About This Chapter
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.
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.
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.
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.
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.
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!
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.
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.
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.
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!
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.
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.
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Other chapters within the NDA Exam Preparation & Study Guide course
- About the NDA Exam
- Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards