 ## Math 1 Skills

VIEW ALL SKILLS

• Algebra Foundations
• Real Number System
• 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
• 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
• 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
• 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
• Scientific Notation
• 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
• 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
• Expressions & Operations
• 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
• 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
• 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
• Equations
• 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
• 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
• 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
• 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
• 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
• Inequalities
• One-Variable Inequalities
• 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
• 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
• Linear Inequalities
• 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
• 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
• 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
• 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
• Functions
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Linear Concepts
• 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
• Slope of Line
• 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
• 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
• 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
• 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
• 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
• Writing Equation of Line
• 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
• 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
• 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
• Writing Equation Given Graph
• 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
• 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
• 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
• Equations, Tables, & Graphs
• 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
• Equation to Graph
• Standard Form to Graph
• Given linear equation in standard form, graph
• Given linear equation in standard form, graph, scrambled variable terms
• Determine linear equation in standard form & graph, real-world context
• Condensed: Determine linear equation in standard form & graph, including real-world context
• Slope-Intercept Form to Graph
• 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
• Basic Graphing
• Given table, graph proportional linear equation
• Given point & integer slope, graph line
• Given point & slope, graph line
• 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
• 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
• 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
• 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
• Perpendicular, Parallel, or Neither
• 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
• 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
• Linear Word Problems
• 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
• 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
• 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
• 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
• Systems
• Systems of Equations
• 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
• 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
• 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
• 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
• 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
• Systems of Inequalities
• 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
• 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
• Exponents
• Product Rule of Exponents
• 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
• Product of Power, Including Coefficients
• 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
• 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
• Negative Exponents
• Basic Negative Exponents
• Express negative power using positive exponent
• 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
• 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
• 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
• Mixed Rules of Exponents
• 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
• 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
• 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
• 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
• Application of Exponents
• Determine algebraic expressions for perimeter & area of rectangles
• Given algebraic expressions for area & side of rectangles, determine expression for missing side
• 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
• 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
• 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, 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
• Multiply radical expressions, numbers & variables
• 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
• Data Analysis
• Graphical Displays of Data
• 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
• Histograms
• Solve problems involving interpretation of histograms
• Given various representations of data, determine histogram
• Bar Graphs
• Determine or interpret percentage bar graphs
• 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
• 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
• Measures of Center & Spread
• 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
• 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
• Linear Modeling
• 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
• 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
• Correlation
• Identify correlation & causation
• Identify association & causation
• Given table, determine & interpret correlation coefficient
• 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
• Given graph of quadratic function, determine roots/zeros
• 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 = #
• Given quadratic equation in standard form, determine discriminant
• Given quadratic equation in standard form, determine number of solutions
• Given quadratic equation in standard form, determine solutions rounded to nearest hundredth
• Given quadratic equation, determine solutions rounded to nearest hundredth, constant on one side
• Given quadratic equation, determine solutions rounded to nearest hundredth, combine like terms first
• Given quadratic equation in standard form, determine attributes & solutions rounded to nearest hundredth
• Given proportion, solve resulting quadratic equation, b = 0
• Given proportion, solve resulting quadratic equation, b ≠ 0
• Given quadratic equation in standard form, determine exact solutions
• Given quadratic equation in standard form, determine exact solutions, combine like terms first
• Solving 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
• Determine or use quadratic equations, real-world context
• 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
• 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
• Identifying Key Features of Quadratic Functions
• 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
• 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
• 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
• Given quadratic equation, determine graph, b = 0
• Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
• 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
• 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
• 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
• 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
• Exponential & Logarithmic Functions
• Exponential Functions
• Evaluating Exponential Functions
• Given exponential function, determine function value, non-negative input
• Given exponential function, determine function value, negative input
• Given exponential function, determine function value, rational coefficient
• Given exponential function, determine function value, rational base
• Given exponential function, determine function value, rational base & coefficient
• Domain & Range of Exponential Functions
• Given equation, determine domain & range of exponential function
• 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
• 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
• 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
• Transformations of Exponential Functions
• Identify & graph reflections of exponential functions
• Identify & graph vertical & horizontal shifts of exponential functions
• Identify & graph vertical & horizontal stretches & compressions of exponential functions
• Given table, identify transformations of exponential functions
• Given exponential equation, identify description of transformations
• Writing Exponential Functions
• Given table, determine linear or exponential growth function
• Given table, determine exponential growth function
• Given table, determine exponential decay function
• Given graph, determine equation of exponential function
• Solving Exponential 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
• 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
• Logarithmic Functions
• 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
• 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
• Write Equations of Logarithmic Functions
• Given graph, determine equation of log function
• Exponential & Logarithmic Equations
• Given log equation, determine exponential equation
• Given exponential equation, determine log equation
• Condensed: Convert between exponential & log equations
• Sequences
• Arithmetic Sequences
• Determine terms in arithmetic sequences
• Given arithmetic sequence, determine common difference & next term
• Given formula, determine specific term of arithmetic sequence
• Determine common difference, first term, & formula of arithmetic sequences
• Condensed: Determine formula & specific terms of arithmetic sequences
• Geometric Sequences
• Given formula, determine specific term of geometric sequence
• Determine formula & specific term of geometric sequences
• Condensed: Determine formula or specific term of geometric sequences
• Determine function & specific term for geometric sequences, real-world context
• 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
• Foundations of Geometry
• 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
• Distance & Midpoint
• 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
• 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
• Distance & Midpoint Combined
• Given midpoint or distance between points, determine missing endpoint
• Condensed: Determine distance or midpoint on number line
• 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
• Properties of Triangles
• 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
• 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
• 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
• 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
• 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
• Triangle Similarity & Congruence
• 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
• 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
• Geometric Transformations
• 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
• 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
• 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
• Dilations
• Identify characteristics of dilations
• Identify rule or dilated point on coordinate plane, including variable scale factors
• Mixed Transformations
• 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
• 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
• 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
• 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
• Probaility
• Determine conditional probabilities from two-way frequency tables
• Determine conditional probabilities, including two-way frequency tables