Arkansas

CNC Complex Numbers and Conic Sections

• Complex Numbers: Students apply properties to complex numbers.

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

    • Complex conjugates (PC-V.2)
    • Multiply and divide complex numbers (PC-V.5)

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

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

    • Convert equations of conic sections from general to standard form (PC-U.13)

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

    • Find properties of parabolas (PC-U.1)
    • Write equations of parabolas in vertex form (PC-U.2)
    • Graph parabolas (PC-U.3)
    • Find properties of circles (PC-U.4)
    • Write equations of circles in standard form (PC-U.5)
    • Graph circles (PC-U.6)
    • Find properties of ellipses (PC-U.7)
    • Find the eccentricity of an ellipse (PC-U.8)
    • Write equations of ellipses in standard form (PC-U.9)
    • Find properties of hyperbolas (PC-U.10)
    • Find the eccentricity of a hyperbola (PC-U.11)
    • Write equations of hyperbolas in standard form (PC-U.12)

FN Functions

• Compositions: Students compose and compare functions.

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

    • Add, subtract, multiply, and divide functions (PC-A.7)
    • Composition of functions (PC-A.8)

• Inverses: Students find inverse functions.

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

    • Identify inverse functions (PC-B.1)
    • Check whether two rational functions are inverses (PC-G.3)

  • A3.FN.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.

    • Find values of inverse functions from tables (PC-B.2)
    • Find values of inverse functions from graphs (PC-B.3)

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

• Transformations: Students graph function transformations.

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

    • Transformations of absolute value functions (A2-H.4)
    • Transformations of quadratic functions (A2-N.4)
    • Function transformation rules (PC-C.1)
    • Translations of functions (PC-C.2)
    • Reflections of functions (PC-C.3)
    • Dilations of functions (PC-C.4)
    • Transformations of functions (PC-C.5)
    • Describe function transformations (PC-C.6)

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

    • Even and odd functions (PC-F.12)

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

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

    • Write a formula for an arithmetic sequence (A2-MM.6)
    • Write a formula for a geometric sequence (A2-MM.7)
    • Find terms of a sequence (PC-AA.1)
    • Find terms of a recursive sequence (PC-AA.2)
    • Identify a sequence as explicit or recursive (PC-AA.3)
    • Find a recursive formula (PC-AA.4)
    • Find recursive and explicit formulas (PC-AA.5)
    • Convert a recursive formula to an explicit formula (PC-AA.6)
    • Convert an explicit formula to a recursive formula (PC-AA.7)
    • Convert between explicit and recursive formulas (PC-AA.8)

MAT Matrices

• Operations: Students represent and perform operations with matrices.

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

    • Matrix vocabulary (PC-Q.1)

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

    • Multiply a matrix by a scalar (PC-Q.4)

  • A3.MAT.3 Add and subtract matrices.

    • Add and subtract matrices (PC-Q.3)
    • Add and subtract scalar multiples of matrices (PC-Q.5)

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

    • Matrix operation rules (PC-Q.2)
    • Multiply two matrices (PC-Q.6)
    • Simplify matrix expressions (PC-Q.7)
    • Properties of matrices (PC-Q.8)

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

    • Determinant of a matrix (PC-Q.10)
    • Is a matrix invertible? (PC-Q.11)
    • Identify inverse matrices (PC-Q.14)
    • Solve matrix equations using inverses (PC-Q.15)

• Systems: Students use matrices to solve systems of equations.

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

    • Solve a system of equations using augmented matrices (PC-N.8)
    • Solve a system of equations using augmented matrices: word problems (PC-N.9)

ELF Exponential and Logarithmic Functions

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

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

    • Domain and range of exponential functions (PC-H.1)
    • Match exponential functions and graphs (PC-H.2)
    • Domain and range of logarithmic functions (PC-J.1)
    • Graph logarithmic functions (PC-J.2)

• Solve: Students solve problems with exponential and logarithmic functions.

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

    • Convert between exponential and logarithmic form (PC-I.1)
    • Product property of logarithms (PC-I.4)
    • Quotient property of logarithms (PC-I.5)
    • Power property of logarithms (PC-I.6)
    • Properties of logarithms: mixed review (PC-I.7)
    • Solve exponential equations using logarithms (PC-K.2)
    • Solve logarithmic equations with one logarithm (PC-K.3)
    • Solve logarithmic equations with multiple logarithms (PC-K.4)

PRF Polynomial & Rational Functions

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

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

    • Graph a quadratic function (PC-D.3)
    • Match polynomials and graphs using end behavior (PC-F.8)
    • Match polynomials and graphs using zeros (PC-F.9)
    • Match polynomials and graphs (PC-F.10)
    • Domain and range of polynomials (PC-F.11)

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

    • Rational functions: asymptotes and excluded values (PC-G.1)
    • Determine end behavior of rational functions (PC)

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