Algebra 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 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 rational numbers
- Determine relationships between subsets of real numbers
- Determine result of adding & multiplying rational & irrational numbers
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Algebraic Properties
- Identify properties used in numerical expressions
- Identify properties used to solve linear equations
- Identify properties used in numerical & algebraic expressions
- Identify steps to solve linear equations
- Evaluate & identify equivalent numerical expressions, including real-world context
- Identify equivalent algebraic expressions, including real-world context
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Numerical Absolute Value
- Determine absolute value of integers
- Determine absolute value of integers, including real-world context
- Determine absolute value of numeric expression
- Determine absolute value of rational numbers
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Order of Operations
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Order of Operations, Only Postives
- Evaluate numerical expressions, # + #(#)
- Evaluate numerical expressions, #/# + #
- Evaluate numerical expressions, #/# + #, decimals
- Evaluate numerical expressions, # ± #(#), decimals
- Evaluate numerical expressions, #(# + #), decimals
- Evaluate numerical expressions, # + #(#)^#
- Evaluate numerical expressions, #(#)^# + #/#
- Evaluate numerical expressions, # + #(# + #)^#
- Evaluate numerical expressions, up to four operations
- Evaluate numerical expressions, including rationals & up to two sets of grouping symbols
- Identify first steps in evaluating numerical expressions using grouping symbols
- Evaluate numerical expressions, up to two sets of grouping symbols, real-world context
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Order of Operations, Three or Four Integers
- Evaluate sum or difference of three integers, at least one difference
- Evaluate sum or difference of four integers, at least one difference
- Evaluate sum or difference of four integers, two grouped in parentheses, at least one difference
- Evaluate sum or difference of four integers, two grouped in absolute value, at least one difference
- Evaluate numerical expressions, three or four integers, including multiplication & division
- Evaluate numerical expressions, three or four integers, including multiplication & division as fraction
- Evaluate numerical expressions, three or four integers, one exponent, including multiplication
- Evaluate numerical expressions, four integers, including multiplication & exponents
- Evaluate numerical expressions, real-world context
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Order of Operations, Five or More Integers
- Evaluate sum or difference of six integers, two grouped in parentheses, two grouped in absolute value, at least one difference
- Evaluate numerical expressions, five integers, two grouped in parentheses, including multiplication & division
- Evaluate numerical expressions, five integers, two grouped in absolute value, including multiplication & division
- Evaluate numerical expressions, five integers, one exponent, two grouped in parentheses, including multiplication & division
- Evaluate numerical expression quotients, five to seven integers, including multiplication, division, & absolute value
- Evaluate numerical expression quotients, five to seven integers, one exponent, including multiplication, division, & absolute value
- Condensed: Evaluate numerical expressions
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Order of Operations, Rational Numbers
- Identify equivalent expressions using order of operations
- Evaluate numerical expressions, fractions, no exponents
- Evaluate numerical expressions, decimals, no exponents
- Evaluate numerical expressions, decimals & fractions, no exponents
- Evaluate numerical expressions, fractions
- Evaluate numerical expressions, decimals
- Evaluate numerical expressions, decimals & fractions
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Scientific Notation
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Basic Scientific Notation
- Identify correct conversion of number from scientific notation with positive exponent to standard form
- Identify correct conversion of number from scientific notation with negative exponent to standard form
- Convert number from scientific notation with positive exponent to standard form
- Convert number from scientific notation with negative exponent to standard form
- Identify correct conversion of number from standard form to scientific notation with positive exponent
- Identify correct conversion of number from standard form to scientific notation with negative exponent
- Convert number from standard form to scientific notation with positive exponent
- Convert number from standard form to scientific notation with negative exponent
- Condensed: Identify correct conversion of number between scientific notation & standard form
- Condensed: Convert number between scientific notation & standard form
- Convert number from word form to scientific notation
- Compare two numbers in scientific notation
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Scientific Notation, Round First
- Round & convert number from standard form to scientific notation with positive exponent
- Round & convert number from standard form to scientific notation with negative exponent
- Condensed: Round & convert number from standard form to scientific notation
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Basic Operations with Scientific Notation
- Add numbers in scientific notation
- Subtract numbers in scientific notation
- 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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Coordinate Plane
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Basic Coordinate Plane
- Plot integer points
- Plot integer points on coordinate plane, point on axis
- Given integer point on graph, determine coordinates
- Given integer point on graph, determine coordinates, point on axis
- Given lattice point, determine coordinates
- Plot points on coordinate plane, student selects scales
- Condensed: Plot integer points or determine coordinates
- Given rational point, determine location on coordinate plane
- Plot rational points on coordinate plane
- Plot or identify rational points on coordinate plane
- Plot rational points on coordinate plane, graph scale at most one-half
- Condensed: Plot or identify points on coordinate plane
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Application of Coordinate Plane
- Identify first quadrant points or parts of coordinate plane
- Identify locations or parts of coordinate plane using first quadrant points
- Identify description of process to plot first quadrant points
- Determine or identify first quadrant points, real-world context
- Determine or identify first quadrant points, including cardinal directions, real-world context
- Condensed: Plot or determine coordinates of first quadrant rational points
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Inferential Reasoning 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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Expressions
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Evaluating Expressions
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Evaluating Expressions, Only Positives
- Evaluate addition expressions for specified value, one variable, whole numbers
- Evaluate addition expressions for specified value, one variable, at least one fraction
- Evaluate addition expressions for specified value, one variable, at least one decimal
- Evaluate subtraction expressions for specified value, one variable, whole numbers
- Evaluate subtraction expressions for specified value, one variable, at least one fraction
- Evaluate subtraction expressions for specified value, one variable, at least one decimal
- Evaluate expressions for specified value, one variable, including multiple operations, at least one decimal
- Evaluate expressions for specified values, two variables, multiple operations, including powers & real-world context
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Evaluating Expressions, Including Negatives
- Evaluate expressions for specified value, one variable, two terms, only sums & differences
- Evaluate expressions for specified value, one variable, one term, two factors
- Evaluate linear expressions for specific values
- Evaluate expressions for specified value, one variable, one term, three factors
- Evaluate expressions for specified value, one variable, two terms
- Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
- Evaluate expressions for specified value, one variable, two terms, multiple operations, including powers of absolute values
