Math 3 Skills
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Functions
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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
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Composition of Functions
- Evaluate compositions of functions
- Determine if functions are inverses using composition
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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, real-world 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
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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
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Interpreting Features of Functions Through Modeling
- Interpret & solve problems involving function notation, real-world context
- Determine discrete domain & range, real-world context
- Determine graph or information from graph, real-world context
- Determine continuous domain & range, real-world context
- Condensed: Determine domain & range, including real-world context
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Graph Mixed Functions
- Given various functions, identify graph
- Given graph, identify various functions
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Equations & Inequalities
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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
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Solving Linear Inequalities in Two or More Variables
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Writing & Solving Inequalities
- Given linear inequality, determine solutions & non-solutions, slope-intercept form
- Given linear inequality graph, determine solutions & non-solutions
- Given linear inequality & x-value, determine y-value
- Given graph, identify linear inequality, slope-intercept form
- Given graph, determine linear inequality
- Given graph, determine inequalities in standard form, real-world context
- Given description, determine linear inequalities in standard form, including tables, real-world context
- Given description, determine linear inequalities in standard form & specific solutions, real-world context
- Solve linear programming problems, real-world context
- Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
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Graphing Linear Inequalities
- Graph linear inequalities, slope-intercept form, only oblique lines
- Graph linear inequalities, vertical & horizontal lines
- Graph linear inequalities, slope-intercept form, including vertical & horizontal lines
- Given linear inequality, identify correct graph, slope-intercept form
- Given linear inequality, determine graph, slope-intercept form
- Given description & table, graph linear inequality, real-world context
- Given description, determine linear inequality in standard form, graph, & determine specific solutions, real-world context
- Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
- Graph linear inequalities, various forms
- Condensed: Determine equivalent linear inequalities & graphical solutions
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Systems of Equations
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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
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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, real-world context
- Solve systems of three linear equations using matrices
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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
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Application of Solving Systems of Equations
- Determine & justify solutions to systems of linear equations, real-world context
- Graph systems of linear equations & determine solutions, including real-world context
- Condensed: Given system of linear equations, identify solution, including real-world context
- Condensed: Determine systems of linear equations & solutions
- Condensed: Determine systems of linear equations & solutions, including real-world context
- Condensed: Given system of linear equations or description, graph system, including real-world context
- Condensed: Solve or determine system of equations, both equations in standard form
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Systems of Inequalities
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Solving Systems of Inequalities
- Graph systems of two linear inequalities, slope-intercept 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, real-world 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, slope-intercept form
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Application of Solving Systems of Inequalities
- Given description, determine system of linear inequalities in standard form & identify graph, real-world context
- Given description, determine system of linear inequalities in standard form & graph, real-world context
- Given description, determine system of linear inequalities in standard form & solution point, real-world context
- Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
- Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
- Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
- Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
- Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
- Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
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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
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Quadratic Functions
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Writing Equations of Quadratic Functions
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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
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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
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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
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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
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Key Features of Quadratic Functions
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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
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Determining Intercepts of Quadratic Functions
- Determine x-intercept(s) of quadratic functions
- Determine zero(s) of quadratic functions
- Determine y-intercept of quadratic functions
- Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
- Determine x-intercepts/zeros & y-intercepts of quadratic functions, vertex form
- Given graph or table of quadratic function, determine x- & y- intercepts
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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
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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, real-world 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
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Modeling with Quadratic Functions
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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
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Modeling by Solving Without Writing Function
- Determine effects of parameter changes in quadratic relationships, real-world 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
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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
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Absolute Value Functions
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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, real-world context
- Solve linear absolute value equations, variable on both sides
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Absolute Value Inequalities
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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
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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, real-world context
- Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
- Condensed: Solve & graph linear absolute value inequalities
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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
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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
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Key Features of Absolute Value Functions
- Determine x- & y-intercepts 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
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Piecewise Functions
- Given graph of piece-wise function, determine equation
- Graph piece-wise functions
- Graph step functions
- Given graph of step function, determine equation
- Condensed: Determine graphs & equations of piece-wise & step functions
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Complex Numbers
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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
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Operations with Complex Numbers
- Square complex numbers
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Radical Functions
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Solving Radical Equations
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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, multi-step
- Condensed: Solve square root equations, one-step & two-step
- Condensed: Solve square root equations
- Identify extraneous solutions of square root equations
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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, multi-step
- Condensed: Solve cube root equations, one-step & two-step
- Condensed: Solve square root & cube root equations
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Graphing Square Root Functions
- Determine x- and y-intercepts 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
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Graphing Cube Root Functions
- Determine x- & y-intercepts 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
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Polynomial Expressions & Functions
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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
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Interpreting Polynomials
- Interpret terms or factors in expressions, including real-world context
- Identify & apply polynomial identities
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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
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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
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Multiplying Polynomials
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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
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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
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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
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Factoring Expressions with One Variable
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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
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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
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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
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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
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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
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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
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Graphing Polynomial Functions
- Determine points of intersection of two polynomial functions
- Given table, determine attributes of polynomial function
- Determine x-intercepts/zeros & y-intercepts 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
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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, real-world context
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Exponential & Logarithmic Expressions & Functions
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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
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Converting Between Exponential & Logarithmic Equations
- Given exponential equation, determine log equation
- Condensed: Convert between exponential & log equations
- Given log equation, determine exponential equation
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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
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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
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Solving Exponential Models
- Exponential growth & decay, real-world 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, real-world context
- Interpret values in exponential functions, real-world context
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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
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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
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Key Features of Exponential Functions
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Domain & Range of Exponential Functions
- Determine domain & range of discrete exponential functions
- Determine domain & range of discrete exponential functions, real-world 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
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Key Attributes of Exponential Functions
- Determine x-intercepts/zeros & y-intercepts of exponential functions
- Determine y-intercept of exponential function, real-world 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, real-world context
- Determine end behavior of exponential functions
- Given table, determine attributes of exponential function
- Condensed: Determine graphical attributes of exponential functions
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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
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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
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Key Features of Logarithmic Functions
- Determine x-intercepts/zeros & y-intercepts 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
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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
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Graphing Logarithmic Functions
- Given equation, graph log function
- Given graph, determine equation of log function
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Rational Expressions & Functions
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Rational Function Values
- Identify value that makes rational expression undefined
- Determine values that make rational expressions undefined
- Given rational function, determine function value
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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
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Solving Rational Equations
- Solve equations involving rational exponents, one- or two-step
- Solve equations involving rational exponents, multi-step
- 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
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Modeling Rational Functions
- Determine rational equations, real-world context
- Determine if solution to rational equation is reasonable
- Determine rational inequalities, real-world context
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Multiplying & Dividing Rational Expressions
- Multiply rational expressions
- Divide rational expressions
- Condensed: Multiply & divide rational expressions
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Adding & Subtracting Rational Expressions
- Add rational expressions
- Subtract rational expressions
- Condensed: Add & subtract rational expressions
- Condensed: Add, subtract, multiply, & divide rational expressions
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Graphing Rational Functions
- Graph rational functions
- Compare rational functions represented differently
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Foundations of Geometry
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Two- & Three-Dimensional 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
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Geometric Modeling
- Apply concepts of density based on area & volume, real-world context
- Apply geometric methods to solve design problems, real-world context
- Describe objects using geometric shapes, measures, & properties
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Finite Geometric Series
- Determine sum of finite geometric series
- Determine sum of finite geometric series, real-world context
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Circles & Conic Sections
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Equations of Circles
- Complete the square & graph, circle equations
- Equations of Parabolas
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Equations of Circles & Parabolas
- Condensed: Complete the square & graph, circle & parabola equations
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Chords, Tangents, & Secants
- Given chord, secant, & tangent on same circle, determine angles & arcs
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Trigonometry
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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
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Solving Right Triangles
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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
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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
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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
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Unit Circle
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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
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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
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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
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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, real-world context
- Determine sides & angles of triangles using law of cosines, real-world context
- Condensed: Determine sides & angles of triangles using law of sines or law of cosines, real-world 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
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Trigonometric Modeling
- Given right triangle, determine angle, real-world context
- Determine angles using special right triangle relationships, real-world context
- Determine sides using special right triangle relationships, real-world context
- Condensed: Determine angles or sides using special right triangle relationships, real-world context
- Given legs of right triangle, determine angle using arctangent, real-world context
- Given right triangle, determine side, real-world context
- Condensed: Given right triangle, determine sides or angles, real-world context
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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, real-world context
- Determine graph of trig functions, tan & cot
- Determine graph of trig functions, sec & csc
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Data Analysis & Probability
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Conditional Probability
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
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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
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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
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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
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Normal Distributions
- Given mean & standard deviation, determine z-score, real-world context
- Given z-score, determine probability
- Given mean, determine z-score & probability, real-world context
- Given proportion, determine z-score & probability, real-world context
- Condensed: Given mean or proportion, determine z-score & probability, real-world context
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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
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Hypothesis Tests
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Hypothesis Tests, One Mean
- Identify hypotheses for hypothesis test, one mean
- Determine test statistics, one mean
- Identify & determine hypothesis test steps, one mean
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Hypothesis Tests, Two Means
- Identify hypotheses for hypothesis test, two means
- Determine test statistics, two means
- Identify & determine hypothesis test steps, two means
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Hypothesis Tests, One Proportion
- Determine test statistics, one proportion
- Identify hypotheses for hypothesis test, one proportion
- Identify & determine hypothesis test steps, one proportion
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Hypothesis Tests, Two Proportions
- Determine test statistics, two proportions
- Identify hypotheses for hypothesis test, two proportions
- Identify & determine hypothesis test steps, two proportions
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Hypothesis Tests, Mixed
- Determine critical z-score & p-value
- Given critical z-score & 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
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