Algebra 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 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 rational numbers
 Determine relationships between subsets of real numbers
 Determine result of adding & multiplying rational & irrational numbers


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

Numerical Absolute Value
 Determine absolute value of integers
 Determine absolute value of integers, including realworld context
 Determine absolute value of numeric expression
 Determine absolute value of rational numbers

Order of Operations

Order of Operations, Only Postives
 Evaluate numerical expressions, # + #(#)
 Evaluate numerical expressions, #/# + #
 Evaluate numerical expressions, #/# + #, decimals
 Evaluate numerical expressions, # ± #(#), decimals
 Evaluate numerical expressions, #(# + #), decimals
 Evaluate numerical expressions, # + #(#)^#
 Evaluate numerical expressions, #(#)^# + #/#
 Evaluate numerical expressions, # + #(# + #)^#
 Evaluate numerical expressions, up to four operations
 Evaluate numerical expressions, including rationals & up to two sets of grouping symbols
 Identify first steps in evaluating numerical expressions using grouping symbols
 Evaluate numerical expressions, up to two sets of grouping symbols, realworld context

Order of Operations, Three or Four Integers
 Evaluate sum or difference of three integers, at least one difference
 Evaluate sum or difference of four integers, at least one difference
 Evaluate sum or difference of four integers, two grouped in parentheses, at least one difference
 Evaluate sum or difference of four integers, two grouped in absolute value, at least one difference
 Evaluate numerical expressions, three or four integers, including multiplication & division
 Evaluate numerical expressions, three or four integers, including multiplication & division as fraction
 Evaluate numerical expressions, three or four integers, one exponent, including multiplication
 Evaluate numerical expressions, four integers, including multiplication & exponents
 Evaluate numerical expressions, realworld context

Order of Operations, Five or More Integers
 Evaluate sum or difference of six integers, two grouped in parentheses, two grouped in absolute value, at least one difference
 Evaluate numerical expressions, five integers, two grouped in parentheses, including multiplication & division
 Evaluate numerical expressions, five integers, two grouped in absolute value, including multiplication & division
 Evaluate numerical expressions, five integers, one exponent, two grouped in parentheses, including multiplication & division
 Evaluate numerical expression quotients, five to seven integers, including multiplication, division, & absolute value
 Evaluate numerical expression quotients, five to seven integers, one exponent, including multiplication, division, & absolute value
 Condensed: Evaluate numerical expressions

Order of Operations, Rational Numbers
 Identify equivalent expressions using order of operations
 Evaluate numerical expressions, fractions, no exponents
 Evaluate numerical expressions, decimals, no exponents
 Evaluate numerical expressions, decimals & fractions, no exponents
 Evaluate numerical expressions, fractions
 Evaluate numerical expressions, decimals
 Evaluate numerical expressions, decimals & fractions


Scientific Notation

Basic Scientific Notation
 Identify correct conversion of number from scientific notation with positive exponent to standard form
 Identify correct conversion of number from scientific notation with negative exponent to standard form
 Convert number from scientific notation with positive exponent to standard form
 Convert number from scientific notation with negative exponent to standard form
 Identify correct conversion of number from standard form to scientific notation with positive exponent
 Identify correct conversion of number from standard form to scientific notation with negative exponent
 Convert number from standard form to scientific notation with positive exponent
 Convert number from standard form to scientific notation with negative exponent
 Condensed: Identify correct conversion of number between scientific notation & standard form
 Condensed: Convert number between scientific notation & standard form
 Convert number from word form to scientific notation
 Compare two numbers in scientific notation

Scientific Notation, Round First
 Round & convert number from standard form to scientific notation with positive exponent
 Round & convert number from standard form to scientific notation with negative exponent
 Condensed: Round & convert number from standard form to scientific notation

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

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


Coordinate Plane

Basic Coordinate Plane
 Plot integer points
 Plot integer points on coordinate plane, point on axis
 Given integer point on graph, determine coordinates
 Given integer point on graph, determine coordinates, point on axis
 Given lattice point, determine coordinates
 Plot points on coordinate plane, student selects scales
 Condensed: Plot integer points or determine coordinates
 Given rational point, determine location on coordinate plane
 Plot rational points on coordinate plane
 Plot or identify rational points on coordinate plane
 Plot rational points on coordinate plane, graph scale at most onehalf
 Condensed: Plot or identify points on coordinate plane

