Math 1 Skills

Algebra Foundations

Real Number System

Comparing Real Numbers
 Order positive decimals
 Order positive fractions
 Condensed: Order positive decimals & fractions
 Order decimals & fractions
 Order positive rational numbers, no radicals, no exponents
 Order rational numbers, no radicals, no exponents
 Order real numbers, no exponents
 Order real numbers, exponents are positive
 Order real numbers
 Comparing expressions on given interval

Application of Comparing Real Numbers
 Order real numbers, positive exponents, percents are whole, including realworld context
 Order real numbers, positive exponents, percents are whole, including realworld context
 Given table, order rational numbers, realworld context
 Given set or list, order rational numbers, realworld context

Classifying Real Numbers
 Determine relationships between subsets of real numbers
 Determine relationships between subsets of rational numbers
 Determine result of adding & multiplying rational & irrational numbers


Algebraic Properties
 Identify properties used in numerical expressions
 Identify properties used in numerical & algebraic expressions
 Identify properties used to solve linear equations
 Identify steps to solve linear equations
 Identify equivalent algebraic expressions, including realworld context
 Evaluate & identify equivalent numerical expressions, including realworld context

Scientific Notation

Operations with Scientific Notation
 Add numbers in scientific notation
 Subtract numbers in scientific notation, realworld context
 Multiply numbers in scientific notation
 Divide numbers in scientific notation
 Condensed: Add, subtract, multiply, & divide numbers in scientific notation

Application of Scientific Notation
 Convert number from standard form to scientific notation, realworld context
 Convert numbers between standard form & scientific notation, realworld context
 Add numbers in scientific notation, realworld context
 Subtract numbers in scientific notation, realworld context
 Multiply numbers in scientific notation, realworld context
 Divide numbers in scientific notation, realworld context
 Compare magnitude of numbers in scientific notation, realworld context


Expressions & Operations

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

Simplifying Expressions
 Simplify algebraic expressions, one variable, distribute once & combine like terms
 Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
 Simplify algebraic expressions, one variable, distribute once & product of two factors
 Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
 Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
 Simplify algebraic expressions, one variable, distribute once, fraction multiplier
 Simplify algebraic expressions, one variable, distribute once, decimal multiplier
 Simplify algebraic expressions, one variable, distribute once, including rationals
 Simplify algebraic expressions, one variable, distribute twice
 Simplify algebraic expressions, two variables, integer coefficients
 Simplify algebraic expressions, two variables, distribute twice
 Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
 Identify equivalent numerical & algebraic expressions, including distribution, including realworld context
 Identify equivalent expressions involving distribution, two or more terms
 Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
 Identify equivalent expressions involving distribution


Inferential Reasonings Word Problems
 Identify appropriate steps to solve problem, realworld context
 Determine reasonable estimates, linear relationships, realworld context
 Determine reasonable estimates, multistep, realworld context


Equations

TwoStep Equations
 Solve ax ± b = c
 Solve twostep linear equations, fractional answers
 Solve twostep linear equations, fractional coefficients
 Solve twostep linear equations, decimal coefficients
 Condensed: Solve x/a ± b = c
 Condensed: Solve onestep linear equations, including fractional coefficients & fractional answers
 Condensed: Solve one or twostep linear equations, fractional coefficients
 Condensed: Solve twostep linear equations
 Solve twostep linear equations, algebra tiles
 Determine if given value is solution to twostep linear equations
 Determine twostep linear equations, realworld context
 Given twostep linear equation, identify realworld situation represented by equation
 Solve problems that can be represented by twostep equations, realworld context

MultiStep Equations
 Solve linear equations, sum or difference on one side
 Solve linear equations, product on one side
 Solve linear equations, like terms on both sides
 Solve linear equations, distributive property on one side, up to two terms on other side
 Solve threestep linear equations involving distribution of decimal multiplier
 Solve threestep linear equations involving distribution, fractional multiplier cancels if distributed
 Solve threestep linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
 Condensed: Solve threestep linear equations involving distribution, including fractional & decimal answers
 Solve linear equations, term minus distributive property on one side
 Solve linear equations, distributive property & additional term on one side
 Condensed: Solve linear equations involving distributive property on one side
 Determine linear equations & solve problems that can be represented by equations with distributive property on one side, realworld context
 Solve (ax ± b)/c = d

Equations with Variables on Both Sides
 Solve linear equations, variables on both sides
 Solve linear equations, distributive property on both sides, integers
 Solve multistep linear equations
 Solve linear equations, distributive property on both sides, additional term on one side
 Solve linear equations, distributive property & additional term on one side & binomial on other side
 Solve linear equations, binomials on both sides, decimals
 Solve linear equations, variables as numerators on both sides
 Solve linear equations, binomials on both sides, fractions
 Solve linear equations, distributive property on both sides, rationals
 Condensed: Solve linear equations, variables on both sides or like terms
 Condensed: Solve linear equations, variables on both sides, rationals
 Determine equations with variables on both sides, 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

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

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


Inequalities

OneVariable Inequalities

Basic OneVariable Inequalities
 Graph inequalities on number line
 Determine graph from inequality or inequality from graph
 Given graph, determine inequality
 Solve & graph onestep inequalities, whole number coefficients
 Solve & graph onestep inequalities, integer coefficients
 Solve & graph onestep inequalities, including fractional coefficients
 Solve & graph onestep inequalities, including negative & fractional coefficients
 Solve & graph twostep inequalities
 Solve multistep inequalities, including variables on both sides
 Solve multistep inequalities using distributive property
 Solve & graph inequalities, variables on both sides, including distributive property
 Condensed: Solve & graph inequalities
 Determine equivalence of inequalities & solution set

Application of OneVariable Inequalities
 Determine inequalities with variables on both sides, realworld context
 Given inequality with variable on both sides, identify realworld problem modeled by inequality
 Identify onestep inequalities that model realworld problems or interpret inequality components
 Determine onestep inequalities, including realworld context
 Determine onestep inequalities, rational numbers, including realworld context
 Given onestep inequality, identify realworld problem modeled by inequality
 Given onestep inequality, identify realworld problem modeled by inequality, rational numbers
 Determine & solve twostep inequalities, greater than, realworld context
 Determine & solve twostep inequalities, less than, realworld context
 Determine twostep inequalities, rational numbers, including realworld context
 Given twostep inequality, identify realworld problem modeled by inequality


Linear Inequalities

Basic Linear Inequalities
 Graph linear inequalities, slopeintercept form, only oblique lines
 Graph linear inequalities, vertical & horizontal lines
 Graph linear inequalities, slopeintercept form, including vertical & horizontal lines
 Graph linear inequalities, various forms
 Given linear inequality, identify correct graph, slopeintercept form
 Given linear inequality, determine graph, slopeintercept form
 Given linear inequality, determine solutions & nonsolutions, slopeintercept form
 Given linear inequality graph, determine solutions & nonsolutions
 Given linear inequality & xvalue, determine yvalue
 Given graph, identify linear inequality, slopeintercept form
 Given graph, determine linear inequality
 Condensed: Determine equivalent linear inequalities & graphical solutions
 Condensed: Given linear inequalities & graphs, determine solutions & nonsolutions

Application of Linear Inequalities
 Given description, determine linear inequalities in standard form & specific solutions, realworld context
 Given description, determine linear inequalities in standard form, including tables, realworld context
 Given description, determine linear inequality in standard form, graph, & determine specific solutions, realworld context
 Given description, determine linear inequality in various forms, graph, & determine specific solutions, realworld context
 Given description & table, graph linear inequality, realworld context
 Given graph, determine inequalities in standard form, realworld context
 Solve linear programming problems, realworld context


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

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


Functions

Independent & Dependent Variables
 Given table, identify dependent or independent variable
 Given table or graph, identify dependent or independent variable
 Given equation, identify dependent or independent variable
 Given description, identify dependent or independent variable

Identifying Functions
 Determine function definition, fill in the blank
 Determine & justify functions, mapping representations, no domain & range language
 Determine functions, mapping representations
 Identify & determine functions, set & table representations
 Determine functions, set & table representations
 Determine functions, graphical representations
 Given relation & additional point, determine functions, multiple representations
 Determine functions, multiple representations, including justification, no domain & range language
 Identify functions, description representations

Identifying & Justifying Functions
 Determine & justify functions, mapping representations
 Determine & justify functions, set representations
 Determine & justify functions, set representations, no domain & range language
 Determine & justify functions, table representations
 Determine & justify functions, table representations, no domain & range language
 Determine & justify functions, graphical representations
 Determine functions, mapping representations, no domain & range language
 Identify & justify functions & nonfunctions, graphical representations
 Identify functions using equivalent mapping diagrams & sets of ordered pairs
 Identify functions, multiple representations, including justification
 Condensed: Identify, justify, & determine functions

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

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

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

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


Linear Concepts

Determining Solution of a Linear Equation
 Given graph of linear equation, identify point on line
 Given linear equation in slopeintercept form, determine if point is on line
 Given linear equation in standard form, determine if point is on line
 Given linear equation in slopeintercept form, identify point on line
 Given linear equation in standard form, identify point on line
 Given horizontal or vertical linear equation, determine if point is on line
 Given horizontal or vertical linear equation, identify point on line
 Condensed: Given linear equation in slopeintercept form & graph, identify point on line
 Given linear equation in slopeintercept form & value of one variable, determine value of other variable
 Given linear equation in slopeintercept form & yvalue, determine xvalue, fractional coefficients or constants

Slope of Line

Find & Use Slope
 Given equation in slopeintercept form, determine next value in table, Δx = 1
 Given equation in slopeintercept form, determine next value in table
 Given equation in slopeintercept form, determine values in table
 Given table of linear equation, determine rate of change & specific value
 Given table, determine rate of change & specific value, function notation
 Given table, determine rate of change & specific value, function notation, integer rate of change
 Given linear graph, determine slope & yintercept, integer slope
 Given table of linear function, determine slope & yintercept

