A2.N: Number & Operations

A2.N.1: Extend the understanding of number and operations to include complex numbers, matrices, radical expressions, and expressions written with rational exponents.

A2.N.1.2: Simplify, add, subtract, multiply, and divide complex numbers.

Points in the Complex Plane

A2.N.1.3: Use matrices to organize and represent data. Identify the order (dimension) of a matrix, add and subtract matrices of appropriate dimensions, and multiply a matrix by a scalar to create a new matrix to solve problems.

Translations

A2.A: Algebraic Reasoning & Algebra

A2.A.1: Represent and solve mathematical and real-world problems using nonlinear equations and systems of linear equations; interpret the solutions in the original context.

A2.A.1.1: Represent real-world or mathematical problems using quadratic equations and solve using various methods (including graphing calculator or other appropriate technology), factoring, completing the square, and the quadratic formula. Find non-real roots when they exist.

Addition and Subtraction of Functions
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Roots of a Quadratic
Translating and Scaling Functions

A2.A.1.2: Represent real-world or mathematical problems using exponential equations, such as compound interest, depreciation, and population growth, and solve these equations graphically (including graphing calculator or other appropriate technology) or algebraically.

Exponential Functions

A2.A.1.4: Solve polynomial equations with real roots using various methods and tools that may include factoring, polynomial division, synthetic division, graphing calculators or other appropriate technology.

Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors

A2.A.1.5: Solve square root equations with one variable and check for extraneous solutions.

Operations with Radical Expressions

A2.A.1.8: Represent real-world or mathematical problems using systems of linear equations with a maximum of three variables and solve using various methods that may include substitution, elimination, and graphing (may include graphing calculators or other appropriate technology).

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

A2.A.2: Represent and analyze mathematical situations and structures using algebraic symbols using various strategies to write equivalent forms of expressions.

A2.A.2.1: Factor polynomial expressions including but not limited to trinomials, differences of squares, sum and difference of cubes, and factoring by grouping using a variety of tools and strategies.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A2.A.2.2: Add, subtract, multiply, divide, and simplify polynomial and rational expressions.

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions II

A2.A.2.3: Recognize that a quadratic function has different equivalent representations [f(x) = ax² + bx + c, f(x)= a(x − h)² + k, and f(x) = (x − h)(x − k)]. Identify and use the representation that is most appropriate to solve real-world and mathematical problems.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form

A2.F: Functions

A2.F.1: Understand functions as descriptions of covariation (how related quantities vary together).

A2.F.1.1: Use algebraic, interval, and set notations to specify the domain and range of functions of various types and evaluate a function at a given point in its domain.

Introduction to Functions
Logarithmic Functions
Radical Functions

A2.F.1.2: Recognize the graphs of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x + c), f(x) + c, f(cx), and cf(x), where c is a positive or negative real-valued constant] algebraically and graphically, using various methods and tools that may include graphing calculators or other appropriate technology.

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Radical Functions

A2.F.1.3: Graph a quadratic function. Identify the x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.

Addition and Subtraction of Functions
Exponential Functions
Graphs of Polynomial Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

A2.F.1.4: Graph exponential and logarithmic functions. Identify asymptotes and x- and y-intercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A2.F.1.5: Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form

A2.F.1.6: Graph a rational function and identify the x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology. (Excluding slant or oblique asymptotes and holes.)

General Form of a Rational Function
Rational Functions

A2.F.1.7: Graph a radical function (square root and cube root only) and identify the x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.

Radical Functions

A2.F.1.8: Graph piecewise functions with no more than three branches (including linear, quadratic, or exponential branches) and analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant.

Absolute Value with Linear Functions

A2.F.2: Analyze functions through algebraic combinations, compositions, and inverses, if they exist.

A2.F.2.3: Find and graph the inverse of a function, if it exists, in real-world and mathematical situations. Know that the domain of a function f is the range of the inverse function f-¹, and the range of the function f is the domain of the inverse function f-¹.

Logarithmic Functions

A2.F.2.4: Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

Logarithmic Functions

A2.D: Data & Probability

A2.D.1: Display, describe, and compare data. For linear and nonlinear relationships, make predictions and assess the reliability of those predictions.

A2.D.1.1: Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve).

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

A2.D.1.2: Collect data and use scatterplots to analyze patterns and describe linear, exponential or quadratic relationships between two variables. Using graphing calculators or other appropriate technology, determine regression equation and correlation coefficients; use regression equations to make predictions and correlation coefficients to assess the reliability of those predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

A2.D.2: Analyze statistical thinking to draw inferences, make predictions, and justify conclusions.

A2.D.2.1: Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Given spreadsheets, tables, or graphs, recognize and analyze distortions in data displays. Show how graphs and data can be distorted to support different points of view.

Correlation
Polling: City
Stem-and-Leaf Plots