Academic Standards
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.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
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.
Operations with Radical Expressions
Simplifying Radical Expressions
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.
Points in the Complex Plane
Roots of a Quadratic
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.
Points in the Complex Plane
Roots of a Quadratic
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.
Points in the Complex Plane
Roots of a Quadratic
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.
Solving Linear Systems (Matrices and Special Solutions)
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.S.A: Understand and use sequences and series.
P.A.S.A.1: Demonstrate an understanding of sequences by representing them recursively and explicitly.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
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.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.
Solving Linear Systems (Matrices and Special Solutions)
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).
Solving Linear Systems (Matrices and Special Solutions)
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.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.
Circles
Ellipses
Hyperbolas
Parabolas
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.
Circles
Ellipses
Hyperbolas
Parabolas
P.A.C.A.4: Transform equations of conic sections to convert between general and standard form.
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.
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Polynomial Form
Quadratics in Vertex Form
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
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.
Addition and Subtraction 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.A: Analyze functions using different representations.
P.F.IF.A.1: Determine whether a function is even, odd, or neither.
Cosine Function
Graphs of Polynomial Functions
Sine Function
Tangent Function
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).
Compound Interest
Cosine Function
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Rational Functions
Sine Function
Tangent Function
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).
General Form of a Rational Function
Graphs of Polynomial Functions
Polynomials and Linear Factors
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.
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Polynomial Form
Radical Functions
Rational Functions
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.
Cosine Function
Exponential Functions
Graphs of Polynomial Functions
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Sine Function
Tangent Function
P.F.IF.A.7: Graph rational functions, identifying zeros, asymptotes (including slant), and holes (when suitable factorizations are available) and showing end-behavior.
General Form of a Rational Function
Rational Functions
P.F.IF.A.8: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
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.
Cosine Function
Radians
Sine Function
Tangent Function
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.
Cosine Function
Sine Function
Tangent Function
P.F.TF.A.3: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Cosine Function
Sine Function
Tangent Function
P.F.TF.A.4: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Translating and Scaling Sine and Cosine Functions
P.F.GT.A: Model periodic phenomena with trigonometric functions.
P.F.GT.A.1: Interpret transformations of trigonometric functions.
Translating and Scaling Sine and Cosine Functions
P.F.GT.A.2: Determine the difference made by choice of units for angle measurement when graphing a trigonometric function.
Cosine Function
Sine Function
Tangent Function
P.F.GT.A.3: Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes.
Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions
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.
Sine, Cosine, and Tangent Ratios
P.G.AT.A.4: Calculate the arc length of a circle subtended by a central angle.
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.
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
P.G.TI.A.2: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Sum and Difference Identities for Sine and Cosine
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.
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
P.S.MD.A.2: Determine a regression equation to model a set of bivariate data. Justify why this equation best fits the data.
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
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.
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Correlation last revised: 2/1/2022