Compare Slopes
 Identify linear table with most extreme rate of change
 Identify linear graph with most extreme rate of change
 Given description, compare rates of change, realworld context
 Compare rates of changes represented differently
 Condensed: Compare rates of change

Identify Slope Category
 Given linear graph, identify type of slope
 Given linear equation, identify type of slope
 Identify linear graph with specific type of slope
 Given table of linear equation, identify type of slope
 Given graph of horizontal or vertical line, determine rate of change
 Condensed: Identify type of slope

Find Slope
 Given equation in slopeintercept form, determine rate of change, integer solution
 Given equation in slopeintercept form, determine rate of change
 Given linear equation in standard form, determine rate of change
 Given equation of horizontal or vertical line, determine rate of change
 Given equation in pointslope form, identify slope
 Given two points with integer coordinates, determine rate of change
 Given two points, determine rate of change, integer solution, including undefined
 Given two points, determine rate of change, one coordinate is fraction
 Given two points, determine rate of change, two coordinates are fractions
 Given table of linear equation, determine rate of change
 Given linear graph, determine rate of change, integer solution
 Given linear graph, determine rate of change
 Given linear graph, determine rate of change, various scales
 Given linear graph, determine slope & yintercept
 Given graph of piecewise function, determine rate of change over specific interval

Application of Slope
 Given graph or table of linear function, determine slope or yintercept, realworld context
 Given right triangle, use legs to determine slope, realworld context
 Given graph of similar right triangles, identify equivalent slopes


Writing Equation of Line

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

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

Writing Equation Given Graph

Write Equation Given Graph Through Origin
 Given linear graph through origin with points shown on line, determine equation in 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

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



Intercepts
 Given linear graph, plot yintercept
 Given linear graph, plot xintercept
 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 linear equation in slopeintercept form, determine coordinates of yintercept
 Given linear equation in standard form, determine coordinates of yintercept
 Given linear equation in slopeintercept form, determine coordinates of xintercept
 Given equation of horizontal or vertical line, determine coordinates of yintercept
 Given equation of horizontal or vertical line, determine coordinates of xintercept
 Given linear equation, determine intercepts
 Given linear equation in slopeintercept form, plot yintercept
 Given equation of horizontal or vertical line, plot yintercept

Equations, Tables, & Graphs

Equation to Table
 Given linear equation, fill missing value in table, m = 1
 Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
 Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
 Given linear equation, fill missing value in table, integer slope, b = 0
 Given linear equation, fill missing value in table, integer slope, b = 0, Δx ≥ 5
 Given linear equation & table, determine another point, integer slope, b = 0
 Given linear equation, fill missing value in table, integer slope
 Given linear equation & table, determine another point, m = 1
 Given linear equation & one xvalue, determine yvalue in table
 Given linear equation, determine table values
 Given linear equation & two xvalues, determine yvalues 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, realworld context

Equation to Graph

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

SlopeIntercept Form to Graph
 Graph linear equations, m = 1
 Graph linear equations, m = 1, various scales
 Given equation in slopeintercept form, graph line, m = ±1, various scales
 Graph proportional linear equation
 Graph linear equations, integer slope not including one & negative one, b = 0
 Graph linear equations, integer slope not including one & negative one
 Graph linear equations, integer slope, various scales
 Graph linear equations, fractional slope, various scales
 Graph linear equations, including horizontal & vertical, integer slope, various scales
 Graph linear equations, fractional slope
 Given description of linear equation, identify graph, fractional slope, realworld context
 Condensed: Graph linear equations, including horizontal & vertical, various scales
 Condensed: Given linear equation or description, determine graph, fractional slope, including realworld context


Basic Graphing
 Given table, graph proportional linear equation
 Given point & integer slope, graph line
 Given point & slope, graph line

Graph to Table
 Given linear graph, determine table value, m = 1, table point off graph
 Given linear graph, determine table value, table point off graph
 Given linear graph with points shown on line, determine table value
 Given linear graph through origin with points shown on line, determine table value, table point off graph
 Given linear graph through origin with points shown on line, determine table values, one table point off graph
 Given linear graph through origin, determine table value
 Given linear graph through origin, determine table value, table point off graph
 Given linear graph through origin, determine table values, one table point off graph

Table to Equation
 Given table representing horizontal linear equation, determine equation
 Given table representing vertical linear equation, determine equation
 Given table, determine linear equation, m = 1
 Given table, determine linear equation, integer slope, b = 0
 Given table, determine linear equation, integer slope
 Given table, identify linear equation in slopeintercept form, rational constants & coefficients
 Given description, determine linear equation, fill table, & determine solution, realworld context


