# Algebra II GRADE-12

## Duration

## 10 Months

## Prerequisites

## Student Must Have Completed Grade 11

## Requirements

## Graphing calculator or graphing software of student’s choice

## Course Summary

## Starting with a review of introductory algebra, you will learn polynomials, quadratic equations, exponential and logarithmic relations, probability, and statistics. Throughout the course, these mathematical concepts are applied to everyday occurrences to demonstrate how the world around us functions.

## MAJOR TOPICS AND CONCEPTS

**Review of Algebra**

- Introduction to Functions
- Graphing Linear Equations and Inequalities
- Writing the Equation of a Line
- Comparing Functions

**Rational, Complex, and Polynomials**

- Rational Exponents
- Properties of Rational Exponents
- Solving Radical Equations
- Complex Numbers
- Operations of Complex Numbers
- Review of Polynomials
- Polynomial Operations

**Factoring and Quadratics**

- Greatest Common Factors and Special Products
- Factoring by Grouping
- Sum and Difference of Cubes
- Graphing Quadratics
- Completing the Square
- Solving Quadratic Equations
- Solving Quadratic Equations with Complex Solutions
- Investigating Quadratics

**Dividing and Solving Polynomials**

- Polynomial Long Division
- Polynomial Synthetic Division
- Theorems of Algebra
- Rational Root Theorem and Descartes’ Rule of Signs
- Solving Polynomial Equations
- Graphing Polynomial Functions
- Polynomial Identities and Proofs

**Rational Expressions**

- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Simplifying Complex Fractions
- Discontinuities of Rational Expressions
- Asymptotes of Rational Functions
- Solving Rational Equations
- Applications of Rational Equations

**Systems of Equations and Inequalities**

- Solving Systems of Equations Algebraically
- Solving Systems of Non-Linear Equations
- Graphing Systems of Linear Equations
- Graphing Systems of Non-Linear Equations

**Exponential and Logarithmic Functions**

- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- Solving Exponential Equations with Unequal Bases
- Graphing Exponential Functions
- Graphing Logarithmic Functions
- Exponential and Logarithmic Functions

**Sequences and Series**

- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Sigma Notation
- Infinite, Convergent, and Divergent Series
- Graphing Sequences and Series

**Statistics**

- Events and Outcomes in a Sample Space
- Independent Probability
- Conditional Probability
- Normal Distribution
- Models of Populations
- Using Surveys
- Using Experiments

**Trigonometry**

- Introduction to the Unit Circle
- Unit Circle and the Coordinate Plane
- Trigonometric Functions with Periodic Phenomena
- Pythagoras, Trigonometry, and Quadrants
- Functions of All Types