Algebra 2 Skills

Algebra Foundations

Real Number System & Properties
 Determine relationships between subsets of real numbers
 Determine relationships between subsets of rational numbers
 Determine result of adding & multiplying rational & irrational numbers
 Order real numbers, no exponents
 Order real numbers, positive exponents, percents are whole, including realworld context
 Order real numbers, positive exponents, percents are whole, including realworld context
 Order irrational numbers
 Comparing expressions on given interval
 Compare irrational numbers
 Condensed: Compare & order irrational numbers

Expressions & Operations

Evaluating Expressions
 Evaluate expressions for specified value, one variable, two terms
 Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
 Evaluate expressions for specified value, one variable, two terms, multiple operations, including powers of absolute values
 Evaluate expressions for specified values, two variables, two terms
 Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
 Evaluate expressions for specified values, two variables, two terms, one term with three factors
 Evaluate expressions for specified values, two variables, quotient of expressions
 Identify values that solve inequalities, expression on left side
 Identify values that solve inequalities, expression on right side

Simplifying Expressions, One Variable
 Simplify algebraic expressions, one variable, distribute once, fraction multiplier
 Simplify algebraic expressions, one variable, distribute once, decimal multiplier
 Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
 Simplify algebraic expressions, one variable, distribute once, including rationals
 Simplify algebraic expressions, one variable, distribute once & combine like terms
 Simplify algebraic expressions, one variable, distribute once & product of two factors
 Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
 Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
 Simplify algebraic expressions, one variable, distribute twice
 Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
 Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors

Simplifying Expressions, Two Variable
 Simplify algebraic expressions, two variables, positive integer coefficients
 Simplify algebraic expressions, two variables, distribute twice

Identifying Equivalent Expressions
 Identify equivalent expressions involving distribution
 Identify equivalent expressions involving distribution, two or more terms
 Identify equivalent numerical & algebraic expressions, including distribution, including realworld context


Equations

Solving Equations
 Determine number of solutions in linear equations, distribute at most one time
 Determine number of solutions in linear equations, distribute up to two times
 Condensed: Determine number of solutions in linear equations
 Condensed: Solve linear equations, variables on both sides or like terms
 Solve linear equations, distributive property & additional term on one side
 Solve linear equations, term minus distributive property on one side
 Solve linear equations, distributive property & additional term on one side & binomial on other side
 Solve linear equations, including no solution & infinitely many solutions
 Condensed: Solve linear equations involving distributive property on one side
 Solve linear equations, distributive property on both sides, rationals
 Solve linear equations, distributive property on both sides, additional term on one side

Solving for Specified Variable
 Given linear equation of form ay = bx, solve for y
 Given linear equation of form ay = bx + c, solve for y
 Given linear equation of form a + by = cx, solve for y
 Given linear equation in standard form, solve for y
 Given linear equation with two terms on each side, solve for specified variable
 Given linear equation with three terms on one side, solve for specified variable
 Condensed: Given linear equation in various forms, solve for specified variable
 Solve literal equation for variable
 Solve literal equation for variable, variable may appear twice, linear terms
 Solve for specific variable in mathematical formula
 Solve for specific variable in scientific formula

Application of Equations
 Solve problems that can be represented by twostep equations, realworld context
 Determine equations or identify realworld situations represented by onestep or twostep equations
 Determine linear equations & solve problems that can be represented by equations with distributive property on one side, realworld context
 Determine equations with variables on both sides, realworld context
 Determine & solve linear equations with variables on both sides, realworld context
 Given equation with variables on both sides, identify realworld situation represented by equation

Literal Equations
 Solve literal equation for variable
 Solve literal equation for variable, variable may appear twice, linear terms
 Determine how change to one variable affects another variable


Inequalities

Solving Inequalities Algebraically
 Condensed: Given linear inequalities & graphs, determine solutions & nonsolutions
 Given linear inequality & xvalue, determine yvalue
 Solve linear programming problems, realworld context
 Given description, determine linear inequality in standard form, graph, & determine specific solutions, realworld context
 Given description, determine linear inequalities in standard form, including tables, realworld context
 Given description, determine linear inequalities in standard form & specific solutions, realworld context
 Given description, determine linear inequality in various forms, graph, & determine specific solutions, realworld context

Solving Inequalities Graphically
 Graph linear inequalities, slopeintercept form, only oblique lines
 Graph linear inequalities, vertical & horizontal lines
 Graph linear inequalities, slopeintercept form, including vertical & horizontal lines
 Given linear inequality, identify correct graph, slopeintercept form
 Given linear inequality, determine graph, slopeintercept form
 Condensed: Determine equivalent linear inequalities & graphical solutions
 Given description & table, graph linear inequality, realworld context
 Graph linear inequalities, various forms
 Condensed: Graph linear equations or inequalities
 Given description & graph, determine system of linear inequalities in standard form & shaded region, realworld context

Solving Inequalities, Given Graph
 Given linear inequality graph, determine solutions & nonsolutions
 Given graph, determine linear inequality
 Determine equivalent systems of linear inequalities & graphical solutions
 Condensed: Determine points that are solutions to linear equations or inequalities

Writing Inequalities
 Given graph, identify linear inequality, slopeintercept form
 Given graph, determine inequalities in standard form, realworld context

Compound Inequalities
 Solve compound inequalities, “and” solutions, multiple choice
 Solve & graph compound inequalities, “and” solutions
 Solve & graph compound inequalities, “and” solutions, including realworld context
 Solve & graph compound inequalities, “or” solutions
 Condensed: Solve & graph compound inequalities
 Given description, determine compound inequality, graph, & possible solutions
 Given description, determine graph of inequality


Systems of Equations

Solving Systems of Equations, Graphing
 Given system of linear equations, determine point of intersection, slopeintercept form
 Given system of linear equations, graph & determine point of intersection, slopeintercept form
 Given system of linear equations, graph system, including tables
 Given description of system of linear equations, graph & determine equations or tables
 Given graph of system of linear equations, determine equations in slopeintercept form
 Given graph of system of linear equations, determine solution, rays on graph to establish pattern

Solving Systems of Equations, Substitution
 Given system of linear equations with same isolated variable, determine point of intersection, integer coordinates
 Given system of linear equations, determine point of intersection, integer coordinates, one horizontal or vertical & one slopeintercept form
 Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
 Solve systems of linear equations, infinite possibilities or no solution
 Condensed: Given system of linear equations, determine solution, substitution bias
 Determine solutions of linear equations, substitution bias, including given system, realworld context
 Determine systems of linear equations & solutions, substitution bias, realworld context
 Condensed: Solve or determine system of equations, likely to have same variable isolated
 Solve, interpret, or determine systems of linear equations, slopeintercept form, realword context
 Solve, interpret, or determine systems of linear equations, standard form, realword context

Solving Systems of Equations, Elimination
 Given system of linear equations in standard form, determine point of intersection, integer coordinates
 Solve systems of linear equations, multiply at most one equation
 Solve systems of linear equations, multiply one or both equations
 Determine systems of linear equations & solutions, elimination bias, realworld context
 Condensed: Solve or determine system of equations, both equations in standard form

Solving Systems of Equations, Mixed Methods
 Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
 Determine system of two equations, one linear & one quadratic
 Condensed: Determine systems of linear equations & solutions
 Solve systems of two equations, algebraic, one linear & one quadratic
 Solve systems of two equations, graphical, one linear & one quadratic
 Condensed: Solve systems of two equations, one linear & one quadratic

Determining Solution to System of Equations
 Given system of linear equations, identify solution or x or yvalue of solution
 Given system of linear equations, identify x or yvalue of solution
 Given system of linear equations, identify solution
 Given tables, determine system of linear equations
 Determine reasonableness of solutions to systems of linear & quadratic equations

Application of Determining Solution to System of Equations
 Given table representing system of linear equations, determine solution, realworld context
 Given system of linear equations & description, identify solution, realworld context
 Condensed: Given system of linear equations, identify solution, including realworld context
 Determine systems of linear equations & solutions, realworld context
 Determine & justify solutions to systems of linear equations, realworld context
 Condensed: Determine systems of linear equations & solutions, including realworld context
 Given graph of system of linear equations, identify specific domain value, realworld context
 Graph systems of linear equations & determine solutions, including realworld context

