Math 2 Skills

Algebra Foundations

Classifying Rational & Irrational Numbers
 Classify numbers as rational or irrational
 Classify rational numbers by definitions
 Classify rational numbers using graphic organizers
 Classify rational numbers, including graphic organizers
 Determine result of adding & multiplying rational & irrational numbers

Ordering & Comparing Irrational Numbers
 Estimate irrational values
 Estimate irrational values, including negatives
 Estimate irrational values, multiple terms or factors
 Estimate irrational values, including cube roots & number line representations
 Order irrational numbers
 Compare irrational numbers
 Condensed: Compare & order irrational numbers


Rational Exponents & Radicals

Rational Exponents
 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
 Simplify rational exponent expressions using power rule, with coefficients
 Condensed: Simplify rational exponents using product & power rules
 Condensed: Evaluate rational exponent expressions
 Convert from rational exponent to radical, single value base
 Convert from rational exponent to radical, algebraic base
 Condensed: Convert from rational exponent to radical

Properties of Exponents
 Simplify rational exponent expressions using power rule, no coefficients
 Simplify rational exponent expressions using product rule, no coefficients
 Simplify rational exponent expressions using product rule, coefficients not with base
 Simplify rational exponent expressions using product rule, coefficients with base
 Simplify rational exponent expressions using quotient rule, no coefficients
 Simplify rational exponent expressions using quotient rule, with coefficients
 Create equivalent exponential expressions using exponent properties

Evaluating Expressions
 Evaluate rational exponent expressions, positive exponents
 Evaluate rational exponent expressions, negative exponents

Solving Exponential Expressions
 Solve equations involving rational exponents, one or twostep
 Solve equations involving rational exponents, multistep
 Condensed: Solve equations involving rational exponents
 Solve simple exponential equations
 Solve exponential equations, common bases given
 Solve exponential equations, one base reduces to common base
 Solve exponential equations, both bases reduce to common base
 Solve exponential equations, no logs required
 Solve exponential equations, two different bases, no common base possible
 Solve exponential equations, one variable & one base

Radicals
 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
 Condensed: Add & subtract radical expressions
 Multiply radical expressions, numbers & variables


Complex Numbers

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

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

Quadratic Equations with Complex Solutions
 Calculate discriminant, then determine number of real or complex solutions
 Solve using quadratic formula, complex solutions
 Factor sum of squares using complex factors
 Determine complex solutions by factoring sum of squares
 Determine number of complex & real roots of quadratic functions
 Solve quadratic equations using square root method, complex solutions
 Solve quadratic equations, complete the square, integers, a = 1, complex solutions
 Condensed: Solve quadratic equations, complex solutions
 Solve quadratic equations, complete the square, integers, a > 1, complex solutions
 Condensed: Solve quadratic equations, complete the square, integers, complex solutions
 Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
 Condensed: Solve quadratic equations, complete the square, integers, including complex solutions
 Solve quadratic equations, complete the square, integers, a = 1, including complex solutions


Expressions

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

Rewriting Equivalent Expressions
 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, including rationals
 Simplify algebraic expressions, one variable, distribute twice
 Simplify algebraic expressions, two variables, distribute twice


Equations & Inequalities

Creating & Solving Equations in One Variable

TwoStep Equations
 Solve twostep linear equations, decimal coefficients
 Solve twostep linear equations, fractional coefficients
 Solve twostep linear equations, fractional answers
 Solve problems that can be represented by twostep equations, realworld context
 Determine equations or identify realworld situations represented by onestep or twostep equations
 Condensed: Solve one or twostep linear equations, including fractional answers
 Condensed: Solve one or twostep linear equations, fractional coefficients
 Condensed: Solve twostep linear equations

ThreeStep Equations
 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

MultiStep Equations
 Solve linear equations, distributive property on one side
 Solve multistep linear equations

Equations with Variables on Both Sides
 Solve linear equations, binomials on both sides, decimals
 Solve linear equations, binomials on both sides, fractions
 Solve linear equations, variables as numerators on both sides
 Solve linear equations, distributive property on both sides, integers
 Solve linear equations, distributive property on both sides, rationals
 Determine linear equations & solve problems that can be represented by equations with distributive property on one side, realworld context
 Solve linear equations, distributive property on both sides, additional term on one side
 Solve linear equations, including no solution & infinitely many solutions
 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

Determining 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


Creating & Solving Inequalities in One Variable

Basic OneVariable Inequalities
 Solve & graph twostep inequalities, integers
 Solve & graph twostep inequalities, decimals
 Solve & graph twostep inequalities, fractions
 Solve twostep inequalities, integers
 Solve twostep inequalities, decimals
 Solve twostep inequalities, fractions
 Determine if given value is solution to twostep inequality
 Condensed: Solve twostep inequalities
 Condensed: Solve & graph twostep inequalities

Application of OneVariable Inequalities
 Determine inequalities with variables on both sides, realworld context
 Determine & solve twostep inequalities, less than, realworld context
 Determine & solve twostep inequalities, greater than, realworld context
 Given twostep inequality, identify realworld problem modeled by inequality
 Determine twostep inequalities, rational numbers, including realworld context
 Given inequality with variable on both sides, identify realworld problem modeled by inequality


Creating & Solving Equations & Inequalities in Two or More Variables

Direct & Inverse Variation
 Solve word problems involving joint variation
 Solve word problems involving combined variation
 Given point & "y varies directly with x & inversely with z", determine equation
 Given point, "y varies jointly with x & z", & another value, determine equation
 Solve word problems involving direct variation
 Condensed: Determine direct, inverse, joint, or combined variation equations

Graphing Linear Inequalities
 Given linear inequality, identify correct graph, slopeintercept form
 Graph linear inequalities, slopeintercept form, only oblique lines
 Graph linear inequalities, vertical & horizontal lines
 Graph linear inequalities, slopeintercept form, including vertical & horizontal lines
 Given graph, identify linear inequality, slopeintercept form
 Graph systems of three linear inequalities, slopeintercept form
 Given linear inequality, determine graph, slopeintercept form
 Graph linear inequalities, various forms
 Given description & table, graph linear inequality, realworld context

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


Solving for Specified Variable
 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

Solving Systems of Equations

Solving Systems of Two Linear Equations
 Condensed: Given system of linear equations, determine point of intersection, integer coordinates
 Condensed: Given system of linear equations, determine solution, substitution bias
 Condensed: Given system of linear equations, identify solution, including realworld context
 Condensed: Determine systems of linear equations & solutions
 Condensed: Determine systems of linear equations & solutions, including realworld context
 Condensed: Given system of linear equations or description, graph system, including realworld context
 Condensed: Solve or determine system of equations, likely to have same variable isolated
 Condensed: Solve or determine system of equations, both equations in standard form
 Determine & justify solutions to systems of linear equations, realworld context
 Graph systems of linear equations & determine solutions, including realworld context

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

Solving Systems of Linear & Quadratic Equations
 Identify ordered pair solutions to systems of two equations, one linear & one quadratic
 Solve systems of two equations, algebraic, one linear & one quadratic
 Determine system of two equations, one linear & one quadratic
 Determine reasonableness of solutions to systems of linear & quadratic equations
 Solve systems of two equations, graphical, one linear & one quadratic
 Condensed: Solve systems of two equations, one linear & one quadratic


Solving Systems of Inequalities

Basic System of Inequalities
 Solve systems of linear 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
 Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, realworld context
 Condensed: Graph system of linear inequalities & determine system of linear inequalities, including realworld context
 Given linear system of inequalities graph, identify true statements
 Given description of system of linear inequalities, identify graph of system
 Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, realworld context
 Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, realworld context

Application of Systems of Inequalities
 Given description, determine system of linear inequalities in standard form & identify graph, realworld context
 Given description, determine system of linear inequalities in standard form & graph, realworld context
 Given description, determine system of linear inequalities in standard form & solution point, 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
 Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, realworld context



Functions

Domain & Range of Functions

Determining Domain & Range of Functions
 Determine if value is in domain or range, set & table representations
 Determine restricted domain & range of linear functions
 Given graph, determine domain & range
 Determine if value is in domain or range, graphical representations
 Determine restricted domain & range of quadratic functions
 Determine asymptotic domain restrictions of rational functions
 Determine domain & range of rational functions using inequalities, interval notation & set notation
 Determine domain & range of various functions using various notations

Application of Domain & Range of Functions
 Determine continuous domain & range, realworld context
 Determine discrete domain & range, realworld context
 Condensed: Determine domain & range, including realworld context


Determining & Justifying Functions
 Determine & justify functions, set representations, no domain & range language
 Determine & justify functions, table representations, no domain & range language
 Determine & justify functions, mapping representations, no domain & range language
 Determine functions, mapping representations, no domain & range language
 Determine functions, multiple representations, including justification, no domain & range language

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

Composition of Functions
 Determine if functions are inverses using composition
 Evaluate compositions of functions