Identifying Key Features of Linear Functions
 Given table of linear equation, determine slope & intercepts
 Given graph of linear equation, determine slope & intercepts
 Given linear equation, determine slope & intercepts
 Given positive point & whole number slope, determine yintercept, equation, & specific value
 Given point & integer slope, determine yintercept, equation, & specific value
 Given linear graph, determine equation in slopeintercept form & specific value, various scales
 Given equation in slopeintercept form, identify slope & yintercept
 Given linear equation in standard form, solve for y
 Given linear equation in standard form, determine slope
 Condensed: Given linear equation in standard form, solve for y or determine slope
 Condensed: Given linear equation in various forms, determine slope or convert to slopeintercept form

Vertical & Horizontal Lines
 Given vertical linear equation, determine graph
 Given horizontal linear equation, determine graph
 Given graph of vertical line, determine equation
 Given graph of horizontal line, determine equation
 Condensed: Given graph of horizontal or vertical line, determine equation

Perpendicular, Parallel, or Neither

Identify Parallel or Perpendicular Lines
 Given equation in slopeintercept form, determine slope of parallel line
 Given equation in various forms, determine slope of parallel line
 Given equation in slopeintercept form, determine slope of perpendicular line
 Given equation in various forms, determine slope of perpendicular line
 Condensed: Given equation in slopeintercept form, determine slope of parallel or perpendicular line
 Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
 Identify equation that is parallel or perpendicular to line through two given points
 Given two slopeintercept form equations, identify as parallel or perpendicular
 Given two equations in standard form, identify as parallel or perpendicular
 Given two pairs of points, determine if lines containing points are parallel or perpendicular

Write Equations of Parallel or Perpendicular Lines
 Given equation in slopeintercept form, determine equation of parallel line through specified point
 Given equation in various forms, determine equation of parallel line through specified point
 Given equation in slopeintercept form, determine equation of perpendicular line through specified point
 Given equation in various forms, determine equation of perpendicular line through specified point
 Given equation in slopeintercept form, determine equation of parallel or perpendicular line through specified point
 Given equation in various forms, determine equation of parallel or perpendicular line through specified point
 Determine equation of line through specified point parallel or perpendicular to 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


Linear Word Problems

Identifying Key Features Given Verbal Description
 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
 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
 Form 6 – Given linear graph, interpret linear relationship & determine slopeintercept equation
 Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slopeintercept equation, & graph
 Given slope & intercept, interpret linear relationship & determine slopeintercept equation, including negative slope
 Given description of linear relationship, determine slope, yintercept, & equation, realworld context
 Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
 Determine linear equation in standard form & graph, realworld context

Choosing Correct Model Given Verbal Description
 Identify equivalent representations of linear relationship, including realworld context
 Given linear word problem, identify graph
 Given description of linear equation, identify graph, integer slope, realworld context
 Given description or table, determine linear graph, realworld context
 Given description of linear relationship, identify graph, table, or equation, realworld context
 Given linear equation, interpret slope & yintercept, realworld context


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

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


Systems

Systems of Equations

Determining Solutions to Systems of Equations
 Given system of linear equations, identify x or yvalue of solution
 Given system of linear equations & description, identify solution, realworld context
 Given system of linear equations, identify solution
 Given graph of system of linear equations, identify specific domain value, realworld context
 Determine systems of linear equations & solutions, realworld context
 Determine & justify solutions to systems of linear equations, realworld context
 Given system of linear equations, identify solution or x or yvalue of solution
 Given table representing system of linear equations, determine solution, realworld context
 Given tables, determine system of linear equations
 Graph systems of linear equations & determine solutions, including realworld context
 Condensed: Given system of linear equations, identify solution, including realworld context
 Condensed: Determine systems of linear equations & solutions, including realworld context

Solving Systems of Equations, Graphing
 Given system of linear equations, graph system, including tables
 Given description of system of linear equations, graph & determine equations or tables
 Given graph of system of linear equations, determine solution, rays on graph to establish pattern
 Given graph of system of linear equations, determine equations in slopeintercept form
 Determine & verify graphical solutions to systems of linear equations, slopeintercept form
 Condensed: Given system of linear equations or description, graph system, including realworld context
 Given system of linear equations, graph & determine point of intersection, slopeintercept form
 Given system of linear equations, determine point of intersection, slopeintercept form

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

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

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


Systems of Inequalities

Basic Systems of Inequalities
 Graph systems of two linear inequalities, slopeintercept form
 Determine equivalent systems of linear inequalities & graphical solutions
 Graph systems of three linear inequalities, slopeintercept form
 Given graph, determine solution of systems of linear inequalities
 Solve systems of linear inequalities

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



Exponents

Product Rule of Exponents

Product of Power, Only Variables
 Express repeated variables as powers, single variable
 Express repeated variables as powers, multiple variables
 Express powers as repeated variables
 Apply product rule of exponents, one variable, positive exponents
 Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
 Simplify single variable powers, negative base or coefficient
 Apply product rule of exponents, two variables, three to four factors, positive exponents
 Apply product rule of exponents, two variables, four to six factors, positive exponents
 Product of Power, Including Coefficients


