About This Chapter
Algebraic Expressions & Patterns - Chapter Summary
In this engaging chapter, our instructors present algebraic expressions and patterns, including continuing patterns that involve decimals, fractions and whole numbers. These lessons explain how to graph linear equations and simplify algebraic expressions. You'll also learn how to solve linear equations using graphing. This chapter is also designed to help you:
- Understand the formulas associated with arithmetic and geometric sequences
- Solve linear equation with intercepts
- Plot points in order to graph functions
- Solve equations and manipulate functions for different variables
- Work with simultaneous equations
Our video and text lessons are short, fun and make studying enjoyable and flexible. Each lesson is accompanied by a handy quiz that tests your knowledge of what you've just learned. If you want to go back and review just one part of a video lesson, it's easy using the video tabs feature. You're welcome to reach out to an instructor if you need any assistance as you study the lessons.
1. Continuing Patterns With Fractions, Decimals & Whole Numbers
This lesson will have a quick review of the definitions of whole numbers, fractions, and decimals. Then, we will look at patterns of these types of numbers and the process of continuing these patterns based on identifying rules that a pattern follows.
2. Geometric Sequence: Formula & Examples
After completing this lesson, you will be able to recognize a geometric sequence. You will also be able to use the general formula for finding a term in a geometric sequence and will be able to write a custom formula for a given geometric sequence.
3. Arithmetic Sequence: Formula & Definition
After completing this lesson, you will be able to recognize an arithmetic sequence. You will also be able to use the general formula for finding a term in an arithmetic sequence and be able to write a custom formula for a given arithmetic sequence.
4. Solving Linear Equations: Practice Problems
With practice, linear equations can be straightforward to solve. In this lesson, we'll define linear equations and learn how to solve them. We'll look at multiple practice problems and walk through solving each one.
5. Linear Equations: Intercepts, Standard Form and Graphing
Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.
6. Practice Simplifying Algebraic Expressions
In this lesson, we'll practice simplifying a variety of algebraic expressions. We'll use two key concepts, combining like terms and the distributive property, to help us simplify.
7. Graph Functions by Plotting Points
Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.
8. How to Solve Linear Equations By Graphing
This lesson will give a quick review of systems of linear equations and their solutions. We will then look at taking an example through a step-by-step process that allows us to solve a system of linear equations by graphing.
9. Manipulating Functions and Solving Equations for Different Variables
Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.
10. How to Solve Simultaneous Equations
In this lesson, you'll learn what simultaneous equations are and discover methods for solving them, including graphing, the elimination method and the substitution method.
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