# ALGEBRA 2, PART 1

## Price: $125 | Credits: One Semester | Dept: Math | Course ID# 222-1

This course builds upon the body of knowledge and skill set learned from Algebra 1 and moves beyond. The course is the first semester of Algebra 2 and includes the topics: Equations and Inequalities, Linear Functions & Inequalities, Systems of Linear Equations and Inequalities, Matrices and Determinants, Quadratic Equations, Graphing Quadratic Functions, Polynomials, Rational Expressions. Algebra 2 is approved by the University of California A-G as mathematics (category C).

Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course in an accelerated rate.

### LEARNING OBJECTIVES

In this module, students gain a comprehension of the following:

- How to write equations from real life situations.
- How to solve one step equations.
- How to solve inequalities.
- How to graph inequalities on a number line.
- How to solve absolute value equations and get two solutions, in most cases.
- How to solve absolute value inequalities and find infinte solutions.
- To identify relations and determine which are functions, as well as to indentify their domains, and ranges.
- How to graph linear functions, both from standard form and slope intercept form.
- To find the slope of a line from two points or from an equation.
- To identify parallel and perpindicular lines given their slopes.
- To solve for and graph from the form y=mx + b.
- How to write equations of lines given their slope and y intercept, or given two points.
- How to graph inequalities, understanding that the solution set includes infinite points.
- How to solve systems of equations using the graphing method, the substitution method, and the addition/elimination method.
- How to graph linear equations with three variables.
- How to solve for systems of linear equations given 3 variables and 3 equations.
- How to work with matrices and perform matrix operations.
- How to multiply matrices and to determine whether or not a solution exists.
- To find and work with determinants of matrices.
- To use Cramer’s rule to solve systems of equations with 2 and 3 variables.
- How to find the inverses of 2×2 matrices and to use these inverses to solve for systems of equations.
- How identify and manipulate quadratic functions.
- To find solutions to quadratic functions by graphing, completing the square, factoring, and by using the quadratic formula.
- To understand and perform operations with complex roots and the imaginary number i.
- How to graph basic parabolas.
- How to graph quadratics using the table method, the vertex method, and by using intercepts.
- How to add and subtract polynomials.
- How to multiply and divide polynomials, focusing on domain problems.
- How to factor special polynomials, including the difference of squares, of cubes, and the sum of cubes.
- How to perform long division with polynomials, as well as synthetic division with polynomials.
- How to identify and simplify complex fractions.
- How to simplify rational expressions.
- How to perform operations with rational expressions, including adding, subtracting, multiplying, and dividing them.

### TOPICS COVERED

- This course covers the following topics:
- Writing Equations
- Solving One-Step Equations
- Solving Multi-Step Equations
- Solving Inequalities
- Graphing on Number Lines
- Solving Absolute Value Equations
- Solving Absolute Value Inequalities
- Relations, Functions, Domain & Range
- Graphs of Linear Functions
- The Slope of a Line
- Parallel and Perpendicular Lines
- y=mx+b
- Writing Equations of Lines
- Graphing Inequalities
- The Graphing Method -Two Variables
- The Substitution Method -Two Variables
- The Addition Method -Two Variables
- Graphing Linear Equations – 3 Variables
- Solving Systems of Linear Equations – 3 Variables
- Matrix Operations
- Multiplication of Matrices
- Determinants
- Cramer’s Rule
- Inverses of 2×2 Matrices
- Solving Systems Using Matrices
- Quadratic Functions: ax^2+bx+c
- Solutions to Quadratic Functions; Factoring
- Completing the Square
- The Quadratic Formula
- Complex Roots: i
- Graphing Basic Parabolas (Positive & Negative)
- Graphing Quadratics (Table Method)
- Graphing Quadratics Using Vertex & Intercepts
- Addition and Subtraction of Polynomials
- Products of Polynomials
- Factoring Special Polynomials
- Division of Polynomials; Long Division
- Divison of Polynomials: Synthetic Division
- Complex Fractions
- Simplifying Rational Expressions
- Adding & Subtracting Rational Expressions
- Multiplying & Dividing Rational Expressions