AII.1: The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.

AII.1.1: Rational Exponents

AII.1.1.b: Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents.

Operations with Radical Expressions
Simplifying Radical Expressions

AII.1.2: Polynomial and Rational Expressions

AII.1.2.a: Divide polynomial expressions by lower degree polynomials.

Dividing Polynomials Using Synthetic Division

AII.1.3: Complex Numbers

AII.1.3.a: Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers.

Points in the Complex Plane

AII.1.3.b: Add, subtract, multiply, divide, and simplify expressions involving complex numbers.

Points in the Complex Plane

AII.2: The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.

AII.2.1: Functions and Function Notation

AII.2.1.d: Use algebraic, interval, and set notations to specify the domain and range of functions of various types.

Introduction to Functions
Logarithmic Functions
Radical Functions

AII.2.1.e: Find and graph the inverse of a function, if it exists.

Exponential Functions
Linear Functions
Logarithmic Functions

AII.2.2: Systems of Equations

AII.2.2.a: Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation.

Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

AII.2.2.b: Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators.

Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

AII.2.3: Quadratic Equations and Functions

AII.2.3.a: Solve quadratic equations by graphing, factoring, completing the square and quadratic formula.

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

AII.2.3.b: Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator.

Quadratics in Factored Form
Quadratics in Vertex Form
Zap It! Game

AII.2.4: Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola, and hyperbola).

Circles
Ellipses
Hyperbolas
Parabolas
Zap It! Game

AII.2.5: Exponential and Logarithmic Functions

AII.2.5.a: Graph exponential and logarithmic functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

AII.2.5.b: Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

Logarithmic Functions

AII.2.5.c: Model a situation that can be described by an exponential or logarithmic function and use the model to answer questions about the situation.

Compound Interest

AII.2.6: Polynomial Equations and Functions

AII.2.6.a: Solve polynomial equations using various methods and tools which may include factoring and synthetic division.

Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

AII.2.6.c: Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator.

Graphs of Polynomial Functions
Polynomials and Linear Factors

AII.2.7: Rational Equations and Functions

AII.2.7.c: Given the graph of a rational function, identify the x- and y-intercepts, asymptotes, using various methods and tools which may include a graphing calculator.

General Form of a Rational Function

AII.2.7.d: Model a situation that can be described by a rational function and use the model to answer questions about the situation.

General Form of a Rational Function
Rational Functions

AII.3: The student will use data analysis and statistics to formulate and justify predictions from a set of data.

AII.3.1: Analysis of Collected Data Involving Two Variables

AII.3.1.b: Interpret results using a linear, exponential or quadratic model/equation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

AII.3.2: Measures of Central Tendency and Variability

AII.3.2.a: Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average).

Describing Data Using Statistics
Polling: City
Populations and Samples

AII.3.2.b: Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation).

Describing Data Using Statistics
Polling: City
Populations and Samples
Real-Time Histogram

AII.3.2.c: Use the characteristics of the Gaussian normal distribution (bell-shaped curve) to solve problems.

Polling: City
Populations and Samples

AII.3.2.d: Identify how given outliers affect representations of data.

Mean, Median, and Mode

AII.3.3: Identify and use arithmetic and geometric sequences and series to solve problems.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences