## Review Videos Required to Succeed in Intermediate Algebra

Since these videos are only for purposes of review, there is no detailed development of concepts. If you need a deeper development of certain review topics, either refer to your elementary algebra textbook or let me know and I will try my best to (eventually) create a video for that topic.

It would be best to view these videos in the order listed to gain a complete review.

Each video has a list of prerequisite skills. You should have mastered (or, at the very least, be competent with) each of the prerequisite skills listed

It would be best to view these videos in the order listed to gain a complete review.

**A note about prerequisite skills**Each video has a list of prerequisite skills. You should have mastered (or, at the very least, be competent with) each of the prerequisite skills listed

*prior*to watching that video. In many cases, I provide links to the relevant prerequisite skill video.

__Prerequisite Skills__- arithmetic

__Video Description__In this video, I

*very*briefly review the number systems (sans the complex numbers) and discuss, in some detail, how to determine whether a given number belongs to a certain number system. Finally, I discuss the axioms that make our system of mathematics work so well.

__Why Learn This Stuff?__Mathematics can be clumsily split into two major islands with a bridge connection. The two islands are called "theory" and "application." The bridge is called "computation." Many high school courses focus on the computational bridge and, sadly, most people view mathematics as being entirely this bridge connection; however, the college-level demands that you can think "outside the box" and follow rigorous theoretical strictures. Hence, you should spend part of your college career on the "theory" island. On the other hand, many of you will be asked to implement the concepts you have learned in your math courses in a work environment (e.g., engineering or accounting). This requires that you spend some time on the "application" island.

The content in this video is definitely more on the theoretical side of mathematics. Those who enjoy problem-solving and puzzles will generally enjoy this material. Believe it or not, there is a

*lot*of hidden advanced mathematics behind this seemingly simple topic.

**Prerequisite Skills:**

- arithmetic
- ability to recognize grouping symbols

This video is dedicated to a brief review of the order of operations (an essential topic prior to tackling the topic of algebraic expressions). It is assumed that the viewer has already had an elementary algebra course (and, therefore, a course in arithmetic).

*I cannot stress enough how important this topic is to your future success in mathematics.*

**Prerequisite Skills:**

- arithmetic
- order of operations
- previous exposure to application/word problems (specifically number-value, distance-rate-time, and average-value problems)
- good reading comprehension and basic critical thinking skills
- exposure to unit/dimensional analysis would be helpful, but is not required

There are quite a few topics in this video (it should be broken into at least two videos); however, since this is supposed to be a review of elementary college algebra, I assume that you are somewhat familiar with algebraic expressions. This video is centered around developing a proper way to write an algebraic expression for a given word problem. I also define variables and algebraic expressions here. Finally, some time is spent evaluating algebraic expressions for given values.

**Prerequisite Skills:**

- arithmetic
- knowledge of, and ability to simplify, algebraic expressions

This video focuses on a review of how to solve algebraic equations for intermediate algebra students. I focus on solving linear equations in one variable using a technique I call "untying the knot." This incredibly powerful technique is useful for all math students (up to, and including, calculus students). I also introduce the idea of a contradiction. Finally, we solve some algebraic formulas for given variables.

**Prerequisite Skills:**

- arithmetic
- knowledge of, and ability to simplify, algebraic expressions
- previous exposure to application/word problems (specifically number-value, distance-rate-time, average-value, and percent markup/markdown problems)
- good reading comprehension and basic critical thinking skills
- ability to solve linear equations in one variable (including those containing multiple grouping symbols, decimal coefficients, and/or fractional coefficients)

The goal of this video is single-minded - develop a method to attack applications (word problems) that require linear equations to solve. This method, called Polya's Method, will be used throughout many of my videos.

**Prerequisite Skills:**

- good reading comprehension and basic critical thinking skills
- knowledge of number systems (for axes)
- previous exposure to graphs in mathematics (just data graphs, not linear or quadratic graphs)
- order of operations and evaluating expressions for given values

We begin with a real-world graph and dissect this to get useful information. After this brief introduction, we then describe the parts of a graph (axes, origin, points, etc.). Finally, we graph solution sets to equations in two variables and also use graphs to find solutions of equations.