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K–12 Standards

Algebra III

Other Arkansas Mathematics Standards sets

Complex Numbers and Conic Sections CNC

  •  

    Complex Numbers: Students apply properties to complex numbers. 

    1. 1

      Find the conjugate of a complex number; use conjugates to find quotients of complex numbers. A3.CNC.1

  •  

    Conic Sections: Students relate the equations and graphs of conic sections.

    1. 2

      Generate an equivalent form of an equation for a conic section by completing the square to identify key characteristics. A3.CNC.2

      1. 1

        Conic sections include: circles, ellipses, parabolas, and hyperbolasA3.CNC.2.1

    2. 3

      Identify, graph, write, and analyze equations of each type of conic section using properties and technology when appropriate. A3.CNC.3

      1. 1

        Conic sections include: circles, ellipses, parabolas, and hyperbolas A3.CNC.3.1

      2. 2

        Properties include: symmetry, intercepts, foci, asymptotes, and eccentricityA3.CNC.3.2

FunctionsFN

  •  

    Compositions: Students compose and compare functions. 

    1. 1

      Combine functions by addition, subtraction, multiplication, division, and composition to model the relationship between two quantities in real-world and mathematical contexts. A3.FN.1

  •  

    Inverses: Students find inverse functions. 

    1. 2

      Verify if two functions are inverses of each other using composition of functions. A3.FN.2

    2. 3

      For a function with an inverse, explain how to read the ordered pairs of the inverse function when given a graph or table of values.A3.FN.3

    3. 4

      Construct an invertible function from a non-invertible function by restricting the domain.A3.FN.4

  •  

    Transformations: Students graph function transformations. 

    1. 5

      Graph and generalize the effect of transformations on quadratic, absolute value, square root, cube root, cubic, and step functions.A3.FN.5

      1. 1

        Transformations include: stretches, compressions, vertical shifts, and horizontal shiftsA3.FN.5.1

    2. 6

      Determine if a function is even, odd, or neither from a graph or an algebraic expression.A3.FN.6

  •  

    Sequences: Students use sequences to model and analyze mathematical situations. 

    1. 7

      Write and use arithmetic and geometric sequences recursively and explicitly to model situations, translating between the two forms.A3.FN.7

      1. 1

        Forms include: when given a graph, a description of the relationship, or two input-output pairsA3.FN.7.1

MatricesMAT

  •  

    Operations: Students represent and perform operations with matrices.

    1. 1

      Use matrices to describe, list, and manipulate data in different situations.A3.MAT.1

    2. 2

      Multiply matrices by scalars to solve real-world and mathematical problems. A3.MAT.2

    3. 3

      Add and subtract matrices.A3.MAT.3

    4. 4

      Multiply matrices, understanding that matrix multiplication for square matrices is not commutative.A3.MAT.4

    5. 5

      Calculate the determinant of a square matrix to determine if it has an inverse. A3.MAT.5

  •  

    Systems: Students use matrices to solve systems of equations.

    1. 6

      Solve systems of linear equations using augmented matrices.A3.MAT.6

Exponential and Logarithmic Functions ELF

  •  

    Analyze & Interpret: Students analyze and interpret exponential and logarithmic functions. 

    1. 1

      Analyze and interpret exponential and logarithmic functions, identifying key characteristics. A3.ELF.1

      1. 1

        Functions should be represented numerically, graphically, and algebraically.A3.ELF.1.1

      2. 2

        Key features include asymptotes, end behavior, intercepts, domain, and range.A3.ELF.1.2

  •  

    Solve: Students solve problems with exponential and logarithmic functions. 

    1. 2

      Understand and apply the inverse relationship between exponents and logarithms to solve problems.A3.ELF.2

Polynomial & Rational Functions PRF

  •  

    Analyze, Interpret, & Graph: Students analyze, interpret, and graph polynomial and rational functions. 

    1. 1

      Analyze and interpret polynomial functions, identifying key characteristics.A3.PRF.1

      1. 1

        Functions should be represented numerically, graphically, and algebraically. A3.PRF.1.1

      2. 2

        Key features include end behavior, intercepts, domain, range, relative and absolute maximum and minimum, and intervals over which the function is increasing or decreasing.A3.PRF.1.2

    2. 2

      Analyze and interpret rational functions, identifying key characteristics. A3.PRF.2

      1. 1

        Functions should be represented numerically, graphically, and algebraically. A3.PRF.2.1

      2. 2

        Key features include asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, domain, and range.A3.PRF.2.2

    3. 3

      Graph rational functions showing zeros, asymptotes, and end behavior.A3.PRF.3

Frequently asked questions

What grade levels do these standards cover?
Grade 9, Grade 10, Grade 11, and Grade 12
Where can I read the official document?
ARKANSAS MATHEMATICS STANDARDS

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