Comparing Properties of Two Functions
 Compare rates of changes represented differently
 Determine whether given table represents linear or exponential function
 Determine whether given table represents linear, exponential, or quadratic function
 Compare linear functions represented differently
 Calculate average rate of change of function from table
 Calculate average rate of change of function, realworld context
 Calculate average rate of change of function from graph
 Condensed: Calculate average rate of change of function
 Calculate average rate of change of a function from an equation
 Determine whether given graph represents linear, exponential, or quadratic function
 Condensed: Determine what function given table or graph represents

Interpreting Functions Given Context

Determining Function Value
 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

Identifying Functions, Mixed Representations
 Determine function definition, fill in the blank
 Determine & justify functions, set representations
 Determine & justify functions, table representations
 Identify & determine functions, set & table representations
 Determine functions, set & table representations
 Determine functions, mapping representations
 Determine & justify functions, mapping representations
 Identify functions using equivalent mapping diagrams & sets of ordered pairs
 Identify functions, multiple representations, including justification
 Given relation & additional point, determine functions, multiple representations
 Condensed: Identify, justify, & determine functions
 Identify functions, description representations

Identifying Functions, Graphical Representations
 Determine functions, graphical representations
 Identify & justify functions & nonfunctions, graphical representations
 Determine & justify functions, graphical representations
 Given step graphs, identify functions


Building Functions to Model Relationships
 Add functions, (f + g)(x)
 Subtract functions, (f – g)(x)
 Multiply functions, (f * g)(x)
 Divide functions, (f / g)(x)
 Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
 Add function values, (f + g)(#)
 Subtract function values, (f – g)(#)
 Multiply function values, (f * g)(#)
 Divide function values, (f / g)(#)
 Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)

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


Absolute Value Functions

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

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

Graphing Absolute Value Functions
 Graph absolute value functions using vertex & intercepts
 Given absolute value equation, identify description of transformation
 Graph absolute value functions using all transformations
 Condensed: Graph absolute value functions using any transformation

Transformations of Absolute Value Functions
 Identify & graph vertical & horizontal shifts of absolute value functions
 Identify & graph reflections of absolute value functions
 Identify & graph vertical & horizontal stretches & compressions 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
 Compare absolute value functions represented differently

Key Features of Absolute Value Functions
 Determine x & yintercepts of absolute value functions
 Determine minimum & maximum of absolute value functions
 Determine points of intersection of absolute value functions
 Condensed: Determine graphical attributes of absolute value functions

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


Piecewise Functions
 Given graph of piecewise function, determine equation
 Graph piecewise functions

Quadratic Equations & Inequalities

Solving Quadratic Equations

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, 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 = 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, a ≤ 10, c ≤ 40, terms on both sides
 Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
 Solve quadratic equations using factoring, perfect square trinomial
 Solve quadratic equations using factoring, difference of squares

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

Solving Quadratics, Quadratic Formula
 Given quadratic equation in standard form, determine discriminant
 Given quadratic equation in standard form, determine number of solutions
 Given proportion, solve resulting quadratic equation, b = 0
 Given proportion, solve resulting quadratic equation, b ≠ 0
 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
 Solve quadratic equations, complete the square, a = 1, real solutions
 Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
 Solve quadratic equations, perfect square trinomial
 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, complete the square, a > 1, real solutions
 Solve quadratic equations, complete the square, integers, a > 1, real solutions
 Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
 Condensed: Solve quadratic equations, complete the square, integers, including complex solutions
 Solve quadratic equations, complete the square, integers, a = 1, real solutions
 Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
 Condensed: Solve quadratic equations, complete the square, integers, real solutions


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


Quadratic Functions

Writing Equations of Quadratic Functions

Standard Form
 Given graph of quadratic function, determine 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 graph of quadratic function, determine equation in standard form
 Given vertex & point, determine quadratic equation, standard form
 Given three points in plane, determine quadratic equation
 Given quadratic equation in vertex form, determine standard form of equation

Vertex Form
 Given vertex & point, determine quadratic equation, vertex form
 Given quadratic equation in standard form, determine vertex form of equation
 Given graph of quadratic function, determine equation
 Given description of transformation, determine quadratic function
 Given graphical attributes, determine equation of parabola


Graphing Quadratic Functions
 Given quadratic equation, determine graph, b = 0
 Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
 Given quadratic equation in vertex form, determine graph
 Given quadratic equation in standard form, determine graph
 Graph quadratic equations
 Given equation, graph quadratic function
 Condensed: Given quadratic equation, determine attributes & graph

Transformations of Quadratic Functions
 Identify & graph vertical & horizontal shifts of quadratic functions
 Identify & graph reflections 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
 Graph quadratic functions using all transformations
 Condensed: Graph quadratic functions using any transformation
 Compare quadratic functions represented differently

