world context
- Given description, determine linear inequality in standard form, graph, & determine specific solutions, real-world context
- Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
- Given description & table, graph linear inequality, real-world context
- Given graph, determine inequalities in standard form, real-world context
- Solve linear programming problems, real-world context
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Compound Inequalities
- Solve & graph compound inequalities, “and” solutions
- Solve & graph compound inequalities, “and” solutions, including real-world context
- Solve & graph compound inequalities, “or” solutions
- Solve compound inequalities, “and” solutions, multiple choice
- Condensed: Solve & graph compound inequalities
- Given description, determine graph of inequality
- Given description, determine compound inequality, graph, & possible solutions
- Interpret meaning of inequality, real-world context
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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, “and” solutions
- Solve & graph linear absolute value inequalities, “or” solutions, including setup
- Solve & graph linear absolute value inequalities, “or” solutions
- Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
- Solve & graph linear absolute value inequalities, including setup
- Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
- Condensed: Solve & graph linear absolute value inequalities, including setup
- Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
- Solve & graph linear absolute value inequalities, including extra constant or coefficient
- Condensed: Solve & graph linear absolute value inequalities
- Create linear absolute value inequalities, real-world context
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Functions
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Independent & Dependent Variables
- Given table, identify dependent or independent variable
- Given table or graph, identify dependent or independent variable
- Given equation, identify dependent or independent variable
- Given description, identify dependent or independent variable
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Identifying Functions
- Determine function definition, fill in the blank
- Determine & justify functions, mapping representations, no domain & range language
- Determine functions, mapping representations
- Identify & determine functions, set & table representations
- Determine functions, set & table representations
- Determine functions, graphical representations
- Given relation & additional point, determine functions, multiple representations
- Determine functions, multiple representations, including justification, no domain & range language
- Identify functions, description representations
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Identifying & Justifying Functions
- Determine & justify functions, mapping representations
- Determine & justify functions, set representations
- Determine & justify functions, set representations, no domain & range language
- Determine & justify functions, table representations
- Determine & justify functions, table representations, no domain & range language
- Determine & justify functions, graphical representations
- Determine functions, mapping representations, no domain & range language
- Identify & justify functions & non-functions, graphical representations
- Identify functions using equivalent mapping diagrams & sets of ordered pairs
- Identify functions, multiple representations, including justification
- Condensed: Identify, justify, & determine functions
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Domain & Range of Functions
- Determine if value is in domain or range, set & table representations
- Determine if value is in domain or range, graphical representations
- Determine restricted domain & range of linear functions
- Determine discrete domain & range, real-world context
- Determine continuous domain & range, real-world context
- Given graph, determine domain & range
- Condensed: Determine domain & range, including real-world context
- Determine asymptotic domain restrictions of rational functions
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Function Notation
- Given set or table, determine function value
- Given graph, determine function value
- Given linear function, determine function value
- Given quadratic function, determine function value
- Condensed: Given graph or linear function, determine function value
- Condensed: Given linear or quadratic function, determine function value
- Interpret & solve problems involving function notation, real-world context
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Inverse Functions
- Determine inverse of linear function
- Determine if functions are inverses using composition
- Determine inverse of various functions
- Graph function and its inverse
- Determine domain & range of inverse functions
- Condensed: Given function, determine equation, graph, & domain & range of inverse
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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)
- Add function values, (f + g)(#)
- Subtract function values, (f – g)(#)
- Multiply function values, (f * g)(#)
- Divide function values, (f / g)(#)
- Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)
- Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
- Evaluate compositions of functions
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Linear Concepts
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Determining Solution of a Linear Equation
- Given graph of linear equation, identify point on line
- Given linear equation in slope-intercept form, determine if point is on line
- Given linear equation in standard form, determine if point is on line
- Given linear equation in slope-intercept form, identify point on line
- Given linear equation in standard form, identify point on line
- Given horizontal or vertical linear equation, determine if point is on line
- Given horizontal or vertical linear equation, identify point on line
- Condensed: Given linear equation in slope-intercept form & graph, identify point on line
- Given linear equation in slope-intercept form & value of one variable, determine value of other variable
- Given linear equation in slope-intercept form & y-value, determine x-value, fractional coefficients or constants
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Slope of Line
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Find & Use Slope
- Given equation in slope-intercept form, determine next value in table, Δx = 1
- Given equation in slope-intercept form, determine next value in table
- Given equation in slope-intercept form, determine values in table
- Given table of linear equation, determine rate of change & specific value
- Given table, determine rate of change & specific value, function notation
- Given table, determine rate of change & specific value, function notation, integer rate of change
- Given linear graph, determine slope & y-intercept, integer slope
- Given table of linear function, determine slope & y-intercept
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Compare Slopes
- Identify linear table with most extreme rate of change
- Identify linear graph with most extreme rate of change
- Given description, compare rates of change, real-world context
- Compare rates of changes represented differently
- Condensed: Compare rates of change
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Identify Slope Category
- Given linear graph, identify type of slope
- Given linear equation, identify type of slope
- Identify linear graph with specific type of slope
- Given table of linear equation, identify type of slope
- Given graph of horizontal or vertical line, determine rate of change
- Condensed: Identify type of slope
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Find Slope
- Given equation in slope-intercept form, determine rate of change, integer solution
- Given equation in slope-intercept form, determine rate of change
- Given linear equation in standard form, determine rate of change
- Given equation of horizontal or vertical line, determine rate of change
- Given equation in point-slope form, identify slope
- Given two points with integer coordinates, determine rate of change
- Given two points, determine rate of change, integer solution, including undefined
- Given two points, determine rate of change, one coordinate is fraction
- Given two points, determine rate of change, two coordinates are fractions
- Given table of linear equation, determine rate of change
- Given linear graph, determine rate of change, integer solution
- Given linear graph, determine rate of change
- Given linear graph, determine rate of change, various scales
- Given linear graph, determine slope & y-intercept
- Given graph of piece-wise function, determine rate of change over specific interval
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Application of Slope
- Given graph or table of linear function, determine slope or y-intercept, real-world context
- Given right triangle, use legs to determine slope, real-world context
- Given graph of similar right triangles, identify equivalent slopes
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Writing Equation of Line
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Writing Equation Given Point & Slope
- Given slope & y-intercept, determine equation
- Given point & integer slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given point & integer slope or rate of change, determine linear equation in slope-intercept form
- 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 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, integer slope, including slope-intercept form conversion
- Given two points, determine linear equation in slope-intercept form, fractional slope
- Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
- Given two points, determine linear equation in point-slope form, fractional slope, including slope-intercept form conversion
- Given linear table, determine slope, y-intercept, & equation
- Given two points, determine linear equation, undefined slope
- Given two points, determine linear equation, zero slope
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Writing Equation Given Various Components
- Given points or slope & point, determine linear equation in point-slope or standard form
- Given points or slope & point, determine linear equation in 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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Write 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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Write Equation Given Graph with Various Y-Intercepts
- Given linear graph, determine equation in slope-intercept form, m = 1
- 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, identify equation in slope-intercept form, integer slopes, various scales
- 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 linear graph, determine equation in slope-intercept form, integer slopes, various scales
- Given equation in slope-intercept form, identify graph, integer slopes, various scales
- Given linear graph, identify equation, slope-intercept form
- Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
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Intercepts
- Given linear graph, plot y-intercept
- Given linear graph, plot x-intercept
- 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 linear equation in slope-intercept form, determine coordinates of y-intercept
- Given linear equation in standard form, determine coordinates of y-intercept
- Given linear equation in slope-intercept form, determine coordinates of x-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 linear equation, determine intercepts
- Given linear equation in slope-intercept form, plot y-intercept
- Given equation of horizontal or vertical line, plot y-intercept
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Equations, Tables, & Graphs
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Equation to Table
- Given linear equation, fill missing value in table, m = 1
- Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
- Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
- Given linear equation, fill missing value in table, integer slope, b = 0
- Given linear equation, fill missing value in table, integer slope, b = 0, Δx ≥ 5
- Given linear equation & table, determine another point, integer slope, b = 0
- Given linear equation, fill missing value in table, integer slope
- Given linear equation & table, determine another point, m = 1
- Given linear equation & one x-value, determine y-value in table
- Given linear equation, determine table values
- Given linear equation & two x-values, determine y-values in table
- Given linear equation, fill table, m = 1
- Given linear equation, fill table, integer slope, b = 0
- Given linear equation, fill table, integer slope
- Given horizontal or vertical linear equation, fill table
- Given description & linear equation, fill table & determine solution, real-world context
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Equation to Graph
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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
- 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 proportional linear equation
- 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, fractional slope, various scales
- Graph linear equations, including horizontal & vertical, integer slope, various scales
- Graph linear equations, fractional slope
- Given description of linear equation, identify graph, fractional slope, real-world context
- Condensed: Graph linear equations, including horizontal & vertical, various scales
- Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
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Basic Graphing
- Given table, graph proportional linear equation
- Given point & integer slope, graph line
- Given point & slope, graph line
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Graph to Table
- Given linear graph, determine table value, m = 1, table point off graph
- Given linear graph, determine table value, table point off graph
- Given linear graph with points shown on line, determine table value
- Given linear graph through origin with points shown on line, determine table value, table point off graph
- Given linear graph through origin with points shown on line, determine table values, one table point off graph
- Given linear graph through origin, determine table value
- Given linear graph through origin, determine table value, table point off graph
- Given linear graph through origin, determine table values, one table point off graph
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Table to Equation
- Given table representing horizontal linear equation, determine equation
- Given table representing vertical linear equation, determine equation
- Given table, determine linear equation, m = 1
- Given table, determine linear equation, integer slope, b = 0