Solving Systems of Equations, Three Equations
 Solve systems of three linear equations using substitution
 Solve systems of three linear equations using Gaussian elimination
 Solve systems of three linear equations using matrices
 Condensed: Solve systems of three linear equations
 Determine system of three linear equations, realworld context


Systems of Inequalities

Solving Systems of Inequalities Graphically
 Given graph, determine solution of systems of linear inequalities
 Given linear system of inequalities graph, identify true statements
 Graph systems of two linear inequalities, slopeintercept form
 Condensed: Determine graphs of linear inequalities or system of linear inequalities
 Solve systems of linear inequalities
 Graph systems of three linear inequalities, slopeintercept form
 Given description of system of linear inequalities, identify graph of system

Application of Solving Systems of Inequalities Graphically
 Condensed: Graph system of linear inequalities & determine system of linear inequalities, including realworld context
 Given description, determine system of linear inequalities in standard form & identify graph, realworld context
 Given description, determine system of linear inequalities in standard form & graph, realworld context
 Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, realworld context
 Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, realworld context
 Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, realworld context

Solving Systems of Inequalities Algebraically
 Given description, determine system of linear inequalities in standard form & solution point, realworld context
 Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, realworld context
 Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, realworld context


Functions

Identifying Functions
 Determine functions, set & table representations
 Identify & determine functions, set & table representations
 Determine functions, mapping representations
 Determine functions, graphical representations
 Given step graphs, identify functions
 Identify functions, description representations
 Given relation & additional point, determine functions, multiple representations

Identifying & Justifying Functions
 Determine & justify functions, set representations
 Determine & justify functions, table representations
 Identify & determine functions, set & table representations
 Determine & justify functions, mapping representations
 Identify functions using equivalent mapping diagrams & sets of ordered pairs
 Determine & justify functions, graphical representations
 Identify & justify functions & nonfunctions, graphical representations
 Identify functions, multiple representations, including justification
 Condensed: Identify, justify, & determine functions

Identifying & Justifying Functions, No Domain & Range Language
 Determine & justify functions, set representations, no domain & range language
 Determine & justify functions, table representations, no domain & range language
 Determine & justify functions, mapping representations, no domain & range language
 Determine functions, multiple representations, including justification, no domain & range language

Function Notation
 Given linear function, determine function value
 Given quadratic function, determine function value
 Condensed: Given linear or quadratic function, determine function value
 Given graph, determine function value
 Condensed: Given graph or linear function, determine function value
 Interpret & solve problems involving function notation, realworld context



Linear Functions

Domain & Range of Linear Functions
 Determine if value is in domain or range, set & table representations
 Determine if value is in domain or range, graphical representations
 Given graph, determine domain & range
 Determine continuous domain & range, realworld context
 Determine restricted domain & range of linear functions
 Determine discrete domain & range, realworld context
 Condensed: Determine domain & range, including realworld context

Graphing Linear Functions

Standard Form to Graph
 Given linear equation in standard form, graph
 Given linear equation in standard form, graph, scrambled variable terms
 Determine linear equation in standard form & graph, realworld context
 Condensed: Determine linear equation in standard form & graph, including realworld context

SlopeIntercept Form to Graph, Integer Slope Only
 Graph linear equations, m = 1
 Graph linear equations, m = 1, various scales
 Given equation in slopeintercept form, graph line, m = ±1, various scales
 Graph linear equations, integer slope not including one & negative one, b = 0
 Graph linear equations, integer slope not including one & negative one
 Graph linear equations, integer slope, various scales
 Graph linear equations, including horizontal & vertical, integer slope, various scales

SlopeIntercept Form to Graph
 Graph linear equations, fractional slope
 Graph linear equations, fractional slope, various scales
 Condensed: Graph linear equations, including horizontal & vertical, various scales
 Given description of linear equation, identify graph, fractional slope, realworld context
 Condensed: Given linear equation or description, determine graph, fractional slope, including realworld context
 Condensed: Identify equivalent equations, graphs, & tables

Vertical & Horizontal Lines to Graph
 Given vertical linear equation, determine graph
 Given horizontal linear equation, determine graph


Identifying Key Features of Linear Function

Identify Linear or NonLinear Relationships
 Identify linear & nonlinear relationships, various representations

Determine or Plot Intercepts, Given Graph
 Given linear graph, determine coordinates of yintercept
 Given linear graph, determine coordinates of xintercept
 Given linear graph, locate intercept or determine coordinates, various scales
 Given graph of linear equation, determine slope & intercepts

Determine or Plot Intercepts, Given Equation
 Given linear equation in slopeintercept form, determine coordinates of yintercept
 Given linear equation in slopeintercept form, determine coordinates of xintercept
 Given linear equation in slopeintercept form, plot yintercept
 Given equation of horizontal or vertical line, determine coordinates of yintercept
 Given equation of horizontal or vertical line, determine coordinates of xintercept
 Given equation of horizontal or vertical line, plot yintercept
 Given linear equation, determine intercepts
 Given linear equation in standard form, determine coordinates of yintercept
 Given linear equation, determine slope & intercepts


Writing Equation of Linear Function

Writing Equation Given Point & Slope
 Given slope & yintercept, determine equation
 Given point & integer slope or rate of change, determine linear equation in slopeintercept form
 Given point & fractional slope, determine linear equation in pointslope form, including slopeintercept form conversion
 Given point & fractional slope, determine linear equation in slopeintercept form, integer yintercept
 Given point & fractional slope, determine linear equation in slopeintercept form, fractional yintercept

Writing Equation Given Two Points
 Given two points, determine linear equation in pointslope form, integer slope, including slopeintercept form conversion
 Given two points, determine linear equation in slopeintercept form, integer slope
 Given two points, determine linear equation in standard form, integer slope, including slopeintercept form conversion
 Given two points, determine linear equation in pointslope form, fractional slope, including slopeintercept form conversion
 Given two points, determine linear equation in standard form, fractional slope, including slopeintercept form conversion

Writing Equation Given Various Components
 Given points or slope & point, determine linear equation in standard form
 Given points or slope & point, determine linear equation in pointslope or standard form
 Given points or slope & point, determine linear equation in various forms
 Condensed: Given two points, determine linear equation in slopeintercept form, including horizontal & vertical lines

Writing Equation Given Graph

Writing Equation Given Graph Through Origin
 Given linear graph through origin with points shown on line, determine equation in slopeintercept form, integer slopes
 Given linear graph through origin, determine equation in slopeintercept form, integer slope, 1 ≤ m ≤ 3
 Given linear graph through origin, determine equation in slopeintercept form, integer slope

Writing Equation Given Graph, Integer Slopes,Various YIntercepts
 Given linear graph, determine equation in slopeintercept form, m = 1, various scales
 Given linear graph, determine equation in slopeintercept form, m = ±1, various scales
 Given linear graph, determine equation in slopeintercept form, integer slopes
 Given linear graph, determine equation in slopeintercept form, integer slopes, various scales
 Given linear graph, identify equation in slopeintercept form, integer slopes, various scales
 Given equation in slopeintercept form, identify graph, integer slopes, various scales
 Condensed: Identify equivalent linear graphs & equations in slopeintercept form, integers slopes, various scales

Writing Equation Given Graph, Various YIntercepts
 Given linear graph, identify equation, slopeintercept form
 Given linear graph, determine equation in slopeintercept form, fractional slopes
 Given linear graph, determine equation in pointslope form
 Given linear graph, determine equation in standard form
 Given linear graph, identify equation, various forms
 Identify equivalent linear graphs & equations in slopeintercept form
 Identify equivalent linear graphs & equations in slopeintercept form, various scales
 Given graph of vertical line, determine equation
 Given graph of horizontal line, determine equation


Writing Equation of Parallel or Perpendicular Line

Identifying Parallel, Perpendicular, or Neither
 Given two slopeintercept form equations, identify as parallel or perpendicular
 Given two pairs of points, determine if lines containing points are parallel or perpendicular

