Gizmos for Tennessee - Mathematics: Precalculus (Academic Standards adopted 2016)

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

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.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: : The Complex Number System

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.A.2: : Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

P.N.VM.A.3: : Solve problems involving velocity and other quantities that can be represented by vectors.

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

P.N.VM.B.4: : Add and subtract vectors.

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.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.8: : Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

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

P.N.VM.C.11: : Understand that 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. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

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.A: : Algebra

P.A.S: : Sequences and Series

P.A.S.A: : Understand and use sequences and series.

P.A.S.A.1: : Demonstrate an understanding of sequences by representing them recursively and explicitly.

P.A.S.A.5: : Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

P.A.REI: : Reasoning with Equations and Inequalities

P.A.REI.A: : Solve systems of equations and nonlinear inequalities.

P.A.REI.A.1: : Represent a system of linear equations as a single matrix equation in a vector variable.

P.A.REI.A.2: : Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

P.A.REI.A.3: : Solve nonlinear inequalities (quadratic, trigonometric, conic, exponential, logarithmic, and rational) by graphing (solutions in interval notation if one-variable), by hand and with appropriate technology.

P.A.C: : Conic Sections

P.A.C.A: : Understand the properties of conic sections and model real-world phenomena.

P.A.C.A.1: : Display all of the conic sections as portions of a cone.

P.A.C.A.2: : Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

P.A.C.A.3: : From an equation in standard form, graph the appropriate conic section: ellipses, hyperbolas, circles, and parabolas. Demonstrate an understanding of the relationship between their standard algebraic form and the graphical characteristics.

P.A.C.A.4: : Transform equations of conic sections to convert between general and standard form.

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.a: : Calculate the inverse of a function, f(x), with respect to each of the functional operations; in other words, the additive inverse, -f(x), the multiplicative inverse, 1/f(x), and the inverse with respect to composition, f^-1(x). Understand the algebraic and graphical implications of each type.

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.IF: : Interpreting Functions

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

P.F.IF.A.1: : Determine whether a function is even, odd, or neither.

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.6: : Visually locate critical points on the graphs of functions and determine if each critical point is a minimum, a maximum, or point of inflection. Describe intervals where the function is increasing or decreasing and where different types of concavity occur.

P.F.IF.A.7: : Graph rational functions, identifying zeros, asymptotes (including slant), and holes (when suitable factorizations are available) and showing end-behavior.

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.1: : Convert from radians to degrees and from degrees to radians.

P.F.TF.A.2: : Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - 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.AT.A.4: : Calculate the arc length of a circle subtended by a central angle.

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: 2/1/2022

Tennessee - Mathematics: Precalculus

Academic Standards | Adopted: 2016

P.N: : Number and Quantity

P.A: : Algebra

P.F: : Functions

P.G: : Geometry

P.S: : Statistics and Probability