Ch 3: Advanced Algebra Concepts

About This Chapter

Develop a deeper understanding of advanced algebra concepts, such as logarithms and Boolean algebra, by using these helpful video and text lessons. This chapter can provide a quick review before you take algebra class, professional certification or even college or military entrance exams.

Advanced Algebra Concepts - Chapter Summary

From arithmetic progressions to logarithms, this chapter is designed to offer a quick overview of advanced topics in algebra. Lessons will address theorems, formulas and problem-solving practices common in advanced algebra. You will learn how to apply these concepts to understand quadratic equations, compound equalities and more. After your review of this chapter, you should be able to:

  • Differentiate between arithmetic, geometric and harmonic progressions
  • Calculate a geometric series and apply formulas to calculate combinations
  • Provide details about the Binomial Theorem
  • Explain how to graph one- and two-variable inequalities
  • Find lead coefficients in quadratic equations
  • Detail standard, intercept and vertex forms of quadratic equations
  • Define logarithms and how to evaluate them
  • Summarize details about Boolean algebra

Lessons are taught by expert instructors who present the material in simple terms and with illustrations and detailed examples. Your Dashboard makes it easy to track your progress through this chapter, and you can contact instructors with any questions about these topics. Assess what you have learned and whether you need further studies by taking the quizzes found in each of these lessons.

11 Lessons in Chapter 3: Advanced Algebra Concepts
Test your knowledge with a 30-question chapter practice test
How to Calculate a Geometric Series

1. How to Calculate a Geometric Series

If you're not satisfied with knowing how many views your YouTube video will get any one day and need to know how many total views you're getting, geometric series are for you! Learn more in this lesson.

Combination: Definition, Formula & Examples

2. Combination: Definition, Formula & Examples

In this lesson, we'll learn how to identify combinations of objects. We'll also look at various formulas that allow us to calculate the number of possible combinations in a given scenario.

Permutation & Combination: Problems & Practice

3. Permutation & Combination: Problems & Practice

In this lesson, we will practice solving various permutation and combination problems using permutation and combination formulas. We can continue our practice when we take a quiz at the end of the lesson.

What is the Binomial Theorem?

4. What is the Binomial Theorem?

While the F.O.I.L. method can be used to multiply any number of binomials together, doing more than three can quickly become a huge headache. Luckily, we've got the Binomial Theorem and Pascal's Triangle for that! Learn all about it in this lesson.

How to Graph 1- and 2-Variable Inequalities

5. How to Graph 1- and 2-Variable Inequalities

So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!

Set Notation, Compound Inequalities, and Systems of Inequalities

6. Set Notation, Compound Inequalities, and Systems of Inequalities

In this lesson, we'll explore the conditions of compound inequalities and learn how to express them using set notation and interval notation. Test you knowledge afterward with a short quiz.

How to Identify Lead Coefficients in Quadratic Equations

7. How to Identify Lead Coefficients in Quadratic Equations

In this lesson, will will go over some basics of quadratic equations and coefficients, specifically leading coefficients and how to find them. We will review examples and special cases.

Parabolas in Standard, Intercept, and Vertex Form

8. Parabolas in Standard, Intercept, and Vertex Form

By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.

What is a Logarithm?

9. What is a Logarithm?

Logarithms can help you solve exponential functions. In this lesson, you will learn about how to work with and recognize logarithms, and how to use logarithm notation with an example problem about earthquakes!

How to Evaluate Logarithms

10. How to Evaluate Logarithms

Using this lesson, you can get practice evaluating logarithms, as well as learn some of the shortcuts behind writing and estimating them. You can also learn how to use your calculator to evaluate logarithms, and learn about a concept called the change of base theory.

Boolean Algebra: Rules, Theorems, Properties & Examples

11. Boolean Algebra: Rules, Theorems, Properties & Examples

In this lesson you will discover and use the rules of Boolean algebra to simplify Boolean expressions (statements that are either True or False). The Rules of Boolean algebra are given in a table, and a few examples show how to use them.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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