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Skills available for Arkansas high school math standards

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Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics
Arkansas Curriculum Framework: Algebra I Arkansas Curriculum Framework: Algebra I
Arkansas Curriculum Framework: Algebra I Part A Arkansas Curriculum Framework: Algebra I Part A
Arkansas Curriculum Framework: Algebra I Part B Arkansas Curriculum Framework: Algebra I Part B
Arkansas Curriculum Framework: Algebra II/Advanced Algebra Arkansas Curriculum Framework: Algebra II/Advanced Algebra
Arkansas Curriculum Framework: Algebra III Arkansas Curriculum Framework: Algebra III
Arkansas Curriculum Framework: Bridge to Algebra II Arkansas Curriculum Framework: Bridge to Algebra II
Arkansas Curriculum Framework: Calculus Arkansas Curriculum Framework: Calculus
Arkansas Curriculum Framework: Computer Science and Mathematics Arkansas Curriculum Framework: Computer Science and Mathematics
Arkansas Curriculum Framework: Geometry Arkansas Curriculum Framework: Geometry
Arkansas Curriculum Framework: Geometry A Arkansas Curriculum Framework: Geometry A
Arkansas Curriculum Framework: Geometry B Arkansas Curriculum Framework: Geometry B
Arkansas Curriculum Framework: Mathematical Applications and Algorithms Arkansas Curriculum Framework: Mathematical Applications and Algorithms
Arkansas Curriculum Framework: Precalculus Arkansas Curriculum Framework: Precalculus
Arkansas Curriculum Framework: Statistics Arkansas Curriculum Framework: Statistics

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MO Matrix Operations

MO.1.AIII Students will perform operations with matrices and use them to solve systems of equations
- MO.1.AIII.1 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).
- MO.1.AIII.2 Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).
- MO.1.AIII.3 Add, subtract, and multiply matrices of appropriate dimensions.
- MO.1.AIII.4 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
  - Properties of matrices (PC-L.8)
- MO.1.AIII.5 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
- MO.1.AIII.6 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector; work with matrices as transformations of vectors.
- MO.1.AIII.7 Work with 2x2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area.
- MO.1.AIII.8 Represent a system of linear equations as a single matrix equation in a vector variable.
- MO.1.AIII.9 Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3x3 or greater.
  - Inverse of a 2 x 2 matrix (PC-L.12)
  - Inverse of a 3 x 3 matrix (PC-L.13)

CS Conic Sections

CS.2.AIII Students will identify, analyze, and sketch the graphs of the conic sections and relate the equations and graphs
- CS.2.AIII.1 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- CS.2.AIII.2 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola.
  - Find the equations for the asymptotes of a hyperbola (A2-X.4)
  - Write equations of ellipses in standard form (PC-P.9)
- CS.2.AIII.3 Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section.
- CS.2.AIII.4 Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.
- CS.2.AIII.5 Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology.
  - Solve a nonlinear system of equations (A2-E.18)

FOP Function Operations and Properties

FOP.3.AIII Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses
- FOP.3.AIII.1 Compose functions (e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).
  - Composition of functions (PC-A.11)
- FOP.3.AIII.2 Verify, by composition, that one function is the inverse of another.
  - Identify inverse functions (PC-A.12)
  - Check whether two rational functions are inverses (PC-E.3)
- FOP.3.AIII.3 Read values of an inverse function from a graph or a table, given that the function has an inverse.
  - Find values of inverse functions from tables (PC-A.13)
  - Find values of inverse functions from graphs (PC-A.14)
- FOP.3.AIII.4 Produce an invertible function from a non-invertible function by restricting the domain.
- FOP.3.AIII.5 Combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model).
  - Add, subtract, multiply, and divide functions (PC-A.10)
- FOP.3.AIII.6 Understand the inverse relationship between exponents and logarithms; use this relationship to solve problems involving logarithms and exponents.
- FOP.3.AIII.7 Graph transformations of functions including quadratic, absolute value, square root, cube root, cubic, and step functions; graph piece-wise defined functions including these transformations.
- FOP.3.AIII.8 Determine numerically, graphically, and algebraically if a function is even, odd, or neither.

IF Interpreting Functions

IF.4.AIII Students will be able to interpret different types of functions and key characteristics including polynomial, exponential, logarithmic, and rational functions
- IF.4.AIII.1 Graph rational functions identifying zeros and asymptotes when suitable factorizations are available; show end behavior.
  - Rational functions: asymptotes and excluded values (PC-E.1)
- IF.4.AIII.2 Analyze and interpret polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases.
- IF.4.AIII.3 Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, and domain and range.
  - Rational functions: asymptotes and excluded values (PC-E.1)
- IF.4.AIII.4 Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.
  - Evaluate exponential functions (A2-T.2)
  - Match exponential functions and graphs (A2-T.4)
- IF.4.AIII.5 Analyze and interpret logarithmic functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.
  - Domain and range of exponential and logarithmic functions (PC-F.1)
- IF.4.AIII.6 Build functions to model real-world applications using algebraic operations on functions and composition of functions, with and without appropriate technology [e.g., profit functions as well as volume and surface area (optimization subject to constraints)].
  - Exponential growth and decay: word problems (PC-F.16)
  - Compound interest: word problems (PC-F.17)

SS Sequences and Series

SS.5.AIII Students will use sequences and series to represent and analyze mathematical situations
- SS.5.AIII.1 Write arithmetic and geometric sequences both recursively and with an explicit formula; translate between the two forms.
- SS.5.AIII.2 Use arithmetic and geometric sequences both recursively and with an explicit formula to model situations.
- SS.5.AIII.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
- SS.5.AIII.4 Use sequences and series to solve real world problems, with and without appropriate technology.

Arkansas

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MO Matrix Operations

MO.1.AIII Students will perform operations with matrices and use them to solve systems of equations

MO.1.AIII.1 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).

MO.1.AIII.2 Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).

MO.1.AIII.3 Add, subtract, and multiply matrices of appropriate dimensions.

MO.1.AIII.4 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

MO.1.AIII.5 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

MO.1.AIII.6 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector; work with matrices as transformations of vectors.

MO.1.AIII.7 Work with 2x2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area.

MO.1.AIII.8 Represent a system of linear equations as a single matrix equation in a vector variable.

MO.1.AIII.9 Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3x3 or greater.

CS Conic Sections

CS.2.AIII Students will identify, analyze, and sketch the graphs of the conic sections and relate the equations and graphs

CS.2.AIII.1 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

CS.2.AIII.2 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola.

CS.2.AIII.3 Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section.

CS.2.AIII.4 Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.

CS.2.AIII.5 Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology.

FOP Function Operations and Properties

FOP.3.AIII Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses

FOP.3.AIII.1 Compose functions (e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).

FOP.3.AIII.2 Verify, by composition, that one function is the inverse of another.

FOP.3.AIII.3 Read values of an inverse function from a graph or a table, given that the function has an inverse.

FOP.3.AIII.4 Produce an invertible function from a non-invertible function by restricting the domain.

FOP.3.AIII.5 Combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model).

FOP.3.AIII.6 Understand the inverse relationship between exponents and logarithms; use this relationship to solve problems involving logarithms and exponents.

FOP.3.AIII.7 Graph transformations of functions including quadratic, absolute value, square root, cube root, cubic, and step functions; graph piece-wise defined functions including these transformations.

FOP.3.AIII.8 Determine numerically, graphically, and algebraically if a function is even, odd, or neither.

IF Interpreting Functions

IF.4.AIII Students will be able to interpret different types of functions and key characteristics including polynomial, exponential, logarithmic, and rational functions

IF.4.AIII.1 Graph rational functions identifying zeros and asymptotes when suitable factorizations are available; show end behavior.

IF.4.AIII.2 Analyze and interpret polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases.

IF.4.AIII.3 Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, and domain and range.

IF.4.AIII.4 Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.

IF.4.AIII.5 Analyze and interpret logarithmic functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.

IF.4.AIII.6 Build functions to model real-world applications using algebraic operations on functions and composition of functions, with and without appropriate technology [e.g., profit functions as well as volume and surface area (optimization subject to constraints)].

SS Sequences and Series

SS.5.AIII Students will use sequences and series to represent and analyze mathematical situations

SS.5.AIII.1 Write arithmetic and geometric sequences both recursively and with an explicit formula; translate between the two forms.

SS.5.AIII.2 Use arithmetic and geometric sequences both recursively and with an explicit formula to model situations.

SS.5.AIII.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

SS.5.AIII.4 Use sequences and series to solve real world problems, with and without appropriate technology.