Application of Coordinate Plane
 Identify first quadrant points or parts of coordinate plane
 Identify locations or parts of coordinate plane using first quadrant points
 Identify description of process to plot first quadrant points
 Determine or identify first quadrant points, realworld context
 Determine or identify first quadrant points, including cardinal directions, realworld context
 Condensed: Plot or determine coordinates of first quadrant rational points


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


Expressions

Evaluating Expressions

Evaluating Expressions, Only Positives
 Evaluate addition expressions for specified value, one variable, whole numbers
 Evaluate addition expressions for specified value, one variable, at least one fraction
 Evaluate addition expressions for specified value, one variable, at least one decimal
 Evaluate subtraction expressions for specified value, one variable, whole numbers
 Evaluate subtraction expressions for specified value, one variable, at least one fraction
 Evaluate subtraction expressions for specified value, one variable, at least one decimal
 Evaluate expressions for specified value, one variable, including multiple operations, at least one decimal
 Evaluate expressions for specified values, two variables, multiple operations, including powers & realworld context

Evaluating Expressions, Including Negatives
 Evaluate expressions for specified value, one variable, two terms, only sums & differences
 Evaluate expressions for specified value, one variable, one term, two factors
 Evaluate linear expressions for specific values
 Evaluate expressions for specified value, one variable, one term, three factors
 Evaluate expressions for specified value, one variable, two terms
 Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
 Evaluate expressions for specified value, one variable, two terms, multiple operations, including powers of absolute values
 Evaluate expressions for specified values, two variables, two terms
 Evaluate expressions for specified values, two variables, two terms, one term with three factors
 Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
 Evaluate expressions for specified values, two variables, quotient of expressions
 Evaluate algebraic expressions, including variable exponents


Simplifying Expressions

Combining Like Terms
 Simplify algebraic expressions, combine two terms, positives
 Simplify algebraic expressions, combine two terms
 Simplify algebraic expressions, one variable, positive integer coefficients
 Simplify algebraic expressions, one variable, integer coefficients
 Simplify algebraic expressions, one variable, rational coefficients
 Simplify algebraic expressions, two variables, positive integer coefficients
 Simplify algebraic expressions, two variables, integer coefficients

Distributive Property
 Simplify algebraic expressions, one variable, distribute once, integer multiplier
 Simplify algebraic expressions, one variable, distribute once, fraction multiplier
 Simplify algebraic expressions, one variable, distribute once, decimal multiplier
 Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
 Identify equivalent numerical & algebraic expressions, including distribution, including realworld context
 Simplify algebraic expressions, one variable, distribute once, variable multiplier
 Simplify algebraic expressions, one variable, distribute once, variable with coefficient multiplier
 Simplify algebraic expressions, one variable, distribute once, including rationals
 Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers

Distributive Property & Combining Like Terms
 Identify equivalent expressions involving distribution
 Simplify algebraic expressions, one variable, distribute once & combine like terms
 Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
 Simplify algebraic expressions, one variable, distribute once & product of two factors
 Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
 Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
 Simplify algebraic expressions, one variable, distribute twice
 Simplify algebraic expressions, two variables, distribute twice

Writing Rational Expression as Two Terms
 Convert linear binomials divided by constants to sum or difference of two terms



Ratios, Rates, & Proportions

Rates
 Determine unit rates, whole numbers, realworld context
 Determine unit rates, fractions, realworld context
 Determine unit rates, mixed numbers, realworld context
 Given unit rate, determine specified value in proportional relationship, realworld context
 Condensed: Determine or apply unit rates, realworld context
 Given rate, convert time unit to determine quantity over time interval, realworld context
 Given rate of travel, determine distance or time
 Given rate & comparison, determine unit rates, realworld context
 Determine & compare unit rates, realworld context
 Given proportional relationship, determine specified quantity, realworld context
 Given proportional relationship, determine specified quantity, including decimals, realworld context

Ratios

Basic Ratios
 Determine part to whole ratio, decimal grids
 Determine part to part ratio, decimal grids
 Identify percents, area models
 Given ratio, identify table
 Given table of proportional relationship, determine value or equivalent ratio
 Compare rates

