# Problem Solving in Algebra

Prerequisites: Qualifying math score and completion of at least one semester of Algebra I

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: PS3

## Course Description

Description

CTY's Problem Solving courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on video lectures provided by Thinkwell, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging quizzes and chapter tests. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.

In Problem Solving in Algebra, students focus on the symbols and rules of algebra and how they are used to represent relationships. Students master skills and concepts through practice problems, interactions within every lesson, and workout questions. Students apply what they have learned to solve sets of questions at varying levels of difficulty. This course provides an excellent foundation for students who will be advancing into Honors Algebra II.

Upon successful completion of this course, a student will be able to understand concepts typically covered in first-semester algebra, such as:

• operations on polynomials
• solving absolute value equations
• working with linear equations
• writing functional relationships
• examining perpendicular and parallel lines
• solving equations using multiple operations
• applications of linear equations and systems
• solving systems of linear equations and inequalities
• working with quadratic equations and expressions

For a detailed list of topics, click the List of Topics tab.

## Materials Needed

There are no required materials for this course.

## List of Topics

### Chapter 1: The Language of Algebra

#### Introduction to Polynomials

• Determining Components and Degree
• Multiplying Polynomials
• The FOIL Method
• Multiplying Big Products
• Using Special Products
• Factoring Perfect Square Trinomials
• Factoring the Difference of Two Squares
• Factoring Sums and Differences of Cubes
• Factoring by Any Method

#### Absolute Value

• Properties of Absolute Value
• Evaluating Absolute Value Expressions
• Matching Number Lines with Absolute Value
• Solving Absolute Value Equations
• Solving Equations with Two Absolute Value Expressions

### Chapter 2: Linear Equations and Functions

#### Graphing and Writing Linear Equations

• An Introduction to Slope
• Finding the Slope Given Two Points
• Graphing Linear Functions
• Graphing Important Functions

#### Introduction to Functions

• Introducing Relations and Functions
• Function Notation and Values
• Functions and the Vertical Line Test
• Using Intercepts to Graph Lines
• Working with Specific Lines
• Writing an Equation in Slope-Intercept Form
• Writing an Equation Given Two Points
• Writing an Equation in Point-Slope Form
• Matching a Slope-Intercept Equation with its Graph
• Slope for Parallel and Perpendicular Lines
• Solving Word Problems Involving Functions

### Chapter 3: Systems of Linear Equations

#### Graphic Solutions of Linear Systems

• An Introduction to Linear Systems
• Solving a System by Graphing

#### Algebraic Solutions of Linear Systems

• Solving a System by Substitution
• Solving a System by Elimination
• Investments

### Chapter 4: Linear Inequalities

#### Inequalities in One Variable

• An Introduction to Solving Inequalities
• Solving Inequalities
• Solving Absolute Value Inequalities
• Solving Word Problems with Inequalities
• Sets, Intersections, and Unions
• Solving Compound Inequalities

#### Inequalities in Two Variables

• An Introduction to Graphing Inequalities in Two Variables
• Graphing Linear and Nonlinear Inequalities
• Graphing the Solution Set of a System of Inequalities

• Finding x- and y-Intercepts
• Nice-Looking Parabolas
• Graphing Parabolas

#### Solving by Completing the Square

• Finding the Vertex by Completing the Square

• Using the Vertex to Write the Equation
• Building a Polynomial from Its Solutions

#### Solving with the Quadratic Formula

• Predicting Types of Solutions from the Discriminant
• Using the Discriminant to Graph Parabolas

• Solving for a Squared Variable
• Finding Real Number Restrictions

#### Formulas and Applications

• Solving a Quadratic Geometry Problem
• Solving with the Pythagorean Theorem
• Solving a Motion Problem
• Solving a Projectile Problem
• Solving Other Problems

## Problem Solving Help Room

Help Room

Each week, all students are invited to a Problem Solving Help Room run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week.

The Problem Solving Help Room meets each Tuesday from 7 – 8 p.m. ET.

Sample Video

## Technical Requirements

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.