About This Chapter
ILTS Mathematics: Variables & Patterns - Chapter Summary
Completing this chapter exposes you to some important concepts dealing with variables and patterns. In turn, you will be better prepared for questions on the ILTS Mathematics exam dealing with:
- Identifying different types of patterns
- Classifying geometric and arithmetic sequences
- Recognizing symmetry graphically, numerically and algebraically
- Calculating arithmetic series and geometric series
- Mathematical induction
- Using words and images to restate a word problem
- The distributive, commutative, and associative properties
- Translating word problems to algebraic expressions
- Domain, range and rings
- Applying group structures to symmetry
Further develop your ability to work with patterns and sequences by watching the video lessons. Their interactive format makes learning and reviewing math principles easy, and you even have access to instructors. They are available to answer any questions that might pop up while you go through the lessons.
1. Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis
When you fold a piece of paper exactly in half, you are creating symmetry. Symmetry is found in many areas of mathematics. In this lesson, learn to recognize symmetry graphically, algebraically, and numerically about the x- and y- axes.
2. Identifying & Extending Different Types of Patterns
In this lesson, we will look at different ways patterns present themselves in the world around us. We will take a look at how to identify patterns and how to extend patterns and use this in some real-world examples.
3. How to Find and Classify an Arithmetic Sequence
Arithmetic sequences are everywhere, and with a few tricks you learn here, you could end up looking like a psychic the next time you go to a movie or a football game!
4. Finding and Classifying Geometric Sequences
Want your YouTube video to get a lot of hits? Besides including a cute baby or an adorable cat, getting your video to have a big common ratio is the key. Learn what I'm talking about here!
5. How to Calculate an Arithmetic Series
In this lesson, you'll learn how to sum up any arithmetic sequence without having to add up each and every term. You'll never guess the circumstances that led to the discovery of this marvelous formula.
6. 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.
7. Mathematical Induction: Uses & Proofs
Watch this video lesson to learn about mathematical induction and how you can use it to prove mathematical statements. See how it is similar to falling dominoes.
8. Translating Words to Algebraic Expressions
When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.
9. Restating Word Problems Using Words or Images
Watch this video lesson to learn how you can use sketches and notes to help you visualize a problem. Watch how easy it becomes to solve your problem once you have visualized it.
10. The Commutative and Associative Properties and Algebraic Expressions
The order of operations is important and useful, but a few mathematical properties highlight cases where order doesn't matter. In this lesson, we'll learn about the commutative and associative properties, which may save you time and effort.
11. The Distributive Property and Algebraic Expressions
The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.
12. What Is Domain and Range in a Function?
The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.
13. The Axiomatic System: Definition & Properties
Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.
14. Rings: Binary Structures & Ring Homomorphism
In this lesson, basic definitions are presented for algebraic rings and ring homomorphisms. These form the foundations for a broader discourse in abstract algebra. Rings are used in more complex algebraic structures and have many applications in computer science, physics, and engineering.
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Other chapters within the ILTS Mathematics (208): Test Practice and Study Guide course
- ILTS Mathematics: Concepts & Skills
- ILTS Mathematics: Logic & Reasoning
- ILTS Mathematics: Using Technology for Math
- ILTS Mathematics: Number Theory
- ILTS Mathematics: Solving Number Problems
- ILTS Mathematics: Real & Complex Numbers
- ILTS Mathematics: Measurement
- ILTS Mathematics: Multidimensional Objects
- ILTS Mathematics: Linear Relations & Functions
- ILTS Mathematics: Quadratic Relations & Functions
- ILTS Mathematics: Absolute Value
- ILTS Mathematics: Polynomials
- ILTS Mathematics: Radical Functions
- ILTS Mathematics: Rational Functions
- ILTS Mathematics: Exponential Functions
- ILTS Mathematics: Logarithmic Functions
- ILTS Mathematics: Trigonometric Functions
- ILTS Mathematics: Calculus
- ILTS Mathematics: Points, Lines, Planes & Space
- ILTS Mathematics: 2D & 3D Shapes
- ILTS Mathematics: Spatial Visualization
- ILTS Mathematics: Congruence, Similarity & Symmetry
- ILTS Mathematics: Probability Theory & Techniques
- ILTS Mathematics: Collecting & Representing Data
- ILTS Mathematics: Using Data to Make Predictions
- ILTS Mathematics Flashcards