Math 2 Skills
-
Algebra Foundations
-
Classifying Rational & Irrational Numbers
- Classify numbers as rational or irrational
- Classify rational numbers by definitions
- Classify rational numbers using graphic organizers
- Classify rational numbers, including graphic organizers
- Determine result of adding & multiplying rational & irrational numbers
-
Ordering & Comparing Irrational Numbers
- Estimate irrational values
- Estimate irrational values, including negatives
- Estimate irrational values, multiple terms or factors
- Estimate irrational values, including cube roots & number line representations
- Order irrational numbers
- Compare irrational numbers
- Condensed: Compare & order irrational numbers
-
-
Rational Exponents & Radicals
-
Rational Exponents
- Convert from radical to rational exponent, single value in radicand
- Convert from radical to rational exponent, algebraic term in radicand
- Convert from radical to rational exponent, algebraic term in radicand, algebraic multiplier
- Simplify radical expression raised to power that is multiple of index
- Condensed: Convert from radical to rational exponent
- Simplify rational exponent expressions using power rule, with coefficients
- Condensed: Simplify rational exponents using product & power rules
- Condensed: Evaluate rational exponent expressions
- Convert from rational exponent to radical, single value base
- Convert from rational exponent to radical, algebraic base
- Condensed: Convert from rational exponent to radical
-
Properties of Exponents
- Simplify rational exponent expressions using power rule, no coefficients
- Simplify rational exponent expressions using product rule, no coefficients
- Simplify rational exponent expressions using product rule, coefficients not with base
- Simplify rational exponent expressions using product rule, coefficients with base
- Simplify rational exponent expressions using quotient rule, no coefficients
- Simplify rational exponent expressions using quotient rule, with coefficients
- Create equivalent exponential expressions using exponent properties
-
Evaluating Expressions
- Evaluate rational exponent expressions, positive exponents
- Evaluate rational exponent expressions, negative exponents
-
Solving Exponential Expressions
- Solve equations involving rational exponents, one- or two-step
- Solve equations involving rational exponents, multi-step
- Condensed: Solve equations involving rational exponents
- Solve simple exponential equations
- Solve exponential equations, common bases given
- Solve exponential equations, one base reduces to common base
- Solve exponential equations, both bases reduce to common base
- Solve exponential equations, no logs required
- Solve exponential equations, two different bases, no common base possible
- Solve exponential equations, one variable & one base
-
Radicals
- Simplify radical expressions, perfect powers
- Add & subtract radical expressions, one or two variables, simplified radicals
- Add & subtract radical expressions, one or two variables, radicals to simplify
- Condensed: Add & subtract radical expressions
- Multiply radical expressions, numbers & variables
-
-
Complex Numbers
-
Simplifying Complex Numbers
- Simplify powers of i
- Express square roots of negatives using i
- Simplify imaginary numbers
-
Operations with Complex Numbers
- Add & subtract complex numbers
- Add or subtract square roots of negative numbers
- Multiply complex numbers
- Multiply square roots of negative numbers
- Divide complex number by constant
- Divide complex numbers
- Condensed: Add, subtract, & multiply square roots of negative numbers
- Condensed: Multiply & divide complex numbers
- Condensed: Add, subtract, multiply, & divide complex numbers
- Square complex numbers
-
Quadratic Equations with Complex Solutions
- Calculate discriminant, then determine number of real or complex solutions
- Solve using quadratic formula, complex solutions
- Factor sum of squares using complex factors
- Determine complex solutions by factoring sum of squares
- Determine number of complex & real roots of quadratic functions
- Solve quadratic equations using square root method, complex solutions
- Solve quadratic equations, complete the square, integers, a = 1, complex solutions
- Condensed: Solve quadratic equations, complex solutions
- Solve quadratic equations, complete the square, integers, a > 1, complex solutions
- Condensed: Solve quadratic equations, complete the square, integers, complex solutions
- Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
- Condensed: Solve quadratic equations, complete the square, integers, including complex solutions
- Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
-
-
Expressions
-
Interpreting & Identifying Parts of an Expression
- Identify terms of expressions
- Classify polynomials by degree
- Determine degree of polynomials
- Classify polynomials by degree & number of terms
- Identify leading coefficient of polynomials
- Determine degree, leading coefficient, & type of polynomial
- Condensed: Classify polynomials & identify components of polynomials
- Determine degree of polynomials, including two variables
- Identify leading coefficient of polynomials, including two variables
- Identify polynomial as monomial, binomial, or trinomial, including two variables
- Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables
-
Rewriting Equivalent Expressions
- Simplify algebraic expressions, one variable, distribute once & product of two factors
- Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
- Simplify algebraic expressions, one variable, distribute once, including rationals
- Simplify algebraic expressions, one variable, distribute twice
- Simplify algebraic expressions, two variables, distribute twice
-
-
Equations & Inequalities
-
Creating & Solving Equations in One Variable
-
Two-Step Equations
- Solve two-step linear equations, decimal coefficients
- Solve two-step linear equations, fractional coefficients
- Solve two-step linear equations, fractional answers
- Solve problems that can be represented by two-step equations, real-world context
- Determine equations or identify real-world situations represented by one-step or two-step equations
- Condensed: Solve one- or two-step linear equations, including fractional answers
- Condensed: Solve one- or two-step linear equations, fractional coefficients
- Condensed: Solve two-step linear equations
-
Three-Step Equations
- Solve three-step linear equations involving distribution of decimal multiplier
- Solve three-step linear equations involving distribution, fractional multiplier cancels if distributed
- Solve three-step linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
- Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
-
Multi-Step Equations
- Solve linear equations, distributive property on one side
- Solve multi-step linear equations
-
Equations with Variables on Both Sides
- Solve linear equations, binomials on both sides, decimals
- Solve linear equations, binomials on both sides, fractions
- Solve linear equations, variables as numerators on both sides
- Solve linear equations, distributive property on both sides, integers
- Solve linear equations, distributive property on both sides, rationals
- Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
- Solve linear equations, distributive property on both sides, additional term on one side
- Solve linear equations, including no solution & infinitely many solutions
- Condensed: Solve linear equations, variables on both sides, rationals
- Determine equations with variables on both sides, real-world context
- Determine & solve linear equations with variables on both sides, real-world context
- Given equation with variables on both sides, identify real-world situation represented by equation
-
Determining Number of Solutions
- Determine number of solutions in linear equations, distribute at most one time
- Determine number of solutions in linear equations, distribute up to two times
- Condensed: Determine number of solutions in linear equations
-
-
Creating & Solving Inequalities in One Variable
-
Basic One-Variable Inequalities
- Solve & graph two-step inequalities, integers
- Solve & graph two-step inequalities, decimals
- Solve & graph two-step inequalities, fractions
- Solve two-step inequalities, integers
- Solve two-step inequalities, decimals
- Solve two-step inequalities, fractions
- Determine if given value is solution to two-step inequality
- Condensed: Solve two-step inequalities
- Condensed: Solve & graph two-step inequalities
-
Application of One-Variable Inequalities
- Determine inequalities with variables on both sides, real-world context
- Determine & solve two-step inequalities, less than, real-world context
- Determine & solve two-step inequalities, greater than, real-world context
- Given two-step inequality, identify real-world problem modeled by inequality
- Determine two-step inequalities, rational numbers, including real-world context
- Given inequality with variable on both sides, identify real-world problem modeled by inequality
-
-
Creating & Solving Equations & Inequalities in Two or More Variables
-
Direct & Inverse Variation
- Solve word problems involving joint variation
- Solve word problems involving combined variation
- Given point & “y varies directly with x & inversely with z”, determine equation
- Given point, “y varies jointly with x & z”, & another value, determine equation
- Solve word problems involving direct variation
- Condensed: Determine direct, inverse, joint, or combined variation equations
-
Graphing Linear Inequalities
- Given linear inequality, identify correct graph, slope-intercept form
- 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 graph, identify linear inequality, slope-intercept form
- Graph systems of three linear inequalities, slope-intercept form
- Given linear inequality, determine graph, slope-intercept form
- Graph linear inequalities, various forms
- Given description & table, graph linear inequality, real-world context
-
Writing & Solving Inequalities
- Given linear inequality, determine solutions & non-solutions, slope-intercept form
- Given linear inequality graph, determine solutions & non-solutions
- Given graph, determine linear inequality
- Given linear inequality & x-value, determine y-value
- Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
- Given graph, determine inequalities in standard form, real-world context
- Solve linear programming problems, 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
- Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
- Condensed: Determine equivalent linear inequalities & graphical solutions
- Determine rational inequalities, real-world context
-
-
Solving for Specified Variable
- Given linear equation with two terms on each side, solve for specified variable
- Given linear equation with three terms on one side, solve for specified variable
- Condensed: Given linear equation in various forms, solve for specified variable
- Solve for specific variable in mathematical formula
- Solve for specific variable in scientific formula
-
Solving Systems of Equations
-
Solving Systems of Two Linear Equations
- Condensed: Given system of linear equations, determine point of intersection, integer coordinates
- Condensed: Given system of linear equations, determine solution, substitution bias
- Condensed: Given system of linear equations, identify solution, including 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, likely to have same variable isolated
- Condensed: Solve or determine system of equations, both equations in standard form
- Determine & justify solutions to systems of linear equations, real-world context
- Graph systems of linear equations & determine solutions, including real-world context
-
Solving Systems of Three Linear Equations
- Solve systems of three linear equations using Gaussian elimination
- Solve systems of three linear equations using substitution
- Determine system of three linear equations, real-world context
- Condensed: Solve systems of three linear equations
- Solve systems of three linear equations using matrices
-
Solving Systems of Linear & Quadratic Equations
- Identify ordered pair solutions to systems of two equations, one linear & one quadratic
- Solve systems of two equations, algebraic, one linear & one quadratic
- Determine system of two equations, one linear & one quadratic
- Determine reasonableness of solutions to systems of linear & quadratic equations
- Solve systems of two equations, graphical, one linear & one quadratic
- Condensed: Solve systems of two equations, one linear & one quadratic
-
-
Solving Systems of Inequalities
-
Basic System of Inequalities
- Solve systems of linear inequalities
- Given graph, determine solution of systems of linear inequalities
- Determine equivalent systems of linear inequalities & graphical solutions
- Graph systems of two linear inequalities, slope-intercept form
- Graph systems of three linear inequalities, slope-intercept form
- Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
- Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
- Given linear system of inequalities graph, identify true statements
- Given description of system of linear inequalities, identify graph of system
- Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
- Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
-
Application of 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
-
-
-
Functions
-
Domain & Range of Functions
-
Determining Domain & Range of Functions
- Determine if value is in domain or range, set & table representations
- Determine restricted domain & range of linear functions
- Given graph, determine domain & range
- Determine if value is in domain or range, graphical representations
- Determine restricted domain & range of quadratic functions
- Determine asymptotic domain restrictions of rational functions
- Determine domain & range of rational functions using inequalities, interval notation & set notation
- Determine domain & range of various functions using various notations
-
Application of Domain & Range of Functions
- Determine continuous domain & range, real-world context
- Determine discrete domain & range, real-world context
- Condensed: Determine domain & range, including real-world context
-
-
Determining & Justifying Functions
- Determine & justify functions, set representations, no domain & range language
- Determine & justify functions, table representations, no domain & range language
- Determine & justify functions, mapping representations, no domain & range language
- Determine functions, mapping representations, no domain & range language
- Determine functions, multiple representations, including justification, no domain & range language
-
Inverse Functions
- Determine inverse of linear function
- Determine inverse of various functions
- Determine if functions are inverses using composition
- Determine domain & range of inverse functions
- Graph function and its inverse
- Condensed: Given function, determine equation, graph, & domain & range of inverse
- Determine inverse of quadratic & square root functions
- Determine inverse of cubic & cube root functions
- Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions
-
Composition of Functions
- Determine if functions are inverses using composition
- Evaluate compositions of functions
-
Comparing Properties of Two Functions
- Compare rates of changes represented differently
- Determine whether given table represents linear or exponential function
- Determine whether given table represents linear, exponential, or quadratic function
- Compare linear functions represented differently
- Calculate average rate of change of function from table
- Calculate average rate of change of function, real-world context
- Calculate average rate of change of function from graph
- Condensed: Calculate average rate of change of function
- Calculate average rate of change of a function from an equation
- Determine whether given graph represents linear, exponential, or quadratic function
- Condensed: Determine what function given table or graph represents
-
Interpreting Functions Given Context
-
Determining Function Value
- Given set or table, determine function value
- Given graph, determine function value
- Given linear function, determine function value
- Given quadratic function, determine function value
- Condensed: Given graph or linear function, determine function value
- Condensed: Given linear or quadratic function, determine function value
-
Identifying Functions, Mixed Representations
- Determine function definition, fill in the blank
- Determine & justify functions, set representations
- Determine & justify functions, table representations
- Identify & determine functions, set & table representations
- Determine functions, set & table representations
- Determine functions, mapping representations
- Determine & justify functions, mapping representations
- Identify functions using equivalent mapping diagrams & sets of ordered pairs
- Identify functions, multiple representations, including justification
- Given relation & additional point, determine functions, multiple representations
- Condensed: Identify, justify, & determine functions
- Identify functions, description representations
-
Identifying Functions, Graphical Representations
- Determine functions, graphical representations
- Identify & justify functions & non-functions, graphical representations
- Determine & justify functions, graphical representations
- Given step graphs, identify functions
-
-
Building Functions to Model Relationships
- Add functions, (f + g)(x)
- Subtract functions, (f – g)(x)
- Multiply functions, (f * g)(x)
- Divide functions, (f / g)(x)
- Condensed: Add, subtract, multiply, & divide functions, (f ? g)(x)
- Add function values, (f + g)(#)
- Subtract function values, (f – g)(#)
- Multiply function values, (f * g)(#)
- Divide function values, (f / g)(#)
- Condensed: Add, subtract, multiply, & divide function values, (f ? g)(#)
-
Graph Mixed Functions
- Given various functions, identify graph
- Given graph, identify various functions
-
-
Absolute Value Functions
-
Absolute Value Equations
- Solve linear absolute value equations
- Solve linear absolute value equations, extra constant or coefficient
- Condensed: Solve linear absolute value equations, including extra constant or coefficient
- Create linear absolute value equations, real-world context
- Solve linear absolute value equations, variable on both sides
-
Absolute Value Inequalities
- Solve & graph linear absolute value inequalities, “and” solutions
- Solve & graph linear absolute value inequalities, “or” solutions
- Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
- Solve & graph linear absolute value inequalities, including extra constant or coefficient
- Condensed: Solve & graph linear absolute value inequalities, including setup
- Condensed: Solve & graph linear absolute value inequalities
- Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
- Given linear absolute value inequality, determine compound inequality
- Create linear absolute value inequalities, real-world context
-
Graphing Absolute Value Functions
- Graph absolute value functions using vertex & intercepts
- Given absolute value equation, identify description of transformation
- Graph absolute value functions using all transformations
- Condensed: Graph absolute value functions using any transformation
-
Transformations of Absolute Value Functions
- Identify & graph vertical & horizontal shifts of absolute value functions
- Identify & graph reflections of absolute value functions
- Identify & graph vertical & horizontal stretches & compressions of absolute value functions
- Graph absolute value functions using all transformations
- Given absolute value equation, identify description of transformation
- Condensed: Graph absolute value functions using any transformation
- Compare absolute value functions represented differently
-
Key Features of Absolute Value Functions
- Determine x- & 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
-
Writing Equation of Absolute Value Functions
- Given description of transformation, determine absolute value equation
- Given graph, determine absolute value equation
-
-
Piecewise Functions
- Given graph of piece-wise function, determine equation
- Graph piece-wise functions
-
Quadratic Equations & Inequalities
-
Solving Quadratic Equations
-
Solving Quadratics, Factoring
- Apply zero product property to solve factored quadratic equations
- Identify zeros of factored quadratics
- Determine relationship between zeros & linear factors of quadratic functions
- Solve quadratic equations using factoring, a = 1, b ≠0, |c| ≤ 40, zero on one side
- Solve quadratic equations using factoring, |a| ≤ 10, b ≠0, |c| ≤ 40, zero on one side
- Solve quadratic equations using factoring, a = 1, b ≠0, c ≤ 40, terms on both sides
- Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
- Solve quadratic equations using factoring, |a| ≤ 10, |c| ≤ 40, terms on both sides
- Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
- Solve quadratic equations using factoring, perfect square trinomial
- Solve quadratic equations using factoring, difference of squares
-
Solving Quadratics, Square Root Method
- Determine solutions to quadratic equations, a ≠±1, b = 0, integer or rounded solutions
- Solve quadratic equations using square root method, a(cx ± h)^2 + k = #
- Condensed: Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
- Condensed: Determine solutions to quadratic equations, a ≠±1, b = 0
- Solve quadratic equations using square root method, (x ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, (cx ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, (x ± h)^2 + k = #, rational solutions
- Solve quadratic equations using square root method, a(x ± h)^2 = #, rational solutions
- Solve quadratic equations using square root method, a(x ± h)^2 + k = #, rational solutions
- Solve quadratic equations using square root method, a(cx ± h)^2 + k = #, rational solutions
-
Solving Quadratics, Quadratic Formula
- Given quadratic equation in standard form, determine discriminant
- Given quadratic equation in standard form, determine number of solutions
- Given proportion, solve resulting quadratic equation, b = 0
- Given proportion, solve resulting quadratic equation, b ≠0
- Given quadratic equation in standard form, determine solutions rounded to nearest hundredth
- Given quadratic equation, determine solutions rounded to nearest hundredth, constant on one side
- Given quadratic equation, determine solutions rounded to nearest hundredth, combine like terms first
- Given quadratic equation in standard form, determine attributes & solutions rounded to nearest hundredth
- Given quadratic equation in standard form, determine exact solutions
- Given quadratic equation in standard form, determine exact solutions, combine like terms first
-
Solving Quadratics, Completing the Square
- Solve quadratic equations, complete the square, a = 1, real solutions
- Solve quadratic equations, complete the square, a > 1, real solutions, multiple choice
- Solve quadratic equations, perfect square trinomial
- Condensed: Solve quadratic equations, complete the square, real solutions
- Solve quadratic equations, complete the square, integers, a = 1, radical form solutions
- Determine constant required to complete the square, a ≥ 1, including fractions
- Solve quadratic equations, complete the square, a > 1, real solutions
- Solve quadratic equations, complete the square, integers, a > 1, real solutions
- Solve quadratic equations, complete the square, integers, a > 1, including complex solutions
- Condensed: Solve quadratic equations, complete the square, integers, including complex solutions
- Solve quadratic equations, complete the square, integers, a = 1, real solutions
- Solve quadratic equations, complete the square, integers, a = 1, including complex solutions
- Condensed: Solve quadratic equations, complete the square, integers, real solutions
-
-
Solving Quadratic Inequalities
- Solve quadratic inequalities, “and” solutions
- Solve quadratic inequalities, “or” solutions
- Condensed: Solve quadratic inequalities
-
-
Quadratic Functions
-
Writing Equations of Quadratic Functions
-
Standard Form
- Given graph of quadratic function, determine equation
- Given integer solutions of quadratic equation, determine function in standard form
- Given zeros of quadratic function, determine quadratic equation with integer coefficients
- Given rational solutions of quadratic equation, determine function in standard form
- Given graph of quadratic function, determine equation in standard form
- Given vertex & point, determine quadratic equation, standard form
- Given three points in plane, determine quadratic equation
- Given quadratic equation in vertex form, determine standard form of equation
-
Vertex Form
- Given vertex & point, determine quadratic equation, vertex form
- Given quadratic equation in standard form, determine vertex form of equation
- Given graph of quadratic function, determine equation
- Given description of transformation, determine quadratic function
- Given graphical attributes, determine equation of parabola
-
-
Graphing Quadratic Functions
- Given quadratic equation, determine graph, b = 0
- Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
- Given quadratic equation in vertex form, determine graph
- Given quadratic equation in standard form, determine graph
- Graph quadratic equations
- Given equation, graph quadratic function
- Condensed: Given quadratic equation, determine attributes & graph
-
Transformations of Quadratic Functions
- Identify & graph vertical & horizontal shifts of quadratic functions
- Identify & graph reflections of quadratic functions
- Identify & graph vertical & horizontal stretches & compressions of quadratic functions
- Given quadratic equation, identify description of transformation
- Identify descriptions of graphs of quadratic parent functions & transformed functions
- Graph quadratic functions using all transformations
- Condensed: Graph quadratic functions using any transformation
- Compare quadratic functions represented differently
-
Key Features of Quadratic Functions
-
Determining Domain & Range of Quadratic Functions
- Given graph of quadratic function, determine domain & range
- Given equation of quadratic function, determine domain & range
- Given description of domain & range of quadratic function, choose graph
- Condensed: Determine domain & range of quadratic function
-
Determining Intercepts of Quadratic Functions
- Determine 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
-
Determining Vertex, Axis of Symmetry, & Extrema of Quadratic Functions
- Determine vertex of quadratic functions
- Determine minimum & maximum of quadratic functions
- Given graph of quadratic function, determine minimum or maximum value
- Given quadratic equation, determine minimum or maximum value
- Determine symmetry of quadratic functions
- Determine intervals of increase & decrease of quadratic functions
- Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
- Determine end behavior of quadratic functions
-
Determining Attributes of Quadratic Functions
- Given quadratic equation, determine attributes & graph, a = 1
- Given quadratic equation, determine attributes & graph, a = -1
- Given quadratic equation, determine attributes & graph, a ≠±1
- Given quadratic equation, vertex, & point, graph function & determine attributes
- Given graph of quadratic function, determine attributes
- Describe parameter changes to quadratic parent functions
- Given table, determine attributes of quadratic function, real-world context
- Condensed: Determine graphical attributes of quadratic functions
- Condensed: Given graph, equation, or table, determine attributes of quadratic function
- Determine intervals where quadratic function is positive or negative
-
-
Modeling with Quadratic Functions
-
Modeling by First Writing Quadratic Function
- Given initial height & velocity of object in vertical motion, determine function, table, & graph of position
- Given initial height & velocity of object in vertical motion, determine position function & maximum height
- Given initial height & velocity of object in vertical motion, determine position function & time to maximum height
- Given initial height & velocity of object in vertical motion, determine position function & time to ground
- Given initial height & velocity of object in vertical motion, determine position function & specific time
- Given initial height & negative velocity of object in vertical motion, determine position function & specific time
- Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
- Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
-
Modeling by Solving Without Writing Function
- Determine effects of parameter changes in quadratic relationships, 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
-
-
-
Polynomial Expressions
-
Interpreting Polynomials
- Interpret terms or factors in expressions, including real-world context
-
Adding & Subtracting Polynomials
- Add binomials & trinomials, degrees zero to two
- Subtract binomials & trinomials, degrees zero to two
- Add binomials & trinomials, degrees zero to three
- Subtract binomials & trinomials, degrees zero to three
- Condensed: Add or subtract binomials & trinomials
- Determine sums of polynomials or missing polynomial addends
- Determine differences of polynomials or missing polynomial subtrahends
- Condensed: Determine sums or differences of polynomials or missing polynomial operands
- Add & subtract polynomials to determine expressions for perimeter of various shapes
- Given polynomial & sum of polynomials, determine missing polynomial
- Given polynomial & difference of polynomials, determine missing polynomial
- Determine missing value to make polynomial statement true, addition & subtraction
- Add & subtract binomials & trinomials, two variables
-
Multiplying Polynomials
-
Multiplying Polynomials Basic
- Multiply monomial times binomial or trinomial, mixed degrees
- Multiply monomial times binomial or trinomial, two variables
- Condensed: Multiply binomial times binomial
- Multiply binomial times trinomial, mixed degrees
- Multiply linear binomial times quadratic trinomial
- Apply binomial theorem to expand (x ± y)^3
- Multiply monomial times binomial or trinomial, degrees zero to two
- Multiply binomial times binomial, both degree one
- Multiply binomial times binomial, mixed degrees
- Square linear binomial
- Simplify monomial minus product of monomial & binomial or trinomial
- Multiply binomial times binomial, two variables
- Multiply binomial times trinomial, two variables
- Condensed: Multiply monomials, binomials, & trinomials, two variables
-
Application of Multiplying Polynomials
- Given monomial & binomial or trinomial, multiply or identify missing value
- Determine missing value to make polynomial statement true, multiplication
- Multiply polynomials to determine expressions for areas of rectangles & triangles
- Given monomial & binomial or trinomial, multiply or identify missing value
- Multiply monomial times binomial or trinomial, mixed degrees
- Multiply monomial times binomial or trinomial, two variables
- Condensed: Multiply binomial times binomial
- Determine missing value to make polynomial statement true, multiplication
- Multiply binomial times trinomial, mixed degrees
- Multiply linear binomial times quadratic trinomial
- Apply binomial theorem to expand (x ± y)^3
- Multiply polynomials to determine expressions for areas of rectangles & triangles
- Multiply monomial times binomial or trinomial, degrees zero to two
- Multiply binomial times binomial, both degree one
- Multiply binomial times binomial, mixed degrees
- Square linear binomial
-
-
Dividing Polynomials
- Divide polynomials, degree three or four by degree one
- Divide polynomials, degree three or four by degree two
- Divide polynomials, degree one or two by degree one or two
- Divide polynomials, divisor supports synthetic division
- Condensed: Divide polynomials, degree three or four by degree one or two
- Divide quadratic trinomial by linear binomial, word problem context
- Condensed: Divide polynomials
- Apply remainder theorem
-
Mixed Operations of Polynomials
- Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
- Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
- Determine missing operation to make polynomial statement true
- Condensed: Determine missing value to make polynomial statement true
-
Factoring Polynomials
-
GCF & LCM of Polynomials
- Determine GCF in polynomials, one variable
- Determine GCF of two monomials, two variables
- Determine LCM of two monomials, two variables
- Condensed: Determine GCF or LCM of two monomials, two variables
- Determine missing component of GCF
- Factor GCF in polynomials, one variable
- Factor GCF in polynomials, including two variables
- Given GCF & one monomial, identify second monomial
-
Factoring Trinomials
- Factor quadratic trinomials, a = 1
- Factor quadratic trinomials, a = 1, b > 0, c > 0
- Factor quadratic trinomials, a = 1, terms scrambled
- Factor quadratic trinomials, 1 < a ≤ 10, no GCF
- Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
- Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < |c| ≤ 10
- Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
- Factor quadratic trinomials, 1 < |a| ≤ 10, 0 < |c| ≤ 30
- Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
- Factor quadratic trinomials, 1 < |a| ≤ 30, 0 < |c| ≤ 40
- Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
-
Factoring GCF & Remaining Trinomial
- Factor GCF in polynomials, degree one or two, one variable
- Factor GCF & remaining quadratic expression, a = 1, one variable
- Factor GCF & remaining quadratic expression, a ≥ 1, one variable
-
Factoring Difference of Squares & Perfect Square Trinomials
- Factor difference of two squares, degree two, one variable, coefficient one
- Factor difference of two squares, degree two, one variable, terms scrambled
- Factor difference of two squares, degree two, one variable
- Factor difference of two squares, two variables
- Factor perfect square trinomials, degree two, one variable
- Factor perfect square trinomials, degree two, two variables
- Condensed: Factor perfect square trinomials, degree two
- Factor difference of two squares, one or two variables
- Condensed: Factor difference of two squares, degree two
- Factor perfect square trinomials, fraction coefficients
-
Factoring Common Binomial
- Factor common binomial
- Factor binomial & its opposite
-
Factoring Cubic Polynomials
- Factor cubic polynomial by grouping, one variable
- Factor cubic polynomial by grouping & difference of two squares, one variable
- Factor sum & difference of two cubes, degree three, one variable
- Condensed: Factor sum & difference of two cubes, degree three
- Factor sum & difference of two cubes, degree three, two variables
- Factor sum & difference of two cubes, degree six, one variable
- Factor sum & difference of two cubes, degree six, two variables
- Condensed: Factor sum & difference of two cubes, degree six
-
Determining Factors of Polynomials
- Determine linear factors of polynomials, degree three
- Determine linear factors of polynomials, degree four
- Condensed: Determine linear factors of polynomials, degree three or four
- Determine quadratic factors of polynomials, degree four
- Determine maximum number of roots for polynomial function
-
-
Graphing Polynomials
- Given table, determine attributes of polynomial function
- Determine x-intercepts/zeros & y-intercepts of polynomial functions
- Determine end behavior of polynomial functions
- Given equation, graph polynomial function
- Determine points of intersection of two polynomial functions
- Determine zeros of polynomials & their multiplicities
- Determine intervals of increase & decrease of polynomial functions
- Given graph, determine equation of polynomial function
- Determine minimum & maximum of polynomial functions
-
-
Exponential Functions & Models
-
Interpreting Exponential Models
- Interpret values in exponential functions, real-world context
- Given exponential function, determine function value, non-negative input
- Given exponential function, determine function value, negative input
- Given exponential function, determine function value, rational coefficient
- Given exponential function, determine function value, rational base
- Given exponential function, determine function value, rational base & coefficient
- Determine exponential function, real-world context
-
Solving Exponential Models
- Given graph, identify solution to exponential equation
- Calculate investment value, annual compounding
- Calculate investment value, various compounding
- Calculate depreciating asset value, annual compounding
- Condensed: Calculate investment & depreciating asset values, annual compounding
-
Writing Exponential Functions
- Given table, determine exponential growth function
- Given table, determine exponential decay function
- Given table, determine linear or exponential growth function
- Given graph, determine equation of exponential function
-
Graphing Exponential Functions
- Given equation, graph exponential function
- Given exponential growth function, determine graph
- Given exponential growth function, determine graph, includes fractional coefficients
- Given exponential growth or decay function, determine graph, includes fractional coefficients
- Given equation, graph exponential function, including base e
- Compare exponential functions represented differently
-
Transformations of Exponential Functions
- Identify & graph vertical & horizontal shifts of exponential functions
- Identify & graph reflections of exponential functions
- Identify & graph vertical & horizontal stretches & compressions of exponential functions
- Given table, identify transformations of exponential functions
- Given exponential equation, identify description of transformations
- Graph exponential functions using all transformations
- Condensed: Graph exponential functions & identify transformations
-
Key Features of Exponential Functions
-
Determining Domain & Range
- Given equation, determine domain & range of exponential function
- Given verbal description & graph, determine domain & range of exponential function
- Determine restricted domain & range of exponential functions
- Determine domain & range of discrete exponential functions, real-world context
-
Determining Attributes
- Determine x-intercepts/zeros & y-intercepts of exponential functions
- Determine y-intercept of exponential function, real-world context
- Given exponential equation, determine asymptote
- Given graph, determine asymptote of exponential function
- Determine asymptote of exponential functions
- Determine asymptote of exponential functions, real-world context
- Determine minimum & maximum of exponential functions
- Determine end behavior of exponential functions
- Given table, determine attributes of exponential function
- Condensed: Determine graphical attributes of exponential functions
-
-
-
Foundations of Geometry
-
Congruence
- Given geometric figure, identify correct conjecture
- Identify corresponding parts from congruence statement or determine congruence statement from figures
- Given congruent triangles, determine values from corresponding parts
- Given congruent sides, identify congruent angles of isosceles triangle
- Given congruent angles, identify congruent sides of isosceles triangle
- Determine angle measures in isosceles trapezoid, using congruent base angles
- Identify congruent angles or determine angle measures in kites, algebraic expressions
- Identify congruence transformations
- Given congruent figures, identify description of transformations
- Determine missing steps in proofs involving angles
- Determine missing steps in proofs involving segments
- Determine missing steps in proofs involving parallel lines
-
Similarity
-
Triangle Similarity
- Determine segment lengths in triangles with angle bisectors
- Determine segment lengths using triangle proportionality theorem
- Determine angles of similar triangles using AA similarity
- Determine sides of similar triangles using AA similarity
- Determine similarity of triangles using AA similarity
- Determine angles of similar triangles using AA similarity, algebraic expressions
- Determine parts using similar triangles, including real-world context
- Determine similar triangles using SAS similarity
- Determine similar triangles using SSS similarity
- Condensed: Determine similar triangles using SAS or SSS similarity
- Determine missing steps in proofs involving similar triangles
- Determine missing steps in proofs involving similar triangles, paragraph form
- Given right triangle with altitude from right angle, identify similar triangles
-
Similar Figures
- Identify similar polygons
- Given similar figures, identify proportion of side lengths
- Given similar figures, identify proportion of side lengths, image orientations differ
- Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
- Identify corresponding parts of similar figures
- Determine dimensions in similar figures, whole number dimensions
- Determine dimensions in similar figures
- Determine dimensions using similar figures & indirect measurements
- Given similar figures, identify description of transformations
- Given three parallel lines with two transversals, determine lengths
- Determine edge, surface area, or volume of similar solids
-
-
Scale Factor
-
Scale Factor Determine Dimension, Perimeter or Area
- Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
- Determine scale factor or perimeter of dilated figures
- Determine scale factor or area of dilated figures
- Determine variable scale factor or variable measurement of dilated figures
- Given similar squares, determine area & side length
- Given similar rectangles, determine perimeter
- Given similar triangles, determine perimeter
- Given similar triangles, determine area
- Given similar cones, determine surface area
- Given scale factor, determine dimension
- Condensed: Determine or apply scale factor between circles
- Given similar squares, determine perimeter & side length
- Given similar rectangles, determine area
- Given similar cones, determine volume
- Given similar pyramids, determine surface area
- Given similar prisms, determine surface area
- Given similar spheres, determine volume
- Given similar pyramids, determine volume
- Given similar prisms, determine volume
- Given similar cylinders, determine volume
- Given similar cylinders, determine surface area
- Condensed: Given similar 2D figures, determine area or perimeter
- Given similar spheres, determine surface area
- Condensed: Given similar 3D figures, determine surface area or volume
-
Scale Factor Determine Coordinates
- Condensed: Given scale factor, determine coordinates of image
- Given scale factor, determine coordinates of image, pre-image not centered at origin
- Given scale factor, determine coordinates of image, pre-image centered at origin
- Given scale factor or length of corresponding side, determine perimeter or area of similar triangle
- Determine scale factor or perimeter of dilated figures
- Determine scale factor or area of dilated figures
- Determine variable scale factor or variable measurement of dilated figures
- Given similar squares, determine area & side length
- Given similar rectangles, determine perimeter
- Given similar triangles, determine perimeter
- Given similar triangles, determine area
- Given similar cones, determine surface area
- Given scale factor, determine coordinates of image, pre-image centered at origin
- Given scale factor, determine dimension
- Given scale factor, determine coordinates of image, pre-image not centered at origin
- Condensed: Given scale factor, determine coordinates of image
- Condensed: Determine or apply scale factor between circles
-
-
Two- & Three-Dimensional Objects
-
Two-Dimensional Objects
- Classify quadrilaterals shapes based on attributes
- Classify polygons using graphic organizers
- Classify polygons using graphic organizers, including types of triangles
- Classify polygons based on number of sides or relationship to other shapes
- Classify polygons based on angles & parallel or perpendicular lines
- Classify 2D figures
-
Three-Dimensional Objects
- Classify 3D figures
- Identify 3D figures & their bases
- Determine cross sections of prisms
- Determine cross sections of pyramids
- Determine cross sections of cylinders
- Determine cross sections of 3D figures
- Condensed: Determine cross sections of cylinders, pyramids, & cones
- Determine 2D orthographic representation of 3D blocks
- Determine 3D figures from rotations of 2D figures
-
-
Circumference & Area of a Circle
- Identify approximate formulas for circumference & area of circles
- Determine circumference of circle, exact answers, multiple choice, including real-world context
- Given radius or diameter, determine circumference
- Given circumference of circle, determine radius or diameter
- Estimate diameter or circumference & identify equations using π
- Given radius or diameter, determine area
- Determine area of circle, exact answers, including real-world context
- Given area of circle, determine radius or diameter
- Given radius or diameter, determine area or circumference
- Condensed: Given area or circumference of circle, determine radius or diameter
- Condensed: Determine area or circumference of circle
- Determine areas of semicircles & quarter circles
-
Volume
-
Cylinder Volume
- Determine volume of cylinders
- Given volume, determine dimension of cylinder
- Given base area & height, determine volume of cylinder
-
Pyramid Volume
- Determine volume of pyramids
- Given volume, determine dimension of pyramid
-
Cone Volume
- Determine volume of cones
- Given volume, determine dimension of cone
-
Sphere Volume
- Determine volume of spheres
- Determine volume or radius of spheres
- Given volume, determine radius, diameter, or surface area of sphere
-
Mixed Figure Volume
- Determine volume of composite figures, cylinders & cones
- Determine volume of cylinders, cones, & spheres, including real-world context
- Identify relationship between volume of cone & cylinder with same base & height
-
-
Surface Area
- Determine surface area of pyramids
-
Triangle Relationships
-
Perpendicular & Angle Bisectors
- Given perpendicular bisector in triangle, determine segment lengths
- Given angle bisector in triangle, determine angles
- Given perpendicular bisector in triangle, determine segment lengths, algebraic expressions
- Given angle bisector in triangle, determine angles, algebraic expressions
- Condensed: Given perpendicular or angle bisector in triangle, determine segment lengths or angles, including algebraic expressions
-
Median & Midsegment Theorem
- Given median of triangle, determine variable or length of bisected side, algebraic expressions
- Apply triangle midsegment theorem to determine segment lengths
- Apply triangle midsegment theorem to determine perimeter
- Apply triangle midsegment theorem to determine segment lengths, algebraic expressions
-
Centroid & Hinge Theorem
- Apply centroid theorem
- Determine coordinates of centroid of triangles
- Apply hinge theorem
-
Triangle Theorems
- Apply triangle theorems or determine missing steps in proofs
- Apply triangle inequality theorem to determine side lengths
- Determine missing steps in proofs involving triangles
- Determine missing steps in proofs involving isosceles triangles
-
-
Proving Geometric Theorems Using Coordinates
- Identify or determine parallelograms in coordinate plane
- Identify congruent angles or determine angle measures in kites, algebraic expressions
- Determine angle measures in isosceles trapezoid, using congruent base angles
-
-
Circles & Conic Sections
-
Circle Basics
- Identify components of circles
- Apply arc addition postulate to determine arc measures
- Apply arc addition postulate to determine arc measures, including algebraic expressions
- Determine relationship between congruent arcs & congruent central angles
-
Similarity Ratios
- Given two circles, determine scale factor or missing dimension
- Given two circles, determine scale factor of area or missing area
-
Arc Length & Area of Sector
- Given arc measure & radius, determine arc length
- Given arc length & radius, determine central angle
- Given chord & radius, determine length
- Given two chords of circle, determine length
- Given arc length & central angle, determine circumference
- Condensed: Determine circumferences, arc lengths, & central angles
- Determine area of sector
-
Properties of Inscribed Angles, Radii, & Chords
- Given central angle or arc measure, determine inscribed angle
- Given inscribed angle, determine central angle & arc measure
- Given inscribed angle formed by chord & tangent, determine angle or arc measure
- Given intersecting chords, determine angle or arc measure
- Given two diameters, radius, & two angles, determine angle or arc measure
- Condensed: Determine inscribed angles, central angles, & arc measures
- Determine relationship between congruent chords & congruent central angles
- Determine relationship between congruent chords & congruent arcs
-
Inscribed & Circumscribed Figures
- Determine angles of quadrilateral inscribed in circle, including algebraic expressions
- Given inscribed isosceles triangle, determine base angle
- Given isosceles triangle in circle, determine angle or arc measure
- Given isosceles triangle in circle, determine angle measure at vertex of triangle
- Given inscribed isosceles triangle or isosceles triangle in circle, determine angle or arc measure
- Given inscribed isosceles triangle, determine measure of arc intercepted by base of triangle
- Given inscribed right triangle, determine inscribed angle or arc measure
- Given inscribed right triangle & tangent, determine angle or arc measure
- Condensed: Given inscribed right triangle, determine angle or arc measure
-
Properties of Secants & Tangents
-
Given Secants & Tangents Determine Angles
- Given two tangents to circle, determine angle
- Given secant & tangent to circle, determine angle
- Given two secants intersecting outside circle, determine angle
- Given two secants intersecting inside circle, determine angle
- Given one chord & one secant of circle, determine angle
- Given tangent & secant intersecting at point of tangency, determine angles
- Given tangent & other segments, determine angle
- Condensed: Given secants, tangents, & chords, determine angles
- Given chord, secant, & tangent on same circle, determine angles & arcs
-
Given Secants & Tangents Determine Lengths
- Given secant & tangent to circle, determine length
- Given two secants of circle, determine length, including algebraic expressions
- Given tangents to circles, determine lengths, algebraic expressions
- Given secants, tangents, & chords, determine length
- Given tangent & other segments or circle inscribed in polygon, determine lengths
-
-
Area of Circular Segments
- Given radius & arc measure of 60°, 90°, or 120°, determine area of circular segment
- Given chord length & arc measure of 60°, 90°, or 120°, determine area of circular segment
- Given radius & arc measure, determine area of circular segment
- Determine areas of circular segments
- Given chord length & arc measure, determine area of circular segment
-
Equations of Circles
- Given equation of circle, identify center & radius
- Given center & radius, determine equation of circle
- Given graph, determine equation of circle
- Given equation of circle in standard form, identify graph
- Given equation of circle, determine area
- Given equation of circle in general form, determine standard form
- Condensed: Determine circle equations, centers, radii, & areas
- Complete the square & graph, circle equations
-
Equations of Parabolas
- Given vertex & point, determine quadratic equation, vertex form
- Given vertex & point, determine quadratic equation, standard form
- Given focus & directrix of parabola, determine equation
- Given focus & directrix of parabola, determine equation in standard form
-
Equations of Circles & Parabolas
- Condensed: Complete the square & graph, circle & parabola equations
-
-
Trigonometry
-
Pythagorean Theorem Calculations & Proofs
- Determine Pythagorean triples
- Given triangle with algebraic expressions, apply Pythagorean theorem to determine side
- Classify triangles using Pythagorean inequality theorem
- Apply Pythagorean theorem to find length in kite
- Given ratio of sides & one dimension, apply Pythagorean theorem to determine specified dimension, real-world context
-
Trigonometric Ratios
- Given special right triangle, determine trig function value, sin, cos, & tan
- Given special right triangle, determine trig function value, cot, sec, & csc
- Given right triangle, determine trig ratio, sin, cos, & tan
- Given right triangle, determine angle, real-world context
- Condensed: Given right triangle, determine sides or angles, real-world context
- Given right triangle, determine trig ratio, cot, sec, & csc
- Condensed: Given right triangle, determine trig ratio
- Given sine, cosine, or tangent & quadrant, determine trig function values
- Determine missing steps in proofs of Pythagorean identities
- Given right triangle, determine missing side & trig ratio, sin, cos, & tan
- Given right triangle, determine missing side & trig ratio, cot, sec, & csc
- Identify definitions of trig functions
- Determine relationship between trig ratios of sides of similar triangles, sin, cos, & tan
- Condensed: Given right triangle, determine missing side & trig ratio
-
Special Right Triangles
-
45-45-90 Triangles
- Given 45-45-90 triangle, determine hypotenuse
- Given 45-45-90 triangle, determine leg
- Given 45-45-90 triangle, determine side
-
30-60-90 Triangles
- Given 30-60-90 triangle & short leg, determine long leg
- Given 30-60-90 triangle & short leg, determine hypotenuse
- Given 30-60-90 triangle & long leg, determine short leg
- Given 30-60-90 triangle & long leg, determine hypotenuse
- Given 30-60-90 triangle & hypotenuse, determine short leg
- Given 30-60-90 triangle & hypotenuse, determine long leg
- Given 30-60-90 triangle, determine side
-
Mixed Special Right Triangles
- Condensed: Given special right triangle, determine trig function value
- Condensed: Given special right triangle, determine side
- Condensed: Determine angles or sides using special right triangle relationships, real-world context
- Given 45-45-90 triangle, determine hypotenuse
- Given 45-45-90 triangle, determine leg
- Given 45-45-90 triangle, determine side
- Given 30-60-90 triangle & short leg, determine long leg
- Given 30-60-90 triangle & short leg, determine hypotenuse
- Given 30-60-90 triangle & long leg, determine short leg
- Given 30-60-90 triangle & long leg, determine hypotenuse
- Given 30-60-90 triangle & hypotenuse, determine short leg
- Given 30-60-90 triangle & hypotenuse, determine long leg
- Given 30-60-90 triangle, determine side
- Condensed: Given special right triangle, determine trig function value
- Condensed: Given special right triangle, determine side
- Condensed: Determine angles or sides using special right triangle relationships, real-world context
-
-
Solving Right Triangles
-
Determining Trigonometric Values
- Determine trig function values, degrees, calculator expected
- Determine trig function values, radians, calculator expected
- Condensed: Determine trig function values, calculator expected
-
Solving Sides of Right Triangles
- Determine leg of right triangle using sine
- Determine hypotenuse of right triangle using sine
- Given side & angle, determine specified side using sine
- Determine leg of right triangle using cosine
- Determine hypotenuse of right triangle using cosine
- Given side & angle, determine specified side using cosine
- Given short leg of right triangle, determine long leg using tangent
- Given long leg of right triangle, determine short leg using tangent
- Given side & angle, determine specified side using tangent
- Condensed: Given side & angle, determine specified side using sine, cosine, or tangent
-
Solving Angles of Right Triangles
- Given hypotenuse & leg of right triangle, determine angle using arcsine
- Given hypotenuse & leg of right triangle, determine angle using arccosine
- Given legs of right triangle, determine angle using arctangent
- Given sides of triangle, determine angle using arcsine, arccosine, or arctangent
-
-
Sine & Cosine of Complementary Angles
- Determine equivalent trig cofunction values, sin & cos
- Determine equivalent trig cofunction values, sec & csc
- Determine equivalent trig cofunction values, tan & cot
- Condensed: Determine equivalent trig cofunction values
- Determine equivalent trig cofunction values from triangles
-
Modeling with Right Triangles
- Given legs of right triangle, determine angle using arctangent, real-world context
- 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
- Given right triangle, determine side, real-world context
-
Law of Sines & 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 angles of triangles using law of sines
- Condensed: Determine sides & angles of triangles using law of sines
-
-
Probability
-
Sample Space
- Determine sample spaces
- Determine size of sample spaces, compound events
- Determine sample spaces, compound events
- Determine sample size, various representations
- Identify experiments & observational studies
- Identify systematic, cluster, stratified, & simple random samples
-
Combinations & Permutations
-
Combinations
- Determine number of combinations using fundamental counting principle, real-world context
- Determine number of combinations using fundamental counting principle, including repeated letters & digits, real-world context
- Determine combinations, real-world context
- Given lists, determine combinations, choose from one list, real-world context
- Given lists, determine combinations, choose from two lists, real-world context
-
Permutations
- Given visual model, determine permutations, specified items predetermined
- Determine permutations using all items, real-world context
- Determine permutations, real-world context
- Determine permutations, one nondistinct item, real-world context
- Determine permutations, multiple nondistinct items, real-world context
- Determine permutation of letters in word, distinct letters
- Determine permutation of letters in word, nondistinct letters
- Condensed: Determine permutation of letters in word, including nondistinct letters
-
Combinations & Permutations Combined
- Determine combinations & permutations, two questions, real-world context
- Determine combinations & permutations, four questions, real-world context
-
-
Multiplication Rule
- Determine probabilities of flipping coins & rolling die
- Determine probabilities of flipping coins specified number of times
- Given visual model, determine “and” probability as fraction, decimal, or percent, dependent events
- Determine “and” probabilities, independent events, visuals provided
- Determine “and” probabilities, independent events, two distinct sample spaces
- Determine “and” probabilities, independent events, same sample space
- Determine “and” probabilities, dependent events
- Determine “and” probabilities, dependent events, multiple choice
- Determine “and” probabilities, independent & dependent events
- Determine “and” probabilities, independent & dependent events, including complementary events
-
Addition Rule
- Determine “or” probabilities
- Determine “or” probabilities as fractions
- Determine “or” probabilities as fractions, decimals, or percents
- Given visual model, determine “or” probability
- Given visual model, determine “or” probability as fraction, decimal, or percent
-
Two-Way Frequency Tables
- Interpret two-way frequency tables, conditional distribution
- Interpret two-way frequency tables, joint distribution
- Interpret two-way frequency tables, marginal distribution
- Given two-way frequency tables, identify associations
- Determine two-way frequency tables
- Condensed: Interpret two-way frequency tables
- Determine specified probabilities in two-way frequency tables
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
-
Simulations
- Identify simulations used to acquire simple random samples
- Identify simulations to model probability events
-
Using Probability to Make Predictions
- Determine predicted values, theoretical probability
- Determine predicted values, experimental probability
- Determine predicted values, experimental probability, compound events
- Determine predicted values, theoretical probability, compound events
- Determine predicted values, experimental or theoretical probability
- Determine inferences from samples
- Determine predicted values or compare likelihood of events
-
-
Rational Functions
- Compare rational functions represented differently
-
Radical Functions
- Compare radical functions represented differently