Key Features of Quadratic Functions

Determining 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

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

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

Determining Attributes of Quadratic Functions
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a = 1
 Given quadratic equation, determine attributes & graph, a ≠ ±1
 Given quadratic equation, vertex, & point, graph function & determine attributes
 Given graph of quadratic function, determine attributes
 Describe parameter changes to quadratic parent functions
 Given table, determine attributes of quadratic function, realworld context
 Condensed: Determine graphical attributes of quadratic functions
 Condensed: Given graph, equation, or table, determine attributes of quadratic function
 Determine intervals where quadratic function is positive or negative


Modeling with Quadratic Functions

Modeling by First Writing Quadratic Function
 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 & 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

Modeling by Solving Without Writing Function
 Determine effects of parameter changes in quadratic relationships, realworld context
 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



Polynomial Expressions

Interpreting Polynomials
 Interpret terms or factors in expressions, including realworld context

Adding & Subtracting 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
 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
 Add & subtract polynomials to determine expressions for perimeter of various shapes
 Given polynomial & sum of polynomials, determine missing polynomial
 Given polynomial & difference of polynomials, determine missing polynomial
 Determine missing value to make polynomial statement true, addition & subtraction
 Add & subtract binomials & trinomials, two variables

Multiplying Polynomials

Multiplying Polynomials Basic
 Multiply monomial times binomial or trinomial, mixed degrees
 Multiply monomial times binomial or trinomial, two variables
 Condensed: Multiply binomial times binomial
 Multiply binomial times trinomial, mixed degrees
 Multiply linear binomial times quadratic trinomial
 Apply binomial theorem to expand (x ± y)^3
 Multiply monomial times binomial or trinomial, degrees zero to two
 Multiply binomial times binomial, both degree one
 Multiply binomial times binomial, mixed degrees
 Square linear binomial
 Simplify monomial minus product of monomial & binomial or trinomial
 Multiply binomial times binomial, two variables
 Multiply binomial times trinomial, two variables
 Condensed: Multiply monomials, binomials, & trinomials, two variables

Application of Multiplying Polynomials
 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
 Given monomial & binomial or trinomial, multiply or identify missing value
 Multiply monomial times binomial or trinomial, mixed degrees
 Multiply monomial times binomial or trinomial, two variables
 Condensed: Multiply binomial times binomial
 Determine missing value to make polynomial statement true, multiplication
 Multiply binomial times trinomial, mixed degrees
 Multiply linear binomial times quadratic trinomial
 Apply binomial theorem to expand (x ± y)^3
 Multiply polynomials to determine expressions for areas of rectangles & triangles
 Multiply monomial times binomial or trinomial, degrees zero to two
 Multiply binomial times binomial, both degree one
 Multiply binomial times binomial, mixed degrees
 Square linear binomial


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

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

Factoring Polynomials

GCF & 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
 Determine missing component of GCF
 Factor GCF in polynomials, one variable
 Factor GCF in polynomials, including two variables
 Given GCF & one monomial, identify second monomial

Factoring Trinomials
 Factor quadratic trinomials, a = 1
 Factor quadratic trinomials, a = 1, b > 0, c > 0
 Factor quadratic trinomials, a = 1, terms scrambled
 Factor quadratic trinomials, 1 < a ≤ 10, no GCF
 Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
 Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
 Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
 Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
 Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
 Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
 Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < c ≤ 10

Factoring GCF & Remaining Trinomial
 Factor GCF in polynomials, degree one or two, one variable
 Factor GCF & remaining quadratic expression, a = 1, one variable
 Factor GCF & remaining quadratic expression, a ≥ 1, one variable

Factoring Difference of Squares & Perfect Square Trinomials
 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 perfect square trinomials, degree two, one variable
 Factor perfect square trinomials, degree two, two variables
 Condensed: Factor perfect square trinomials, degree two
 Factor difference of two squares, one or two variables
 Condensed: Factor difference of two squares, degree two
 Factor perfect square trinomials, fraction coefficients

Factoring Common Binomial
 Factor common binomial
 Factor binomial & its opposite

Factoring Cubic Polynomials
 Factor cubic polynomial by grouping, one variable
 Factor cubic polynomial by grouping & difference of two squares, one variable
 Factor sum & difference of two cubes, degree three, one variable
 Condensed: Factor sum & difference of two cubes, degree three
 Factor sum & difference of two cubes, degree three, two variables
 Factor sum & difference of two cubes, degree six, one variable
 Factor sum & difference of two cubes, degree six, two variables
 Condensed: Factor sum & difference of two cubes, degree six

Determining Factors of Polynomials
 Determine linear factors of polynomials, degree three
 Determine linear factors of polynomials, degree four
 Condensed: Determine linear factors of polynomials, degree three or four
 Determine quadratic factors of polynomials, degree four
 Determine maximum number of roots for polynomial function