Writing Equation of Parallel or Perpendicular in SlopeIntercept Form
 Given equation in slopeintercept form, determine slope of parallel line
 Given equation in slopeintercept form, determine slope of perpendicular line
 Condensed: Given equation in slopeintercept form, determine slope of parallel or perpendicular line
 Given equation in slopeintercept form, determine equation of parallel line through specified point
 Given equation in slopeintercept form, determine equation of perpendicular line through specified point
 Given equation in slopeintercept form, determine equation of parallel or perpendicular line through specified point
 Condensed: Determine equations for parallel & perpendicular lines through specified points
 Given slope & point, determine equation for parallel or perpendicular line through specified point
 Given two points for one line, determine equation for parallel or perpendicular line through specified point
 Given graph of line, determine equation for parallel or perpendicular line through specified point

Writing Equation of Parallel or Perpendicular in Various Forms
 Given equation in various forms, determine slope of parallel line
 Given equation in various forms, determine slope of perpendicular line
 Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
 Determine equation of line through specified point parallel or perpendicular to xaxis
 Determine equation of line through specified point parallel or perpendicular to yaxis
 Condensed: Determine equation of line through specified point parallel or perpendicular to x or yaxis
 Given equation in various forms, determine equation of parallel line through specified point
 Given equation in various forms, determine equation of perpendicular line through specified point
 Given equation in various forms, determine equation of parallel or perpendicular line through specified point
 Identify equation that is parallel or perpendicular to line through two given points



Transformations of Linear Functions
 Identify & graph reflections of linear functions
 Identify & graph vertical & horizontal shifts of linear functions
 Identify & graph vertical & horizontal stretches & compressions of linear functions
 Identify descriptions of graphs of linear parent functions & transformed functions
 Graph linear functions using all transformations
 Condensed: Graph linear functions & identify transformations
 Given description of transformation, determine linear function
 Given table, identify transformations of linear functions
 Describe parameter changes to linear parent functions
 Compare linear functions represented differently

Application of Linear Functions, Given SlopeIntercept or Two Points
 Form 1 – Given slope & intercept, interpret linear relationship, determine slopeintercept equation, & graph, positive slope, only input to output questions
 Form 2 – Given slope & intercept, interpret linear relationship, determine slopeintercept equation, & graph, positive slope
 Form 3 – Given slope & intercept, interpret linear relationship, determine slopeintercept equation, & graph, including negative slope
 Given slope & intercept, interpret linear relationship & determine slopeintercept equation, including negative slope
 Form 4 – Given point & slope, interpret linear relationship, determine slopeintercept equation, & graph, including negative slope
 Form 5 – Given two points, interpret linear relationship, determine slopeintercept equation, & graph, including negative slope
 Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slopeintercept equation, & graph

Application of Linear Functions
 Given linear word problem, identify graph
 Form 6 – Given linear graph, interpret linear relationship & determine slopeintercept equation
 Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
 Determine graph or information from graph, realworld context
 Given linear equation, interpret slope & yintercept, realworld context
 Determine effects of parameter changes in linear relationships, realworld context

Linear Regression
 Sketch line of best fit & determine equation, graph scales of one
 Sketch line of best fit & determine equation, various graph scales
 Sketch line of best fit & determine equation, realworld context
 Sketch line of best fit
 Sketch line of best fit & determine predicted value
 Condensed: Sketch line of best fit & determine equation
 Determine residuals


Exponents

Numerical Exponential Expressions
 Evaluate powers, whole number base, nonpositive exponent
 Evaluate powers, integer base, nonpositive exponent, including negative coefficients
 Evaluate powers, fractional base, positive exponent
 Evaluate powers, fractional base, negative exponent
 Evaluate powers, positive fractional base, including nonpositive exponents
 Evaluate powers, fractional bases
 Condensed: Evaluate powers with negative exponents

Simplify Negative Exponents
 Express negative power using positive exponent
 Express negative power using positive exponent, coefficient other than one

Power Rule of Exponents

Power Rule, One Variable
 Apply power rule, one variable, positive exponents
 Apply power rule, one variable, at least one negative exponent
 Apply power rule, one variable, including nonpositive exponents
 Apply power rule, one variable, coefficient of negative one, at least one negative exponent
 Simplify single variable powers, negative base or coefficient

Power Rule, Multiple Variables
 Apply power rule, including multiple variables, positive exponents
 Apply power rule, including multiple variables & negative exponents
 Apply power rule, including multiple variables & negative exponents
 Apply power rule, coefficient of negative one, multiple variables, including negative exponents
 Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
 Apply power rule, negative base or coefficient, multiple variables, including negative exponents
 Apply power rule, multiple variables, coefficients other than one, including negative exponents
 Simplify powers, fractional algebraic base, including negative exponents


Product Rule of Exponents

Product Rule, One Variable
 Apply product rule of exponents, one variable, positive exponents
 Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
 Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
 Apply product rule of exponents, one variable, positive exponents, coefficients other than one

Product Rule, Multiple Variables
 Apply product rule of exponents, two variables, three to four factors, positive exponents
 Apply product rule of exponents, two variables, three to four factors, at least one negative exponent
 Apply product rule of exponents, two variables, three to four factors, one variable cancels
 Apply product rule of exponents, two variables, four to six factors, positive exponents
 Apply product rule of exponents, two variables, four to six factors, at least one negative exponent
 Apply product rule of exponents, two variables, four to six factors, at least one variable cancels
 Apply product rule of exponents, positive exponents
 Apply product rule, multiple variables, coefficients other than one, including negative exponents
 Apply product rule of exponents, negative exponents


Quotient Rule of Exponents

Quotient Rule, One Variable
 Apply quotient rule of exponents, one variable, positive exponents, greater exponent in numerator
 Apply quotient rule of exponents, one variable, positive exponents, greater exponent in denominator
 Apply quotient rule of exponents, one variable, at least one negative exponent

Quotient Rule, Multiple Variables
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents
 Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, positive exponents
 Apply quotient rule of exponents, positive exponents
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, at least one negative exponent
 Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, at least one negative exponent
 Apply quotient rule of exponents, negative exponents
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, including negative exponents, coefficients other than one
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents, coefficients other than one


Power & Product Rules of Exponents
 Apply power rule of exponents, positive exponents

Product & Quotient Rules of Exponents

Multiply Two Fractions
 Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
 Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one nonpositive exponent

Divide Two Fractions
 Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents

Multiply & Divide Two Fractions
 Apply product & quotient rules of exponents, negative exponents
 Apply product & quotient rules of exponents, negative exponents, coefficients other than one
 Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
 Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one nonpositive 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 nonpositive exponent
 Apply product & quotient rules of exponents, negative exponents, coefficients other than one
 Apply product & quotient rules of exponents, negative exponents
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, one or two variables, positive exponents


Power, Product, & Quotient Rule of Exponents Mixed

Exponents Mixed, One Variable
 Apply power & product rules of exponents, one variable, positive exponents
 Apply product & power rules of exponents, one variable, coefficient of negative one
 Apply product, quotient, & power rules of exponents, one variable

Exponents Mixed, Positive Exponents
 Apply product & quotient rules of exponents, one or two variables, positive exponents
 Apply power & product rules of exponents, multiple variables, positive exponents
 Apply power & product rules of exponents, fraction with numerator of one, positive exponents
 Apply power, product, & quotient rules of exponents, positive exponents
 Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
 Apply power, product, & quotient rules of exponents, divide fractions, positive exponents

Exponents Mixed, Including Negative Exponents
 Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
 Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
 Apply power, product, & quotient rules of exponents, including negative exponents
 Apply power rule of exponents, negative exponents
 Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
 Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
 Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
 Apply product rule of exponents, coefficients other than one
 Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents
 Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents
 Apply product, quotient, & power rules of exponents, multiple variables


Application of Exponents
 Determine algebraic expressions for perimeter & area of rectangles
 Given algebraic expressions for area & side of rectangles, determine expression for missing side

