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K–12 Standards

Pre-Calculus

Other Arkansas Mathematics Standards sets

Vectors & MatricesVM

  •  

    Vector Quantities: Students recognize, model, and write vector quantities.

    1. 1

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

    2. 2

      Write vector quantities using appropriate symbols indicating magnitude and direction. PC.VM.2

  •  

    Vector Operations: Students perform operations involving vectors. 

    1. 3

      Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. PC.VM.3

    2. 4

      Solve problems involving velocity and other quantities that can be represented by vectors.PC.VM.4

    3. 5

      Add and subtract vectors graphically and algebraically. PC.VM.5

    4. 6

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

  •  

    Matrix Operations: Students represent and perform operations with matrices.

    1. 7

      Use matrices to list, describe, and manipulate data with and without technology. PC.VM.7

    2. 8

      Multiply matrices, understanding that matrix multiplication for square matrices is not commutative. PC.VM.8

    3. 9

      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. PC.VM.9

    4. 10

      Work with 2 × 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area.PC.VM.10

TrigonometryTR

  •  

    Radians: Students understand, explain, and describe radian measure. 

    1. 1

      Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. PC.TR.1

    2. 2

      Convert between radian and degree measure.PC.TR.2

    3. 3

      Explain how the unit circle can be used to model sine, cosine, tangent, secant, cosecant, and cotangent for all real numbers.PC.TR.3

  •  

    Unit Circle: Students use the unit circle to express and find exact values for trigonometric functions.

    1. 4

      Construct special right triangles on the unit circle to find the exact values of sine, cosine, tangent for 𝜋 3 , 𝜋 4 , 𝜋 6 , and 𝜋 2 .PC.TR.4

    2. 5

      Use the unit circle to express the values of sine, cosine, and tangent for 𝜋– 𝑥,𝜋 + 𝑥, and 2𝜋– 𝑥 in terms of their exact values for 𝑥, where 𝑥 is one of these values: 𝜋 3 , 𝜋 4 , 𝜋 6 , and 𝜋 2 .PC.TR.5

  •  

    Identities, Formulas, & Laws: Students develop and apply identities, formulas, and laws using trigonometry.

    1. 6

      Develop the Pythagorean identity, 𝑠𝑖𝑛2 (𝜃) + 𝑐𝑜𝑠2 (𝜃) = 1.PC.TR.6

    2. 7

      Apply the Pythagorean identity to find the remaining trigonometric functions when given 𝑠𝑖𝑛(𝜃), 𝑐𝑜𝑠(𝜃), or 𝑡𝑎𝑛(𝜃) and the quadrant of the angle.PC.TR.7

    3. 8

      Develop addition, subtraction, double, and half-angle formulas for sine, cosine, and tangent and use them to solve problems, including verifying other identities.PC.TR.8

    4. 9

      Develop the formula for the area of a triangle, 𝐴 = ( 1 2 ) 𝑎𝑏 𝑠𝑖𝑛 𝐶 , using trigonometry.PC.TR.9

    5. 10

      Develop and apply the Law of Sines and the Law of Cosines to solve real-world and mathematical problems including finding unknown measurements in right and non-right triangles.PC.TR.10

    6. 11

      Define and use reciprocal functions, cosecant, secant, and cotangent to solve problems.PC.TR.11

  •  

    Solve & Graph: Students explore, solve, and sketch the graphs of periodic trigonometric functions. 

    1. 12

      Explain whether a trigonometric function is even or odd and recognize the periodicity of the graph using the unit circle. PC.TR.12

    2. 13

      Graph trigonometric and inverse trigonometric functions and show period, midline, and amplitude. PC.TR.13

    3. 14

      Select a trigonometric function that models real-world contexts. PC.TR.14

    4. 15

      Explain how restricting the domain of a trigonometric function allows the creation of its inverse.PC.TR.15

    5. 16

      Solve and evaluate the solution of trigonometric equations in real-world contexts; interpret the solution in terms of its context.PC.TR.16

    6. 17

      Recognize that some trigonometric equations have infinitely many solutions and be able to state a general formula to represent the infinite solutions.PC.TR.17

    7. 18

      Calculate and interpret the average rate of change over a specified interval of a trigonometric function represented in a table, graph, or as an equation in the context of real-world and mathematical problems.PC.TR.18

Conic SectionsCS

  •  

    Derive Equations: Students derive equations for conic sections.

    1. 1

      Derive the general form of the equation of a circle using the Distance Formula or Pythagorean Theorem.PC.CS.1

    2. 2

      Derive the equation of a parabola given a focus and directrix. PC.CS.2

    3. 3

      Derive the equations of ellipses and hyperbolas given the foci using the Distance Formula. PC.CS.3

  •  

    Explore Equations: Students identify, analyze, and sketch the graphs of the conic sections and relate their equations and graphs. 

    1. 4

      Find the equations for the asymptotes of a hyperbola. PC.CS.4

    2. 5

      Generate an equivalent form of an equation for a conic section by completing the square to identify key characteristics. PC.CS.5

      1. 1

        Conic sections include: circles, ellipses, parabolas, and hyperbolasPC.CS.5.1

    3. 6

      Identify, graph, write, and analyze equations of each type of conic section using properties and technology when appropriate.PC.CS.6

      1. 1

        Conic sections include: circles, ellipses, parabolas, and hyperbolasPC.CS.6.1

      2. 2

        Properties include: symmetry, intercepts, foci, asymptotes, and eccentricityPC.CS.6.2

  •  

    Systems of Equations & Inequalities: Students solve systems of equations and inequalities involving conic sections. 

    1. 7.

      Solve systems of equations and inequalities involving conics and other types of equations, with and without technology.PC.CS.7

      1. 1

        Equations include: conic-conic and conic-linearPC.CS.7.1

FunctionsFN

  •  

    Solve Problems: Students derive and apply functions. 

    1. 1

      Understand that sequences are functions, sometimes defined recursively, whose domains are a subset of the integers.PC.FN.1

    2. 2

      Derive the formula for the sum of a finite geometric series; apply the formula to solve conceptual problems.PC.FN.2

    3. 3

      Apply the Binomial Theorem for the expansion of (𝑎 + 𝑏) 𝑛 in powers of 𝑎 and 𝑏 for a positive integer 𝑛, where 𝑎 and 𝑏 are any number.PC.FN.3

    4. 4

      Build functions to model real-world contexts using algebraic operations on functions and composition, with and without appropriate technology. PC.FN.4

  •  

    Explore Graphing: Students graph and interpret functions. 

    1. 5

      Graph power and polynomial functions, identify zeros (when suitable factorizations are available), and show end behavior.PC.FN.5

    2. 6

      Graph rational functions, identify zeros, holes and asymptotes (when suitable factorizations are available), and show end behavior. PC.FN.6

      1. 1

        Asymptotes include: horizontal, vertical, and obliquePC.FN.6.1

    3. 7

      Graph exponential and logarithmic functions; show intercepts and end behavior. PC.FN.7

    4. 8

      Compare key features of two functions each represented in a different way.PC.FN.8

      1. 1

        Representations include: algebraic, graphic, numeric in tables, and verbal descriptionsPC.FN.8.1

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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