- Evaluate expressions for specified values, two variables, two terms
- Evaluate expressions for specified values, two variables, two terms, one term with three factors
- Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
- Evaluate expressions for specified values, two variables, quotient of expressions
- Evaluate algebraic expressions, including variable exponents
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Simplifying Expressions
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Combining Like Terms
- Simplify algebraic expressions, combine two terms, positives
- Simplify algebraic expressions, combine two terms
- Simplify algebraic expressions, one variable, positive integer coefficients
- Simplify algebraic expressions, one variable, integer coefficients
- Simplify algebraic expressions, one variable, rational coefficients
- Simplify algebraic expressions, two variables, positive integer coefficients
- Simplify algebraic expressions, two variables, integer coefficients
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Distributive Property
- Simplify algebraic expressions, one variable, distribute once, integer multiplier
- Simplify algebraic expressions, one variable, distribute once, fraction multiplier
- Simplify algebraic expressions, one variable, distribute once, decimal multiplier
- Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
- Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
- Simplify algebraic expressions, one variable, distribute once, variable multiplier
- Simplify algebraic expressions, one variable, distribute once, variable with coefficient multiplier
- Simplify algebraic expressions, one variable, distribute once, including rationals
- Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
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Distributive Property & Combining Like Terms
- Identify equivalent expressions involving distribution
- 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 combine like terms & product of two factors
- Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
- Simplify algebraic expressions, one variable, distribute twice
- Simplify algebraic expressions, two variables, distribute twice
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Writing Rational Expression as Two Terms
- Convert linear binomials divided by constants to sum or difference of two terms
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Ratios, Rates, & Proportions
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Rates
- Determine unit rates, whole numbers, real-world context
- Determine unit rates, fractions, real-world context
- Determine unit rates, mixed numbers, real-world context
- Given unit rate, determine specified value in proportional relationship, real-world context
- Condensed: Determine or apply unit rates, real-world context
- Given rate, convert time unit to determine quantity over time interval, real-world context
- Given rate of travel, determine distance or time
- Given rate & comparison, determine unit rates, real-world context
- Determine & compare unit rates, real-world context
- Given proportional relationship, determine specified quantity, real-world context
- Given proportional relationship, determine specified quantity, including decimals, real-world context
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Ratios
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Basic Ratios
- Determine part to whole ratio, decimal grids
- Determine part to part ratio, decimal grids
- Identify percents, area models
- Given ratio, identify table
- Given table of proportional relationship, determine value or equivalent ratio
- Compare rates
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Application of Ratios
- Determine part to whole ratio, strip diagrams, real-world context
- Determine part to part ratio, strip diagrams, real-world context
- Determine part to whole ratio, double number lines, real-world context
- Determine part to part ratio, including double number lines, including real-world context
- Determine specified values in ratios, strip diagrams, real-world context
- Determine specified values in proportional relationships, real-world context
- Determine ratios or specified quantities from table or identify table from given ratio, real-world context
- Compare rates or determine specified values in proportional relationships, real-world context
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Proportions
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Basic Proportions
- Solve proportions, whole numbers
- Solve proportions
- Solve proportions, mixed number components, whole number cross products
- Solve proportions, mixed number components
- Solve proportions, one binomial expression
- Solve proportions, two binomial expressions
- Condensed: Solve proportions, binomial expressions
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Application of Proportions
- Solve proportions, exact answers, real-world context
- Solve proportions, rounded answers, real-world context
- Solve proportions involving time, real-world context
- Condensed: Solve proportions, including real-world context
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Equations
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One-Step Equations
- Condensed: Solve one-step linear equations, addition or subtraction
- Condensed: Solve one-step linear equations, multiplication or division
- Solve one-step linear equations, fractional answers
- Solve one-step linear equations, fractional coefficients
- Solve one-step linear equations, fractional coefficients & constants
- Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
- Determine one-step linear equations, real-world context
- Determine one-step equations, including decimals, real-world context
- Given one-step linear equation, identify real-world situation represented by equation
- Given one-step equation, identify real-world situation represented by equation
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Two-Step Equations
- Solve two-step linear equations, algebra tiles
- Determine if given value is solution to two-step linear equations
- Solve ax ± b = c
- Condensed: Solve x/a ± 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 two-step linear equations
- Condensed: Solve one- or two-step linear equations, fractional coefficients
- Condensed: Solve one- or two-step linear equations, including fractional answers
- Determine two-step linear equations, real-world context
- Given two-step linear equation, identify real-world situation represented by equation
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Multi-Step Equations
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Multi-Step Equations, no Distribution
- 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 (ax ± b)/c = d
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Multi-Step Equations, with Distribution
- Solve linear equations, distributive property on one side
- 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
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Equations with Variables on Both Sides
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Equations with Variables on Both Sides
- Solve linear equations, variables on both sides
- 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
- Condensed: Solve linear equations, variables on both sides or like terms
- Condensed: Solve linear equations, variables on both sides, rationals
- Solve multi-step linear equations
- Solve linear equations, distributive property on both sides, integers
- Solve linear equations, distributive property on both sides, rationals
- 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
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Application of Equations with Variables on Both Sides
- 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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Solving for Specified Variable
- Given linear equation of form ay = bx, solve for y
- Given linear equation of form ay = bx + c, solve for y
- Given linear equation of form a + by = cx, solve for y
- Given linear equation with two terms on each side, solve for specified variable
- Given linear equation with three terms on one side, solve for specified variable
- Condensed: Given linear equation in various forms, solve for specified variable
- Solve for specific variable in mathematical formula
- Solve for specific variable in scientific formula
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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
- Solve linear absolute value equations, variable on both sides
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Identifying Number of Solutions
- Determine number of solutions in linear equations, distribute at most one time
- Determine number of solutions in linear equations, distribute up to two times
- Condensed: Determine number of solutions in linear equations
- Solve linear equations, including no solution & infinitely many solutions
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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
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Two-Step or Multi-Step One-Variable Inequalities
- Solve & graph two-step inequalities
- Condensed: Solve & graph inequalities
- Determine equivalence of inequalities & solution set
- 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
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Application of One-Variable Inequalities
- Determine one-step inequalities, including real-world context
- Identify one-step inequalities that model real-world problems or interpret inequality components
- 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 one-step inequalities, rational numbers, including real-world context
- Given two-step inequality, identify real-world problem modeled by inequality
- 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
- Determine inequalities with variables on both sides, real-world context
- Given inequality with variable on both sides, identify real-world problem modeled by inequality
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Linear Inequalities
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Linear Inequalities Solutions & Non-Solutions
- Given linear inequality & x-value, determine y-value
- Given linear inequality, determine solutions & non-solutions, slope-intercept form
- Given linear inequality graph, determine solutions & non-solutions
- Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
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Basic Linear Inequalities
- Graph linear inequalities, slope-intercept form, only oblique lines
- Graph linear inequalities, slope-intercept form, including vertical & horizontal lines
- Given linear inequality, identify correct graph, slope-intercept form
- Given linear inequality, determine graph, slope-intercept form
- Given graph, identify linear inequality, slope-intercept form
- Condensed: Determine equivalent linear inequalities & graphical solutions
- Graph linear inequalities, vertical & horizontal lines
- Graph linear inequalities, various forms
- Given graph, determine linear inequality
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Application of Linear Inequalities
- Given description, determine inequality, graph, & possible solutions
- Given graph, determine inequalities in standard form, real-world context
- Given description, determine linear inequalities in standard form, including tables, real-world context
- Given description & table, graph linear inequality, real-world context
- Given description, determine linear inequalities in standard form & specific solutions, 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
- Solve linear programming problems, real-world context
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Compound Inequalities
- Solve compound inequalities, “and” solutions, multiple choice
- Solve & graph compound inequalities, “and” solutions
- Solve & graph compound inequalities, “and” solutions, including real-world context
- Solve & graph compound inequalities, “or” solutions
- Condensed: Solve & graph compound inequalities
- Given description, determine 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
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Absolute Value Inequalities with Setup
- Given linear absolute value inequality, determine compound inequality
- Solve & graph linear absolute value inequalities, “and” solutions, including setup
- Solve & graph linear absolute value inequalities, “or” solutions, including setup
- Solve & graph linear absolute value inequalities, including setup
- Condensed: Solve & graph linear absolute value inequalities, including setup
- Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
- Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
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Absolute Value Inequalities without Setup
- Solve & graph linear absolute value inequalities, “and” solutions
- Solve & graph linear absolute value inequalities, “or” solutions
- Condensed: Solve & graph linear absolute value inequalities
- Solve & graph linear absolute value inequalities, including extra constant or coefficient
- Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
- Create linear absolute value inequalities, real-world context
- Create linear absolute value equations, real-world context
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Functions
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Identifying Functions
- Determine function definition, fill in the blank
- Determine & justify functions, table representations, no domain & range language
- Determine functions, set & table representations
- Identify & determine functions, set & table representations
- Determine functions, mapping representations, no domain & range language
- Determine functions, mapping representations
- Given relation & additional point, determine functions, multiple representations
- Determine functions, graphical representations
- Given step graphs, identify functions
- 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, no domain & range language
- Determine & justify functions, mapping representations
- Determine & justify functions, set representations, no domain & range language
- Determine & justify functions, set representations
- Identify functions using equivalent mapping diagrams & sets of ordered pairs
- Determine & justify functions, table representations
- Determine & justify functions, graphical representations
- Identify & justify functions & non-functions, graphical representations
- Identify functions, multiple representations, including justification
- Condensed: Identify, justify, & determine functions
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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
- Given graph, determine domain & range
- Determine restricted domain & range of linear functions
- Determine discrete domain & range, real-world context
- Determine continuous domain & range, real-world context
- Condensed: Determine domain & range, including real-world context
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Function Notation
- Given set or table, determine function value
- Given linear function, determine function value
- Condensed: Given graph or linear function, determine function value
- Given quadratic function, determine function value
- Condensed: Given linear or quadratic function, determine function value
- Given graph, determine function value
- Interpret & solve problems involving function notation, real-world context
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Determine Parent Functions & Points of Intersection
- Determine whether given table represents linear or exponential function
- Determine points of intersection of various functions, not absolute value or polynomial
- Condensed: Determine points of intersection of functions
- Determine whether given table represents linear, exponential, or quadratic function
- Determine whether given graph represents linear, exponential, or quadratic function
- Condensed: Determine what function given table or graph represents
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Graph Functions
- Given various functions, identify graph
- Given graph, identify various functions
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Inverse Functions
- Determine inverse of linear function
- Determine inverse of quadratic & square root functions
- Determine inverse of cubic & cube root functions
- Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions
- Determine inverse of various functions
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Linear Concepts
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Determining Solution of Linear Equation
- Given linear equation in slope-intercept form, determine if point is on line
- Given linear equation in slope-intercept form, identify point on line
- Given linear equation in standard form, determine if point is 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
- 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
- Condensed: Given linear equation in slope-intercept form & graph, identify point on line
- Given graph of linear equation, identify point on line
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Slope of Line
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Finding & Using 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, integer rate of change
- Given table, determine rate of change & specific value, function notation
- Given table of linear function, determine slope & y-intercept
- Given linear graph, determine slope & y-intercept, integer slope
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Comparing 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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Identifying Slope Category
- Given graph of horizontal or vertical line, determine rate of change
- Given linear graph, identify type of slope
- Identify linear graph with specific type of slope
- Given linear equation, identify type of slope
- Given table of linear equation, identify type of slope
- Condensed: Identify type of slope
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Finding Slope
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Finding Slope Given Points
- 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
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Finding Slope Given Equation or Graph
- Given equation in point-slope form, identify slope
- Given equation in slope-intercept form, determine rate of change, integer solution
- Given equation in slope-intercept form, determine rate of change
- Given equation of horizontal or vertical line, determine rate of change
- Given linear equation in standard form, 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 & integer slope or rate of change, determine linear equation in slope-intercept form
- Given point & integer slope, determine linear equation in slope-intercept form
- Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given point & fractional slope, determine linear equation in slope-intercept form, integer y-intercept
- Given point & fractional slope, determine linear equation in slope-intercept form, fractional y-intercept
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Writing Equation Given Two Points
- Given two points, determine linear equation in slope-intercept form, integer slope
- Given two points, determine linear equation in point-slope form, integer slope, including slope-intercept form conversion
- Given two points, determine linear equation in standard 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 point-slope form, fractional slope, including slope-intercept form conversion
- Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
- Given two points, determine linear equation, undefined slope
- Given two points, determine linear equation, zero slope
- Given linear table, determine slope, y-intercept, & equation
- Given intercepts, determine linear equation in slope-intercept form
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Writing Equation Given Various Components
- Given linear equation, write equation in requested form
- Given points or slope & point, determine linear equation in standard form
- Given points or slope & point, determine linear equation in point-slope or standard form
- Given points or slope & point, determine linear equation in various forms
- Condensed: Given two points, determine linear equation in slope-intercept form, including horizontal & vertical lines
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Writing Equation Given Graph
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Writing Equation Given Graph Through Origin
- Given linear graph through origin, determine equation in slope-intercept form, integer slope, 1 ≤ |m| ≤ 3
- Given linear graph through origin, determine equation in slope-intercept form, integer slope
- Given linear graph through origin with points shown on line, determine equation in slope-intercept form, integer slopes
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Writing Equation Given Graph, Slope-Intercept Form
- 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, integer slopes, various scales
- Given linear graph, determine equation in slope-intercept form, fractional slopes
- Given linear graph, determine slope, y-intercept, & equation
- Given linear graph, identify equation, slope-intercept form
- Condensed: Given linear graph, determine equation in slope-intercept form & specific value, various scales, including real-world context
- Given equation in slope-intercept form, identify graph, integer slopes, various scales
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Writing Equation Given Graph, Various Forms
- Given linear graph, determine equation in point-slope form
- Given linear graph, determine equation in standard form
- Given linear graph, identify equation, various forms
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Identify Equivalent Graphs & Equations
- Identify equivalent linear graphs & equations in slope-intercept form
- Identify equivalent linear graphs & equations in slope-intercept form, various scales
- Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
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Intercepts
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Intercepts, Given Graph
- 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 graph, identify equation, various forms
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Intercepts, Given Equation
- Given linear equation in slope-intercept form, plot y-intercept
- Given equation of horizontal or vertical line, plot y-intercept
- Given linear equation in slope-intercept form, determine coordinates of y-intercept
- Given linear equation in slope-intercept form, determine coordinates of x-intercept
- Given linear equation in standard form, determine coordinates of y-intercept
- Given equation of horizontal or vertical line, determine coordinates of y-intercept
- Given equation of horizontal or vertical line, determine coordinates of x-intercept
- Given linear equation, determine intercepts
- Condensed: Given linear equation, determine x- or y-intercepts
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Equations, Tables, & Graphs
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Equation to Table
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Fill Missing Value in 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, fill missing value in table, integer slope
- Given linear equation & one x-value, determine y-value in table
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Fill Table
- Given linear equation & table, determine another point, m = 1
- Given linear equation & table, determine another point, integer slope, b = 0
- 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
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Slope-Interecept Form to Graph Scale of One
- Graph linear equations, m = 1
- Graph linear equations, integer slope not including one & negative one, b = 0
- Graph linear equations, integer slope not including one & negative one
- Graph proportional linear equation
- Graph linear equations, fractional slope
- Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
- Given description of linear equation, identify graph, fractional slope, real-world context
- Condensed: Identify equivalent equations, graphs, & tables
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Slope-Intercept Form to Graph Various Scales
- Graph linear equations, m = 1, various scales
- Given equation in slope-intercept form, graph line, m = ±1, various scales
- Graph linear equations, integer slope, various scales
- Graph linear equations, fractional slope, various scales
- Graph linear equations, including horizontal & vertical, integer slope, various scales
- Condensed: Graph linear equations, including horizontal & vertical, various scales
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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 values, one table point off graph
- Given linear graph through origin with points shown on line, determine table value, 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, determine linear equation, m = 1
- Given table, determine linear equation, integer slope, b = 0
- Given table, determine linear equation, integer slope
- Given table representing horizontal linear equation, determine equation
- Given table representing vertical linear equation, determine equation
- 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 Function
- Given table of linear equation, determine slope & intercepts
- Given graph of linear equation, determine slope & intercepts
- Given linear equation in standard form, determine slope
- Given linear equation in standard form, solve for y
- Given equation in slope-intercept form, identify slope & y-intercept
- Given linear equation, determine slope & intercepts
- 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
- 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
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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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Identifying Parallel or Perpendicular Lines
- Given equation in slope-intercept form, determine slope of parallel line
- Given equation in slope-intercept form, determine slope of perpendicular line
- Given two slope-intercept form equations, identify as parallel or perpendicular
- Condensed: Given equation in slope-intercept form, determine slope of parallel or perpendicular line
- Given equation in various forms, determine slope of parallel line
- Given equation in various forms, determine slope of perpendicular line
- Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
- 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
- Identify equation that is parallel or perpendicular to line through two given points
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Writing Equations of Parallel or Perpendicular Lines
- Given equation in slope-intercept form, determine equation of parallel line through specified point
- Given equation in slope-intercept form, determine equation of perpendicular line through specified point
- Given equation in slope-intercept form, determine equation of parallel or perpendicular line through specified point
- Determine equation of line through specified point parallel or perpendicular to x-axis
- Determine equation of line through specified point parallel or perpendicular to y-axis
- Condensed: Determine equation of line through specified point parallel or perpendicular to x- or y-axis
- Given equation in various forms, determine equation of parallel line through specified point
- Given equation in various forms, determine equation of perpendicular line through specified point
- Given equation in various forms, determine equation of parallel or perpendicular line through specified point
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Line of Best Fit & Scatter Plots
- Identify positive & negative correlations in scatter plots
- Identify linear & nonlinear associations in scatter plots
- Condensed: Interpret scatter plots
- Sketch line of best fit
- Sketch line of best fit & determine equation, graph scales of one
- Sketch line of best fit & determine equation, various graph scales
- Condensed: Sketch line of best fit & determine equation
- Sketch line of best fit & determine predicted value
- Sketch line of best fit & determine equation, real-world context
- Determine residuals
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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
- Given slope & intercept, interpret linear relationship & determine slope-intercept equation, including negative 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 description of linear relationship, determine slope, y-intercept, & equation, real-world context
- Determine linear equation in standard form & graph, real-world context
- Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
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Choosing Correct Model Given Verbal Description
- Given description of linear equation, identify graph, integer slope, real-world context
- Given description or table, determine linear graph, real-world context
- Given description, determine equation & specific value, real-world context
- Given description of linear relationship, identify graph, table, or equation, real-world context
- Identify equivalent representations of linear relationship, including real-world context
- Given linear word problem, identify graph
- Given linear equation, interpret slope & y-intercept, real-world context
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Absolute Value Functions
- Determine x- & y-intercepts of absolute value functions
- Determine minimum & maximum of absolute value functions
- Identify & graph reflections of absolute value functions
- Identify & graph vertical & horizontal shifts of absolute value functions
- Identify & graph vertical & horizontal stretches & compressions of absolute value functions
- Given absolute value equation, identify description of transformation
- Condensed: Determine graphical attributes of absolute value functions
- Graph absolute value functions using all transformations
- Condensed: Graph absolute value functions using any transformation
- Graph absolute value functions using vertex & intercepts
- Determine points of intersection 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 Solution to System of Equations
- Given tables, determine system of linear equations
- Given table representing system of linear equations, determine solution, real-world context
- Given graph of system of linear equations, identify specific domain value, real-world context
- Graph systems of linear equations & determine solutions, including real-world context
- Given system of linear equations, identify x- or y-value of solution
- Given system of linear equations, identify solution
- Given system of linear equations, identify solution or x- or y-value of solution
- Given system of linear equations & description, identify solution, real-world context
- Condensed: Given system of linear equations, identify solution, including real-world context
- Determine systems of linear equations & solutions, real-world context
- Determine & justify solutions to systems of linear equations, real-world context
- Condensed: Determine systems of linear equations & solutions, including real-world context
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Solving Systems of Equations, Graphing
- 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
- Given system of linear equations, graph system, including tables
- Given system of linear equations, determine point of intersection, slope-intercept form
- Given system of linear equations, graph & determine point of intersection, slope-intercept form
- Given description of system of linear equations, graph & determine equations or tables
- Condensed: Given system of linear equations or description, graph system, including real-world context
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Solving Systems of Equations, Substitution
- Given system of linear equations with same isolated variable, determine point of intersection, integer coordinates
- Given system of linear equations, determine point of intersection, integer coordinates, one horizontal or vertical & one slope-intercept form
- Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
- Condensed: Given system of linear equations, determine solution, substitution bias
- 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
- Determine systems of linear equations & solutions, substitution bias, real-world context
- Determine solutions of linear equations, substitution bias, including given system, real-world context
- Solve systems of linear equations, infinite possibilities or no solution
- 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
- Solve systems of linear equations, multiply at most one equation
- Solve systems of linear equations, multiply one or both equations
- Condensed: Solve or determine system of equations, both equations in standard form
-
Solving Systems of Equations, Mixed Methods
- Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
- Condensed: Determine systems of linear equations & solutions
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Systems of Inequalties
-
Basic Systems of Inequalities
- Given graph, determine solution of systems of linear inequalities
- Determine equivalent systems of linear inequalities & graphical solutions
- Graph systems of two linear inequalities, slope-intercept form
- Graph systems of three linear inequalities, slope-intercept form
- Solve systems of linear inequalities
-
Application of Systems of Inequalities
- Given linear system of inequalities graph, identify true statements
- Given description, determine system of linear inequalities in standard form & solution point, real-world context
- Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
- Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
- Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
- Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
- Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
- Given description of system of linear inequalities, identify graph of system
- 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
- 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
-
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, 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
- Apply power & product rules of exponents, fraction with numerator of one, positive exponents
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Product Rule of Exponents
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Product of Powers, Only Variables
- Express repeated variables as powers, single variable
- Express repeated variables as powers, multiple variables
- Express powers as repeated variables
- Simplify single variable powers, negative base or coefficient
- Apply product rule of exponents, one variable, positive exponents
- Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
- Apply product rule of exponents, 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 Powers, Including Coefficients
- Express repeated variables as powers or powers as repeated variables
- Express repeated variables as powers, coefficients other than one
- Apply product rule of exponents, positive exponents
- Apply product rule of exponents, one variable, positive exponents, coefficients other than one
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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 quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents
- Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, positive exponents
- Apply product & quotient rules of exponents, one or two variables, positive exponents
-
Negative Exponents
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Basic Negative Exponents
- Express negative power using positive exponent
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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, 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 rule of exponents, negative exponents
- Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
- Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
- Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
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Product Rule with Negative Exponents
- Apply power rule, multiple variables, coefficients other than one, including 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
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Quotient Rule with Negative Exponents
- Apply quotient rule of exponents, one variable, 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
- Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
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Mixed Properties of Exponents
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Simplifying Exponential Expressions
- Express negative power using positive exponent, coefficient other than one
- 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, positive 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 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
- 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
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Multiplying Exponential Expressions
- 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 fractions, one or two variables, coefficients other than one, including negative exponents
- 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 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 two fractions, one or two variables, at least one non-positive exponent
- Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
- Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
- Apply product & quotient rules of exponents, 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, positive fractional base, including non-positive exponents
- Evaluate powers, fractional base, positive exponent
- Evaluate powers, fractional base, negative exponent
- Evaluate powers, fractional bases
- Condensed: Evaluate powers with negative exponents
-
Rational Exponents
- Evaluate numerical expressions with rational exponents
- Simplify numerical expressions with rational exponents
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Radicals & Roots
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Simplifying Radicals
- Determine square roots of perfect squares
- Determine principal square root 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
- Simplify radical expressions, perfect powers
- Multiply radical expressions, numbers & variables
- Add & subtract radical expressions, one or two variables, simplified radicals
- Add & subtract radical expressions, one or two variables, radicals to simplify
- Condensed: Add & subtract radical expressions
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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
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Quadratic Functions
-
Identifying Key Features of Quadratic Functions
-
Determine Intercepts
- Determine x-intercept(s) of quadratic functions
- Determine y-intercept of quadratic functions
- Determine x-intercepts/zeros & y-intercepts of quadratic functions, vertex form
- Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
- Determine zero(s) of quadratic functions
- Given graph or table of quadratic function, determine x- & y- intercepts
-
Determine Maximum & Minimum Values
- Given graph of quadratic function, determine minimum or maximum value
- Given quadratic equation, determine minimum or maximum value
- Determine minimum & maximum of quadratic functions
-
Determine Vertex, Symmetry, Increase & Decrease, & End Behavior
- Determine vertex of quadratic functions
- Determine symmetry of quadratic functions
- Determine intervals of increase & decrease of quadratic functions
- Determine intervals where quadratic function is positive or negative
- Determine end behavior of quadratic functions
-
Determine Attributes & Graph
- Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
- Given graph of quadratic function, determine attributes
- Condensed: Determine graphical attributes of quadratic functions
- Condensed: Given graph, equation, or table, determine attributes of quadratic function
- Given quadratic equation, determine attributes & graph, a ≠ ±1
- Given quadratic equation, determine attributes & graph, a = 1
- Given quadratic equation, determine attributes & graph, a = -1
- Condensed: Given quadratic equation, determine attributes & graph
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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 vertex form, determine graph
- Given quadratic equation in standard form, determine graph
- Graph quadratic functions using all transformations
- Given equation, graph quadratic function
- Given quadratic equation, vertex, & point, graph function & determine attributes
- Condensed: Graph quadratic functions using any transformation
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Writing Equations of Quadratic Functions
- Given graph of quadratic function, determine equation
- Given graph of quadratic function, determine equation
- Given vertex & point, determine quadratic equation, vertex form
- Given quadratic equation in standard form, determine vertex form of equation
- Given vertex & point, determine quadratic equation, standard form
- Given graphical attributes, determine equation of parabola
- Given quadratic equation in vertex form, determine standard form of equation
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Solving Quadratic Functions
-
Solving Quadratics, Zero Product
- Apply zero product property to solve factored quadratic equations
- Identify zeros of factored quadratics
- Determine relationship between zeros & linear factors of quadratic functions
-
Solving Quadratics, Factoring GCF
- Solve quadratic binomial equation by factoring out GCF
- Solve quadratic binomial equation by factoring out GCF, one term on each side
- Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
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Solving Quadratics, Factoring Trinomials & Difference of Squares
- Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
- Solve quadratic equations using factoring, a = 1, b ≠ 0, |c| ≤ 40, zero on one side
- Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
- Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
- Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
- Solve quadratic equations using factoring, |a| ≤ 10, b ≠ 0, |c| ≤ 40, zero on one side
- Solve quadratic equations using factoring, |a| ≤ 10, |c| ≤ 40, terms on both sides
- Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
- Solve quadratic equations using factoring, difference of squares
- Factor perfect square trinomials, degree two, one variable
- Factor perfect square trinomials, degree two, two variables
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Solving Quadratics, 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 solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
- Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
- Determine exact solution to quadratic equations, a = ±1, b = 0
- Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
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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 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
- Determine constant required to complete the square, a ≥ 1, including fractions
- Solve quadratic equations, complete the square, integers, a = 1, real solutions
- Solve quadratic equations, complete the square, integers, a > 1, real solutions
- Solve quadratic equations, complete the square, a > 1, real solutions
- Condensed: Solve quadratic equations, complete the square, integers, real solutions
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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
- Given quadratic equation, identify description of transformation
- Identify descriptions of graphs of quadratic parent functions & transformed functions
- Given description of transformation, determine quadratic function
- Describe parameter changes to quadratic parent functions
- Determine effects of parameter changes in quadratic relationships, real-world context
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Vertical Motion Problems
- Given initial height & velocity of object in vertical motion, determine function, table, & graph of position
- Given initial height & velocity of object in vertical motion, determine position function & maximum height
- Given initial height & velocity of object in vertical motion, determine position function & time to maximum height
- Given initial height & velocity of object in vertical motion, determine position function & time to ground
- Given initial height & velocity of object in vertical motion, determine position function & specific time
- Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
- Given initial height & negative velocity of object in vertical motion, determine position function & specific time
- Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
- Given height of dropped object, determine position function & specific time
- Condensed: Given initial height & velocity of object in vertical motion, determine position function, maximum height, or time to maximum height
- Condensed: Given initial height & velocity of object in vertical motion, determine position function & specific times
- Condensed: Given initial height & velocity of object in vertical motion, determine position graph, position function, & specific times
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Domain & Range of Quadratic Functions
- Given description of domain & range of quadratic function, choose graph
- Given graph of quadratic function, determine domain & range
- Given equation of quadratic function, determine domain & range
- Condensed: Determine domain & range of quadratic function
- Determine restricted domain & range of quadratic functions
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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
-
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 base
- Given exponential function, determine function value, rational coefficient
- Given exponential function, determine function value, rational base & coefficient
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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 graph, determine equation of exponential function
- Given equation, graph exponential function
- Given equation, graph exponential function, including base e
-
Writing Exponential Functions
- Given table, determine exponential growth function
- Given table, determine exponential decay function
- Given table, determine linear or exponential growth function
- Given graph, determine equation of exponential function
-
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
- Determine exponential function, real-world context
- Given table, determine attributes of exponential function
- Interpret values in exponential functions, real-world context
- Given absolute value equation, identify description of transformation
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Polynomials
-
Standard Form of Polynomials
- Identify leading coefficient of polynomials
- Identify leading coefficient of polynomials, including two variables
- Identify terms of expressions
- Determine degree, leading coefficient, & type of polynomial
- Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables
- Determine standard form of polynomial, no like terms
- Determine standard form of polynomial, like terms
- Determine standard form of polynomial, no like terms, including two variables
- Determine standard form of polynomial, like terms, including two variables
-
Classifying Polynomials
- Determine degree of polynomials
- Determine degree of polynomials, including two variables
- Identify polynomial as monomial, binomial, or trinomial
- Identify polynomial as monomial, binomial, or trinomial, including two variables
- Classify polynomials by degree
- Classify polynomials by degree & number of terms
- Condensed: Classify polynomials & identify components of polynomials
-
Operations of Polynomials
-
Addition & Subtraction of Polynomials
- Add binomials & trinomials, degrees zero to two
- Subtract binomials & trinomials, degrees zero to two
- Add binomials & trinomials, degrees zero to three
- Subtract binomials & trinomials, degrees zero to three
- Condensed: Add or subtract binomials & trinomials
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Multiplication & Division of Polynomials
- Multiply monomial times binomial or trinomial, degrees zero to two
- Multiply monomial times binomial or trinomial, mixed degrees
- Multiply binomial times binomial, both degree one
- Square linear binomial
- Condensed: Multiply binomial times binomial
- Multiply binomial times binomial, mixed degrees
- Multiply linear binomial times quadratic trinomial
- Multiply binomial times trinomial, mixed degrees
- Divide polynomials, degree one or two by degree one or two
- Divide polynomials, degree three or four by degree one
- Divide polynomials, divisor supports synthetic division
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Mixed Operations of Polynomials
- Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
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Factoring Polynomials
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GCF or LCM of Polynomials
- Determine GCF in polynomials, one variable
- Determine GCF of two monomials, two variables
- Determine LCM of two monomials, two variables
- Condensed: Determine GCF or LCM of two monomials, two variables
- Factor GCF in polynomials, degree one or two, one variable
- Factor GCF in polynomials, one variable
- Factor GCF in polynomials, including two variables
- Determine missing component of GCF
- Given GCF & one monomial, identify second monomial
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Factoring Trinomials, a=1
- Factor quadratic trinomials, a = 1, b > 0, c > 0
- Factor quadratic trinomials, a = 1
- Factor quadratic trinomials, a = 1, terms scrambled
- Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
- Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < |c| ≤ 10
- Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
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Factoring Trinomials, a>1
- Factor quadratic trinomials, 1 < a ≤ 10, no GCF
- Factor quadratic trinomials, 1 < |a| ≤ 10, 0 < |c| ≤ 30
- Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
- Factor quadratic trinomials, 1 < |a| ≤ 30, 0 < |c| ≤ 40
- Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
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Factoring Using Difference of Squares
- Factor difference of two squares, degree two, one variable, coefficient one
- Factor difference of two squares, degree two, one variable, terms scrambled
- Factor difference of two squares, degree two, one variable
- Factor difference of two squares, two variables
- Factor difference of two squares, one or two variables
- Condensed: Factor difference of two squares, degree two
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Mixed Factoring
- Factor GCF & remaining quadratic expression, a = 1, one variable
- Factor GCF & remaining quadratic expression, a ≥ 1, one variable
- Factor common binomial
- Factor binomial & its opposite
- Factor cubic polynomial by grouping, one variable
- Factor cubic polynomial by grouping & difference of two squares, one variable
- Identify factors of polynomials
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Application of Polynomials
- Determine sums of polynomials or missing polynomial addends
- Determine differences of polynomials or missing polynomial subtrahends
- Condensed: Determine sums or differences of polynomials or missing polynomial operands
- Given polynomial & sum of polynomials, determine missing polynomial
- Given polynomial & difference of polynomials, determine missing polynomial
- Add & subtract polynomials to determine expressions for perimeter of various shapes
- Given monomial & binomial or trinomial, multiply or identify missing value
- Determine missing value to make polynomial statement true, multiplication
- Multiply polynomials to determine expressions for areas of rectangles & triangles
- Divide quadratic trinomial by linear binomial, word problem context
- Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
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Rational Expressions & Functions
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Operations of Rational Expressions
- Multiply rational expressions
- Divide rational expressions
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Simplifying Rational Expressions
- Simplify rational expressions by factoring GCF, one monomial & one binomial
- Simplify rational expressions by factoring GCF, two binomials
- Simplify rational expressions by factoring GCF, two binomials, remaining binomials cancel