- Given table, determine linear equation, integer slope
- Given table, identify linear equation in slope-intercept form, rational constants & coefficients
- Given description, determine linear equation, fill table, & determine solution, real-world context
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Identifying Key Features of Linear Functions
- Given table of linear equation, determine slope & intercepts
- Given graph of linear equation, determine slope & intercepts
- Given linear equation, determine slope & intercepts
- Given positive point & whole number slope, determine y-intercept, equation, & specific value
- Given point & integer slope, determine y-intercept, equation, & specific value
- Given linear graph, determine equation in slope-intercept form & specific value, various scales
- Given equation in slope-intercept form, identify slope & y-intercept
- Given linear equation in standard form, solve for y
- Given linear equation in standard form, determine slope
- Condensed: Given linear equation in standard form, solve for y or determine slope
- Condensed: Given linear equation in various forms, determine slope or convert to slope-intercept form
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Vertical & Horizontal Lines
- Given vertical linear equation, determine graph
- Given horizontal linear equation, determine graph
- Given graph of vertical line, determine equation
- Given graph of horizontal line, determine equation
- Condensed: Given graph of horizontal or vertical line, determine equation
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Perpendicular, Parallel, or Neither
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Identify Parallel or Perpendicular Lines
- Given equation in slope-intercept form, determine slope of parallel line
- Given equation in various forms, determine slope of parallel line
- Given equation in slope-intercept form, determine slope of perpendicular line
- Given equation in various forms, determine slope of perpendicular line
- Condensed: Given equation in slope-intercept form, determine slope of parallel or perpendicular line
- Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
- Identify equation that is parallel or perpendicular to line through two given points
- Given two slope-intercept form equations, identify as parallel or perpendicular
- Given two equations in standard form, identify as parallel or perpendicular
- Given two pairs of points, determine if lines containing points are parallel or perpendicular
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Write Equations of Parallel or Perpendicular Lines
- Given equation in slope-intercept form, determine equation of parallel line through specified point
- Given equation in various forms, 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 various forms, determine equation of perpendicular line through specified point
- Given equation in slope-intercept form, determine equation of parallel or perpendicular line through specified point
- Given equation in various forms, determine equation of parallel or perpendicular line through specified point
- 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
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Linear Word Problems
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Identifying Key Features Given Verbal Description
- 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
- 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
- Form 6 – Given linear graph, interpret linear relationship & determine slope-intercept equation
- Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
- Given slope & intercept, interpret linear relationship & determine slope-intercept equation, including negative slope
- Given description of linear relationship, determine slope, y-intercept, & equation, real-world context
- Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
- Determine linear equation in standard form & graph, real-world context
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Choosing Correct Model Given Verbal Description
- Identify equivalent representations of linear relationship, including real-world context
- Given linear word problem, identify graph
- Given description of linear equation, identify graph, integer slope, real-world context
- Given description or table, determine linear graph, real-world context
- Given description of linear relationship, identify graph, table, or equation, real-world context
- Given linear equation, interpret slope & y-intercept, real-world context
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Transformations of Linear Functions
- Identify & graph vertical & horizontal shifts of linear functions
- Identify & graph vertical & horizontal stretches & compressions of linear functions
- Identify & graph reflections of linear functions
- Given description of transformation, determine linear function
- Graph linear functions using all transformations
- Describe parameter changes to linear parent functions
- Identify descriptions of graphs of linear parent functions & transformed functions
- Given table, identify transformations of linear functions
- Condensed: Graph linear functions & identify transformations
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Absolute Value Functions
- Determine x- & y-intercepts of absolute value functions
- Identify & graph vertical & horizontal stretches & compressions of absolute value functions
- Determine minimum & maximum of absolute value functions
- Determine points of intersection of absolute value functions
- Identify & graph vertical & horizontal shifts of absolute value functions
- Identify & graph reflections of absolute value functions
- Graph absolute value functions using all transformations
- Given absolute value equation, identify description of transformation
- Condensed: Graph absolute value functions using any transformation
- Graph absolute value functions using vertex & intercepts
- Condensed: Determine graphical attributes of absolute value functions
- Compare absolute value functions represented differently
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Systems
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Systems of Equations
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Determining Solutions to Systems of Equations
- Given system of linear equations, identify x- or y-value of solution
- Given system of linear equations & description, identify solution, real-world context
- Given system of linear equations, identify solution
- Given graph of system of linear equations, identify specific domain value, real-world context
- Determine systems of linear equations & solutions, real-world context
- Determine & justify solutions to systems of linear equations, real-world context
- Given system of linear equations, identify solution or x- or y-value of solution
- Given table representing system of linear equations, determine solution, real-world context
- Given tables, determine system of linear equations
- Graph systems of linear equations & determine solutions, including real-world context
- Condensed: Given system of linear equations, identify solution, including real-world context
- Condensed: Determine systems of linear equations & solutions, including real-world context
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Solving Systems of Equations, Graphing
- 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 solution, rays on graph to establish pattern
- Given graph of system of linear equations, determine equations in slope-intercept form