Rational Exponents

Power Rule
 Evaluate rational exponent expressions, positive exponents
 Evaluate rational exponent expressions, negative exponents
 Condensed: Evaluate rational exponent expressions
 Simplify rational exponent expressions using power rule, no coefficients
 Simplify rational exponent expressions using power rule, with coefficients

Product Rule
 Simplify rational exponent expressions using product rule, no coefficients
 Simplify rational exponent expressions using product rule, coefficients not with base
 Simplify rational exponent expressions using product rule, coefficients with base

Quotient Rule
 Simplify rational exponent expressions using quotient rule, no coefficients
 Simplify rational exponent expressions using quotient rule, with coefficients

Exponent Rules Mixed
 Evaluate numerical expressions with rational exponents
 Simplify numerical expressions with rational exponents
 Condensed: Simplify rational exponents using product & power rules

Convert Rational Exponents & Radicals
 Convert from rational exponent to radical, single value base
 Convert from rational exponent to radical, algebraic base
 Condensed: Convert from rational exponent to radical



Polynomials

Classifying Polynomials
 Identify terms of expressions
 Identify polynomial as monomial, binomial, or trinomial
 Classify polynomials by degree & number of terms
 Condensed: Classify polynomials & identify components of polynomials
 Determine degree, leading coefficient, & type of polynomial
 Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables

Interpreting Polynomials
 Interpret terms or factors in expressions, including realworld context
 Identify & apply polynomial identities

Operations with Polynomials

Addition & Subtraction of Polynomials

Addition of Polynomials
 Add binomials & trinomials, degrees zero to two
 Add binomials & trinomials, degrees zero to three
 Given polynomial & sum of polynomials, determine missing polynomial
 Determine sums of polynomials or missing polynomial addends

Subtraction of Polynomials
 Subtract binomials & trinomials, degrees zero to two
 Subtract binomials & trinomials, degrees zero to three
 Given polynomial & difference of polynomials, determine missing polynomial
 Determine differences of polynomials or missing polynomial subtrahends

Addition & Subtraction of Polynomials
 Condensed: Add or subtract binomials & trinomials
 Condensed: Determine sums or differences of polynomials or missing polynomial operands
 Add & subtract polynomials to determine expressions for perimeter of various shapes
 Determine missing value to make polynomial statement true, addition & subtraction
 Add & subtract binomials & trinomials, two variables


Multiplication of Polynomials

Multiplication of Polynomials, One Variable
 Multiply monomial times binomial or trinomial, mixed degrees
 Multiply binomial times binomial, both degree one
 Square linear binomial
 Multiply binomial times binomial, mixed degrees
 Condensed: Multiply binomial times binomial
 Multiply linear binomial times quadratic trinomial
 Multiply binomial times trinomial, mixed degrees
 Simplify monomial minus product of monomial & binomial or trinomial
 Given monomial & binomial or trinomial, multiply or identify missing value
 Determine missing value to make polynomial statement true, multiplication
 Multiply polynomials to determine expressions for areas of rectangles & triangles

Multiplication of Polynomials, Two Variables
 Multiply monomial times binomial or trinomial, two variables
 Multiply binomial times binomial, two variables
 Multiply binomial times trinomial, two variables
 Condensed: Multiply monomials, binomials, & trinomials, two variables

Binomial Theorem
 Apply binomial theorem to expand (x ± y)^3
 Apply binomial theorem to expand (x ± y)^n, n ≥ 4
 Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
 Multiply monomial times binomial or trinomial, mixed degrees
 Multiply monomial times binomial or trinomial, two variables
 Multiply binomial times binomial, both degree one
 Square linear binomial
 Multiply binomial times binomial, mixed degrees
 Multiply linear binomial times quadratic trinomial
 Multiply binomial times trinomial, mixed degrees
 Condensed: Multiply binomial times binomial
 Given monomial & binomial or trinomial, multiply or identify missing value
 Apply binomial theorem to expand (x ± y)^3
 Multiply polynomials to determine expressions for areas of rectangles & triangles
 Determine missing value to make polynomial statement true, multiplication
 Apply binomial theorem to expand (x ± y)^n, n ≥ 4
 Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
 Simplify monomial minus product of monomial & binomial or trinomial
 Multiply binomial times binomial, two variables
 Multiply binomial times trinomial, two variables
 Condensed: Multiply monomials, binomials, & trinomials, two variables


Division of Polynomials
 Divide polynomials, degree one or two by degree one or two
 Divide polynomials, degree three or four by degree one
 Divide polynomials, degree three or four by degree two
 Divide polynomials, divisor supports synthetic division
 Condensed: Divide polynomials, degree three or four by degree one or two
 Condensed: Divide polynomials
 Divide quadratic trinomial by linear binomial, word problem context
 Apply remainder theorem

Mixed Operations of Polynomials
 Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
 Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
 Determine missing operation to make polynomial statement true
 Condensed: Determine missing value to make polynomial statement true


Factoring Polynomials

Factoring Trinomials, a=1
 Factor quadratic trinomials, a = 1, b > 0, c > 0
 Factor quadratic trinomials, a = 1
 Factor quadratic trinomials, a = 1, terms scrambled
 Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
 Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
 Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < c ≤ 10

Factoring Trinomials, a>1
 Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
 Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
 Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
 Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
 Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < c ≤ 10

Factor Perfect Square Trinomials
 Factor perfect square trinomials, degree two, one variable
 Factor perfect square trinomials, degree two, two variables
 Condensed: Factor perfect square trinomials, degree two
 Factor perfect square trinomials, fraction coefficients

Factoring Difference of Squares
 Factor difference of two squares, degree two, one variable
 Factor difference of two squares, degree two, one variable, terms scrambled
 Factor difference of two squares, degree two, one variable, coefficient one
 Condensed: Factor difference of two squares, degree two
 Factor difference of two squares, two variables
 Factor difference of two squares, one or two variables

Factor GCF & Remaining Quadratic
 Factor GCF & remaining quadratic expression, a = 1, one variable
 Factor GCF & remaining quadratic expression, a ≥ 1, one variable

Factor Common Binomial
 Factor common binomial
 Factor binomial & its opposite

Factor by Grouping
 Factor cubic polynomial by grouping, one variable
 Factor cubic polynomial by grouping & difference of two squares, one variable

Factor Sum & Difference of Cubes
 Factor sum & difference of two cubes, degree three, one variable
 Factor sum & difference of two cubes, degree six, one variable
 Factor sum & difference of two cubes, degree three, two variables
 Condensed: Factor sum & difference of two cubes, degree three
 Factor sum & difference of two cubes, degree six, two variables
 Condensed: Factor sum & difference of two cubes, degree six

Identify Factors
 Identify factors of polynomials
 Determine linear factors of polynomials, degree three
 Determine linear factors of polynomials, degree four
 Determine quadratic factors of polynomials, degree four
 Condensed: Determine linear factors of polynomials, degree three or four

Determine Number of Roots
 Determine maximum number of roots for polynomial function


Interpreting Graphs of Polynomials

Intercepts & Multiplicities
 Determine x & yintercepts of cubic functions
 Determine xintercepts/zeros & yintercepts of polynomial functions
 Determine zeros of polynomials & their multiplicities

Extrema, Increase & Decrease, End Behavior, & Symmetry
 Determine minimum & maximum of polynomial functions
 Determine intervals of increase & decrease of polynomial functions
 Determine end behavior of polynomial functions
 Determine symmetry of various functions

Determine Attributes
 Given table, determine attributes of polynomial function
 Given cubic equation, identify descriptions of transformations
 Condensed: Determine graphical attributes of polynomial functions

Determine Graph or Equation
 Given zeros, determine graph of polynomial function
 Given equation, graph polynomial function
 Given graph, determine equation of polynomial function

Determine Points of Intersection of Two Functions
 Determine points of intersection of two polynomial functions



Function Operations, Inverses, & Solutions

Operations with Functions
 Add functions, (f + g)(x)
 Subtract functions, (f – g)(x)
 Multiply functions, (f * g)(x)
 Divide functions, (f / g)(x)
 Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
 Add function values, (f + g)(#)
 Subtract function values, (f – g)(#)
 Multiply function values, (f * g)(#)
 Divide function values, (f / g)(#)
 Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)
 Evaluate compositions of functions

Inverse Functions
 Determine inverse of linear function
 Determine inverse of quadratic & square root functions
 Determine inverse of cubic & cube root functions
 Determine inverse of various functions
 Determine if functions are inverses using composition
 Graph function and its inverse
 Determine domain & range of inverse functions
 Condensed: Given function, determine equation, graph, & domain & range of inverse
 Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions

Identifying Function, Solutions, & Points of Intersection
 Determine whether given table represents linear or exponential function
 Determine whether given table represents linear, exponential, or quadratic function
 Determine whether given graph represents linear, exponential, or quadratic function
 Condensed: Determine what function given table or graph represents
 Identify ordered pair solutions to systems of two equations, one linear & one quadratic
 Perform operations on functions represented graphically, graphical solution
 Perform operations on functions represented graphically, numerical solution
 Determine points of intersection of various functions, not absolute value or polynomial
 Condensed: Determine points of intersection of functions


Complex Numbers

Simplify Complex Numbers
 Express square roots of negatives using i
 Simplify imaginary numbers
 Simplify powers of i

Operations with Complex Numbers
 Add & subtract complex numbers
 Add or subtract square roots of negative numbers
 Multiply complex numbers
 Square complex numbers
 Multiply square roots of negative numbers
 Divide complex number by constant
 Divide complex numbers
 Condensed: Multiply & divide complex numbers
 Condensed: Add, subtract, multiply, & divide complex numbers
 Condensed: Add, subtract, & multiply square roots of negative numbers

Quadratic Equations with Complex Solutions
 Factor sum of squares using complex factors
 Calculate discriminant, then determine number of real or complex solutions
 Determine number of complex & real roots of quadratic functions
 Determine complex solutions by factoring sum of squares
 Solve quadratic equations using square root method, complex solutions
 Solve using quadratic formula, complex solutions
 Condensed: Solve quadratic equations, complex solutions
 Solve quadratic equations, complete the square, integers, a = 1, complex solutions
 Solve quadratic equations, complete the square, integers, a > 1, complex solutions
 Condensed: Solve quadratic equations, complete the square, integers, complex solutions
 Given two complex solutions, determine quadratic equation of form x^2 + # = 0


Quadratic Functions

Domain & Range of Quadratic Functions
 Given graph of quadratic function, determine domain & range
 Given equation of quadratic function, determine domain & range
 Given description of domain & range of quadratic function, choose graph
 Condensed: Determine domain & range of quadratic function
 Determine restricted domain & range of quadratic functions

Graphing Quadratic Functions
 Given quadratic equation, determine graph, b = 0
 Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
 Graph quadratic functions using all transformations
 Given quadratic equation, vertex, & point, graph function & determine attributes
 Given quadratic equation in vertex form, determine graph
 Given quadratic equation in standard form, determine graph
 Graph quadratic equations
 Given equation, graph quadratic function
 Condensed: Graph quadratic functions using any transformation
 Given table, determine attributes of quadratic function, realworld context

Identifying Key Features of Quadratic Functions

Vertex, Axis of Symmetry, Increase & Decrease, & Extrema of Quadratic Functions
 Determine vertex of quadratic functions
 Determine minimum & maximum of quadratic functions
 Given graph of quadratic function, determine minimum or maximum value
 Given quadratic equation, determine minimum or maximum value
 Determine symmetry of quadratic functions
 Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
 Determine end behavior of quadratic functions
 Determine intervals of increase & decrease of quadratic functions
 Determine intervals where quadratic function is positive or negative

Intercepts of Quadratic Functions
 Determine xintercept(s) of quadratic functions
 Determine zero(s) of quadratic functions
 Determine zero(s)/xintercept(s) of quadratic functions, b = 0
 Determine yintercept of quadratic functions
 Determine xintercepts/zeros & yintercepts of quadratic functions, vertex form
 Given graph or table of quadratic function, determine x & y intercepts

Mixed Key Attributes of Quadratic Functions
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a ≠ ±1
 Given graph of quadratic function, determine attributes
 Condensed: Given graph, equation, or table, determine attributes of quadratic function
 Condensed: Determine graphical attributes of quadratic functions
 Condensed: Given quadratic equation, determine attributes & graph


Transformations of Quadratic Functions
 Identify & graph reflections of quadratic functions
 Identify & graph vertical & horizontal shifts of quadratic functions
 Identify & graph vertical & horizontal stretches & compressions of quadratic functions
 Identify descriptions of graphs of quadratic parent functions & transformed functions
 Given quadratic equation, identify description of transformation
 Given description of transformation, determine quadratic function
 Describe parameter changes to quadratic parent functions
 Determine effects of parameter changes in quadratic relationships, realworld context
 Compare quadratic functions represented differently

Writing Equations of Quadratic Functions

Standard & Vertex Form
 Given quadratic equation in standard form, determine vertex form of equation
 Given quadratic equation in vertex form, determine standard form of equation

Given Vertex, Zeros, or Points
 Given vertex & point, determine quadratic equation, vertex form
 Given vertex & point, determine quadratic equation, standard form
 Given zeros of quadratic function, determine quadratic equation with integer coefficients
 Given integer solutions of quadratic equation, determine function in standard form
 Given rational solutions of quadratic equation, determine function in standard form
 Given three points in plane, determine quadratic equation

Given Graph, Determine Equation
 Given graph of quadratic function, determine equation
 Given graph of quadratic function, determine equation
 Given graph of quadratic function, determine equation in standard form

Focus & Directrix
 Given focus & directrix of parabola, determine equation
 Given focus & directrix of parabola, determine equation in standard form
 Given graphical attributes, determine equation of parabola


Solving Quadratic Equations

Solving Quadratic Equations, Zeros
 Apply zero product property to solve factored quadratic equations
 Identify zeros of factored quadratics
 Determine relationship between zeros & linear factors of quadratic functions

Solving Quadratic Equations, GCF
 Solve quadratic binomial equation by factoring out GCF
 Solve quadratic binomial equation by factoring out GCF, one term on each side
 Solve quadratic binomial equation by factoring out GCF, combining like terms necessary

Solving Quadratic Equations, Factoring
 Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
 Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
 Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
 Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a ≤ 10, b ≠ 0, c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a ≤ 10, c ≤ 40, terms on both sides
 Solve quadratic equations using factoring, perfect square trinomial
 Solve quadratic equations, perfect square trinomial
 Solve quadratic equations using factoring, difference of squares

Solving Quadratic Equations, Graphing
 Given graph of quadratic function, determine roots/zeros

Solving Quadratic Equations, Square Root Method
 Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
 Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
 Solve quadratic equations using square root method, a(cx ± h)^2 + k = #
 Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
 Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions

Solving Quadratic Equations, Quadratic Formula
 Given quadratic equation in standard form, determine discriminant
 Given quadratic equation in standard form, determine number of solutions
 Given quadratic equation in standard form, determine solutions rounded to nearest hundredth
 Given quadratic equation, determine solutions rounded to nearest hundredth, constant on one side
 Given quadratic equation, determine solutions rounded to nearest hundredth, combine like terms first
 Given quadratic equation in standard form, determine attributes & solutions rounded to nearest hundredth
 Given proportion, solve resulting quadratic equation, b = 0
 Given proportion, solve resulting quadratic equation, b ≠ 0
 Given quadratic equation in standard form, determine exact solutions
 Given quadratic equation in standard form, determine exact solutions, combine like terms first

Solving Quadratic Equations, Completing the Square
 Determine constant required to complete the square, a ≥ 1, including fractions
 Solve quadratic equations, complete the square, integers, a = 1, real solutions
 Solve quadratic equations, complete the square, integers, a > 1, real solutions
 Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
 Condensed: Solve quadratic equations, complete the square, integers, real solutions
 Solve quadratic equations, complete the square, a = 1, real solutions
 Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
 Solve quadratic equations, complete the square, a > 1, real solutions
 Condensed: Solve quadratic equations, complete the square, real solutions
 Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
 Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
 Condensed: Solve quadratic equations, complete the square, integers, including complex solutions