- Simplify rational expressions by factoring GCF, one trinomial or difference of squares
- Simplify rational expressions by factoring GCF, trinomials & differences of squares
- Simplify rational expressions by factoring GCF, remaining leading coefficient one
- Condensed: Simplify rational expressions
- Condensed: Simplify rational expressions, including trinomials
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Rational Functions
- Identify value that makes rational expression undefined
- Determine values that make rational expressions undefined
- Given rational function, determine function value
- Graph rational functions
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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
- Determine function & specific term for geometric sequences, real-world context
- Condensed: Determine formula or specific term of geometric sequences
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Arithmetic & Geometric 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
- Determine function & specific term for arithmetic & geometric sequences, real-world context
- Condensed: Identify arithmetic & geometric sequences & determine components of sequences
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Data Analysis & Probability
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Counting Methods
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Fundamental Counting Principle
- Determine number of combinations using fundamental counting principle, real-world context
- Determine number of combinations using fundamental counting principle, including repeated letters & digits, real-world context
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Permutations
- Given visual model, determine permutations, specified items predetermined
- Determine permutations using all items, real-world context
- Determine permutations, real-world context
- Determine permutation of letters in word, nondistinct letters
- Determine permutation of letters in word, distinct letters
- Determine permutations, one nondistinct item, real-world context
- Determine permutations, multiple nondistinct items, real-world context
- Condensed: Determine permutation of letters in word, including nondistinct letters
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Combinations
- Given lists, determine combinations, choose from one list, real-world context
- Given lists, determine combinations, choose from two lists, real-world context
- Determine combinations, real-world context
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Permutations & Combinations
- Determine combinations & permutations, two questions, real-world context
- Determine combinations & permutations, four questions, real-world context
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Probabiltiy
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Basic Probability
- Determine sample spaces
- Classify probabilities by levels of likelihood
- Determine odds
- Determine probabilities & odds, including visual models
- Determine equivalent probabilities & odds
- Determine theoretical probabilities
- Determine theoretical probabilities, fraction answers
- Determine probabilities of single events
- Determine probabilities & complementary probabilities of single events, including visual models
- Determine probabilities & complementary probabilities of single events as fractions, decimals, or percents, including visual models
- Determine probabilities of flipping coins specified number of times
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Compound Probability
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Determine AND Probabilities
- Given visual model, determine “and” probability as fraction, decimal, or percent, dependent events
- Determine “and” probabilities, independent events, visuals provided
- Determine “and” probabilities, independent events, same sample space
- Determine “and” probabilities, independent events, two distinct sample spaces
- Determine probabilities of flipping coins & rolling die
- Determine “and” probabilities, dependent events, multiple choice
- Determine “and” probabilities, dependent events
- Determine “and” probabilities, independent & dependent events
- Determine “and” probabilities, independent & dependent events, including complementary events
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Determine OR Probabilities
- Given visual model, determine “or” probability
- Given visual model, determine “or” probability as fraction, decimal, or percent
- Determine “or” probabilities as fractions
- Determine “or” probabilities as fractions, decimals, or percents
- Determine “or” probabilities
- Given visual model, determine “or” probability
- Given visual model, determine “or” probability as fraction, decimal, or percent
- Determine “and” probabilities, independent events, visuals provided
- Determine “and” probabilities, independent events, same sample space
- Determine “and” probabilities, independent events, two distinct sample spaces
- Determine “and” probabilities, dependent events, multiple choice
- Determine “and” probabilities, dependent events
- Given visual model, determine “and” probability as fraction, decimal, or percent, dependent events
- Determine probabilities of flipping coins & rolling die
- Determine “or” probabilities as fractions
- Determine “or” probabilities as fractions, decimals, or percents
- Determine “and” probabilities, independent & dependent events
- Determine “and” probabilities, independent & dependent events, including complementary events
- Determine “or” probabilities
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Experimental Probability & Sampling
- Identify samples & populations
- Identify biased samples & questions
- Identify variables of interest
- Identify simulations used to acquire simple random samples
- Identify simulations to model probability events
- Identify statistical inferences
- Condensed: Identify samples, populations, variables of interest, & statistical inferences
- Determine size of sample spaces, compound events
- Determine sample spaces, compound events
- Determine experimental probabilities
- Determine experimental probabilities, fraction answers
- Compare data from two samples, various representations
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Predictions from Probabilities
- Determine inferences from samples
- Determine predicted values or compare likelihood of events
- Determine predicted values, theoretical probability
- Determine predicted values, experimental probability
- Determine predicted values, experimental or theoretical probability
- Determine predicted values, theoretical probability, compound events
- Determine predicted values, experimental probability, compound events
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Mixed Probability
- Determine “or” probabilities
- Determine “or” probabilities, including “and” situations
- Condensed: Determine probabilities
- Condensed: Determine experimental & theoretical probabilities
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Conditional Probaility
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
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Data Analysis
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Measures of Center & Spread
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Calculating Measures of Center & Spread
- Identify definition of mean, median, mode, or range
- Determine mean, median, mode, & range
- Determine mean, median, mode, or range
- Determine mean, median, mode, or range from various graphs
- Given various representations of data, identify mean, median, mode, & range
- Given mean, median, or range, determine missing or additional value in data set
- Given mean, median, mode, or range, determine missing 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 & interpret measures of center
- Identify & interpret measures of variability
- Identify measures of center based on data distribution
- Identify measures of variability based on data distribution
- Determine or interpret shapes & features of graphs
- Determine or interpret measures of center & spread from graphs
- Given various representations of data, identify outlier
- Identify outliers in scatter plots
- Identify scatterplots with clustered data
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Stem-&-Leaf Plots
- Determine mean, median, mode, & range from stem-&-leaf plots
- Determine mean, median, mode, or range from stem-&-leaf plots
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Box Plots
- Determine five-number summary
- Given boxplot, determine values from five-number summary
- Determine characteristics of boxplots
- Solve problems involving interpretation of box plots
- Solve problems involving 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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