Common Planner
K–12 Standards

Precalculus

Other North Carolina Mathematics sets

Number and Quantity N

  • 1

    Apply properties of complex numbers and the complex number system. PC.N.1.

    1. 1

      Execute the sum and difference algorithms to combine complex numbers.PC.N.1.1

    2. 2

       Execute the multiplication algorithm with complex numbers.PC.N.1.2

  • 2

     Apply properties and operations with matrices. PC.N.2

    1. 1

       Execute the sum and difference algorithms to combine matrices of appropriate dimensions. PC.N.2.1

    2. 2

       Execute associative and distributive properties to matrices. PC.N.2.2

    3. 3

       Execute commutative property to add matrices. PC.N.2.3 

    4. 4

       Execute properties of matrices to multiply a matrix by a scalar. PC.N.2.4

    5. 5

       Execute the multiplication algorithm with matrices. PC.N.2.5

  • 3

     Understand properties and operations with vectors. PC.N.3

    1. 1

       Represent a vector indicating magnitude and direction. PC.N.3.1

    2. 2

       Execute sum and difference algorithms to combine vectors. PC.N.3.2

Algebra  A

  • 1

     Apply properties of solving inequalities that include rational and polynomial expressions in one variable. PC.A.1

    1. 1

      Implement algebraic (sign analysis) methods to solve rational and polynomial inequalities.  PC.A.1.1

    2. 2

      Implement graphical methods to solve rational and polynomial inequalities. PC.A.1.2

  • 2

     Apply properties of solving equations involving exponential, logarithmic, and trigonometric functions. PC.A.2

    1. 1

      Use properties of logarithms to rewrite expressions. PC.A.2.1 

    2. 2

      Implement properties of exponentials and logarithms to solve equations. PC.A.2.2 

    3. 3

      Implement properties of trigonometric functions to solve equations includingPC.A.2.3 

      1. a

        inverse trigonometric functionsPC.A.2.3a

      2. b

        double angle formulasPC.A.2.3b

      3. c

        Pythagorean identities. PC.A.2.3c

    4. 4

      Implement algebraic techniques to rewrite parametric equations in cartesian form by eliminating the parameter.PC.A.2.4

Functions 

  • 1

    Understand key features of sine, cosine, tangent, cotangent, secant and cosecant functions. PC.F.1

    1. 1

      Interpret algebraic and graphical representations to determine key features of transformed sine and cosine functions. Key features include: amplitude, domain, midline, phase shift, frequency, period, intervals where the function is increasing, decreasing, positive or negative, relative maximums and minimums.   PC.F.1.1 

    2. 2

      Interpret algebraic and graphical representations to determine key features of tangent, cotangent, secant, and cosecant. Key features include: domain, frequency, period, intervals where the function is increasing, decreasing, positive or negative, relative maximums and minimums, and asymptotes.PC.F.1.2 

    3. 3

      Integrate information to build trigonometric functions with specified amplitude, frequency, period, phase shift, or midline with or without context.PC.F.1.3 

    4. 4

      Implement graphical and algebraic methods to solve trigonometric equations and inequalities in context with support from technology.PC.F.1.4 

  • 2

    Apply properties of a unit circle with center (0,0) to determine the values of sine, cosine, tangent, cotangent, secant, and cosecant. PC.F.2 

    1. 1

      Use a unit circle to find values of sine, cosine, and tangent for angles in terms of reference angles. PC.F.2.1 

    2. 2

      Explain the relationship between the symmetry of a unit circle and the periodicity of trigonometric functions.PC.F.2.2 

  • 3

    Apply properties of trigonometry to solve problems involving all types of triangles. PC.F.3 

    1. 1

      Implement a strategy to solve equations using inverse trigonometric functions.PC.F.3.1 

    2. 2

      Implement the Law of Sines and the Law of Cosines to solve problems.PC.F.3.2

    3. 3

      Implement the Pythagorean identity to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. PC.F.3.3 

  • 4

    Understand the relationship of algebraic and graphical representations of exponential, logarithmic, rational, power functions, and conic sections to their key features. PC.F.4 

    1. 1

      Interpret algebraic and graphical representations to determine key features of exponential functions. Key features include: domain, range, intercepts, intervals where the function is increasing, decreasing, positive or negative, concavity, end behavior, limits, and asymptotes. PC.F.4.1

    2. 2

      Integrate information to build exponential functions to model phenomena involving growth or decay. PC.F.4.2 

    3. 3

      Interpret algebraic and graphical representations to determine key features of logarithmic functions. Key features include: domain, range, intercepts, intervals where the function is increasing, decreasing, positive or negative, concavity, end behavior, continuity, limits, and asymptotes. PC.F.4.3 

    4. 4

      Implement graphical and algebraic methods to solve exponential and logarithmic equations in context with support from technology. PC.F.4.4 

    5. 5

      PC.F.4.5 Interpret algebraic and graphical representations to determine key features of rational functions. Key features include: domain, range, intercepts, intervals where the function is increasing, decreasing, positive or negative, concavity, end behavior, continuity, limits, and asymptotes. PC.F.4.5 

    6. 6

      Implement graphical and algebraic methods to solve optimization problems given rational and polynomial functions in context with support from technology.PC.F.4.6 

    7. 7

      Construct graphs of transformations of power, exponential, and logarithmic functions showing key features.PC.F.4.7 

    8. 8

      Identify the conic section (ellipse, hyperbola, parabola) from its algebraic representation in standard form.PC.F.4.8 

    9. 9

      Interpret algebraic and graphical representations to determine key features of conic sections (ellipse: center, length of the major and minor axes; hyperbola: vertices, transverse axis; parabola: vertex, axis of symmetry).PC.F.4.9 

  • 5

    Apply properties of function composition to build new functions from existing functions.PC.F.5 

    1. 1

      Implement algebraic procedures to compose functions. PC.F.5.1 

    2. 2

      Execute a procedure to determine the value of a composite function at a given value using algebraic, graphical, and tabular representations.PC.F.5.2 

    3. 3

      Implement algebraic methods to find the domain of a composite function. PC.F.5.3 

    4. 4

      Organize information to build models involving function composition. PC.F.5.4 

    5. 5

      Deconstruct a composite function into two functions. PC.F.5.5

    6. 6

      Implement algebraic and graphical methods to find an inverse function of an existing function, restricting domains if necessary.PC.F.5.6 

    7. 7

      Use composition to determine if one function is the inverse of another function. PC.F.5.7 

  • 6

    Apply mathematical reasoning to build recursive functions to model and solve problems.PC.F.6 

    1. 1

      Use algebraic representations to build recursive functions. PC.F.6.1 

    2. 2

      Construct a recursive function for a sequence represented numerically. PC.F.6.2 

  • 7

    Apply mathematical reasoning to build parametric functions and solve problems.PC.F.7 

    1. 1

      Implement algebraic methods to write parametric equations in context.PC.F.7.1 

    2. 2

      Implement technology to solve contextual problems involving parametric equations.PC.F.7.2 

Frequently asked questions

What grade levels do these standards cover?
Grade 10, Grade 11, and Grade 12
Where can I read the official document?
Public Schools of North Carolina

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