Solving Quadratic Equations, Determine Solutions
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
 Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
 Determine exact solution to quadratic equations, a = ±1, b = 0
 Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0

Application of Solving Quadratic Equations
 Determine or use quadratic equations, realworld context


Solving Quadratic Inequalities
 Solve quadratic inequalities, “and” solutions
 Solve quadratic inequalities, “or” solutions
 Condensed: Solve quadratic inequalities

Vertical Motion Problems
 Given initial height & velocity of object in vertical motion, determine function, table, & graph of position
 Given initial height & velocity of object in vertical motion, determine position function & maximum height
 Given initial height & velocity of object in vertical motion, determine position function & time to maximum height
 Given initial height & velocity of object in vertical motion, determine position function & time to ground
 Given initial height & velocity of object in vertical motion, determine position function & specific time
 Given height of dropped object, determine position function & specific time
 Given initial height & negative velocity of object in vertical motion, determine position function & specific time
 Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
 Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
 Condensed: Given initial height & velocity of object in vertical motion, determine position function, maximum height, or time to maximum height
 Condensed: Given initial height & velocity of object in vertical motion, determine position function & specific times
 Condensed: Given initial height & velocity of object in vertical motion, determine position graph, position function, & specific times


Absolute Value Functions

Solving Absolute Value Equations
 Solve linear absolute value equations
 Solve linear absolute value equations, extra constant or coefficient
 Solve linear absolute value equations, variable on both sides
 Condensed: Solve linear absolute value equations, including extra constant or coefficient
 Create linear absolute value equations, realworld context

Solving Absolute Value Inequalities
 Given linear absolute value inequality, determine compound inequality
 Solve & graph linear absolute value inequalities, “and” solutions, including setup
 Solve & graph linear absolute value inequalities, “or” solutions, including setup
 Solve & graph linear absolute value inequalities, including setup
 Condensed: Solve & graph linear absolute value inequalities, including setup
 Solve & graph linear absolute value inequalities, “and” solutions
 Solve & graph linear absolute value inequalities, “or” solutions
 Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
 Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
 Solve & graph linear absolute value inequalities, including extra constant or coefficient
 Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
 Condensed: Solve & graph linear absolute value inequalities

Graphing Absolute Value Functions
 Determine x & yintercepts of absolute value functions
 Determine minimum & maximum of absolute value functions
 Identify & graph reflections of absolute value functions
 Identify & graph vertical & horizontal shifts of absolute value functions
 Identify & graph vertical & horizontal stretches & compressions of absolute value functions
 Given absolute value equation, identify description of transformation
 Graph absolute value functions using all transformations
 Condensed: Graph absolute value functions using any transformation
 Graph absolute value functions using vertex & intercepts
 Condensed: Determine graphical attributes of absolute value functions
 Compare absolute value functions represented differently
 Determine points of intersection of absolute value functions

Writing Equation of Absolute Value Functions
 Given graph, determine absolute value equation
 Given description of transformation, determine absolute value equation


Piecewise & Step Functions
 Graph piecewise functions
 Given graph of piecewise function, determine equation
 Graph step functions
 Given graph of step function, determine equation
 Condensed: Determine graphs & equations of piecewise & step functions

Cubic Functions

Graphing Cubic Functions
 Determine minimum & maximum of cubic functions
 Identify & graph reflections of cubic functions
 Identify & graph vertical & horizontal shifts of cubic functions
 Identify & graph vertical & horizontal stretches & compressions of cubic functions
 Graph cubic functions using all transformations
 Condensed: Graph cubic functions using any transformation
 Condensed: Determine graphical attributes of cubic functions
 Graph cubic functions using key points & intercepts


Rational Expressions & Functions

Simplifying Rational Expressions
 Simplify rational expressions by factoring GCF, one monomial & one binomial
 Simplify rational expressions by factoring GCF, two binomials
 Simplify rational expressions by factoring GCF, two binomials, remaining binomials cancel
 Simplify rational expressions by factoring GCF, one trinomial or difference of squares
 Simplify rational expressions by factoring GCF, trinomials & differences of squares
 Simplify rational expressions by factoring GCF, remaining leading coefficient one
 Condensed: Simplify rational expressions
 Condensed: Simplify rational expressions, including trinomials

Operations with Rational Expressions
 Multiply rational expressions
 Divide rational expressions
 Condensed: Multiply & divide rational expressions
 Add rational expressions
 Subtract rational expressions
 Condensed: Add & subtract rational expressions
 Condensed: Add, subtract, multiply, & divide rational expressions

Domain of Rational Functions
 Given rational function, determine function value
 Identify value that makes rational expression undefined
 Determine values that make rational expressions undefined
 Determine asymptotic domain restrictions of rational functions
 Determine domain & range of rational functions using inequalities, interval notation & set notation

Key Attributes of Rational Functions
 Determine x & yintercepts of reciprocal functions
 Determine symmetry of reciprocal functions
 Determine asymptotes of reciprocal functions
 Determine minimum & maximum of reciprocal functions
 Condensed: Determine graphical attributes of reciprocal functions

Graphing Rational Functions
 Identify & graph reflections of reciprocal functions
 Identify & graph vertical & horizontal shifts of reciprocal functions
 Identify & graph vertical & horizontal stretches & compressions of reciprocal functions
 Given reciprocal equation, identify description of transformations
 Graph reciprocal functions using all transformations
 Graph rational functions
 Condensed: Graph reciprocal functions using any transformation
 Graph reciprocal functions using asymptotes, intercepts, & domain & range
 Compare rational functions represented differently

Solving Rational Equations & Inequalities
 Solve equations involving rational exponents, one or twostep
 Solve equations involving rational exponents, multistep
 Solve rational equations, one term each side
 Solve rational equations, multiple terms on one side
 Condensed: Solve rational equations
 Condensed: Solve equations involving rational exponents
 Determine if solution to rational equation is reasonable
 Determine rational equations, realworld context
 Determine rational inequalities, realworld context


Radical Expressions & Functions

Simplifying Radical Expressions
 Identify steps to simplify square roots
 Simplify square roots
 Simplify square roots, coefficient greater than one
 Given square root expression, evaluate for specific value
 Condensed: Simplify square roots, including algebraic expressions
 Evaluate perfect cube roots
 Solve perfect cube root equations
 Condensed: Determine cube roots of perfect cubes
 Compare perfect square & cube roots
 Simplify radical expression raised to power that is multiple of index
 Simplify radical expressions, perfect powers

Operations with Radicals
 Add & subtract radical expressions, one or two variables, simplified radicals
 Add & subtract radical expressions, one or two variables, radicals to simplify
 Condensed: Add & subtract radical expressions
 Multiply radical expressions, numbers & variables

Convert Radicals & Rationals
 Convert from radical to rational exponent, single value in radicand
 Convert from radical to rational exponent, algebraic term in radicand
 Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
 Condensed: Convert from radical to rational exponent

Solving Radical Equations

Square Root
 Solve perfect square root equations
 Condensed: Determine square roots of perfect squares
 Solve square root equations, square root = #
 Solve square root equations, square root = square root
 Solve square root equations, add & subtract from root
 Solve square root equations, divide by coefficient of root
 Solve square root equations, multistep
 Solve square root equations, square root = x ± #
 Solve square root equations, square root ± square root = #
 Condensed: Solve square root equations, onestep & twostep
 Condensed: Solve square root equations
 Identify extraneous solutions of square root equations

Cube Root
 Solve perfect cube root equations
 Solve cube root equations, cube root = #
 Solve cube root equations, cube root = cube root
 Solve cube root equations, multistep
 Solve cube root equations, cube root = variable
 Condensed: Solve cube root equations, onestep & twostep

Square Root & Cube Root Mixed
 Compare perfect square & cube roots
 Condensed: Evaluate & compare perfect square & cube roots
 Condensed: Solve square root & cube root equations


