Gizmos for Tennessee - Mathematics: Precalculus (Academic Standards adopted 2021)

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

1: : 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: : Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

P.N.CN.A.2: : Perform arithmetic operations with complex numbers expressing answers in the form a + bi.

P.N.CN.A.3: : Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

P.N.CN.A.4: : 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.5: : Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation (for example, (–1 + 3i) 3 = 8 because (–1 + 3i) has modulus 2 and argument 120°).

P.N.CN.A.6: : Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

P.N.CN.B: : Use complex numbers in polynomial identities and equations.

P.N.CN.B.7: : Extend polynomial identities to the complex numbers (for example, rewrite x² + 4 as (x + 2i)(x – 2i).

P.N.CN.B.8: : Solve quadratic equations with real coefficients that have complex solutions.

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.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: : 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.10: : Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

2: : 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.4: : 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: : Know and write the equation of a circle of given center and radius using the Pythagorean Theorem.

P.A.C.A.3: : 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.4: : 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.5: : Transform equations of conic sections to convert between general and standard form.

3: : 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 (for example, given a function, describe the transformation of the graph resulting from the manipulation of the algebraic properties of the equation such as translations, stretches, reflections, and changes in periodicity and amplitude).

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.6: : Explain why the graph of a function and its inverse are reflections of one another over the line y = x.

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.3: : 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.4: : Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c.

P.F.IF.A.5: : 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.

Correlation last revised: 4/17/2023

Tennessee - Mathematics: Precalculus

Academic Standards | Adopted: 2021

1: : Number and Quantity

2: : Algebra

3: : Functions