Graphing Polynomials
 Given table, determine attributes of polynomial function
 Determine xintercepts/zeros & yintercepts of polynomial functions
 Determine end behavior of polynomial functions
 Given equation, graph polynomial function
 Determine points of intersection of two polynomial functions
 Determine zeros of polynomials & their multiplicities
 Determine intervals of increase & decrease of polynomial functions
 Given graph, determine equation of polynomial function
 Determine minimum & maximum of polynomial functions


Exponential Functions & Models

Interpreting Exponential Models
 Interpret values in exponential functions, realworld context
 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
 Determine exponential function, realworld context

Solving Exponential Models
 Given graph, identify solution to exponential equation
 Calculate investment value, annual compounding
 Calculate investment value, various compounding
 Calculate depreciating asset value, annual compounding
 Condensed: Calculate investment & depreciating asset values, annual compounding

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

Graphing Exponential Functions
 Given equation, graph exponential function
 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 equation, graph exponential function, including base e
 Compare exponential functions represented differently

Transformations of Exponential Functions
 Identify & graph vertical & horizontal shifts of exponential functions
 Identify & graph reflections 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
 Graph exponential functions using all transformations
 Condensed: Graph exponential functions & identify transformations

Key Features of Exponential Functions

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

Determining Attributes
 Determine xintercepts/zeros & yintercepts of exponential functions
 Determine yintercept of exponential function, realworld context
 Given exponential equation, determine asymptote
 Given graph, determine asymptote of exponential function
 Determine asymptote of exponential functions
 Determine asymptote of exponential functions, realworld context
 Determine minimum & maximum of exponential functions
 Determine end behavior of exponential functions
 Given table, determine attributes of exponential function
 Condensed: Determine graphical attributes of exponential functions



Foundations of Geometry

Congruence
 Given geometric figure, identify correct conjecture
 Identify corresponding parts from congruence statement or determine congruence statement from figures
 Given congruent triangles, determine values from corresponding parts
 Given congruent sides, identify congruent angles of isosceles triangle
 Given congruent angles, identify congruent sides of isosceles triangle
 Determine angle measures in isosceles trapezoid, using congruent base angles
 Identify congruent angles or determine angle measures in kites, algebraic expressions
 Identify congruence transformations
 Given congruent figures, identify description of transformations
 Determine missing steps in proofs involving angles
 Determine missing steps in proofs involving segments
 Determine missing steps in proofs involving parallel lines

Similarity

Triangle Similarity
 Determine segment lengths in triangles with angle bisectors
 Determine segment lengths using triangle proportionality theorem
 Determine angles of similar triangles using AA similarity
 Determine sides of similar triangles using AA similarity
 Determine similarity of triangles using AA similarity
 Determine angles of similar triangles using AA similarity, algebraic expressions
 Determine parts using similar triangles, including realworld context
 Determine similar triangles using SAS similarity
 Determine similar triangles using SSS similarity
 Condensed: Determine similar triangles using SAS or SSS similarity
 Determine missing steps in proofs involving similar triangles
 Determine missing steps in proofs involving similar triangles, paragraph form
 Given right triangle with altitude from right angle, identify similar triangles

Similar Figures
 Identify similar polygons
 Given similar figures, identify proportion of side lengths
 Given similar figures, identify proportion of side lengths, image orientations differ
 Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
 Identify corresponding parts of similar figures
 Determine dimensions in similar figures, whole number dimensions
 Determine dimensions in similar figures
 Determine dimensions using similar figures & indirect measurements
 Given similar figures, identify description of transformations
 Given three parallel lines with two transversals, determine lengths
 Determine edge, surface area, or volume of similar solids


Scale Factor

Scale Factor Determine Dimension, Perimeter or Area
 Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
 Determine scale factor or perimeter of dilated figures
 Determine scale factor or area of dilated figures
 Determine variable scale factor or variable measurement of dilated figures
 Given similar squares, determine area & side length
 Given similar rectangles, determine perimeter
 Given similar triangles, determine perimeter
 Given similar triangles, determine area
 Given similar cones, determine surface area
 Given scale factor, determine dimension
 Condensed: Determine or apply scale factor between circles
 Given similar squares, determine perimeter & side length
 Given similar rectangles, determine area
 Given similar cones, determine volume
 Given similar pyramids, determine surface area
 Given similar prisms, determine surface area
 Given similar spheres, determine volume
 Given similar pyramids, determine volume
 Given similar prisms, determine volume
 Given similar cylinders, determine volume
 Given similar cylinders, determine surface area
 Condensed: Given similar 2D figures, determine area or perimeter
 Given similar spheres, determine surface area
 Condensed: Given similar 3D figures, determine surface area or volume