Key Attributes of Radical Functions
 Determine x and yintercepts of square root functions
 Determine minimum & maximum of square root functions
 Condensed: Determine graphical attributes of square root functions
 Determine x & yintercepts of cube root functions
 Determine minimum & maximum of cube root functions
 Condensed: Determine graphical attributes of cube root functions

Transformations of Radical Functions
 Identify & graph reflections of square root functions
 Identify & graph vertical & horizontal shifts of square root functions
 Identify & graph vertical & horizontal stretches & compressions of square root functions
 Given square root equation, identify description of transformations
 Identify & graph reflections of cube root functions
 Identify & graph vertical & horizontal shifts of cube root functions
 Identify & graph vertical & horizontal stretches & compressions of cube root functions
 Given cube root equation, identify descriptions of transformations
 Compare radical functions represented differently

Graphing Radical Functions
 Graph square root functions using key point & intercepts
 Graph square root functions using all transformations
 Condensed: Graph square root functions using any transformation
 Graph cube root functions using key points & intercepts
 Graph cube root functions using all transformations
 Condensed: Graph cube root functions using any transformation


Mixed Functions
 Calculate average rate of change of function from table
 Calculate average rate of change of function from graph
 Calculate average rate of change of a function from an equation
 Calculate average rate of change of function, realworld context
 Condensed: Calculate average rate of change of function
 Given graph, identify various functions
 Given various functions, identify graph
 Condensed: Graph various functions
 Determine domain & range of various functions using various notations

Logarithms

Evaluating Logarithmic Expressions
 Evaluate log expressions, whole number base
 Evaluate log expressions, fractional bases
 Evaluate log expressions, using change of base
 Evaluate log expressions, natural log
 Condensed: Evaluate log expressions

Solving Logarithmic Equations
 Solve log equations, log = #
 Solve log equations, log = log
 Solve log equations, log + log = #, same base, using product rule
 Solve log equations, log – log = #, same base, using quotient rule
 Condensed: Solve log equations, log = #, using product & quotient rules
 Condensed: Solve log equations
 Solve natural log equations, ln = #
 Solve natural log equations, ln = ln
 Solve natural log equations, ln + ln = #
 Solve natural log equations, ln – ln = #
 Condensed: Solve natural log equations
 Determine if solution to logarithmic equation is reasonable

Condensing & Expanding Logarithms
 Apply power rule to expand or condense log expressions
 Apply product rule to expand or condense log expressions
 Apply quotient rule to expand or condense log expressions
 Apply product, quotient, & power rules to expand or condense log expressions
 Condensed: Expand or condense log expressions


Exponential & Logarithmic Functions

Exponential Functions

Evaluating Exponential Functions
 Given exponential function, determine function value, nonnegative input
 Given exponential function, determine function value, negative input
 Given exponential function, determine function value, rational coefficient
 Given exponential function, determine function value, rational base
 Given exponential function, determine function value, rational base & coefficient

Domain & Range of Exponential Functions
 Given equation, determine domain & range of exponential function
 Determine domain & range of discrete exponential functions
 Determine restricted domain & range of exponential functions
 Given verbal description & graph, determine domain & range of exponential function
 Determine domain & range of discrete exponential functions, realworld context

Graphing Exponential Functions
 Given graph, identify solution to exponential equation
 Given exponential growth function, determine graph
 Graph exponential functions using all transformations
 Given exponential growth function, determine graph, includes fractional coefficients
 Given exponential growth or decay function, determine graph, includes fractional coefficients
 Given equation, graph exponential function
 Given equation, graph exponential function, including base e
 Given graph, determine equation of exponential function
 Compare exponential functions represented differently

Identifying Key Features of Exponential Functions
 Determine xintercepts/zeros & yintercepts of exponential functions
 Determine yintercept of exponential function, realworld context
 Determine minimum & maximum of exponential functions
 Determine asymptote of exponential functions
 Given graph, determine asymptote of exponential function
 Given exponential equation, determine asymptote
 Determine asymptote of exponential functions, realworld context
 Determine end behavior of exponential functions
 Condensed: Determine graphical attributes of exponential functions
 Graph exponential functions using all transformations
 Condensed: Graph exponential functions & identify transformations

Transformations of Exponential Functions
 Identify & graph reflections of exponential functions
 Identify & graph vertical & horizontal shifts of exponential functions
 Identify & graph vertical & horizontal stretches & compressions of exponential functions
 Given table, identify transformations of exponential functions
 Given exponential equation, identify description of transformations

Writing Equations of Exponential Functions
 Given table, determine linear or exponential growth function
 Given table, determine exponential growth function
 Given table, determine exponential decay function
 Given graph, determine equation of exponential function

Solving Exponential Equations
 Solve exponential equations, no logs required
 Solve exponential equations, common bases given
 Solve exponential equations, both bases reduce to common base
 Solve simple exponential equations
 Solve exponential equations, one base reduces to common base
 Solve exponential equations, two different bases, no common base possible
 Solve exponential equations, one variable & one base
 Solve exponential equations, base e
 Create equivalent exponential expressions using exponent properties

Application of Exponential Functions
 Calculate investment value, annual compounding
 Calculate depreciating asset value, annual compounding
 Calculate investment value, various compounding
 Condensed: Calculate investment & depreciating asset values, annual compounding
 Exponential growth & decay, realworld context
 Determine exponential function, realworld context
 Determine asymptote of exponential functions, realworld context
 Given table, determine attributes of exponential function
 Interpret values in exponential functions, realworld context


Logarithmic Functions

Graphing Logarithmic Functions
 Identify & graph reflections of log functions
 Identify & graph vertical & horizontal shifts of log functions
 Identify & graph vertical & horizontal stretches & compressions of log functions
 Given log equation, identify description of transformations
 Graph log functions using all transformations
 Given equation, graph log function
 Condensed: Graph log functions & identify transformations

Identifying Key Features of Logarithmic Functions
 Determine xintercepts/zeros & yintercepts of log functions
 Determine asymptote of log functions
 Determine minimum & maximum of log functions
 Determine end behavior of log functions
 Given table, determine attributes of log function
 Condensed: Determine graphical attributes of log functions

Writing Equations of Logarithmic Functions
 Given graph, determine equation of log function


Exponential & Logarithmic Equations
 Given log equation, determine exponential equation
 Given exponential equation, determine log equation
 Condensed: Convert between exponential & log equations


Direct & Inverse Variation

Direct & Inverse Variation

Direct & Inverse Variation, Multiple Choice
 Determine direct variation table, multiple choice
 Determine direct variation equation, multiple choice
 Determine inverse variation table, multiple choice
 Determine variation equation type, multiple choice
 Determine direct or inverse variation, multiple choice

Direct & Inverse Variation, Determine Equation or Missing Number
 Given point & “y varies directly with x”, determine equation
 Given point & “y varies directly with x & inversely with z”, determine equation
 Given point, “y varies directly with x”, & another value, determine missing number
 Given point, “y varies directly with x”, & another value, determine equation & missing number
 Given point, “y varies directly with x”, & another value, determine equation & missing number, rational numbers
 Given point & “y varies inversely with x”, determine equation
 Given point, “y varies jointly with x & z”, & another value, determine equation
 Given point, “y varies inversely with x”, & another value, determine equation & missing number
 Condensed: Determine direct, inverse, joint, or combined variation equations
 Determine direct variation table, multiple choice
 Determine inverse variation table, multiple choice
 Determine variation equation type, multiple choice
 Determine direct or inverse variation, multiple choice
 Given point & “y varies directly with x”, determine equation
 Given point & “y varies inversely with x”, determine equation
 Given point, “y varies directly with x”, & another value, determine equation & missing number
 Given point, “y varies inversely with x”, & another value, determine equation & missing number
 Determine direct variation equation, multiple choice
 Given point, “y varies directly with x”, & another value, determine equation & missing number, rational numbers
 Given point & “y varies directly with x & inversely with z”, determine equation
 Given point, “y varies directly with x”, & another value, determine missing number
 Given point, “y varies jointly with x & z”, & another value, determine equation
 Condensed: Determine direct, inverse, joint, or combined variation equations