- Determine & verify graphical solutions to systems of linear equations, slope-intercept form
- Condensed: Given system of linear equations or description, graph system, including real-world context
- Given system of linear equations, graph & determine point of intersection, slope-intercept form
- Given system of linear equations, determine point of intersection, slope-intercept form
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Solving Systems of Equations, Substitution
- Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
- 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
- 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
- Solve systems of linear equations, infinite possibilities or no solution
- 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: Given system of linear equations, determine solution, substitution bias
- Condensed: Solve or determine system of equations, likely to have same variable isolated
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Solving Systems of Equations, Elimination
- Given system of linear equations in standard form, determine point of intersection, integer coordinates
- Determine systems of linear equations & solutions, elimination bias, real-world context
- Condensed: Solve or determine system of equations, both equations in standard form
- Solve systems of linear equations, multiply at most one equation
- Solve systems of linear equations, multiply one or both equations
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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
- Condensed: Determine systems of linear equations & solutions
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Systems of Inequalities
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Basic Systems of Inequalities
- Graph systems of two linear inequalities, slope-intercept form
- Determine equivalent systems of linear inequalities & graphical solutions
- Graph systems of three linear inequalities, slope-intercept form
- Given graph, determine solution of systems of linear inequalities
- Solve systems of linear inequalities
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Application of Systems of Inequalities
- Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
- Given description, determine system of linear inequalities in standard form & solution point, real-world context
- Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
- Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
- Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
- Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, 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 linear system of inequalities graph, identify true statements
- Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
- Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
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Exponents
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Product Rule of Exponents
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Product of Power, Only Variables
- Express repeated variables as powers, single variable
- Express repeated variables as powers, multiple variables
- Express powers as repeated variables
- Apply product rule of exponents, one variable, positive exponents
- Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
- Simplify single variable powers, negative base or coefficient
- Apply product rule of exponents, two variables, three to four factors, positive exponents
- Apply product rule of exponents, two variables, four to six factors, positive exponents
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Product of Power, Including Coefficients
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Quotient Rule of Exponents
- 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, positive exponents
- Apply product & quotient rules of exponents, one or two variables, positive exponents
- 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
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Power Rule of Exponents
- Apply power rule, one variable, positive exponents
- Apply power rule, including multiple variables, positive exponents
- Apply power & product rules of exponents, fraction with numerator of one, positive exponents
- Apply power & product rules of exponents, one variable, positive exponents
- Apply product & power rules of exponents, one variable, coefficient of negative one
- Apply power & product rules of exponents, multiple variables, positive exponents
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Negative Exponents
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Basic Negative Exponents
- Express negative power using positive exponent
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Product Rule with Negative Exponents
- Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
- Apply product rule of exponents, negative 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, at least one negative exponent
- Apply product rule of exponents, two variables, four to six factors, at least one variable cancels
- Apply product rule, multiple variables, coefficients other than one, including negative exponents
- Apply power rule, multiple variables, coefficients other than one, including negative exponents
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Quotient Rule with Negative Exponents
- Apply quotient rule of exponents, one variable, at least one negative exponent
- Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
- 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
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Power Rule with Negative 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
- Apply power rule of exponents, 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, negative base or coefficient, multiple variables, including negative exponents
- Apply power rule, including multiple variables & negative exponents
- Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
- Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
- Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
- Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
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Mixed Rules of Exponents
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Simplifying Exponential Expressions
- Apply power rule of exponents, positive exponents
- Simplify powers, fractional algebraic base, including negative exponents
- Apply product rule of exponents, coefficients other than one
- 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
- Express negative power using positive exponent, coefficient other than one
- Apply power, product, & quotient rules of exponents, positive exponents
- Apply power, product, & quotient rules of exponents, including negative exponents
- Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
- Apply product, quotient, & power rules of exponents, one variable
- Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one non-positive exponent
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Multiplying Exponential Expressions
- Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive 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
- 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, divide two fractions, one or two variables, at least one non-positive exponent
- Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
- Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents
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Dividing Exponential Expressions
- 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 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, divide two fractions, multiple variables, at least one non-positive exponent
- Apply power, product, & quotient rules of exponents, divide fractions, positive exponents
- Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents
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MIxed Operations of Exponential Expressions
- Apply product & quotient rules of exponents, negative exponents
- Apply product & quotient rules of exponents, negative exponents, coefficients other than one
- 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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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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Rational Exponents
- Evaluate numerical expressions with rational exponents
- Simplify numerical expressions with rational exponents
- Evaluate rational exponent expressions, positive exponents
- Simplify rational exponent expressions using product rule, coefficients not with base
- Evaluate rational exponent expressions, negative exponents
- Simplify rational exponent expressions using quotient rule, with coefficients
- Simplify rational exponent expressions using product rule, coefficients with base
- Simplify rational exponent expressions using power rule, with coefficients
- Condensed: Simplify rational exponents using product & power rules
- Condensed: Evaluate rational exponent expressions
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Radicals & Roots
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Simplifying Radicals
- Determine square roots of perfect squares
- Simplify square roots
- Simplify square roots, coefficient greater than one
- Identify steps to simplify square roots
- Given square root expression, evaluate for specific value
- Condensed: Simplify square roots, including algebraic expressions
- Evaluate perfect cube roots
- Convert from radical to rational exponent, single value in radicand
- Convert from radical to rational exponent, algebraic term in radicand
- Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
- Simplify radical expression raised to power that is multiple of index
- Condensed: Convert from radical to rational exponent
- Convert from rational exponent to radical, single value base
- Convert from rational exponent to radical, algebraic base
- Condensed: Convert from rational exponent to radical
- Determine principal square root of perfect squares
- Simplify radical expressions, perfect powers
- Add & subtract radical expressions, one or two variables, simplified radicals
- Add & subtract radical expressions, one or two variables, radicals to simplify
- Multiply radical expressions, numbers & variables
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Solving Radicals
- Solve perfect square root equations
- Condensed: Determine square roots of perfect squares
- Solve perfect cube root equations
- Condensed: Determine cube roots of perfect cubes
- Condensed: Evaluate & compare perfect square & cube roots
- 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, multi-step
- Solve square root equations, divide by coefficient of root
- Condensed: Solve square root equations, one-step & two-step
- Solve square root equations, square root = x ± #
- Condensed: Solve square root equations
- Solve square root equations, square root ± square root = #
- Identify extraneous solutions of square root equations
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Data Analysis
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Graphical Displays of Data
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Dot Plots
- Determine mean from dot plots
- Determine median from dot plots
- Determine mean absolute deviation from dot plots
- Determine & compare means from two dot plots
- Determine & compare medians from two dot plots
- Compare mean absolute deviations from two dot plots
- Compare characteristics of side-by-side dot plots
- Solve one-step problems from dot plots, real-world context
- Solve multi-step problems from dot plots, real-world context
- Given data, identify dot plot
- Given data represented in various ways, identify dot plot
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Histograms
- Solve problems involving interpretation of histograms
- Given various representations of data, determine histogram
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Bar Graphs
- Determine or interpret percentage bar graphs
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Box Plots
- Solve problems involving interpretation of box plots
- Solve problems involving five-number summary
- Determine five-number summary
- Given boxplot, determine values from five-number summary
- Solve problems involving interpretation of stacked box plots, real-world context
- Condensed: Determine five-number summary, including box plots
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Frequency Tables
- Interpret two-way frequency tables, marginal distribution
- Interpret two-way frequency tables, conditional distribution
- Interpret two-way frequency tables, joint distribution
- Given two-way frequency tables, identify associations
- Determine two-way frequency tables
- Condensed: Interpret two-way frequency tables
- Determine specified probabilities in two-way frequency tables
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Measures of Center & Spread
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Calculating Measures of Center & Spread
- Determine mean, median, mode, & range
- Identify definition of mean, median, mode, or range
- Determine mean, median, mode, or range
- Given various representations of data, identify mean, median, mode, & range
- Determine mean, median, mode, or range from various graphs
- Given mean, median, mode, or range, determine missing value in data set
- Given mean, median, or range, determine missing or additional value in data set
- Given additional value in data set, determine change in mean, median, mode, or range
- Condensed: Determine mean, median, mode, or range, including graphs
- Determine interquartile range of data
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Interpreting Measures of Center & Spread
- Identify measures of center based on data distribution
- Identify measures of variability based on data distribution
- Identify & interpret measures of center
- Identify & interpret measures of variability
- Determine or interpret shapes & features of graphs
- Determine or interpret measures of center & spread from graphs
- Given various representations of data, identify outlier
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Linear Modeling
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Scatterplots
- Identify positive & negative correlations in scatter plots
- Identify linear & nonlinear associations in scatter plots
- Identify scatterplots with clustered data
- Identify outliers in scatter plots
- Given data, determine scatter plot
- Condensed: Interpret scatter plots
- 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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Regression
- Determine linear regression equations, calculator expected
- Determine quadratic regression equations, calculator expected
- Determine exponential regression equations, calculator expected
- Condensed: Determine linear, quadratic, or exponential equations, calculator expected
- Given regression equation, determine predicted value
- Given table, identify as linear, quadratic, or exponential
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Correlation
