About This Chapter
Expressions, Functions & Operations - Chapter Summary
In this engaging chapter, you'll discover how to use exponential notation and identify the five main exponent properties. Logarithmic functions are also addressed.
After working your way through this chapter, you'll know more about working with complex numbers and solving problems using fractions, mixed numbers and decimal numbers. Once you complete this chapter, you should be capable of:
- Defining logarithm
- Adding, subtracting, multiplying and dividing complex numbers
- Solving quadratics that include complex numbers
- Working with inequalities
- Solving exponential expressions
- Identifying logarithmic functions
- Performing operations on vectors
The videos in this chapter average around 5-10 minutes, and are taught by qualified instructors. As you go through this chapter, use the quizzes to see if you are retaining the information from the lessons. Additionally, if a topic from this chapter seems to be confusing, you can get help from one of the instructors.
1. How to Use Exponential Notation
Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.
2. What Are the Five Main Exponent Properties?
We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents here!
3. Simplifying and Solving Exponential Expressions
What do we do with an exponent? In this lesson, we'll learn how to simplify and solve expressions containing exponents. We'll solve a variety of types of exponential expressions.
4. Performing Operations on Vectors in the Plane
After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.
5. 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!
6. Logarithmic Function: Definition & Examples
Exponential functions and logarithmic functions are closely tied. In fact, they are so closely tied we could say a logarithm is actually an exponent in disguise. A logarithm, or log, is just another way to write an exponential function in reverse.
7. How to Add, Subtract and Multiply Complex Numbers
Knowing that complex numbers exist is the first step. But that knowledge alone won't help you do much with them. Learn the basics of complex number addition, subtraction and multiplication here!
8. How to Divide Complex Numbers
While adding, subtracting and multiplying complex numbers is pretty straightforward, dividing them can be pretty tricky. It comes down to the process of multiplying by the complex conjugate. Learn about what that is, and how to do it, here.
9. How to Solve Quadratics with Complex Numbers as the Solution
When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!
10. The Order of Real Numbers: Inequalities
An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.
11. Solving Problems using Fractions and Mixed Numbers
Fractions don't just live in math problems. They're all around us, helping us through our lives. In this lesson, we'll look at real scenarios where your ability to work with fractions can save the day.
12. Solving Problems Using Decimal Numbers
Problems involving decimal numbers might sound like a way to torture you, but learning how important these types of problems are in the real world is important. In this lesson, you will see a couple areas in life where you routinely encounter decimal number problems.
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Other chapters within the MTTC Professional Readiness Examination (096): Practice & Study Guide course
- Basic Number Sense
- Fundamentals of Calculation
- Mathematical Reasoning & Problem-Solving
- Logic in Mathematics
- Expressions & Equations in Algebra
- Understanding Algebraic Functions
- Using Algebraic Functions
- Polynomials, Rational Equations & Trigonometric Equations
- Introduction to Basic Geometry
- Measuring Geometric Figures
- Relationships Between Figures in Geometry
- Basics of Trigonometry
- Fundamentals of Statistics
- Bivariate Relationships in Statistics
- Using Tables & Graphs
- Interpreting Statistical Data
- Probability Overview
- Introduction to Conditional Probability & Diagrams
- Structure, Analysis & Word Meanings in English
- Literary Themes & Main Ideas
- Strategies for Effective Writing
- Reading Strategies & Literary Analysis
- Critical Reasoning for Test-Taking
- Conventions in Writing: Effective Usage
- Constructing Sentences & Paragraphs
- Argumentative Writing Overview
- Structuring Informational & Explanatory Texts
- MTTC Professional Readiness Flashcards