Quotient Rule of Exponents
 Apply quotient rule of exponents, one variable, positive exponents, greater exponent in numerator
 Apply quotient rule of exponents, one variable, positive exponents, greater exponent in denominator
 Apply quotient rule of exponents, positive exponents
 Apply product & quotient rules of exponents, one or two variables, positive exponents
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents
 Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, positive exponents

Power Rule of Exponents
 Apply power rule, one variable, positive exponents
 Apply power rule, including multiple variables, positive exponents
 Apply power & product rules of exponents, fraction with numerator of one, positive exponents
 Apply power & product rules of exponents, one variable, positive exponents
 Apply product & power rules of exponents, one variable, coefficient of negative one
 Apply power & product rules of exponents, multiple variables, positive exponents

Negative Exponents

Basic Negative Exponents
 Express negative power using positive exponent

Product Rule with Negative Exponents
 Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
 Apply product rule of exponents, negative exponents
 Apply product rule of exponents, two variables, three to four factors, at least one negative exponent
 Apply product rule of exponents, two variables, three to four factors, one variable cancels
 Apply product rule of exponents, two variables, four to six factors, at least one negative exponent
 Apply product rule of exponents, two variables, four to six factors, at least one variable cancels
 Apply product rule, multiple variables, coefficients other than one, including negative exponents
 Apply power rule, multiple variables, coefficients other than one, including negative exponents

Quotient Rule with Negative Exponents
 Apply quotient rule of exponents, one variable, at least one negative exponent
 Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, at least one negative exponent
 Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, at least one negative exponent
 Apply quotient rule of exponents, negative exponents

Power Rule with Negative Exponents
 Apply power rule, one variable, at least one negative exponent
 Apply power rule, one variable, including nonpositive exponents
 Apply power rule, one variable, coefficient of negative one, at least one negative exponent
 Apply power rule of exponents, negative exponents
 Apply power rule, including multiple variables & negative exponents
 Apply power rule, coefficient of negative one, multiple variables, including negative exponents
 Apply power rule, negative base or coefficient, multiple variables, including negative exponents
 Apply power rule, including multiple variables & negative exponents
 Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
 Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
 Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
 Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one


Mixed Rules of Exponents

Simplifying Exponential Expressions
 Apply power rule of exponents, positive exponents
 Simplify powers, fractional algebraic base, including negative exponents
 Apply product rule of exponents, coefficients other than one
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, including negative exponents, coefficients other than one
 Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents, coefficients other than one
 Express negative power using positive exponent, coefficient other than one
 Apply power, product, & quotient rules of exponents, positive exponents
 Apply power, product, & quotient rules of exponents, including negative exponents
 Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
 Apply product, quotient, & power rules of exponents, one variable
 Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one nonpositive exponent

Multiplying Exponential Expressions
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one 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 nonpositive exponent
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
 Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one nonpositive exponent
 Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
 Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents

Dividing Exponential Expressions
 Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
 Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
 Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one nonpositive exponent
 Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one nonpositive exponent
 Apply power, product, & quotient rules of exponents, divide fractions, positive exponents
 Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents

MIxed Operations of Exponential Expressions
 Apply product & quotient rules of exponents, negative exponents
 Apply product & quotient rules of exponents, negative exponents, coefficients other than one
 Apply product, quotient, & power rules of exponents, multiple variables


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

Numerical Exponential Expressions
 Evaluate powers, whole number base, 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

Rational Exponents
 Evaluate numerical expressions with rational exponents
 Simplify numerical expressions with rational exponents
 Evaluate rational exponent expressions, positive exponents
 Simplify rational exponent expressions using product rule, coefficients not with base
 Evaluate rational exponent expressions, negative exponents
 Simplify rational exponent expressions using quotient rule, with coefficients
 Simplify rational exponent expressions using product rule, coefficients with base
 Simplify rational exponent expressions using power rule, with coefficients
 Condensed: Simplify rational exponents using product & power rules
 Condensed: Evaluate rational exponent expressions


Radicals & Roots

Simplifying Radicals
 Determine square roots of perfect squares
 Simplify square roots
 Simplify square roots, coefficient greater than one
 Identify steps to simplify square roots
 Given square root expression, evaluate for specific value
 Condensed: Simplify square roots, including algebraic expressions
 Evaluate perfect cube roots
 Convert from radical to rational exponent, single value in radicand
 Convert from radical to rational exponent, algebraic term in radicand
 Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
 Simplify radical expression raised to power that is multiple of index
 Condensed: Convert from radical to rational exponent
 Convert from rational exponent to radical, single value base
 Convert from rational exponent to radical, algebraic base
 Condensed: Convert from rational exponent to radical
 Determine principal square root of perfect squares
 Simplify radical expressions, perfect powers
 Add & subtract radical expressions, one or two variables, simplified radicals
 Add & subtract radical expressions, one or two variables, radicals to simplify
 Multiply radical expressions, numbers & variables

Solving Radicals
 Solve perfect square root equations
 Condensed: Determine square roots of perfect squares
 Solve perfect cube root equations
 Condensed: Determine cube roots of perfect cubes
 Condensed: Evaluate & compare perfect square & cube roots
 Solve square root equations, square root = #
 Solve square root equations, square root = square root
 Solve square root equations, add & subtract from root
 Solve square root equations, multistep
 Solve square root equations, divide by coefficient of root
 Condensed: Solve square root equations, onestep & twostep
 Solve square root equations, square root = x ± #
 Condensed: Solve square root equations
 Solve square root equations, square root ± square root = #
 Identify extraneous solutions of square root equations


Data Analysis

Graphical Displays of Data

Dot Plots
 Determine mean from dot plots
 Determine median from dot plots
 Determine mean absolute deviation from dot plots
 Determine & compare means from two dot plots
 Determine & compare medians from two dot plots
 Compare mean absolute deviations from two dot plots
 Compare characteristics of sidebyside dot plots
 Solve onestep problems from dot plots, realworld context
 Solve multistep problems from dot plots, realworld context
 Given data, identify dot plot
 Given data represented in various ways, identify dot plot

Histograms
 Solve problems involving interpretation of histograms
 Given various representations of data, determine histogram

Bar Graphs
 Determine or interpret percentage bar graphs

Box Plots
 Solve problems involving interpretation of box plots
 Solve problems involving fivenumber summary
 Determine fivenumber summary
 Given boxplot, determine values from fivenumber summary
 Solve problems involving interpretation of stacked box plots, realworld context
 Condensed: Determine fivenumber summary, including box plots

Frequency Tables
 Interpret twoway frequency tables, marginal distribution
 Interpret twoway frequency tables, conditional distribution
 Interpret twoway frequency tables, joint distribution
 Given twoway frequency tables, identify associations
 Determine twoway frequency tables
 Condensed: Interpret twoway frequency tables
 Determine specified probabilities in twoway frequency tables


Measures of Center & Spread

Calculating Measures of Center & Spread
 Determine mean, median, mode, & range
 Identify definition of mean, median, mode, or range
 Determine mean, median, mode, or range
 Given various representations of data, identify mean, median, mode, & range
 Determine mean, median, mode, or range from various graphs
 Given mean, median, mode, or range, determine missing value in data set
 Given mean, median, or range, determine missing or additional value in data set
 Given additional value in data set, determine change in mean, median, mode, or range
 Condensed: Determine mean, median, mode, or range, including graphs
 Determine interquartile range of data

Interpreting Measures of Center & Spread
 Identify measures of center based on data distribution
 Identify measures of variability based on data distribution
 Identify & interpret measures of center
 Identify & interpret measures of variability
 Determine or interpret shapes & features of graphs
 Determine or interpret measures of center & spread from graphs
 Given various representations of data, identify outlier


Linear Modeling

Scatterplots
 Identify positive & negative correlations in scatter plots
 Identify linear & nonlinear associations in scatter plots
 Identify scatterplots with clustered data
 Identify outliers in scatter plots
 Given data, determine scatter plot
 Condensed: Interpret scatter plots
 Sketch line of best fit & determine equation, graph scales of one
 Sketch line of best fit & determine equation, various graph scales
 Sketch line of best fit & determine equation, 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

Regression
 Determine linear regression equations, calculator expected
 Determine quadratic regression equations, calculator expected
 Determine exponential regression equations, calculator expected
 Condensed: Determine linear, quadratic, or exponential equations, calculator expected
 Given regression equation, determine predicted value
 Given table, identify as linear, quadratic, or exponential

Correlation
 Identify correlation & causation
 Identify association & causation
 Given table, determine & interpret correlation coefficient



Quadratic Functions

Solving Quadratic Functions

Solving Quadratics, Factoring
 Apply zero product property to solve factored quadratic equations
 Identify zeros of factored quadratics
 Determine relationship between zeros & linear factors of quadratic functions
 Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
 Solve quadratic equations using factoring, difference of squares
 Solve quadratic equations using factoring, perfect square trinomial
 Solve quadratic binomial equation by factoring out GCF
 Solve quadratic binomial equation by factoring out GCF, one term on each side
 Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
 Solve quadratic equations using factoring, a ≤ 10, b ≠ 0, c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a ≤ 10, c ≤ 40, terms on both sides
 Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
 Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
 Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
 Factor perfect square trinomials, degree two, one variable
 Factor perfect square trinomials, degree two, two variables

Solving Quadratics, Given Graph
 Given graph of quadratic function, determine roots/zeros

Solving Quadratic Functions, Square Root Method
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
 Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
 Determine exact solution to quadratic equations, a = ±1, b = 0
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
 Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
 Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
 Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
 Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
 Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
 Solve quadratic equations using square root method, a(cx ± h)^2 + k = #

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

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

Application of Solving Quadratics
 Determine or use quadratic equations, realworld context