Application of Ratios
 Determine part to whole ratio, strip diagrams, realworld context
 Determine part to part ratio, strip diagrams, realworld context
 Determine part to whole ratio, double number lines, realworld context
 Determine part to part ratio, including double number lines, including realworld context
 Determine specified values in ratios, strip diagrams, realworld context
 Determine specified values in proportional relationships, realworld context
 Determine ratios or specified quantities from table or identify table from given ratio, realworld context
 Compare rates or determine specified values in proportional relationships, realworld context


Proportions

Basic Proportions
 Solve proportions, whole numbers
 Solve proportions
 Solve proportions, mixed number components, whole number cross products
 Solve proportions, mixed number components
 Solve proportions, one binomial expression
 Solve proportions, two binomial expressions
 Condensed: Solve proportions, binomial expressions

Application of Proportions
 Solve proportions, exact answers, realworld context
 Solve proportions, rounded answers, realworld context
 Solve proportions involving time, realworld context
 Condensed: Solve proportions, including realworld context



Equations

OneStep Equations
 Condensed: Solve onestep linear equations, addition or subtraction
 Condensed: Solve onestep linear equations, multiplication or division
 Solve onestep linear equations, fractional answers
 Solve onestep linear equations, fractional coefficients
 Solve onestep linear equations, fractional coefficients & constants
 Condensed: Solve onestep linear equations, including fractional coefficients & fractional answers
 Determine onestep linear equations, realworld context
 Determine onestep equations, including decimals, realworld context
 Given onestep linear equation, identify realworld situation represented by equation
 Given onestep equation, identify realworld situation represented by equation

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

MultiStep Equations

MultiStep Equations, no Distribution
 Solve linear equations, sum or difference on one side
 Solve linear equations, product on one side
 Solve linear equations, like terms on both sides
 Solve (ax ± b)/c = d

MultiStep Equations, with Distribution
 Solve linear equations, distributive property on one side
 Solve linear equations, distributive property on one side, up to two terms on other side
 Solve 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


Equations with Variables on Both Sides

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

Application of Equations with Variables on Both Sides
 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


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

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

Identifying Number of Solutions
 Determine number of solutions in linear equations, distribute at most one time
 Determine number of solutions in linear equations, distribute up to two times
 Condensed: Determine number of solutions in linear equations
 Solve linear equations, including no solution & infinitely many solutions


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

TwoStep or MultiStep OneVariable Inequalities
 Solve & graph twostep inequalities
 Condensed: Solve & graph inequalities
 Determine equivalence of inequalities & solution set
 Solve multistep inequalities, including variables on both sides
 Solve multistep inequalities using distributive property
 Solve & graph inequalities, variables on both sides, including distributive property

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


Linear Inequalities

Linear Inequalities Solutions & NonSolutions
 Given linear inequality & xvalue, determine yvalue
 Given linear inequality, determine solutions & nonsolutions, slopeintercept form
 Given linear inequality graph, determine solutions & nonsolutions
 Condensed: Given linear inequalities & graphs, determine solutions & nonsolutions

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

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

Absolute Value Inequalities

Absolute Value Inequalities with Setup
 Given linear absolute value inequality, determine compound inequality
 Solve & graph linear absolute value inequalities, "and" solutions, including setup
 Solve & graph linear absolute value inequalities, "or" solutions, including setup
 Solve & graph linear absolute value inequalities, including setup
 Condensed: Solve & graph linear absolute value inequalities, including setup
 Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
 Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup

Absolute Value Inequalities without Setup
 Solve & graph linear absolute value inequalities, "and" solutions
 Solve & graph linear absolute value inequalities, "or" solutions
 Condensed: Solve & graph linear absolute value inequalities
 Solve & graph linear absolute value inequalities, including extra constant or coefficient
 Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
 Create linear absolute value inequalities, realworld context
 Create linear absolute value equations, realworld context



Functions

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

Identifying & Justifying Functions
 Determine & justify functions, mapping representations, no domain & range language
 Determine & justify functions, mapping representations
 Determine & justify functions, set representations, no domain & range language
 Determine & justify functions, set representations
 Identify functions using equivalent mapping diagrams & sets of ordered pairs
 Determine & justify functions, table representations
 Determine & justify functions, graphical representations
 Identify & justify functions & nonfunctions, graphical representations
 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
 Given graph, determine domain & range
 Determine restricted domain & range of linear functions
 Determine discrete domain & range, realworld context
 Determine continuous domain & range, realworld context
 Condensed: Determine domain & range, including realworld context

