N-CN: The Complex Number System

N-CN.1: Know there is a complex number ?? such that ??² = ?1, and every complex number has the form ?? + ???? with ?? and ?? real.

Points in the Complex Plane

N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.

Roots of a Quadratic

A-SSE: Seeing Structure in Expressions

A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

A-SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Exponential Growth and Decay
Simple and Compound Interest
Unit Conversions

A-SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Exponential Growth and Decay
Simple and Compound Interest
Translating and Scaling Functions
Using Algebraic Expressions

A-SSE.2: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A-APR: Arithmetic with Polynomials and Rational Expressions

A-APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Addition of Polynomials

A-APR.2: Know and apply the Remainder Theorem: For a polynomial ??(??) and a number ??, the remainder on division by ?? ? ?? is ??(??), so ??(??) = 0 if and only if (?? ? ??) is a factor of ??(??).

Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors

A-APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Polynomials and Linear Factors
Quadratics in Factored Form

A-APR.5: Know and apply the Binomial Theorem for the expansion of (?? + ??)? in powers of ?? and y for a positive integer ??, where ?? and ?? are any numbers, with coefficients determined for example by Pascal?s Triangle.

Binomial Probabilities

A-CED: Creating Equations

A-CED.1: Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Exploring Linear Inequalities in One Variable
Exponential Growth and Decay
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Simple and Compound Interest
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

2D Collisions
Air Track
Determining a Spring Constant
Golf Range
Points, Lines, and Equations
Simple and Compound Interest
Slope-Intercept Form of a Line

A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

Linear Programming

A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

A-REI: Reasoning with Equations and Inequalities

A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Radical Functions

A-REI.3.1: Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

Absolute Value Equations and Inequalities
Compound Inequalities

A-REI.11: Explain why the ??-coordinates of the points where the graphs of the equations ?? = ??(??) and ?? = ??(??) intersect are the solutions of the equation ??(??) = ??(??); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where ??(??) and/or ??(??) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Cat and Mouse (Modeling with Linear Systems)
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

F-IF: Interpreting Functions

F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions

F-IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions

F-IF.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic

F-IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Exponential Functions
Exponential Growth and Decay
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

F-BF: Building Functions

F-BF.3: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Exponential Functions
Logarithmic Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

F-TF: Trigonometric Functions

F-TF.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function
Sine Function
Tangent Function

F-TF.2.1: Graph all 6 basic trigonometric functions.

Translating and Scaling Functions

F-TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Sound Beats and Sine Waves

G-GPE: Expressing Geometric Properties with Equations

G-GPE.3.1: Given a quadratic equation of the form ax² + by2 + cx + dy + e = 0, use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola, and graph the equation.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas

S-IC: Making Inferences and Justifying Conclusions

S-IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Estimating Population Size
Polling: City
Polling: Neighborhood

S-IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Real-Time Histogram
Sight vs. Sound Reactions