Math 3 Skills

Functions

Combining Functions Using Arithmetic Operations
 Add functions, (f + g)(x)
 Subtract functions, (f – g)(x)
 Multiply functions, (f * g)(x)
 Divide functions, (f / g)(x)
 Add function values, (f + g)(#)
 Subtract function values, (f – g)(#)
 Multiply function values, (f * g)(#)
 Divide function values, (f / g)(#)
 Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)
 Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
 Perform operations on functions represented graphically, graphical solution
 Perform operations on functions represented graphically, numerical solution

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

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

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

Interpreting Features of Functions Through Modeling
 Interpret & solve problems involving function notation, realworld context
 Determine discrete domain & range, realworld context
 Determine graph or information from graph, realworld context
 Determine continuous domain & range, realworld context
 Condensed: Determine domain & range, including realworld context

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


Equations & Inequalities

Direct & Inverse Variation
 Solve word problems involving direct 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
 Condensed: Determine direct, inverse, joint, or combined variation equations

Solving Linear Inequalities in Two or More Variables

Writing & Solving Inequalities
 Given linear inequality, determine solutions & nonsolutions, slopeintercept form
 Given linear inequality graph, determine solutions & nonsolutions
 Given linear inequality & xvalue, determine yvalue
 Given graph, identify linear inequality, slopeintercept form
 Given graph, determine linear inequality
 Given graph, determine inequalities in standard form, 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
 Solve linear programming problems, realworld context
 Condensed: Given linear inequalities & graphs, determine solutions & nonsolutions

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


Systems of Equations

Solving Systems of Two Linear Equations
 Condensed: Given system of linear equations, determine solution, substitution bias
 Condensed: Given system of linear equations, determine point of intersection, integer coordinates
 Condensed: Solve or determine system of equations, likely to have same variable isolated

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

Solving Systems of One Linear & One Quadratic
 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

Application of Solving Systems of Equations
 Determine & justify solutions to systems of linear equations, realworld context
 Graph systems of linear equations & determine solutions, including realworld context
 Condensed: Given system of linear equations, identify solution, including realworld context
 Condensed: Determine systems of linear equations & solutions
 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, both equations in standard form


Systems of Inequalities

Solving Systems of Inequalities
 Graph systems of two linear inequalities, slopeintercept form
 Given graph, determine solution of systems of linear inequalities
 Solve systems of linear inequalities
 Determine equivalent systems of linear inequalities & graphical solutions
 Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, realworld context
 Given linear system of inequalities graph, identify true statements
 Given description of system of linear inequalities, identify graph of system
 Graph systems of three linear inequalities, slopeintercept form

Application of Solving 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
 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
 Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, 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


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

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 end behavior of quadratic functions
 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


Solving Quadratic Functions
 Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
 Solve quadratic equations, complete the square, a = 1, real solutions
 Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
 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, real solutions
 Condensed: Solve quadratic equations, complete the square, integers, real solutions


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

Absolute Value Inequalities with Setup
 Solve & graph linear absolute value inequalities, “and” solutions, including setup
 Solve & graph linear absolute value inequality, extra coefficient or constant, 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

Absolute Value Inequalities without Setup
 Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
 Solve & graph linear absolute value inequalities, including extra constant or coefficient
 Solve & graph linear absolute value inequalities, “and” solutions
 Solve & graph linear absolute value inequalities, “or” solutions
 Given linear absolute value inequality, determine compound inequality
 Create linear absolute value inequalities, realworld context
 Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
 Condensed: Solve & graph linear absolute value inequalities


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 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


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

Complex Numbers

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

Operations with Complex Numbers
 Square complex numbers


Radical Functions

Solving Radical Equations

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

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


Graphing Square Root Functions
 Determine x and yintercepts of square root functions
 Identify & graph vertical & horizontal shifts of square root functions
 Identify & graph reflections of square root functions
 Identify & graph vertical & horizontal stretches & compressions of square root functions
 Determine minimum & maximum of square root functions
 Given square root equation, identify description of transformations
 Condensed: Determine graphical attributes of square root functions
 Graph square root functions using key point & intercepts
 Graph square root functions using all transformations
 Condensed: Graph square root functions using any transformation
 Compare radical functions represented differently

Graphing Cube Root Functions
 Determine x & yintercepts of cube root functions
 Identify & graph vertical & horizontal shifts of cube root functions
 Identify & graph reflections of cube root functions
 Identify & graph vertical & horizontal stretches & compressions of cube root functions
 Determine minimum & maximum of cube root functions
 Condensed: Determine graphical attributes of cube root functions
 Graph cube root functions using key points & intercepts
 Graph cube root functions using all transformations
 Given cube root equation, identify descriptions of transformations
 Condensed: Graph cube root functions using any transformation


Polynomial Expressions & Functions

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

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

Writing Polynomials in Standard Form
 Identify terms of expressions
 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

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
 Add & subtract polynomials to determine expressions for perimeter of various shapes
 Determine sums of polynomials or missing polynomial addends
 Given polynomial & difference of polynomials, determine missing polynomial
 Determine differences of polynomials or missing polynomial subtrahends
 Given monomial & binomial or trinomial, multiply or identify missing value
 Condensed: Determine sums or differences of polynomials or missing polynomial operands
 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, degrees zero to two
 Multiply binomial times binomial, both degree one
 Square linear binomial
 Condensed: Multiply binomial times binomial
 Simplify monomial minus product of monomial & binomial or trinomial

Multiplying Polynomials, Advanced
 Multiply monomial times binomial or trinomial, mixed degrees
 Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
 Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
 Multiply binomial times binomial, mixed degrees
 Multiply binomial times trinomial, mixed degrees
 Multiply linear binomial times quadratic trinomial
 Given monomial & binomial or trinomial, multiply or identify missing value
 Multiply monomial times binomial or trinomial, two variables
 Apply binomial theorem to expand (x ± y)^3
 Determine missing value to make polynomial statement true, multiplication
 Multiply polynomials to determine expressions for areas of rectangles & triangles
 Condensed: Determine missing value to make polynomial statement true
 Apply binomial theorem to expand (x ± y)^n, n ≥ 4
 Condensed: Apply binomial theorem to expand (x ± y)^n, n ≥ 3
 Multiply binomial times binomial, two variables
 Multiply binomial times trinomial, two variables
 Condensed: Multiply monomials, binomials, & trinomials, two variables


Dividing Polynomials
 Divide polynomials, degree one or two by degree one or two
 Divide polynomials, degree three or four by degree one
 Divide polynomials, degree three or four by degree two
 Divide polynomials, divisor supports synthetic division
 Condensed: Divide polynomials, degree three or four by degree one or two
 Divide quadratic trinomial by linear binomial, word problem context
 Identify factors of polynomials
 Condensed: Divide polynomials
 Apply remainder theorem
 Determine missing operation to make polynomial statement true

Factoring Expressions with One Variable

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

Factoring Quadratic Trinomials
 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
 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
 Factor quadratic trinomials, 1 < a ≤ 10, no GCF
 Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < c ≤ 10

Factoring by Grouping
 Factor cubic polynomial by grouping, one variable
 Factor cubic polynomial by grouping & difference of two squares, one variable
 Factor common binomial
 Factor binomial & its opposite

Factoring Special Polynomials
 Factor perfect square trinomials, degree two, one variable
 Condensed: Factor perfect square trinomials, degree two
 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 sum & difference of two cubes, degree three, one variable
 Factor sum & difference of two cubes, degree six, one variable
 Factor sum & difference of two cubes, degree six, two variables
 Condensed: Factor sum & difference of two cubes, degree six

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


Factoring Expressions with Multiple Variables
 Condensed: Determine GCF or LCM of two monomials, two variables
 Factor perfect square trinomials, degree two, two variables
 Factor difference of two squares, one or two variables
 Factor difference of two squares, two variables
 Factor GCF in polynomials, including two variables
 Determine GCF of two monomials, two variables
 Determine LCM of two monomials, two variables
 Condensed: Factor perfect square trinomials, degree two
 Given GCF & one monomial, identify second monomial
 Determine missing component of GCF
 Factor sum & difference of two cubes, degree three, two variables
 Condensed: Factor sum & difference of two cubes, degree three

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

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


Exponential & Logarithmic Expressions & Functions

Logarithms Introduction
 Evaluate log expressions, whole number base
 Evaluate log expressions, natural log
 Evaluate log expressions, fractional bases
 Evaluate log expressions, using change of base
 Condensed: Evaluate log expressions

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

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

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

Solving Exponential Models
 Exponential growth & decay, realworld context
 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
 Interpret values in exponential functions, realworld context

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

Solving Natural Logarithmic Equations
 Solve natural log equations, ln = ln
 Solve natural log equations, ln = #
 Solve natural log equations, ln + ln = #
 Solve natural log equations, ln – ln = #
 Condensed: Solve natural log equations

Key Features of Exponential Functions

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

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


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

Graphing Exponential Functions
 Given equation, graph exponential function, including base e
 Given graph, determine equation of exponential function
 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 graph, identify solution to exponential equation
 Given table, determine exponential growth function
 Given table, determine exponential decay function
 Compare exponential functions represented differently

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

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

Graphing Logarithmic Functions
 Given equation, graph log function
 Given graph, determine equation of log function


Rational Expressions & Functions

Rational Function Values
 Identify value that makes rational expression undefined
 Determine values that make rational expressions undefined
 Given rational function, determine function value

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

Solving Rational Equations
 Solve equations involving rational exponents, one or twostep
 Solve equations involving rational exponents, multistep
 Condensed: Solve equations involving rational exponents
 Solve rational equations, one term each side
 Solve rational equations, multiple terms on one side
 Condensed: Solve rational equations

Modeling Rational Functions
 Determine rational equations, realworld context
 Determine if solution to rational equation is reasonable
 Determine rational inequalities, realworld context

Multiplying & Dividing Rational Expressions
 Multiply rational expressions
 Divide rational expressions
 Condensed: Multiply & divide rational expressions

Adding & Subtracting Rational Expressions
 Add rational expressions
 Subtract rational expressions
 Condensed: Add & subtract rational expressions
 Condensed: Add, subtract, multiply, & divide rational expressions

Graphing Rational Functions
 Graph rational functions
 Compare rational functions represented differently


Foundations of Geometry

Two & ThreeDimensional Figures
 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
 Classify 3D figures
 Determine cross sections of prisms
 Determine cross sections of pyramids
 Determine cross sections of cylinders
 Determine 3D figures from rotations of 2D figures
 Condensed: Determine cross sections of cylinders, pyramids, & cones

Geometric Modeling
 Apply concepts of density based on area & volume, realworld context
 Apply geometric methods to solve design problems, realworld context
 Describe objects using geometric shapes, measures, & properties

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


Circles & Conic Sections

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

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

Chords, Tangents, & Secants
 Given chord, secant, & tangent on same circle, determine angles & arcs


Trigonometry

Radians & Degrees
 Convert radians to degrees
 Convert degrees to radians
 Condensed: Convert between degrees & radians
 Determine trig function values, degrees, calculator expected
 Determine trig function values, radians, calculator expected
 Condensed: Determine trig function values, calculator expected

Solving Right Triangles

Determining Trig Values
 Identify definitions of trig functions
 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 trig ratio, cot, sec, & csc
 Given right triangle, determine missing side & trig ratio, sin, cos, & tan
 Given right triangle, determine missing side & trig ratio, cot, sec, & csc
 Condensed: Given right triangle, determine trig ratio
 Condensed: Given special right triangle, determine trig function value

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


Unit Circle

Trig Function Values, Degrees
 Determine trig function values, unit circle, first quadrant, degrees, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, second quadrant, degrees, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, third quadrant, degrees, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, fourth quadrant, degrees, sin, cos, & tan, exact answers
 Determine sine values, unit circle, degrees, exact answers
 Determine cosine values, unit circle, degrees, exact answers
 Determine tangent values, unit circle, degrees, exact answers
 Determine trig function values, unit circle, axes, degrees, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, degrees, sin, cos, & tan, exact answers

Trig Function Values, Radians
 Determine trig function values, unit circle, first quadrant, radians, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, second quadrant, radians, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, third quadrant, radians, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, fourth quadrant, radians, sin, cos, & tan, exact answers
 Determine trig function values, unit circle, axes, radians, sin, cos, & tan
 Determine sine values, unit circle, radians, exact answers
 Determine cosine values, unit circle, radians, exact answers
 Determine tangent values, unit circle, radians, exact answers
 Given arc length & radius, determine radian measure
 Determine trig function values, unit circle, radians, sin, cos, & tan, exact answers

Trig Function Values, Degrees & Radians
 Determine trig function values, unit circle, cot, csc, & sec, exact answers
 Determine trig function values, unit circle, sin, cos, & tan, exact answers


Solving General Triangles Using Law of Sines & Cosines
 Determine sides of triangles using law of sines
 Determine sides of triangles using law of cosines
 Determine angles of triangles using law of cosines
 Determine sides or angles of triangles using law of cosines, multiple choice
 Condensed: Determine sides & angles of triangles using law of 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 area of triangles using sine formula
 Determine angles of triangles using law of sines
 Condensed: Determine sides & angles of triangles using law of sines

Trigonometric Modeling
 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
 Condensed: Determine angles or sides using special right triangle relationships, realworld context
 Given legs of right triangle, determine angle using arctangent, realworld context
 Given right triangle, determine side, realworld context
 Condensed: Given right triangle, determine sides or angles, realworld context

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


Data Analysis & Probability

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

Interpreting Categorical & Quantitative Data
 Identify descriptive & inferential statistics
 Identify experiments & observational studies
 Identify systematic, cluster, stratified, & simple random samples
 Identify simulations used to acquire simple random samples
 Identify simulations to model probability events

Making Inferences & Justifying Conclusions
 Determine inferences from samples
 Determine expected value & identify conclusion
 Identify variables of interest
 Condensed: Identify samples, populations, variables of interest, & statistical inferences
 Identify statistical inferences
 Identify samples & populations

Using Probability to Make Decisions
 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 predicted values or compare likelihood of events

Normal Distributions
 Given mean & standard deviation, determine zscore, realworld context
 Given zscore, determine probability
 Given mean, determine zscore & probability, realworld context
 Given proportion, determine zscore & probability, realworld context
 Condensed: Given mean or proportion, determine zscore & probability, realworld context

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

Hypothesis Tests

Hypothesis Tests, One Mean
 Identify hypotheses for hypothesis test, one mean
 Determine test statistics, one mean
 Identify & determine hypothesis test steps, one mean

Hypothesis Tests, Two Means
 Identify hypotheses for hypothesis test, two means
 Determine test statistics, two means
 Identify & determine hypothesis test steps, two means

Hypothesis Tests, One Proportion
 Determine test statistics, one proportion
 Identify hypotheses for hypothesis test, one proportion
 Identify & determine hypothesis test steps, one proportion

Hypothesis Tests, Two Proportions
 Determine test statistics, two proportions
 Identify hypotheses for hypothesis test, two proportions
 Identify & determine hypothesis test steps, two proportions

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