Writing Equations of Quadratic Functions
 Given vertex & point, determine quadratic equation, vertex form
 Given vertex & point, determine quadratic equation, standard form
 Given graph of quadratic function, determine equation in standard form
 Given graph of quadratic function, determine equation
 Given quadratic equation in standard form, determine vertex form of equation
 Given integer solutions of quadratic equation, determine function in standard form
 Given zeros of quadratic function, determine quadratic equation with integer coefficients
 Given rational solutions of quadratic equation, determine function in standard form
 Given graphical attributes, determine equation of parabola

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

Identifying Key Features of Quadratic Functions

Identifying Vertex, Axis of Symmetry, & Extrema of Quadratics
 Determine minimum & maximum of quadratic functions
 Given graph of quadratic function, determine minimum or maximum value
 Given quadratic equation, determine minimum or maximum value
 Determine vertex of quadratic functions
 Determine symmetry of quadratic functions
 Problem to be Retired (try 1127324): Determine axis of symmetry of quadratic functions
 Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
 Determine intervals of increase & decrease of quadratic functions
 Determine end behavior of quadratic functions

Identifying Intercepts of Quadratics
 Determine zero(s) of quadratic functions
 Determine zero(s)/xintercept(s) of quadratic functions, b = 0
 Determine xintercept(s) of quadratic functions
 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

Identifying Mixed Key Attributes of Quadratics
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a ≠ ±1
 Given graph of quadratic function, determine attributes
 Condensed: Given quadratic equation, determine attributes & graph
 Condensed: Given graph, equation, or table, determine attributes of quadratic function
 Determine intervals where quadratic function is positive or negative


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

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

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


Polynomial Expressions & Functions
 Interpret terms or factors in expressions, including realworld context
 Condensed: Classify polynomials & identify components of polynomials
 Determine quadratic factors of polynomials, degree four
 Determine linear factors of polynomials, degree four
 Factor sum & difference of two cubes, degree three, one variable
 Condensed: Determine linear factors of polynomials, degree three or four
 Determine xintercepts/zeros & yintercepts of polynomial functions
 Determine symmetry of various functions

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
 Given verbal description & graph, determine domain & range of exponential function
 Determine domain & range of discrete exponential functions, realworld context
 Determine restricted domain & range of exponential functions
 Determine domain & range of discrete exponential functions

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

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

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

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

Solving Exponential Functions
 Solve simple exponential equations
 Solve exponential equations, one variable & one base
 Solve exponential equations, both bases reduce to common base
 Solve exponential equations, two different bases, no common base possible
 Solve exponential equations, base e
 Solve exponential equations, no logs required
 Solve exponential equations, common bases given
 Solve exponential equations, one base reduces to common base

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


Logarithmic Functions

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

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

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


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


Sequences

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

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

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


Foundations of Geometry

Vocabulary
 Determine definitions of undefined terms of geometry, fill in the blank
 Determine definitions of angles & shapes, fill in the blank
 Determine definitions of conjectures, fill in the blank
 Determine definitions of theorems, fill in the blank
 Determine definitions of postulates, fill in the blank
 Condensed: Determine definitions of general geometry vocabulary, fill in the blank

Distance & Midpoint

Distance
 Determine distance between two points on number line
 Determine fractional distance between two points on number line
 Determine distance between points
 Determine distance between points, horizontal or vertical
 Determine distance between points, including coordinate plane
 Given segment on coordinate plane, determine length
 Determine fractional distance or fractional point dividing segment into specified ratio
 Given coordinates for vertices of triangle, determine length of sides
 Given coordinates, use length to determine segment congruence

Midpoint
 Determine midpoint of segment on number line
 Given endpoints, determine midpoint
 Determine midpoint of two points on coordinate plane
 Given midpoint & endpoint, determine other endpoint on coordinate plane
 Condensed: Determine midpoint or endpoint of segment on coordinate plane
 Given endpoint & point dividing segment into specified ratio, determine other endpoint on coordinate plane
 Determine point that divides segment into specified ratio on coordinate plane
 Condensed: Determine endpoint or point dividing segment into specified ratio on coordinate plane

Distance & Midpoint Combined
 Given midpoint or distance between points, determine missing endpoint
 Condensed: Determine distance or midpoint on number line


Angles
 Classify angles from figure
 Identify angle names
 Identify angle pairs
 Identify types of angles in figures
 Estimate angle measures
 Identify 90°, 180°, 270°, & 360° angles
 Measure angles using protractor
 Measure angles using protractor, realworld context
 Identify angles with specified measures
 Apply angle addition postulate to determine angle measures
 Apply angle addition postulate to determine angle measures, algebraic expressions
 Condensed: Apply angle addition postulate to determine angle measures, including algebraic expressions

Properties of Triangles

Classifying Triangles
 Classify triangles by sides
 Classify triangles by angles
 Classify triangle based on given angle measures
 Classify triangles based on angles & sides
 Apply triangle inequality theorem to determine range of values for unknown side
 Apply triangle inequality theorem to determine side lengths