Scale Factor Determine Coordinates
 Condensed: Given scale factor, determine coordinates of image
 Given scale factor, determine coordinates of image, preimage not centered at origin
 Given scale factor, determine coordinates of image, preimage centered at origin
 Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
 Determine scale factor or perimeter of dilated figures
 Determine scale factor or area of dilated figures
 Determine variable scale factor or variable measurement of dilated figures
 Given similar squares, determine area & side length
 Given similar rectangles, determine perimeter
 Given similar triangles, determine perimeter
 Given similar triangles, determine area
 Given similar cones, determine surface area
 Given scale factor, determine coordinates of image, preimage centered at origin
 Given scale factor, determine dimension
 Given scale factor, determine coordinates of image, preimage not centered at origin
 Condensed: Given scale factor, determine coordinates of image
 Condensed: Determine or apply scale factor between circles


Two & ThreeDimensional Objects

TwoDimensional Objects
 Classify quadrilaterals shapes based on attributes
 Classify polygons using graphic organizers
 Classify polygons using graphic organizers, including types of triangles
 Classify polygons based on number of sides or relationship to other shapes
 Classify polygons based on angles & parallel or perpendicular lines
 Classify 2D figures

ThreeDimensional Objects
 Classify 3D figures
 Identify 3D figures & their bases
 Determine cross sections of prisms
 Determine cross sections of pyramids
 Determine cross sections of cylinders
 Determine cross sections of 3D figures
 Condensed: Determine cross sections of cylinders, pyramids, & cones
 Determine 2D orthographic representation of 3D blocks
 Determine 3D figures from rotations of 2D figures


Circumference & Area of a Circle
 Identify approximate formulas for circumference & area of circles
 Determine circumference of circle, exact answers, multiple choice, including realworld context
 Given radius or diameter, determine circumference
 Given circumference of circle, determine radius or diameter
 Estimate diameter or circumference & identify equations using π
 Given radius or diameter, determine area
 Determine area of circle, exact answers, including realworld context
 Given area of circle, determine radius or diameter
 Given radius or diameter, determine area or circumference
 Condensed: Given area or circumference of circle, determine radius or diameter
 Condensed: Determine area or circumference of circle
 Determine areas of semicircles & quarter circles

Volume

Cylinder Volume
 Determine volume of cylinders
 Given volume, determine dimension of cylinder
 Given base area & height, determine volume of cylinder

Pyramid Volume
 Determine volume of pyramids
 Given volume, determine dimension of pyramid

Cone Volume
 Determine volume of cones
 Given volume, determine dimension of cone

Sphere Volume
 Determine volume of spheres
 Determine volume or radius of spheres
 Given volume, determine radius, diameter, or surface area of sphere

Mixed Figure Volume
 Determine volume of composite figures, cylinders & cones
 Determine volume of cylinders, cones, & spheres, including realworld context
 Identify relationship between volume of cone & cylinder with same base & height


Surface Area
 Determine surface area of pyramids

Triangle Relationships

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

Median & Midsegment Theorem
 Given median of triangle, determine variable or length of bisected side, algebraic expressions
 Apply triangle midsegment theorem to determine segment lengths
 Apply triangle midsegment theorem to determine perimeter
 Apply triangle midsegment theorem to determine segment lengths, algebraic expressions

Centroid & Hinge Theorem
 Apply centroid theorem
 Determine coordinates of centroid of triangles
 Apply hinge theorem

Triangle Theorems
 Apply triangle theorems or determine missing steps in proofs
 Apply triangle inequality theorem to determine side lengths
 Determine missing steps in proofs involving triangles
 Determine missing steps in proofs involving isosceles triangles


Proving Geometric Theorems Using Coordinates
 Identify or determine parallelograms in coordinate plane
 Identify congruent angles or determine angle measures in kites, algebraic expressions
 Determine angle measures in isosceles trapezoid, using congruent base angles


Circles & Conic Sections

Circle Basics
 Identify components of circles
 Apply arc addition postulate to determine arc measures
 Apply arc addition postulate to determine arc measures, including algebraic expressions
 Determine relationship between congruent arcs & congruent central angles

Similarity Ratios
 Given two circles, determine scale factor or missing dimension
 Given two circles, determine scale factor of area or missing area

Arc Length & Area of Sector
 Given arc measure & radius, determine arc length
 Given arc length & radius, determine central angle
 Given chord & radius, determine length
 Given two chords of circle, determine length
 Given arc length & central angle, determine circumference
 Condensed: Determine circumferences, arc lengths, & central angles
 Determine area of sector

Properties of Inscribed Angles, Radii, & Chords
 Given central angle or arc measure, determine inscribed angle
 Given inscribed angle, determine central angle & arc measure
 Given inscribed angle formed by chord & tangent, determine angle or arc measure
 Given intersecting chords, determine angle or arc measure
 Given two diameters, radius, & two angles, determine angle or arc measure
 Condensed: Determine inscribed angles, central angles, & arc measures
 Determine relationship between congruent chords & congruent central angles
 Determine relationship between congruent chords & congruent arcs

Inscribed & Circumscribed Figures
 Determine angles of quadrilateral inscribed in circle, including algebraic expressions
 Given inscribed isosceles triangle, determine base angle
 Given isosceles triangle in circle, determine angle or arc measure
 Given isosceles triangle in circle, determine angle measure at vertex of triangle
 Given inscribed isosceles triangle or isosceles triangle in circle, determine angle or arc measure
 Given inscribed isosceles triangle, determine measure of arc intercepted by base of triangle
 Given inscribed right triangle, determine inscribed angle or arc measure
 Given inscribed right triangle & tangent, determine angle or arc measure
 Condensed: Given inscribed right triangle, determine angle or arc measure

Properties of Secants & Tangents

Given Secants & Tangents Determine Angles
 Given two tangents to circle, determine angle
 Given secant & tangent to circle, determine angle
 Given two secants intersecting outside circle, determine angle
 Given two secants intersecting inside circle, determine angle
 Given one chord & one secant of circle, determine angle
 Given tangent & secant intersecting at point of tangency, determine angles
 Given tangent & other segments, determine angle
 Condensed: Given secants, tangents, & chords, determine angles
 Given chord, secant, & tangent on same circle, determine angles & arcs

Given Secants & Tangents Determine Lengths
 Given secant & tangent to circle, determine length
 Given two secants of circle, determine length, including algebraic expressions
 Given tangents to circles, determine lengths, algebraic expressions
 Given secants, tangents, & chords, determine length
 Given tangent & other segments or circle inscribed in polygon, determine lengths


Area of Circular Segments
 Given radius & arc measure of 60°, 90°, or 120°, determine area of circular segment
 Given chord length & arc measure of 60°, 90°, or 120°, determine area of circular segment
 Given radius & arc measure, determine area of circular segment
 Determine areas of circular segments
 Given chord length & arc measure, determine area of circular segment

Equations of Circles
 Given equation of circle, identify center & radius
 Given center & radius, determine equation of circle
 Given graph, determine equation of circle
 Given equation of circle in standard form, identify graph
 Given equation of circle, determine area
 Given equation of circle in general form, determine standard form
 Condensed: Determine circle equations, centers, radii, & areas
 Complete the square & graph, circle equations

Equations of Parabolas
 Given vertex & point, determine quadratic equation, vertex form
 Given vertex & point, determine quadratic equation, standard form
 Given focus & directrix of parabola, determine equation
 Given focus & directrix of parabola, determine equation in standard form

Equations of Circles & Parabolas
 Condensed: Complete the square & graph, circle & parabola equations


Trigonometry

Pythagorean Theorem Calculations & Proofs
 Determine Pythagorean triples
 Given triangle with algebraic expressions, apply Pythagorean theorem to determine side
 Classify triangles using Pythagorean inequality theorem
 Apply Pythagorean theorem to find length in kite
 Given ratio of sides & one dimension, apply Pythagorean theorem to determine specified dimension, realworld context

Trigonometric Ratios
 Given special right triangle, determine trig function value, sin, cos, & tan
 Given special right triangle, determine trig function value, cot, sec, & csc
 Given right triangle, determine trig ratio, sin, cos, & tan
 Given right triangle, determine angle, realworld context
 Condensed: Given right triangle, determine sides or angles, realworld context
 Given right triangle, determine trig ratio, cot, sec, & csc
 Condensed: Given right triangle, determine trig ratio
 Given sine, cosine, or tangent & quadrant, determine trig function values
 Determine missing steps in proofs of Pythagorean identities
 Given right triangle, determine missing side & trig ratio, sin, cos, & tan
 Given right triangle, determine missing side & trig ratio, cot, sec, & csc
 Identify definitions of trig functions
 Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
 Condensed: Given right triangle, determine missing side & trig ratio

Special Right Triangles

454590 Triangles
 Given 454590 triangle, determine hypotenuse
 Given 454590 triangle, determine leg
 Given 454590 triangle, determine side