- Identify correlation & causation
- Identify association & causation
- Given table, determine & interpret correlation coefficient
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Quadratic Functions
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Solving Quadratic Functions
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Solving Quadratics, Factoring
- Apply zero product property to solve factored quadratic equations
- Identify zeros of factored quadratics
- Determine relationship between zeros & linear factors of quadratic functions
- Solve quadratic equations using factoring, a = 1, b > 0, 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, difference of squares
- Solve quadratic equations using factoring, perfect square trinomial
- Solve quadratic binomial equation by factoring out GCF
- Solve quadratic binomial equation by factoring out GCF, one term on each side
- Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
- Solve quadratic equations using factoring, |a| ≤ 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, 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, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
- Factor perfect square trinomials, degree two, one variable
- Factor perfect square trinomials, degree two, two variables
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Solving Quadratics, Given Graph
- Given graph of quadratic function, determine roots/zeros
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Solving Quadratic Functions, Square Root Method
- Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
- Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
- Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
- Determine exact solution to quadratic equations, a = ±1, b = 0
- Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
- Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
- Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
- Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
- Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
- Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, a(cx ± h)^2 + k = #
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Solving Quadratics, 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 Quadratics, Completing the Square
- Solve quadratic equations, complete the square, a = 1, real solutions
- Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
- Condensed: Solve quadratic equations, complete the square, real solutions
- Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
- Determine constant required to complete the square, a ≥ 1, including fractions
- Solve quadratic equations, perfect square trinomial
- Solve quadratic equations, complete the square, integers, a > 1, real solutions
- Solve quadratic equations, complete the square, integers, a = 1, real solutions
- Condensed: Solve quadratic equations, complete the square, integers, real solutions
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Application of Solving Quadratics
- Determine or use quadratic equations, real-world context
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Writing Equations of Quadratic Functions
- Given vertex & point, determine quadratic equation, vertex form
- Given vertex & point, determine quadratic equation, standard form
- Given graph of quadratic function, determine equation in standard form
- Given graph of quadratic function, determine equation
- Given quadratic equation in standard form, determine vertex form of equation
- Given integer solutions of quadratic equation, determine function in standard form
- Given zeros of quadratic function, determine quadratic equation with integer coefficients
- Given rational solutions of quadratic equation, determine function in standard form
- Given graphical attributes, determine equation of parabola
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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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Identifying Key Features of Quadratic Functions
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Identifying Vertex, Axis of Symmetry, & Extrema of Quadratics
- 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 vertex of quadratic functions
- Determine symmetry of quadratic functions
- Problem to be Retired (try 1127324): Determine axis of symmetry of quadratic functions
- Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
- Determine intervals of increase & decrease of quadratic functions
- Determine end behavior of quadratic functions
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Identifying Intercepts of Quadratics
- Determine zero(s) of quadratic functions
- Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
- Determine x-intercept(s) of quadratic functions
- 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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Identifying Mixed Key Attributes of Quadratics
- 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 quadratic equation, determine attributes & graph
- Condensed: Given graph, equation, or table, determine attributes of quadratic function
- Determine intervals where quadratic function is positive or negative
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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 equations
- Given quadratic equation in standard form, determine graph
- Given quadratic equation in vertex form, determine graph
- Given equation, graph quadratic function
- Identify & graph reflections of quadratic functions
- Graph quadratic functions using all transformations
- Given quadratic equation, vertex, & point, graph function & determine attributes
- Given table, determine attributes of quadratic function, real-world context
- Condensed: Graph quadratic functions using any transformation
- Condensed: Determine graphical attributes of quadratic functions
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Transformations of Quadratic Functions
- Identify & graph vertical & horizontal shifts of quadratic functions
- Identify & graph vertical & horizontal stretches & compressions of quadratic functions
- Describe parameter changes to quadratic parent functions
- Identify descriptions of graphs of quadratic parent functions & transformed functions
- Given description of transformation, determine quadratic function
- Given quadratic equation, identify description of transformation
- Determine effects of parameter changes in quadratic relationships, real-world context
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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 height of dropped object, determine position function & specific time
- Given initial height & velocity of object in vertical motion, determine position function & specific time
- Given initial height & negative velocity of object in vertical motion, determine position function & specific time
- Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
- Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
- 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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Polynomial Expressions & Functions
- Interpret terms or factors in expressions, including real-world context
- Condensed: Classify polynomials & identify components of polynomials
- Determine quadratic factors of polynomials, degree four
- Determine linear factors of polynomials, degree four
- Factor sum & difference of two cubes, degree three, one variable
- Condensed: Determine linear factors of polynomials, degree three or four
- Determine x-intercepts/zeros & y-intercepts of polynomial functions
