A2.1: Number Systems and Non-Linear Expressions & Equations

A2.1.1: Operations with Complex Numbers

A2.1.1.1: Represent and/or use imaginary numbers in equivalent forms (e.g., square roots and exponents).

A2.1.1.1.2: Simplify/evaluate expressions involving powers of i (e.g., i to the 6th power + i³ = -1 �i).

Points in the Complex Plane

A2.1.1.2: Apply the order of operations in computation and in problem-solving situations.

A2.1.1.2.1: Add and subtract complex numbers (e.g., (7Â?3i)Â?(2 + i) = 5Â?4i).

Points in the Complex Plane

A2.1.1.2.2: Multiply and divide complex numbers (e.g., (7Â?3i)(2 + i) = 17+i).

Points in the Complex Plane

A2.1.2: Non-Linear Expressions

A2.1.2.1: Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems.

A2.1.2.1.2: Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers-exponents should not exceed power of 10).

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A2.1.3: Non-Linear Equations

A2.1.3.1: Write and/or solve non-linear equations using various methods.

A2.1.3.1.1: Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Roots of a Quadratic

A2.1.3.1.2: Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x � 2) = 1 or the square root of (x² + 21x) = 14).

Operations with Radical Expressions
Radical Functions

A2.1.3.1.3: Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).

Exponential Functions

A2.1.3.1.4: Write, solve, and/or apply linear or exponential growth or decay (including problem situations).

Compound Interest
Dilations
Direct and Inverse Variation

A2.1.3.2: Describe and/or determine change.

A2.1.3.2.1: Determine how a change in one variable relates to a change in a second variable (e.g., y = 4/x; if x doubles, what happens to y?).

Translating and Scaling Functions
Zap It! Game

A2.1.3.2.2: Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).

Area of Triangles
Solving Formulas for any Variable

A2.2: Functions and Data Analysis

A2.2.1: Patterns, Relations, and Functions

A2.2.1.1: Analyze and/or use patterns or relations.

A2.2.1.1.2: Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

A2.2.1.1.3: Determine the domain, range, or inverse of a relation.

Introduction to Functions

A2.2.1.1.4: Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes).

Addition and Subtraction of Functions
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

A2.2.2: Applications of Functions

A2.2.2.1: Create, interpret, and/or use polynomial, exponential, and/or logarithmic functions and their equations, graphs, or tables.

A2.2.2.1.1: Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics).

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

A2.2.2.1.2: Create, interpret, and/or use the equation, graph, or table of an exponential or logarithmic function (including common and natural logarithms).

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A2.2.2.1.3: Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential, or logarithmic function.

Graphs of Polynomial Functions
Quadratics in Factored Form

A2.2.2.2: Describe and/or determine families of functions.

A2.2.2.2.1: Identify or describe the effect of changing parameters within a family of functions (e.g., y = x² and y = x² + 3, or y = x² and y = 3x²).

Introduction to Exponential Functions
Points, Lines, and Equations
Translating and Scaling Functions
Zap It! Game

A2.2.3: Data Analysis

A2.2.3.1: Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.

A2.2.3.1.1: Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.

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

A2.2.3.1.2: Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

A2.2.3.2: Apply probability to practical situations.

A2.2.3.2.1: Use combinations, permutations, and the fundamental counting principle to solve problems involving probability.

Permutations and Combinations

A2.2.3.2.3: Use probability for independent, dependent, or compound events to predict outcomes.

Independent and Dependent Events