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

Determine Parent Functions & Points of Intersection
 Determine whether given table represents linear or exponential function
 Determine points of intersection of various functions, not absolute value or polynomial
 Condensed: Determine points of intersection of functions
 Determine whether given table represents linear, exponential, or quadratic function
 Determine whether given graph represents linear, exponential, or quadratic function
 Condensed: Determine what function given table or graph represents

Graph Functions
 Given various functions, identify graph
 Given graph, identify various functions

Inverse Functions
 Determine inverse of linear function
 Determine inverse of quadratic & square root functions
 Determine inverse of cubic & cube root functions
 Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions
 Determine inverse of various functions


Linear Concepts

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

Slope of Line

Finding & Using 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, integer rate of change
 Given table, determine rate of change & specific value, function notation
 Given table of linear function, determine slope & yintercept
 Given linear graph, determine slope & yintercept, integer slope

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

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

Finding Slope

Finding Slope Given Points
 Given two points with integer coordinates, determine rate of change
 Given two points, determine rate of change, integer solution, including undefined
 Given two points, determine rate of change, one coordinate is fraction
 Given two points, determine rate of change, two coordinates are fractions
 Given table of linear equation, determine rate of change

Finding Slope Given Equation or Graph
 Given equation in pointslope form, identify slope
 Given equation in slopeintercept form, determine rate of change, integer solution
 Given equation in slopeintercept form, determine rate of change
 Given equation of horizontal or vertical line, determine rate of change
 Given linear equation in standard form, determine rate of change
 Given linear graph, determine rate of change, integer solution
 Given linear graph, determine rate of change
 Given linear graph, determine rate of change, various scales
 Given linear graph, determine slope & 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 & integer slope or rate of change, determine linear equation in slopeintercept form
 Given point & integer slope, 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 slopeintercept form, integer slope
 Given two points, determine linear equation in pointslope form, integer slope, including slopeintercept form conversion
 Given two points, determine linear equation in standard 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 pointslope form, fractional slope, including slopeintercept form conversion
 Given two points, determine linear equation in standard form, fractional slope, including slopeintercept form conversion
 Given two points, determine linear equation, undefined slope
 Given two points, determine linear equation, zero slope
 Given linear table, determine slope, yintercept, & equation
 Given intercepts, determine linear equation in slopeintercept form

Writing Equation Given Various Components
 Given linear equation, write equation in requested form
 Given points or slope & point, determine linear equation in standard form
 Given points or slope & point, determine linear equation in 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, determine equation in slopeintercept form, integer slope, 1 ≤ m ≤ 3
 Given linear graph through origin, determine equation in slopeintercept form, integer slope
 Given linear graph through origin with points shown on line, determine equation in slopeintercept form, integer slopes

Writing Equation Given Graph, SlopeIntercept Form
 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, integer slopes, various scales
 Given linear graph, determine equation in slopeintercept form, fractional slopes
 Given linear graph, determine slope, yintercept, & equation
 Given linear graph, identify equation, slopeintercept form
 Condensed: Given linear graph, determine equation in slopeintercept form & specific value, various scales, including realworld context
 Given equation in slopeintercept form, identify graph, integer slopes, various scales

Writing Equation Given Graph, Various Forms
 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 Graphs & Equations
 Identify equivalent linear graphs & equations in slopeintercept form
 Identify equivalent linear graphs & equations in slopeintercept form, various scales
 Condensed: Identify equivalent linear graphs & equations in slopeintercept form, integers slopes, various scales



Intercepts

Intercepts, Given Graph
 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 graph, identify equation, various forms

Intercepts, Given Equation
 Given linear equation in slopeintercept form, plot yintercept
 Given equation of horizontal or vertical line, plot yintercept
 Given linear equation in slopeintercept form, determine coordinates of yintercept
 Given linear equation in slopeintercept form, determine coordinates of xintercept
 Given linear equation in standard form, determine coordinates of yintercept
 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
 Condensed: Given linear equation, determine x or yintercepts


Equations, Tables, & Graphs

Equation to Table

Fill Missing Value in Table
 Given linear equation, fill missing value in table, m = 1
 Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
 Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
 Given linear equation, fill missing value in table, integer slope, b = 0
 Given linear equation, fill missing value in table, integer slope, b = 0, Δx ≥ 5
 Given linear equation, fill missing value in table, integer slope
 Given linear equation & one xvalue, determine yvalue in table

