### P.N: Number and Quantity

#### P.N.NE: Number Expressions

P.N.NE.A: Represent, interpret, compare, and simplify number expressions.

P.N.NE.A.1: Use the laws of exponents and logarithms to expand or collect terms in expressions; simplify expressions or modify them in order to analyze them or compare them.

P.N.NE.A.2: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

P.N.NE.A.3: Classify real numbers and order real numbers that include transcendental expressions, including roots and fractions of ? and e.

P.N.NE.A.4: Simplify complex radical and rational expressions; discuss and display understanding that rational numbers are dense in the real numbers and the integers are not.

#### P.N.CN: Complex Numbers

P.N.CN.A: Perform complex number arithmetic and understand the representation on the complex plane.

P.N.CN.A.1: Perform arithmetic operations with complex numbers expressing answers in the form a + bi.

P.N.CN.A.2: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

P.N.CN.A.3: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

P.N.CN.A.4: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

#### P.N.VM: Vector and Matrix Quantities

P.N.VM.A: Represent and model with vector quantities.

P.N.VM.A.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

P.N.VM.B: Understand the graphic representation of vectors and vector arithmetic.

P.N.VM.B.4.a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

P.N.VM.B.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

P.N.VM.B.4.c: Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

P.N.VM.B.6: Calculate and interpret the dot product of two vectors.

P.N.VM.C: Perform operations on matrices and use matrices in applications.

P.N.VM.C.9: Add, subtract, and multiply matrices of appropriate dimensions.

P.N.VM.C.13: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

### P.F: Functions

#### P.F.BF: Building Functions

P.F.BF.A: Build new functions from existing functions.

P.F.BF.A.1: Understand how the algebraic properties of an equation transform the geometric properties of its graph.

P.F.BF.A.2: Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.

P.F.BF.A.5: Find inverse functions (including exponential, logarithmic, and trigonometric).

P.F.BF.A.5.c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

P.F.BF.A.5.d: Recognize a function is invertible if and only if it is one-to-one. Produce an invertible function from a non-invertible function by restricting the domain.

#### P.F.IF: Interpreting Functions

P.F.IF.A: Analyze functions using different representations.

P.F.IF.A.2: Analyze qualities of exponential, polynomial, logarithmic, trigonometric, and rational functions and solve real-world problems that can be modeled with these functions (by hand and with appropriate technology).

P.F.IF.A.4: Identify the real zeros of a function and explain the relationship between the real zeros and the x-intercepts of the graph of a function (exponential, polynomial, logarithmic, trigonometric, and rational).

P.F.IF.A.5: Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c.

P.F.IF.A.8: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

#### P.F.TF: Trigonometric Functions

P.F.TF.A: Extend the domain of trigonometric functions using the unit circle.

P.F.TF.A.2: Use special triangles to determine geometrically the values of sine, cosine, tangent for ?/3, ?/4 and ?/6, and use the unit circle to express the values of sine, cosine, and tangent for ?–x, ?+x, and 2?–x in terms of their values for x, where x is any real number.

P.F.TF.A.3: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

P.F.TF.A.4: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

#### P.F.GT: Graphing Trigonometric Functions

P.F.GT.A: Model periodic phenomena with trigonometric functions.

P.F.GT.A.1: Interpret transformations of trigonometric functions.

P.F.GT.A.2: Determine the difference made by choice of units for angle measurement when graphing a trigonometric function.

P.F.GT.A.3: Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes.

### P.G: Geometry

#### P.G.AT: Applied Trigonometry

P.G.AT.A: Use trigonometry to solve problems.

P.G.AT.A.1: Use the definitions of the six trigonometric ratios as ratios of sides in a right triangle to solve problems about lengths of sides and measures of angles.

#### P.G.TI: Trigonometric Identities

P.G.TI.A: Apply trigonometric identities to rewrite expressions and solve equations.

P.G.TI.A.1: Apply trigonometric identities to verify identities and solve equations. Identities include: Pythagorean, reciprocal, quotient, sum/difference, double-angle, and half-angle.

P.G.TI.A.2: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

### P.S: Statistics and Probability

#### P.S.MD: Model with Data

P.S.MD.A: Model data using regressions equations.

P.S.MD.A.1: Create scatter plots, analyze patterns, and describe relationships for bivariate data (linear, polynomial, trigonometric, or exponential) to model real-world phenomena and to make predictions.

P.S.MD.A.2: Determine a regression equation to model a set of bivariate data. Justify why this equation best fits the data.

P.S.MD.A.3: Use a regression equation, modeling bivariate data, to make predictions. Identify possible considerations regarding the accuracy of predictions when interpolating or extrapolating.

Correlation last revised: 11/21/2018

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