Application of Direct & Inverse Variation
 Solve word problems involving direct variation
 Determine & apply inverse variation equation, realworld context
 Solve word problems involving joint variation
 Solve word problems involving combined variation


Sequences

Arithmetic Sequences
 Determine terms in arithmetic sequences
 Given arithmetic sequence, determine common difference & next term
 Given formula, determine specific term of arithmetic sequence
 Determine common difference, first term, & formula of arithmetic sequences
 Condensed: Determine formula & specific terms of arithmetic sequences

Geometric Sequences
 Given formula, determine specific term of geometric sequence
 Determine formula & specific term of geometric sequences
 Condensed: Determine formula or specific term of geometric sequences

Application of Sequences
 Given table, determine difference in terms in arithmetic sequence, realworld context
 Identify arithmetic & geometric sequences & determine common difference or common ratio
 Given formula, determine terms in arithmetic & geometric sequences
 Condensed: Identify arithmetic & geometric sequences & determine components of sequences
 Determine function & specific term for arithmetic & geometric sequences, realworld context

Finite Geometric Series
 Determine sum of finite geometric series
 Determine sum of finite geometric series, realworld context


Data Analysis

Samples & Populations
 Identify samples & populations
 Identify biased samples & questions
 Determine sample spaces
 Identify statistical questions
 Identify variables of interest
 Identify statistical inferences
 Condensed: Identify samples, populations, variables of interest, & statistical inferences
 Identify experiments & observational studies
 Identify systematic, cluster, stratified, & simple random samples
 Identify simulations used to acquire simple random samples
 Identify simulations to model probability events
 Identify descriptive & inferential statistics

Probability

Addition Rule
 Given visual model, determine “or” probability
 Given visual model, determine “or” probability as fraction, decimal, or percent
 Determine “or” probabilities as fractions
 Determine “or” probabilities as fractions, decimals, or percents
 Determine “or” probabilities
 Determine “or” probabilities
 Determine “or” probabilities, including “and” situations

Multiplication Rule
 Given visual model, determine “and” probability as fraction, decimal, or percent, dependent events
 Determine probabilities of flipping coins & rolling die
 Determine probabilities of flipping coins specified number of times
 Determine “and” probabilities, independent events, visuals provided
 Determine “and” probabilities, independent events, same sample space
 Determine “and” probabilities, independent events, two distinct sample spaces
 Determine “and” probabilities, dependent events, multiple choice
 Determine “and” probabilities, dependent events
 Determine “and” probabilities, independent & dependent events
 Determine “and” probabilities, independent & dependent events, including complementary events

Conditional Probability
 Determine conditional probabilities from twoway frequency tables
 Determine conditional probabilities, including twoway frequency tables


Permutations
 Given visual model, determine permutations, specified items predetermined
 Determine permutation of letters in word, nondistinct letters
 Determine permutation of letters in word, distinct letters
 Condensed: Determine permutation of letters in word, including nondistinct letters
 Determine permutations, one nondistinct item, realworld context
 Determine permutations, multiple nondistinct items, realworld context
 Determine permutations using all items, realworld context
 Determine permutations, realworld context

Combinations
 Given lists, determine combinations, choose from one list, realworld context
 Given lists, determine combinations, choose from two lists, realworld context
 Determine number of combinations using fundamental counting principle, realworld context
 Determine number of combinations using fundamental counting principle, including repeated letters & digits, realworld context
 Determine combinations, realworld context

Determine zScore & Probability
 Given mean & standard deviation, determine zscore, realworld context
 Given zscore, determine probability
 Given mean, determine zscore & probability, realworld context
 Given proportion, determine zscore & probability, realworld context
 Condensed: Given mean or proportion, determine zscore & probability, realworld context

Confidence Intervals
 Determine margin of error for confidence interval
 Given sample data, estimate population mean using confidence intervals
 Given sample data, estimate population proportion using confidence intervals
 Condensed: Given sample data, estimate population proportion or mean using confidence intervals

Normal Distributions

Determine Test Statistic or Hypotheses, One Mean or Proportion
 Determine test statistics, one mean
 Determine test statistics, one proportion
 Condensed: Determine test statistics, one mean or proportion
 Identify hypotheses for hypothesis test, one mean
 Identify hypotheses for hypothesis test, one proportion
 Condensed: Identify hypotheses for hypothesis test, one mean or proportion

Determine Test Statistic or Hypotheses, Two Means or Proportions
 Determine test statistics, two means
 Determine test statistics, two proportions
 Condensed: Determine test statistics, two means or proportions
 Identify hypotheses for hypothesis test, two means
 Identify hypotheses for hypothesis test, two proportions
 Condensed: Identify hypotheses for hypothesis test, two means or proportions

Steps in Hypothesis Testing, One Mean or Proportion
 Identify & determine hypothesis test steps, one mean
 Identify & determine hypothesis test steps, one proportion
 Condensed: Identify & determine hypothesis test steps, one mean or proportion
 Determine critical zscore & pvalue

Steps in Hypothesis Testing, Two Means or Proportions
 Identify & determine hypothesis test steps, two means
 Identify & determine hypothesis test steps, two proportions
 Condensed: Identify & determine hypothesis test steps, two means or proportions

Determine Conclusions
 Determine conclusion from statistical summaries
 Given critical zscore & test statistic, determine conclusion for null hypothesis
 Identify hypotheses for hypothesis test, one mean
 Identify hypotheses for hypothesis test, one proportion
 Condensed: Identify hypotheses for hypothesis test, one mean or proportion
 Identify hypotheses for hypothesis test, two means
 Identify hypotheses for hypothesis test, two proportions
 Condensed: Identify hypotheses for hypothesis test, two means or proportions
 Determine test statistics, one mean
 Determine test statistics, one proportion
 Determine test statistics, two proportions
 Condensed: Determine test statistics, one mean or proportion
 Determine critical zscore & pvalue
 Given critical zscore & test statistic, determine conclusion for null hypothesis
 Determine test statistics, two means
 Identify & determine hypothesis test steps, two means
 Condensed: Identify & determine hypothesis test steps, two means or proportions
 Identify & determine hypothesis test steps, two proportions
 Identify & determine hypothesis test steps, one proportion


Regression
 Determine linear regression equations, calculator expected
 Determine exponential regression equations, calculator expected
 Determine quadratic regression equations, calculator expected
 Given table, use technology to determine radical equation
 Given regression equation, determine predicted value


Trigonometry

Graphing Trigonometric Functions
 Given graph or equation, determine amplitude of trig function
 Given graph or equation, determine midline of trig function
 Given graph or equation, determine period of trig function
 Condensed: Given graph or equation, determine characteristics of trig function
 Determine graph of trig functions, sin, one transformation
 Determine graph of trig functions, sin, multiple transformations
 Determine graph of trig functions, cos, one transformation
 Determine graph of trig functions, cos, multiple transformations
 Determine graph of trig functions, tan & cot
 Determine graph of trig functions, sec & csc
 Identify trigonometric functions to model periodic data, realworld context

Trigonometric Ratios
 Identify definitions of trig functions
 Given right triangle, determine missing side & trig ratio, sin, cos, & tan
 Given right triangle, determine missing side & trig ratio, cot, sec, & csc
 Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
 Condensed: Given right triangle, determine missing side & trig ratio

Trigonometric Identities
 Determine missing steps in proofs of Pythagorean identities
 Given graph or equation, determine period of trig function
 Given graph or equation, determine midline of trig function
 Given graph or equation, determine amplitude of trig function
 Condensed: Given graph or equation, determine characteristics of trig function
 Determine graph of trig functions, sin, one transformation
 Determine graph of trig functions, sin, multiple transformations
 Determine graph of trig functions, cos, one transformation
 Determine graph of trig functions, cos, multiple transformations
 Determine graph of trig functions, tan & cot
 Determine graph of trig functions, sec & csc
 Identify trigonometric functions to model periodic data, realworld context
 Identify definitions of trig functions
 Given right triangle, determine missing side & trig ratio, sin, cos, & tan
 Given right triangle, determine missing side & trig ratio, cot, sec, & csc
