Gizmos for Arizona - Mathematics: Precalculus (High Academic Standards for Students adopted 2018)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

PC.RFR: Reasoning with Functions and Relations

PC.RFR.AF: Analyze functions

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.5: Sketch the graph of all six trigonometric functions, identifying key features.

PC.RFR.AF.b: Calculate, interpret, and use average rate of change.

PC.RFR.AF.c: Use multiple representations of function models appropriately.

PC.RFR.AF.d: Work with different families of functions beyond linear and quadratic functions including but not limited to exponential, logarithmic, rational, polynomial, logistic, radical, and piecewise-defined functions.

PC.RFR.AF.e: Graph rational functions including those whose graphs contain horizontal asymptotes, vertical asymptotes, oblique asymptotes, and/or holes.

PC.RFR.AF.f: Make sense of radian measure.

PC.RFR.AF.g: Use the unit circle as a tool to graph the trig functions in radians and degrees.

PC.RFR.AF.h: Develop fluency with the unit circle. Include opportunities beyond the special angles, for example, explain why sin(1.1) > sin(0.3) in radians.

PC.RFR.AF.i: Graph sine, cosine, tangent functions in radians and degrees and analyze/explain the characteristics of each.

PC.RFR.BF: Building Functions

PC.RFR.BF.1: Model relationships between quantities that require adding, subtracting, multiplying, and/or dividing 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.BF.a: Model real-world situations with the sum, difference, product, or quotient of other function models.

PC.RFR.BF.b: Describe relationships of quantities in functions and within a composition of those functions.

PC.RFR.BF.c: Find an inverse algebraically, for example given y = f(x) algebraically find x = f⁻¹ (y). Work with exponential and logarithmic functions, and quadratic and square root functions at a minimum.

PC.RFR.IC: Interpreting Conics

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.IC.a: Explore conics as loci of points satisfying stipulated conditions.

PC.RFR.IC.b: Explore conic sections with technology and manipulatives.

PC.RFR.IC.c: Connect the geometric and algebraic relationships of conics.

PC.RFR.IC.d: Use the method of completing the square to put the equation of the conic section into standard form.

PC.RFR.ISS: Interpreting Sequences and Series

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.a: Become fluent in working with arithmetic and geometric sequences and series.

PC.RFR.ISS.b: Explore several types of sequences, including but not limited to Fibonacci, telescoping, harmonic, alternating.

PC.RT: Reasoning with Trigonometry

PC.RT.ETT: Extending Triangle Trigonometry

PC.RFR.ETT.1: Model real-world situations involving trigonometry.

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.RT.ETT.a: Go beyond using the mnemonic SohCahToa by interpreting the meaning of the trigonometric ratios as multiplicative comparisons of the appropriate sides of a right triangle. Situations should involve unknown sides and/or angles, as well as periodic functions and their inverses.

PC.RT.RTS: Reasoning with Trigonometric Structure

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.a: Recognize that a single identity can be manipulated into another identity.

PC.RT.RTS.b: Apply the Pythagorean, sum, difference, double angle, and half angle formulas for sine and cosine to reveal and explain properties.

PC.RT.EPE: Exploring Polar Equations

PC.RT.EPE.a: Convert points between polar and rectangular forms.

PC.RT.EPE.b: Determine equivalent polar representations for a given point.

PC.RV: Reasoning with Vectors

PC.RV.EV: Exploring 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.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.EV.a: Distinguish vector quantities from scalar quantities. For example, distinguish the difference between velocity and speed.

PC.RV.EV.b: Make sense of operations with vectors.

PC.RM: Reasoning with Matrices

PC.RM.UM: Using 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.

PC.RM.UM.b: Explain that the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

PC.RM.UM.c: Explore the roles of the zero matrix, identity matrix, inverse matrix, and the determinant of a matrix.

PC.RM.UM.d: Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

PC.RM.UM.e: Use 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.

PC.RM.UM.f: Use matrices as a tool. Including but not limited to: producing new vectors from old vectors, creating transformations in the plane, calculating the area of geometric figures.

PC.RM.UM.g: Explore matrices and solve problems with and without technology, as appropriate.

Correlation last revised: 4/13/2026

Arizona - Mathematics: Precalculus

High Academic Standards for Students | Adopted: 2018

PC.RFR: Reasoning with Functions and Relations

PC.RT: Reasoning with Trigonometry

PC.RV: Reasoning with Vectors

PC.RM: Reasoning with Matrices