- Determine symmetry of various functions
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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
- Given verbal description & graph, determine domain & range of exponential function
- Determine domain & range of discrete exponential functions, real-world context
- Determine restricted domain & range of exponential functions
- Determine domain & range of discrete exponential functions
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Graphing Exponential Functions
- Given exponential growth function, determine graph
- Given exponential growth function, determine graph, includes fractional coefficients
- Given exponential growth or decay function, determine graph, includes fractional coefficients
- Given graph, identify solution to exponential equation
- Given equation, graph exponential function, including base e
- Graph exponential functions using all transformations
- Given graph, determine equation of exponential function
- Given equation, graph exponential function
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Identifying Key Features of Exponential Functions
- Determine minimum & maximum of exponential functions
- Determine asymptote of exponential functions
- Given exponential equation, determine asymptote
- Given graph, determine asymptote of exponential function
- Determine asymptote of exponential functions, real-world context
- Determine y-intercept of exponential function, real-world context
- Determine x-intercepts/zeros & y-intercepts of exponential functions
- Determine end behavior of exponential functions
- Condensed: Graph exponential functions & identify transformations
- Graph exponential functions using all transformations
- Condensed: Determine graphical attributes of exponential functions
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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 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 Functions
- Solve simple exponential equations
- Solve exponential equations, one variable & one base
- Solve exponential equations, both bases reduce to common base
- Solve exponential equations, two different bases, no common base possible
- Solve exponential equations, base e
- Solve exponential equations, no logs required
- Solve exponential equations, common bases given
- Solve exponential equations, one base reduces to common base
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Application of Exponential Functions
- Calculate investment value, annual compounding
- Calculate investment value, various compounding
- Calculate depreciating asset value, annual compounding
- Condensed: Calculate investment & depreciating asset values, annual compounding
- Interpret values in exponential functions, real-world context
- Given table, determine attributes of exponential function
- Determine asymptote of exponential functions, real-world context
- Exponential growth & decay, real-world context
- Determine exponential function, real-world context
- Compare exponential functions represented differently
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Logarithmic Functions
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Graph Logarithmic Functions
- Given log equation, identify description of transformations
- Identify & graph reflections of log functions
- Identify & graph vertical & horizontal shifts of log functions
- Given equation, graph log function
- Graph log functions using all transformations
- Condensed: Graph log functions & identify transformations
- Identify & graph vertical & horizontal stretches & compressions of log functions
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Identify Key Features of Logarithmic Functions
- Determine x-intercepts/zeros & y-intercepts of log functions
- Determine asymptote of log functions
- Determine end behavior of log functions
- Given table, determine attributes of log function
- Determine minimum & maximum of log functions
- Condensed: Determine graphical attributes of log functions
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Write 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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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
- Determine function & specific term for geometric sequences, real-world context
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Application of Sequences
- Identify arithmetic & geometric sequences & determine common difference or common ratio
- Given table, determine difference in terms in arithmetic sequence, real-world context
- 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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Foundations of Geometry
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Vocabulary
- Determine definitions of undefined terms of geometry, fill in the blank
- Determine definitions of angles & shapes, fill in the blank
- Determine definitions of conjectures, fill in the blank
- Determine definitions of theorems, fill in the blank
- Determine definitions of postulates, fill in the blank
- Condensed: Determine definitions of general geometry vocabulary, fill in the blank
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Distance & Midpoint
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Distance
- Determine distance between two points on number line
- Determine fractional distance between two points on number line
- Determine distance between points
- Determine distance between points, horizontal or vertical
- Determine distance between points, including coordinate plane
- Given segment on coordinate plane, determine length
- Determine fractional distance or fractional point dividing segment into specified ratio
- Given coordinates for vertices of triangle, determine length of sides
- Given coordinates, use length to determine segment congruence
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Midpoint
- Determine midpoint of segment on number line
- Given endpoints, determine midpoint
- Determine midpoint of two points on coordinate plane
- Given midpoint & endpoint, determine other endpoint on coordinate plane
- Condensed: Determine midpoint or endpoint of segment on coordinate plane
- Given endpoint & point dividing segment into specified ratio, determine other endpoint on coordinate plane
- Determine point that divides segment into specified ratio on coordinate plane
- Condensed: Determine endpoint or point dividing segment into specified ratio on coordinate plane
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Distance & Midpoint Combined
- Given midpoint or distance between points, determine missing endpoint
- Condensed: Determine distance or midpoint on number line
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Angles
- Classify angles from figure
- Identify angle names
- Identify angle pairs
- Identify types of angles in figures
- Estimate angle measures
- Identify 90°, 180°, 270°, & 360° angles
- Measure angles using protractor
- Measure angles using protractor, real-world context
- Identify angles with specified measures
- Apply angle addition postulate to determine angle measures
- Apply angle addition postulate to determine angle measures, algebraic expressions
- Condensed: Apply angle addition postulate to determine angle measures, including algebraic expressions
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Properties of Triangles
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Classifying Triangles
- Classify triangles by sides
- Classify triangles by angles