Fill Table
 Given linear equation & table, determine another point, m = 1
 Given linear equation & table, determine another point, integer slope, b = 0
 Given linear equation, determine table values
 Given linear equation & two 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

SlopeInterecept Form to Graph Scale of One
 Graph linear equations, m = 1
 Graph linear equations, integer slope not including one & negative one, b = 0
 Graph linear equations, integer slope not including one & negative one
 Graph proportional linear equation
 Graph linear equations, fractional slope
 Condensed: Given linear equation or description, determine graph, fractional slope, including realworld context
 Given description of linear equation, identify graph, fractional slope, realworld context
 Condensed: Identify equivalent equations, graphs, & tables

SlopeIntercept Form to Graph Various Scales
 Graph linear equations, m = 1, various scales
 Given equation in slopeintercept form, graph line, m = ±1, various scales
 Graph linear equations, integer slope, various scales
 Graph linear equations, fractional slope, various scales
 Graph linear equations, including horizontal & vertical, integer slope, various scales
 Condensed: Graph linear equations, including horizontal & vertical, various scales



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 values, one table point off graph
 Given linear graph through origin with points shown on line, determine table value, table point off graph
 Given linear graph through origin, determine table value
 Given linear graph through origin, determine table value, table point off graph
 Given linear graph through origin, determine table values, one table point off graph

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


Identifying Key Features of Linear Function
 Given table of linear equation, determine slope & intercepts
 Given graph of linear equation, determine slope & intercepts
 Given linear equation in standard form, determine slope
 Given linear equation in standard form, solve for y
 Given equation in slopeintercept form, identify slope & yintercept
 Given linear equation, determine slope & intercepts
 Condensed: Given linear equation in standard form, solve for y or determine slope
 Condensed: Given linear equation in various forms, determine slope or convert to slopeintercept form
 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

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

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

Writing Equations of Parallel or Perpendicular Lines
 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
 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


Line of Best Fit & Scatter Plots
 Identify positive & negative correlations in scatter plots
 Identify linear & nonlinear associations in scatter plots
 Condensed: Interpret scatter plots
 Sketch line of best fit
 Sketch line of best fit & determine equation, graph scales of one
 Sketch line of best fit & determine equation, various graph scales
 Condensed: Sketch line of best fit & determine equation
 Sketch line of best fit & determine predicted value
 Sketch line of best fit & determine equation, realworld context
 Determine residuals

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
 Given slope & intercept, interpret linear relationship & determine slopeintercept equation, including negative 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 description of linear relationship, determine slope, yintercept, & equation, realworld context
 Determine linear equation in standard form & graph, realworld context
 Form 7 – Given linear word problem, graph & interpret relationship, four quadrants

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


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
 Condensed: Determine graphical attributes of absolute value functions
 Graph absolute value functions using all transformations
 Condensed: Graph absolute value functions using any transformation
 Graph absolute value functions using vertex & intercepts
 Determine points of intersection of absolute value functions
 Compare absolute value functions represented differently


Systems

Systems of Equations

Determining Solution to System of Equations
 Given tables, determine system of linear equations
 Given table representing system of linear equations, determine solution, 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
 Given system of linear equations, identify x or yvalue of solution
 Given system of linear equations, identify solution
 Given system of linear equations, identify solution or x or yvalue of solution
 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

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

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
 Condensed: Given system of linear equations, determine solution, substitution bias
 Solve, interpret, or determine systems of linear equations, slopeintercept form, realword context
 Solve, interpret, or determine systems of linear equations, standard form, realword context
 Determine systems of linear equations & solutions, substitution bias, realworld context
 Determine solutions of linear equations, substitution bias, including given system, realworld context
 Solve systems of linear equations, infinite possibilities or no solution
 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
 Solve systems of linear equations, multiply at most one equation
 Solve systems of linear equations, multiply one or both equations
 Condensed: Solve or determine system of equations, both equations in standard form

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


Systems of Inequalties

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

Application of Systems of Inequalities
 Given linear system of inequalities graph, identify true statements
 Given description, determine system of linear inequalities in standard form & solution point, 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
 Given description & graph, determine system of linear inequalities in standard form & shaded region, 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
 Given description of system of linear inequalities, identify graph of system
 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
 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