306090 Triangles
 Given 306090 triangle & short leg, determine long leg
 Given 306090 triangle & short leg, determine hypotenuse
 Given 306090 triangle & long leg, determine short leg
 Given 306090 triangle & long leg, determine hypotenuse
 Given 306090 triangle & hypotenuse, determine short leg
 Given 306090 triangle & hypotenuse, determine long leg
 Given 306090 triangle, determine side

Mixed Special Right Triangles
 Condensed: Given special right triangle, determine trig function value
 Condensed: Given special right triangle, determine side
 Condensed: Determine angles or sides using special right triangle relationships, realworld context
 Given 454590 triangle, determine hypotenuse
 Given 454590 triangle, determine leg
 Given 454590 triangle, determine side
 Given 306090 triangle & short leg, determine long leg
 Given 306090 triangle & short leg, determine hypotenuse
 Given 306090 triangle & long leg, determine short leg
 Given 306090 triangle & long leg, determine hypotenuse
 Given 306090 triangle & hypotenuse, determine short leg
 Given 306090 triangle & hypotenuse, determine long leg
 Given 306090 triangle, determine side
 Condensed: Given special right triangle, determine trig function value
 Condensed: Given special right triangle, determine side
 Condensed: Determine angles or sides using special right triangle relationships, realworld context


Solving Right Triangles

Determining Trigonometric Values
 Determine trig function values, degrees, calculator expected
 Determine trig function values, radians, calculator expected
 Condensed: Determine trig function values, calculator expected

Solving Sides of Right Triangles
 Determine leg of right triangle using sine
 Determine hypotenuse of right triangle using sine
 Given side & angle, determine specified side using sine
 Determine leg of right triangle using cosine
 Determine hypotenuse of right triangle using cosine
 Given side & angle, determine specified side using cosine
 Given short leg of right triangle, determine long leg using tangent
 Given long leg of right triangle, determine short leg using tangent
 Given side & angle, determine specified side using tangent
 Condensed: Given side & angle, determine specified side using sine, cosine, or tangent

Solving Angles of Right Triangles
 Given hypotenuse & leg of right triangle, determine angle using arcsine
 Given hypotenuse & leg of right triangle, determine angle using arccosine
 Given legs of right triangle, determine angle using arctangent
 Given sides of triangle, determine angle using arcsine, arccosine, or arctangent


Sine & Cosine of Complementary Angles
 Determine equivalent trig cofunction values, sin & cos
 Determine equivalent trig cofunction values, sec & csc
 Determine equivalent trig cofunction values, tan & cot
 Condensed: Determine equivalent trig cofunction values
 Determine equivalent trig cofunction values from triangles

Modeling with Right Triangles
 Given legs of right triangle, determine angle using arctangent, realworld context
 Given right triangle, determine angle, realworld context
 Determine angles using special right triangle relationships, realworld context
 Determine sides using special right triangle relationships, realworld context
 Given right triangle, determine side, realworld context

Law of Sines & Cosines
 Determine sides & angles of triangles using law of sines, realworld context
 Determine sides & angles of triangles using law of cosines, realworld context
 Condensed: Determine sides & angles of triangles using law of sines or law of cosines, realworld context
 Determine angles of triangles using law of sines
 Condensed: Determine sides & angles of triangles using law of sines


Probability

Sample Space
 Determine sample spaces
 Determine size of sample spaces, compound events
 Determine sample spaces, compound events
 Determine sample size, various representations
 Identify experiments & observational studies
 Identify systematic, cluster, stratified, & simple random samples

Combinations & Permutations

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

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

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


Multiplication Rule
 Determine probabilities of flipping coins & rolling die
 Determine probabilities of flipping coins specified number of times
 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, two distinct sample spaces
 Determine "and" probabilities, independent events, same sample space
 Determine "and" probabilities, dependent events
 Determine "and" probabilities, dependent events, multiple choice
 Determine "and" probabilities, independent & dependent events
 Determine "and" probabilities, independent & dependent events, including complementary events

Addition Rule
 Determine "or" probabilities
 Determine "or" probabilities as fractions
 Determine "or" probabilities as fractions, decimals, or percents
 Given visual model, determine "or" probability
 Given visual model, determine "or" probability as fraction, decimal, or percent

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

Simulations
 Identify simulations used to acquire simple random samples
 Identify simulations to model probability events

Using Probability to Make Predictions
 Determine predicted values, theoretical probability
 Determine predicted values, experimental probability
 Determine predicted values, experimental probability, compound events
 Determine predicted values, theoretical probability, compound events
 Determine predicted values, experimental or theoretical probability
 Determine inferences from samples
 Determine predicted values or compare likelihood of events


Rational Functions
 Compare rational functions represented differently

Radical Functions
 Compare radical functions represented differently