- Classify triangle based on given angle measures
- Classify triangles based on angles & sides
- Apply triangle inequality theorem to determine range of values for unknown side
- Apply triangle inequality theorem to determine side lengths
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Isosceles & Equilateral Triangles
- Given congruent sides, identify congruent angles of isosceles triangle
- Given congruent angles, identify congruent sides of isosceles triangle
- Solve problems involving perimeter of equilateral triangles
- Solve problems involving perimeter of isosceles triangles
- Given equilateral triangle & algebraic expressions for sides, solve for variable or determine side length
- Given equilateral triangle & algebraic expression for angle, solve for variable
- Determine angle measure in isosceles triangle, at most one algebraic expression
- Determine angle measure in isosceles triangle, up to two algebraic expressions
- Condensed: Solve problems involving perimeter of equilateral & isosceles triangles
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Triangle Angle Sum & Exterior Angles
- Given two angle measures in triangle, determine angle measure
- Given two angle measures in triangle, determine & justify angle measure
- Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions
- Apply triangle angle sum theorem to determine angles, algebraic expressions
- Apply triangle angle sum theorem to determine angles, multiple algebraic expressions
- Given description, apply triangle angle sum theorem to determine angles, algebraic expressions
- Apply triangle exterior angle theorem to determine angles, including algebraic expressions
- Condensed: Apply triangle angle sum theorem & exterior angle theorem to determine angles, including algebraic expressions
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Perpendicular & Angle Bisectors
- Given perpendicular bisector in triangle, determine segment lengths
- Given perpendicular bisector in triangle, determine segment lengths, algebraic expressions
- Given angle bisector in triangle, determine angles
- Given angle bisector in triangle, determine angles, algebraic expressions
- Determine segment lengths in triangles with angle bisectors
- Condensed: Given perpendicular or angle bisector in triangle, determine segment lengths or angles, including algebraic expressions
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Area & Perimeter on the Coordinate Plane
- Determine area of polygons in coordinate plane
- Determine area of polygons in coordinate plane, real-world context
- Given coordinates of vertices, determine side lengths & perimeter of polygons
- Given coordinates of vertices, determine area of triangle or rectangle
- Determine area of composite figures on coordinate plane, no circular shapes
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Triangle Similarity & Congruence
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Similar Triangles
- Identify corresponding parts of similar figures
- Determine angles of similar triangles using AA similarity
- Determine similarity of triangles using AA similarity
- Determine similar triangles using SAS similarity
- Determine similar triangles using SSS similarity
- Determine missing steps in proofs involving similar triangles
- Determine missing steps in proofs involving similar triangles, paragraph form
- Determine sides of similar triangles using AA similarity
- Determine angles of similar triangles using AA similarity, algebraic expressions
- Determine segment lengths using triangle proportionality theorem
- Condensed: Determine similar triangles using SAS or SSS similarity
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Proofs
- Determine missing steps in proofs involving SSS in triangles
- Determine missing steps in proofs involving SAS in triangles
- Determine missing steps in proofs involving AAS in triangles
- Determine missing steps in proofs involving ASA in triangles
- Determine missing steps in proofs involving triangle congruence theorems
- Determine missing steps in proofs involving triangle congruence theorems, paragraph form
- Determine missing steps in proofs involving corresponding parts
- Determine missing steps in proofs involving corresponding parts, paragraph form
- Determine missing steps in proofs involving quadrilaterals
- Apply triangle theorems or determine missing steps in proofs
- Determine missing steps in proofs involving quadrilaterals, paragraph form
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Geometric Transformations
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Translations
- Given coordinate vertices of figure, determine translated image
- Given figure on coordinate plane, determine translated coordinates
- Identify rule or determine translated point on coordinate plane
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Reflections
- Determine coordinates of reflected points
- Given coordinate vertices of figure, determine reflected image
- Identify rule or reflected point on coordinate plane
- Given figure on coordinate plane, determine reflected coordinates
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Rotations
- Given coordinate vertices of figure, determine rotated image
- Given figure on coordinate plane, determine rotated coordinates
- Identify rule or rotated point on coordinate plane
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Dilations
- Identify characteristics of dilations
- Identify rule or dilated point on coordinate plane, including variable scale factors
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Mixed Transformations
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Transformations of Angles, Lines, & Segments
- Identify characteristics of transformed lines
- Identify characteristics of transformed line segments
- Identify characteristics of transformed parallel lines
- Identify characteristics of transformed angles
- Identify characteristics of transformed lines, segments, & angles
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Transformations of Figures
- Given congruent figures, identify description of transformations
- Given similar figures, identify description of transformations
- Identify congruence transformations
- Identify rule or determine transformed point on coordinate plane
- Identify rule for transformed shape on coordinate plane
- Composition of transformations on coordinate plane
- Identify characteristics of transformations
- Identify reflections & rotations on coordinate plane
- Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates
- Condensed: Given similar or congruent figures, identify description of transformations
- Condensed: Identify rule or determine transformed point on coordinate plane
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Absolute Value Functions
- Given graph, determine absolute value equation
- Given description of transformation, determine absolute value equation
- Condensed: Graph absolute value functions using any transformation
- Given absolute value equation, identify description of transformation
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Trigonometry
- Identify definitions of trig functions
- Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
- Given right triangle, determine missing side & trig ratio, sin, cos, & tan
- Given right triangle, determine missing side & trig ratio, cot, sec, & csc
- Condensed: Given right triangle, determine missing side & trig ratio
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Probaility
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables