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K–12 Standards

Advanced Topics and Modeling in Mathematics

Other Arkansas Mathematics Standards sets

FunctionsFN

  •  

    Interpreting Functions: Students extend previous knowledge of functions beyond linear and quadratic. 

    1. 1

      Interpret key features of graphs and tables in terms of two quantities, which extend to function families beyond linear and quadratic, that model a relationship between the quantities in a contextual application and/or student-generated data. AT.FN.1

    2. 2

      Interpret the parameters of functions beyond the level of linear and quadratic in terms of a given context. AT.FN.2

  •  

    Graphing Functions: Students analyze functions using graphing. 

    1. 3

      Graph functions expressed symbolically and show key features of the graph using technology.AT.FN.3

      1. 1

        Functions include exponential, logarithmic, and trigonometric functions.AT.FN.3.1

    2. 4

      Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions, with or without the appropriate technology. Contextual situations may include:AT.FN.4

      1. 1

        Cube root (e.g., minimizing packaging on cubic boxes, geostationary satellites)AT.FN.4.1

      2. 2

        Piecewise (e.g., postage stamp function, teacher salary, GPS for distance)AT.FN.4.2

      3. 3

        Square root (distance via Pythagorean Theorem) AT.FN.4.3

    3. 5

      Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior, with or without the appropriate technology.AT.FN.5

    4. 6

      Graph rational functions, identifying zeros and asymptotes (vertical, horizontal, and/or oblique) when suitable factorizations are available and showing end behavior, with or without the appropriate technology.AT.FN.6

    5. 7

      Graph exponential and logarithmic functions, showing intercepts and end behavior.AT.FN.7

    6. 8

      Graph trigonometric functions showing period, midline, and amplitude. AT.FN.8

Vectors & Matrices VM

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    Vectors: Students represent and model vector quantities and perform operations on vectors. 

    1. 1

      Recognize that vector quantities have both magnitude and direction and can be represented by directed line segments.AT.VM.1

    2. 2

      Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. AT.VM.2

    3. 3

      Solve problems involving velocity and other quantities that can be represented by vectors.AT.VM.3

    4. 4

      Add and subtract vectors graphically and algebraically.AT.VM.4

    5. 5

      Given two vectors in magnitude and direction form, determine the magnitude and direction of the sum. AT.VM.5

    6. 6

      Multiply a vector by a scalar graphically and analytically; reverse their direction when possible.AT.VM.6

    7. 7

      Compute the magnitude and direction of a vector by multiplying a vector by a scalar. AT.VM.7

  •  

    Matrices: Students perform operations on matrices and use matrices in applications.

    1. 8

      Use matrices to represent, list, describe and manipulate data with technology.AT.VM.8

    2. 9

      Multiply a matrix by a scalar.AT.VM.9

    3. 10

      Add and subtract matrices.AT.VM.10

    4. 11

      Multiply matrices, understanding that matrix multiplication for square matrices is not commutative.AT.VM.11

    5. 12

      Represent a system of linear equations as a single matrix equation in a vector variable.AT.VM.12

    6. 13

      Find and use the inverse of a matrix to solve systems of linear equations; solve 3 × 3 or greater systems of equations with technology. AT.VM.13

Statistics & Probability 

  •  

    Expected Value: Students calculate and use expected values to solve problems.

    1. 1

      Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.AT.SP.1

    2. 2

      Calculate the expected value for a random variable and describe the expected value as the mean of the probability distribution in context.AT.SP.2

    3. 3

      Create a probability distribution using theoretical probabilities; calculate the expected value.AT.SP.3

    4. 4

      Create a probability distribution using experimental or observational data; calculate the expected value. AT.SP.4

  •  

    Decisions Using Probability: Students use probability to evaluate outcomes of decisions. 

    1. 5

      Analyze the costs and benefits of possible outcomes of making a decision by assigning probabilities to particular payoff values; calculate expected values. AT.SP.5

    2. 7

      Analyze decisions and strategies using probability concepts.AT.SP.7

Frequently asked questions

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

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