Arizona flagArizona: Precalculus Math Standards

46 standards · 4 domains

REASONING WITH FUNCTIONS AND RELATIONS (RFR)

  • PC.RFR.AF.1 Interpret parameters of a function defined by an expression in the context of the situation.
  • PC.RFR.AF.2 Sketch the graph of a function that models a relationship between two quantities, identifying key features.
  • PC.RFR.AF.3 Interpret key features of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.
  • PC.RFR.AF.4 Use limits to describe long-range behavior, asymptotic behavior, and points of discontinuity.
  • PC.RFR.AF.5 Sketch the graph of all six trigonometric functions, identifying key features.
  • PC.RFR.BF.1 Model relationships between quantities that require adding, subtracting, multiplying, and/or dividing functions
  • PC.RFR.BF.2 Model relationships through composition and attend to the restrictions of the domain.
  • PC.RFR.BF.3 Rewrite a function as a composition of functions.
  • PC.RFR.BF.4 Determine if a function has an inverse. If so, find the inverse. If not, define a restriction on the domain that meets the requirement for invertibility and find the inverse on the restricted domain.
  • PC.RFR.BF.5 Interpret the meanings of quantities involving functions and their inverses.
  • PC.RFR.BF.6 Verify by analytical methods that one function is the inverse of another.
  • PC.RFR.ETT.1 Model real-world situations involving trigonometry.
  • PC.RFR.ETT.2 Apply the Law of Sines and Law of Cosines to solve problems.
  • PC.RFR.ETT.3 Use trigonometry to find the area of triangles.
  • PC.RFR.ETT.4 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and 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 values for x, where x is any real number.
  • PC.RFR.ETT.5 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • PC.RFR.ETT.6 Use inverse functions to solve trigonometric equations utilizing real world context; evaluate the solution and interpret them in terms of context.
  • PC.RFR.IC.1 Model real-world situations which involve conic sections.
  • PC.RFR.IC.2 Identify key features of conic sections (foci, directrix, radii, axes, asymptotes, center) graphically and algebraically.
  • PC.RFR.IC.3 Sketch a graph of a conic section using its key features.
  • PC.RFR.IC.4 Use the key features of a conic section to write its equation.
  • PC.RFR.IC.5 Given a quadratic equation of the form ax2+ by2 + cx + dy + e = 0, determine if the equation is a circle, ellipse, parabola, or hyperbola.
  • PC.RFR.ISS.1 Model real-world situations involving sequences or series using recursive and/or explicit definitions.
  • PC.RFR.ISS.2 Use covariational reasoning to describe sequences and series.
  • PC.RFR.ISS.3 Represent finite or infinite series using sigma notation.
  • PC.RFR.ISS.4 Find the sums of finite or infinite series, if they exist.

REASONING WITH MATRICES

  • PC.RM.UM.1 Use matrices to represent and manipulate data.
  • PC.RM.UM.2 Use matrix operations to solve problems. Add, subtract, and multiply matrices of appropriate dimensions. Multiply matrices by scalars to produce new matrices.
  • PC.RM.UM.3 Find the inverse and determinant of a matrix.
  • PC.RM.UM.4 Use matrices to solve systems of linear equations.

REASONING WITH TRIGONOMETRY

  • PC.RT.EPE.1 Graph polar equations.
  • PC.RT.EPE.2 Analyze and interpret the graphs of polar equations.
  • PC.RT.EPE.3 Use polar equations to solve problems.
  • PC.RT.ETT Extending Triangle Trigonometry
  • PC.RT.RTS.1 Use the structure of a trigonometric expression to identify ways to rewrite it.
  • PC.RT.RTS.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • PC.RT.RTS.3 Solve trigonometric equations.

REASONING WITH VECTORS

  • PC.RV.EV.1 Recognize vector quantities as having both magnitude and direction.
  • PC.RV.EV.2 Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.
  • PC.RV.EV.3 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
  • PC.RV.EV.4 Solve problems involving velocity and other quantities that can be represented by vectors.
  • PC.RV.EV.5 Add and subtract vectors, and multiply a vector by a scalar.
  • PC.RV.MP.1 Model real-world contexts with parametric equations.
  • PC.RV.MP.2 Use parametric equations to solve problems.
  • PC.RV.MP.3 Graph parametric equations and identify orientation.
  • PC.RV.MP.4 Analyze and interpret the graphs of parametric equations.