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Skills available for Florida high school math standards

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Florida's B.E.S.T. Standards: Algebra 1 Florida's B.E.S.T. Standards: Algebra 1
Florida's B.E.S.T. Standards: Algebra 2 Florida's B.E.S.T. Standards: Algebra 2
Florida's B.E.S.T. Standards: Calculus Florida's B.E.S.T. Standards: Calculus
Florida's B.E.S.T. Standards: Discrete Math Honors Florida's B.E.S.T. Standards: Discrete Math Honors
Florida's B.E.S.T. Standards: Fourth Courses Florida's B.E.S.T. Standards: Fourth Courses
Florida's B.E.S.T. Standards: Geometry Florida's B.E.S.T. Standards: Geometry
Florida's B.E.S.T. Standards: Mathematical Thinking and Reasoning Standards Florida's B.E.S.T. Standards: Mathematical Thinking and Reasoning Standards
Florida's B.E.S.T. Standards: Mathematics for College Algebra Florida's B.E.S.T. Standards: Mathematics for College Algebra
Florida's B.E.S.T. Standards: Mathematics for College Liberal Arts Florida's B.E.S.T. Standards: Mathematics for College Liberal Arts

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NSO Number Sense and Operations

MA.912.NSO.1 Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.
- MA.912.NSO.1.3 Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.
- MA.912.NSO.1.5 Add, subtract, multiply and divide algebraic expressions involving radicals.
- MA.912.NSO.1.6 Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents.
- MA.912.NSO.1.7 Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.
MA.912.NSO.2 Represent and perform operations with expressions within the complex number system.
- MA.912.NSO.2.1 Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.

AR Algebraic Reasoning

MA.912.AR.1 Interpret and rewrite algebraic expressions and equations in equivalent forms.
- MA.912.AR.1.1 Identify and interpret parts of an equation or expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.
- MA.912.AR.1.3 Add, subtract and multiply polynomial expressions with rational number coefficients.
  - Add and subtract polynomials (A2-L.2)
  - Multiply polynomials (A2-L.3)
- MA.912.AR.1.5 Divide polynomial expressions using long division, synthetic division or algebraic manipulation.
  - Divide polynomials using long division (A2-L.4)
  - Divide polynomials using synthetic division (A2-L.5)
- MA.912.AR.1.6 Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.
- MA.912.AR.1.8 Rewrite a polynomial expression as a product of polynomials over the real or complex number system.
- MA.912.AR.1.9 Apply previous understanding of rational number operations to add, subtract, multiply and divide rational algebraic expressions.
MA.912.AR.3 Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
- MA.912.AR.3.2 Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
- MA.912.AR.3.3 Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.
  - Graph solutions to quadratic inequalities (A2-O.9)
  - Solve quadratic inequalities (A2-O.10)
- MA.912.AR.3.4 Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
- MA.912.AR.3.8 Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.
- MA.912.AR.3.9 Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.
- MA.912.AR.3.10 Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.
MA.912.AR.4 Write, solve and graph absolute value equations, functions and inequalities in one and two variables.
- MA.912.AR.4.2 Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.
  - Solve absolute value inequalities (A2-G.4)
  - Graph solutions to absolute value inequalities (A2-G.5)
- MA.912.AR.4.4 Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.5 Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
- MA.912.AR.5.2 Solve one-variable equations involving logarithms or exponential expressions. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
- MA.912.AR.5.4 Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
- MA.912.AR.5.5 Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.
  - Exponential functions over unit intervals (A2-Z.6)
  - Describe linear and exponential growth and decay (A2-Z.8)
- MA.912.AR.5.7 Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.
- MA.912.AR.5.8 Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.
  - Domain and range of logarithmic functions (A2-BB.1)
  - Graph logarithmic functions (A2-BB.2)
- MA.912.AR.5.9 Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.6 Solve and graph polynomial equations and functions in one and two variables.
- MA.912.AR.6.1 Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems.
  - Solve polynomial equations (A2-Q.1)
- MA.912.AR.6.5 Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.
  - Match polynomials and graphs (A2-Q.11)
MA.912.AR.7 Solve and graph radical equations and functions in one and two variables.
- MA.912.AR.7.1 Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.
  - Solve radical equations (A2-S.4)
- MA.912.AR.7.2 Given a table, equation or written description of a square root or cube root function, graph that function and determine its key features.
- MA.912.AR.7.3 Solve and graph mathematical and real-world problems that are modeled with square root or cube root functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.8 Solve and graph rational equations and functions in one and two variables.
- MA.912.AR.8.1 Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
  - Solve rational equations (A2-X.8)
- MA.912.AR.8.2 Given a table, equation or written description of a rational function, graph that function and determine its key features.
  - Rational functions: asymptotes and excluded values (A2-X.1)
- MA.912.AR.8.3 Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.9 Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.
- MA.912.AR.9.2 Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically.
  - Solve a system of linear and quadratic equations by graphing: parabolas (A2-P.1)
  - Solve a system of linear and quadratic equations: parabolas (A2-P.2)
- MA.912.AR.9.3 Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.
  - Solve a nonlinear system of equations (A2-P.4)
- MA.912.AR.9.5 Graph the solution set of a system of two-variable inequalities.
  - Solve systems of linear inequalities by graphing (A2-F.4)
- MA.912.AR.9.7 Given a real-world context, represent constraints as systems of linear and non-linear equations or inequalities. Interpret solutions to problems as viable or non-viable options.

F Functions

MA.912.F.1 Understand, compare and analyze properties of functions.
- MA.912.F.1.1 Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.
  - Identify linear, quadratic, and exponential functions from tables (A2)
  - Identify function types from graphs (A2)
- MA.912.F.1.7 Compare key features of two functions each represented algebraically, graphically, in tables or written descriptions.
- MA.912.F.1.9 Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.
  - Even and odd functions (A2-Q.13)
MA.912.F.2 Identify and describe the effects of transformations on functions. Create new functions given transformations.
- MA.912.F.2.2 Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.
  - Function transformation rules (A2-W.1)
  - Describe function transformations (A2-W.6)
- MA.912.F.2.3 Given the graph or table of f(x) and the graph or table of f(x) + k, kf(x), f(kx) and f(x + k), state the type of transformation and find the value of the real number k.
  - Function transformation rules (A2-W.1)
  - Describe function transformations (A2-W.6)
- MA.912.F.2.5 Given a table, equation or graph that represents a function, create a corresponding table, equation or graph of the transformed function defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.
MA.912.F.3 Create new functions from existing functions.
- MA.912.F.3.2 Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.
- MA.912.F.3.4 Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.
- MA.912.F.3.6 Determine whether an inverse function exists by analyzing tables, graphs and equations.
  - Find inverse functions and relations (A2-V.4)
- MA.912.F.3.7 Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.

FL Financial Literacy

MA.912.FL.3 Describe the advantages and disadvantages of short-term and long-term purchases.
- MA.912.FL.3.1 Compare simple, compound and continuously compounded interest over time.
- MA.912.FL.3.2 Solve real-world problems involving simple, compound, and continuously compounded interest.
- MA.912.FL.3.4 Explain the relationship between simple interest and linear growth. Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.

DP Data Analysis and Probability

MA.912.DP.2 Solve problems involving univariate and bivariate numerical data.
- MA.912.DP.2.8 Fit a quadratic function to bivariate numerical data that suggests a quadratic association and interpret any intercepts or the vertex of the model. Use the model to solve real-world problems in terms of the context of the data.
- MA.912.DP.2.9 Fit an exponential function to bivariate numerical data that suggests an exponential association. Use the model to solve real-world problems in terms of the context of the data.
  - Exponential regression (A2-SS.7)

Florida

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NSO Number Sense and Operations

MA.912.NSO.1 Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms.

MA.912.NSO.1.3 Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents.

MA.912.NSO.1.5 Add, subtract, multiply and divide algebraic expressions involving radicals.

MA.912.NSO.1.6 Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents.

MA.912.NSO.1.7 Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.

MA.912.NSO.2 Represent and perform operations with expressions within the complex number system.

MA.912.NSO.2.1 Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.

AR Algebraic Reasoning

MA.912.AR.1 Interpret and rewrite algebraic expressions and equations in equivalent forms.

MA.912.AR.1.1 Identify and interpret parts of an equation or expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.

MA.912.AR.1.3 Add, subtract and multiply polynomial expressions with rational number coefficients.

MA.912.AR.1.5 Divide polynomial expressions using long division, synthetic division or algebraic manipulation.

MA.912.AR.1.6 Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.

MA.912.AR.1.8 Rewrite a polynomial expression as a product of polynomials over the real or complex number system.

MA.912.AR.1.9 Apply previous understanding of rational number operations to add, subtract, multiply and divide rational algebraic expressions.

MA.912.AR.3 Write, solve and graph quadratic equations, functions and inequalities in one and two variables.

MA.912.AR.3.2 Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.

MA.912.AR.3.3 Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.

MA.912.AR.3.4 Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.

MA.912.AR.3.8 Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.3.9 Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.

MA.912.AR.3.10 Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.

MA.912.AR.4 Write, solve and graph absolute value equations, functions and inequalities in one and two variables.

MA.912.AR.4.2 Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.

MA.912.AR.4.4 Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.5 Write, solve and graph exponential and logarithmic equations and functions in one and two variables.

MA.912.AR.5.2 Solve one-variable equations involving logarithms or exponential expressions. Interpret solutions as viable in terms of the context and identify any extraneous solutions.

MA.912.AR.5.4 Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.

MA.912.AR.5.5 Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.

MA.912.AR.5.7 Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.5.8 Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.

MA.912.AR.5.9 Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.6 Solve and graph polynomial equations and functions in one and two variables.

MA.912.AR.6.1 Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems.

MA.912.AR.6.5 Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.

MA.912.AR.7 Solve and graph radical equations and functions in one and two variables.

MA.912.AR.7.1 Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.

MA.912.AR.7.2 Given a table, equation or written description of a square root or cube root function, graph that function and determine its key features.

MA.912.AR.7.3 Solve and graph mathematical and real-world problems that are modeled with square root or cube root functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.8 Solve and graph rational equations and functions in one and two variables.

MA.912.AR.8.1 Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.

MA.912.AR.8.2 Given a table, equation or written description of a rational function, graph that function and determine its key features.

MA.912.AR.8.3 Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the context.

MA.912.AR.9 Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.

MA.912.AR.9.2 Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically.

MA.912.AR.9.3 Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.

MA.912.AR.9.5 Graph the solution set of a system of two-variable inequalities.

MA.912.AR.9.7 Given a real-world context, represent constraints as systems of linear and non-linear equations or inequalities. Interpret solutions to problems as viable or non-viable options.

F Functions

MA.912.F.1 Understand, compare and analyze properties of functions.

MA.912.F.1.1 Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.

MA.912.F.1.7 Compare key features of two functions each represented algebraically, graphically, in tables or written descriptions.

MA.912.F.1.9 Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.

MA.912.F.2 Identify and describe the effects of transformations on functions. Create new functions given transformations.

MA.912.F.2.2 Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.

MA.912.F.2.3 Given the graph or table of f(x) and the graph or table of f(x) + k, kf(x), f(kx) and f(x + k), state the type of transformation and find the value of the real number k.

MA.912.F.2.5 Given a table, equation or graph that represents a function, create a corresponding table, equation or graph of the transformed function defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.

MA.912.F.3 Create new functions from existing functions.

MA.912.F.3.2 Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.

MA.912.F.3.4 Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.

MA.912.F.3.6 Determine whether an inverse function exists by analyzing tables, graphs and equations.

MA.912.F.3.7 Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.

FL Financial Literacy

MA.912.FL.3 Describe the advantages and disadvantages of short-term and long-term purchases.

MA.912.FL.3.1 Compare simple, compound and continuously compounded interest over time.

MA.912.FL.3.2 Solve real-world problems involving simple, compound, and continuously compounded interest.

MA.912.FL.3.4 Explain the relationship between simple interest and linear growth. Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.

DP Data Analysis and Probability

MA.912.DP.2 Solve problems involving univariate and bivariate numerical data.

MA.912.DP.2.8 Fit a quadratic function to bivariate numerical data that suggests a quadratic association and interpret any intercepts or the vertex of the model. Use the model to solve real-world problems in terms of the context of the data.

MA.912.DP.2.9 Fit an exponential function to bivariate numerical data that suggests an exponential association. Use the model to solve real-world problems in terms of the context of the data.