North Carolina flagNorth Carolina: Precalculus Math Standards

44 standards · 3 domains

ALGEBRA

  • PC.A.1.1 Implement algebraic (sign analysis) methods to solve rational and polynomial inequalities.
  • PC.A.1.2 Implement graphical methods to solve rational and polynomial inequalities.
  • PC.A.2.1 Use properties of logarithms to rewrite expressions.
  • PC.A.2.2 Implement properties of exponentials and logarithms to solve equations.
  • PC.A.2.3 Implement properties of trigonometric functions to solve equations including • inverse trigonometric functions, • double angle formulas, and • Pythagorean identities.
  • PC.A.2.4 Implement algebraic techniques to rewrite parametric equations in cartesian form by eliminating the parameter.

FUNCTIONS

  • PC.F.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.1.2 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.1.3 Integrate information to build trigonometric functions with specified amplitude, frequency, period, phase shift, or midline with or without context.
  • PC.F.1.4 Implement graphical and algebraic methods to solve trigonometric equations and inequalities in context with support from technology.
  • PC.F.2.1 Use a unit circle to find values of sine, cosine, and tangent for angles in terms of reference angles.
  • PC.F.2.2 Explain the relationship between the symmetry of a unit circle and the periodicity of trigonometric functions.
  • PC.F.3.1 Implement a strategy to solve equations using inverse trigonometric functions.
  • PC.F.3.2 Implement the Law of Sines and the Law of Cosines to solve problems.
  • PC.F.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.4.1 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.4.2 Integrate information to build exponential functions to model phenomena involving growth or decay.
  • PC.F.4.3 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.4.4 Implement graphical and algebraic methods to solve exponential and logarithmic equations in context with support from technology.
  • 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.4.6 Implement graphical and algebraic methods to solve optimization problems given rational and polynomial functions in context with support from technology.
  • PC.F.4.7 Construct graphs of transformations of power, exponential, and logarithmic functions showing key features.
  • PC.F.4.8 Identify the conic section (ellipse, hyperbola, parabola) from its algebraic representation in standard form.
  • PC.F.4.9 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.5.1 Implement algebraic procedures to compose functions.
  • PC.F.5.2 Execute a procedure to determine the value of a composite function at a given value using algebraic, graphical, and tabular representations.
  • PC.F.5.3 Implement algebraic methods to find the domain of a composite function.
  • PC.F.5.4 Organize information to build models involving function composition.
  • PC.F.5.5 Deconstruct a composite function into two functions.
  • PC.F.5.6 Implement algebraic and graphical methods to find an inverse function of an existing function, restricting domains if necessary.
  • PC.F.5.7 Use composition to determine if one function is the inverse of another function.
  • PC.F.6.1 Use algebraic representations to build recursive functions.
  • PC.F.6.2 Construct a recursive function for a sequence represented numerically.
  • PC.F.7.1 Implement algebraic methods to write parametric equations in context.
  • PC.F.7.2 Implement technology to solve contextual problems involving parametric equations.

NUMBER AND QUANTITY

  • PC.N.1.1 Execute the sum and difference algorithms to combine complex numbers.
  • PC.N.1.2 Execute the multiplication algorithm with complex numbers.
  • PC.N.2.1 Execute the sum and difference algorithms to combine matrices of appropriate dimensions.
  • PC.N.2.2 Execute associative and distributive properties to matrices.
  • PC.N.2.3 Execute commutative property to add matrices.
  • PC.N.2.4 Execute properties of matrices to multiply a matrix by a scalar.
  • PC.N.2.5 Execute the multiplication algorithm with matrices.
  • PC.N.3.1 Represent a vector indicating magnitude and direction.
  • PC.N.3.2 Execute sum and difference algorithms to combine vectors.