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

Product Rule of Exponents

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

Product of Powers, Including Coefficients
 Express repeated variables as powers or powers as repeated variables
 Express repeated variables as powers, coefficients other than one
 Apply product rule of exponents, positive exponents
 Apply product rule of exponents, one variable, positive exponents, coefficients other than one


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

Negative Exponents

Basic Negative Exponents
 Express negative power using positive exponent

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, including multiple variables & negative exponents
 Apply power rule, coefficient of negative one, multiple variables, including negative exponents
 Apply power rule, negative base or coefficient, multiple variables, including negative exponents
 Apply power rule, including multiple variables & negative exponents
 Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
 Apply power rule of exponents, negative exponents
 Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
 Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
 Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one

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

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


Mixed Properties of Exponents

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

Multiplying Exponential Expressions
 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 fractions, one or two variables, coefficients other than one, including negative exponents
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
 Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one 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 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, 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, positive fractional base, including nonpositive exponents
 Evaluate powers, fractional base, positive exponent
 Evaluate powers, fractional base, negative exponent
 Evaluate powers, fractional bases
 Condensed: Evaluate powers with negative exponents

Rational Exponents
 Evaluate numerical expressions with rational exponents
 Simplify numerical expressions with rational exponents


Radicals & Roots

Simplifying Radicals
 Determine square roots of perfect squares
 Determine principal square root of perfect squares
 Simplify square roots
 Simplify square roots, coefficient greater than one
 Identify steps to simplify square roots
 Given square root expression, evaluate for specific value
 Condensed: Simplify square roots, including algebraic expressions
 Evaluate perfect cube roots
 Simplify radical expressions, perfect powers
 Multiply radical expressions, numbers & variables
 Add & subtract radical expressions, one or two variables, simplified radicals
 Add & subtract radical expressions, one or two variables, radicals to simplify
 Condensed: Add & subtract radical expressions

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


Quadratic Functions

Identifying Key Features of Quadratic Functions

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

Determine Maximum & Minimum Values
 Given graph of quadratic function, determine minimum or maximum value
 Given quadratic equation, determine minimum or maximum value
 Determine minimum & maximum of quadratic functions

Determine Vertex, Symmetry, Increase & Decrease, & End Behavior
 Determine vertex of quadratic functions
 Determine symmetry of quadratic functions
 Determine intervals of increase & decrease of quadratic functions
 Determine intervals where quadratic function is positive or negative
 Determine end behavior of quadratic functions

Determine Attributes & Graph
 Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
 Given graph of quadratic function, determine attributes
 Condensed: Determine graphical attributes of quadratic functions
 Condensed: Given graph, equation, or table, determine attributes of quadratic function
 Given quadratic equation, determine attributes & graph, a ≠ ±1
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a = 1
 Condensed: Given quadratic equation, determine attributes & graph


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

Writing Equations of Quadratic Functions
 Given graph of quadratic function, determine equation
 Given graph of quadratic function, determine equation
 Given vertex & point, determine quadratic equation, vertex form
 Given quadratic equation in standard form, determine vertex form of equation
 Given vertex & point, determine quadratic equation, standard form
 Given graphical attributes, determine equation of parabola
 Given quadratic equation in vertex form, determine standard form of equation

Solving Quadratic Functions

Solving Quadratics, Zero Product
 Apply zero product property to solve factored quadratic equations
 Identify zeros of factored quadratics
 Determine relationship between zeros & linear factors of quadratic functions

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

Solving Quadratics, Factoring Trinomials & Difference of Squares
 Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
 Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
 Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a ≤ 10, b ≠ 0, c ≤ 40, zero on one side
 Solve quadratic equations using factoring, a ≤ 10, c ≤ 40, terms on both sides
 Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
 Solve quadratic equations using factoring, difference of squares
 Factor perfect square trinomials, degree two, one variable
 Factor perfect square trinomials, degree two, two variables

Solving Quadratics, Square Root Method
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
 Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
 Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
 Determine exact solution to quadratic equations, a = ±1, b = 0
 Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0

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

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


Transformations of Quadratic Functions
 Identify & graph vertical & horizontal shifts of quadratic functions
 Identify & graph vertical & horizontal stretches & compressions of quadratic functions
 Given quadratic equation, identify description of transformation
 Identify descriptions of graphs of quadratic parent functions & transformed functions
 Given description of transformation, determine quadratic function
 Describe parameter changes to quadratic parent functions
 Determine effects of parameter changes in quadratic relationships, 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 initial height & velocity of object in vertical motion, determine position function & specific time
 Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
 Given initial height & negative velocity of object in vertical motion, determine position function & specific time
 Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
 Given height of dropped object, determine position function & specific time
 Condensed: Given initial height & velocity of object in vertical motion, determine position function, maximum height, or time to maximum height
 Condensed: Given initial height & velocity of object in vertical motion, determine position function & specific times
 Condensed: Given initial height & velocity of object in vertical motion, determine position graph, position function, & specific times

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


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

Exponential Functions

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

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

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

Application of Exponential Functions
 Calculate investment value, annual compounding
 Calculate investment value, various compounding
 Calculate depreciating asset value, annual compounding
 Condensed: Calculate investment & depreciating asset values, annual compounding
 Determine exponential function, realworld context
 Given table, determine attributes of exponential function
 Interpret values in exponential functions, realworld context
 Given absolute value equation, identify description of transformation


Polynomials

Standard Form of Polynomials
 Identify leading coefficient of polynomials
 Identify leading coefficient of polynomials, including two variables
 Identify terms of expressions
 Determine degree, leading coefficient, & type of polynomial
 Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables
 Determine standard form of polynomial, no like terms
 Determine standard form of polynomial, like terms
 Determine standard form of polynomial, no like terms, including two variables
 Determine standard form of polynomial, like terms, including two variables

Classifying Polynomials
 Determine degree of polynomials
 Determine degree of polynomials, including two variables
 Identify polynomial as monomial, binomial, or trinomial
 Identify polynomial as monomial, binomial, or trinomial, including two variables
 Classify polynomials by degree
 Classify polynomials by degree & number of terms
 Condensed: Classify polynomials & identify components of polynomials

Operations of Polynomials

Addition & Subtraction of Polynomials
 Add binomials & trinomials, degrees zero to two
 Subtract binomials & trinomials, degrees zero to two
 Add binomials & trinomials, degrees zero to three
 Subtract binomials & trinomials, degrees zero to three
 Condensed: Add or subtract binomials & trinomials

Multiplication & Division of Polynomials
 Multiply monomial times binomial or trinomial, degrees zero to two
 Multiply monomial times binomial or trinomial, mixed degrees
 Multiply binomial times binomial, both degree one
 Square linear binomial
 Condensed: Multiply binomial times binomial
 Multiply binomial times binomial, mixed degrees
 Multiply linear binomial times quadratic trinomial
 Multiply binomial times trinomial, mixed degrees
 Divide polynomials, degree one or two by degree one or two
 Divide polynomials, degree three or four by degree one
 Divide polynomials, divisor supports synthetic division

Mixed Operations of Polynomials
 Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial


Factoring Polynomials

GCF or LCM of Polynomials
 Determine GCF in polynomials, one variable
 Determine GCF of two monomials, two variables
 Determine LCM of two monomials, two variables
 Condensed: Determine GCF or LCM of two monomials, two variables
 Factor GCF in polynomials, degree one or two, one variable
 Factor GCF in polynomials, one variable
 Factor GCF in polynomials, including two variables
 Determine missing component of GCF
 Given GCF & one monomial, identify second monomial

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, no GCF
 Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
 Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
 Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
 Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40

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

Mixed Factoring
 Factor GCF & remaining quadratic expression, a = 1, one variable
 Factor GCF & remaining quadratic expression, a ≥ 1, one variable
 Factor common binomial
 Factor binomial & its opposite
 Factor cubic polynomial by grouping, one variable
 Factor cubic polynomial by grouping & difference of two squares, one variable
 Identify factors of polynomials


Application of Polynomials
 Determine sums of polynomials or missing polynomial addends
 Determine differences of polynomials or missing polynomial subtrahends
 Condensed: Determine sums or differences of polynomials or missing polynomial operands
 Given polynomial & sum of polynomials, determine missing polynomial
 Given polynomial & difference of polynomials, determine missing polynomial
 Add & subtract polynomials to determine expressions for perimeter of various shapes
 Given monomial & binomial or trinomial, multiply or identify missing value
 Determine missing value to make polynomial statement true, multiplication
 Multiply polynomials to determine expressions for areas of rectangles & triangles
 Divide quadratic trinomial by linear binomial, word problem context
 Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles


Rational Expressions & Functions

Operations of Rational Expressions
 Multiply rational expressions
 Divide rational expressions

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

Rational Functions
 Identify value that makes rational expression undefined
 Determine values that make rational expressions undefined
 Given rational function, determine function value
 Graph rational functions


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
 Determine function & specific term for geometric sequences, realworld context
 Condensed: Determine formula or specific term of geometric sequences

Arithmetic & Geometric 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
 Determine function & specific term for arithmetic & geometric sequences, realworld context
 Condensed: Identify arithmetic & geometric sequences & determine components of sequences


Data Analysis & Probability

Counting Methods

Fundamental Counting Principle
 Determine number of combinations using fundamental counting principle, realworld context
 Determine number of combinations using fundamental counting principle, including repeated letters & digits, realworld context

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

Combinations
 Given lists, determine combinations, choose from one list, realworld context
 Given lists, determine combinations, choose from two lists, realworld context
 Determine combinations, realworld context

Permutations & Combinations
 Determine combinations & permutations, two questions, realworld context
 Determine combinations & permutations, four questions, realworld context


Probabiltiy

Basic Probability
 Determine sample spaces
 Classify probabilities by levels of likelihood
 Determine odds
 Determine probabilities & odds, including visual models
 Determine equivalent probabilities & odds
 Determine theoretical probabilities
 Determine theoretical probabilities, fraction answers
 Determine probabilities of single events
 Determine probabilities & complementary probabilities of single events, including visual models
 Determine probabilities & complementary probabilities of single events as fractions, decimals, or percents, including visual models
 Determine probabilities of flipping coins specified number of times

Compound Probability

Determine AND Probabilities
 Given visual model, determine "and" probability as fraction, decimal, or percent, dependent events
 Determine "and" probabilities, independent events, visuals provided
 Determine "and" probabilities, independent events, same sample space
 Determine "and" probabilities, independent events, two distinct sample spaces
 Determine probabilities of flipping coins & rolling die
 Determine "and" probabilities, dependent events, multiple choice
 Determine "and" probabilities, dependent events
 Determine "and" probabilities, independent & dependent events
 Determine "and" probabilities, independent & dependent events, including complementary events

Determine OR Probabilities
 Given visual model, determine "or" probability
 Given visual model, determine "or" probability as fraction, decimal, or percent
 Determine "or" probabilities as fractions
 Determine "or" probabilities as fractions, decimals, or percents
 Determine "or" probabilities
 Given visual model, determine "or" probability
 Given visual model, determine "or" probability as fraction, decimal, or percent
 Determine "and" probabilities, independent events, visuals provided
 Determine "and" probabilities, independent events, same sample space
 Determine "and" probabilities, independent events, two distinct sample spaces
 Determine "and" probabilities, dependent events, multiple choice
 Determine "and" probabilities, dependent events
 Given visual model, determine "and" probability as fraction, decimal, or percent, dependent events
 Determine probabilities of flipping coins & rolling die
 Determine "or" probabilities as fractions
 Determine "or" probabilities as fractions, decimals, or percents
 Determine "and" probabilities, independent & dependent events
 Determine "and" probabilities, independent & dependent events, including complementary events
 Determine "or" probabilities


Experimental Probability & Sampling
 Identify samples & populations
 Identify biased samples & questions
 Identify variables of interest
 Identify simulations used to acquire simple random samples
 Identify simulations to model probability events
 Identify statistical inferences
 Condensed: Identify samples, populations, variables of interest, & statistical inferences
 Determine size of sample spaces, compound events
 Determine sample spaces, compound events
 Determine experimental probabilities
 Determine experimental probabilities, fraction answers
 Compare data from two samples, various representations

Predictions from Probabilities
 Determine inferences from samples
 Determine predicted values or compare likelihood of events
 Determine predicted values, theoretical probability
 Determine predicted values, experimental probability
 Determine predicted values, experimental or theoretical probability
 Determine predicted values, theoretical probability, compound events
 Determine predicted values, experimental probability, compound events

Mixed Probability
 Determine "or" probabilities
 Determine "or" probabilities, including "and" situations
 Condensed: Determine probabilities
 Condensed: Determine experimental & theoretical probabilities

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


Data Analysis

Measures of Center & Spread

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

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


Stem&Leaf Plots
 Determine mean, median, mode, & range from stem&leaf plots
 Determine mean, median, mode, or range from stem&leaf plots

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