Isosceles & Equilateral Triangles
 Given congruent sides, identify congruent angles of isosceles triangle
 Given congruent angles, identify congruent sides of isosceles triangle
 Solve problems involving perimeter of equilateral triangles
 Solve problems involving perimeter of isosceles triangles
 Given equilateral triangle & algebraic expressions for sides, solve for variable or determine side length
 Given equilateral triangle & algebraic expression for angle, solve for variable
 Determine angle measure in isosceles triangle, at most one algebraic expression
 Determine angle measure in isosceles triangle, up to two algebraic expressions
 Condensed: Solve problems involving perimeter of equilateral & isosceles triangles

Triangle Angle Sum & Exterior Angles
 Given two angle measures in triangle, determine angle measure
 Given two angle measures in triangle, determine & justify angle measure
 Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions
 Apply triangle angle sum theorem to determine angles, algebraic expressions
 Apply triangle angle sum theorem to determine angles, multiple algebraic expressions
 Given description, apply triangle angle sum theorem to determine angles, algebraic expressions
 Apply triangle exterior angle theorem to determine angles, including algebraic expressions
 Condensed: Apply triangle angle sum theorem & exterior angle theorem to determine angles, including algebraic expressions

Perpendicular & Angle Bisectors
 Given perpendicular bisector in triangle, determine segment lengths
 Given perpendicular bisector in triangle, determine segment lengths, algebraic expressions
 Given angle bisector in triangle, determine angles
 Given angle bisector in triangle, determine angles, algebraic expressions
 Determine segment lengths in triangles with angle bisectors
 Condensed: Given perpendicular or angle bisector in triangle, determine segment lengths or angles, including algebraic expressions


Area & Perimeter on the Coordinate Plane
 Determine area of polygons in coordinate plane
 Determine area of polygons in coordinate plane, realworld context
 Given coordinates of vertices, determine side lengths & perimeter of polygons
 Given coordinates of vertices, determine area of triangle or rectangle
 Determine area of composite figures on coordinate plane, no circular shapes


Triangle Similarity & Congruence

Similar Triangles
 Identify corresponding parts of similar figures
 Determine angles of similar triangles using AA similarity
 Determine similarity of triangles using AA similarity
 Determine similar triangles using SAS similarity
 Determine similar triangles using SSS similarity
 Determine missing steps in proofs involving similar triangles
 Determine missing steps in proofs involving similar triangles, paragraph form
 Determine sides of similar triangles using AA similarity
 Determine angles of similar triangles using AA similarity, algebraic expressions
 Determine segment lengths using triangle proportionality theorem
 Condensed: Determine similar triangles using SAS or SSS similarity

Proofs
 Determine missing steps in proofs involving SSS in triangles
 Determine missing steps in proofs involving SAS in triangles
 Determine missing steps in proofs involving AAS in triangles
 Determine missing steps in proofs involving ASA in triangles
 Determine missing steps in proofs involving triangle congruence theorems
 Determine missing steps in proofs involving triangle congruence theorems, paragraph form
 Determine missing steps in proofs involving corresponding parts
 Determine missing steps in proofs involving corresponding parts, paragraph form
 Determine missing steps in proofs involving quadrilaterals
 Apply triangle theorems or determine missing steps in proofs
 Determine missing steps in proofs involving quadrilaterals, paragraph form


Geometric Transformations

Translations
 Given coordinate vertices of figure, determine translated image
 Given figure on coordinate plane, determine translated coordinates
 Identify rule or determine translated point on coordinate plane

Reflections
 Determine coordinates of reflected points
 Given coordinate vertices of figure, determine reflected image
 Identify rule or reflected point on coordinate plane
 Given figure on coordinate plane, determine reflected coordinates

Rotations
 Given coordinate vertices of figure, determine rotated image
 Given figure on coordinate plane, determine rotated coordinates
 Identify rule or rotated point on coordinate plane

Dilations
 Identify characteristics of dilations
 Identify rule or dilated point on coordinate plane, including variable scale factors

Mixed Transformations

Transformations of Angles, Lines, & Segments
 Identify characteristics of transformed lines
 Identify characteristics of transformed line segments
 Identify characteristics of transformed parallel lines
 Identify characteristics of transformed angles
 Identify characteristics of transformed lines, segments, & angles

Transformations of Figures
 Given congruent figures, identify description of transformations
 Given similar figures, identify description of transformations
 Identify congruence transformations
 Identify rule or determine transformed point on coordinate plane
 Identify rule for transformed shape on coordinate plane
 Composition of transformations on coordinate plane
 Identify characteristics of transformations
 Identify reflections & rotations on coordinate plane
 Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates
 Condensed: Given similar or congruent figures, identify description of transformations
 Condensed: Identify rule or determine transformed point on coordinate plane



Absolute Value Functions
 Given graph, determine absolute value equation
 Given description of transformation, determine absolute value equation
 Condensed: Graph absolute value functions using any transformation
 Given absolute value equation, identify description of transformation

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

Probaility
 Determine conditional probabilities from twoway frequency tables
 Determine conditional probabilities, including twoway frequency tables