ABCs of Algebra

Learn the Fundamentals of Algebra at Your Own Pace!

ABCs of Algebra

Learn the Fundamentals of Algebra at Your Own Pace!

Unlock your potential and transform your understanding of mathematics with our revolutionary ABCs of Algebra course. This isn't just another class; it's your gateway to mastering the fundamentals with unmatched clarity and ease. Embrace a journey where complex algebraic operations effortlessly bloom into tangible skills, empowering you to tackle real-world problems with confidence. Discover the joy of turning equations into solutions, and watch as each lesson builds seamlessly upon the last, unveiling a newfound fluency in algebraic thinking. Guided by expert instructors, you'll cultivate a robust mathematical foundation that transcends the classroom, equipping you with tools to thrive in any field you choose. Enroll today--redefine what you thought possible!

Self Paced • Online Class • 22 Hours

$120

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CURRICULUM

ABCs of Algebra

Name: ABCs of Algebra
Price: 95.00 USD

CRN: 9770476

Lesson 1. Understanding Algebra: A Journey Through Numbers and Symbols

Concepts like constants and variables are presented as foundational elements in algebra, illustrating how they function within open and closed sentences. The lesson uses practical examples to demonstrate substitution and evaluation, easing learners into equation-solving with common axioms and properties.

Lesson 2. Identity Elements and Axioms in Action

Lesson Summary 5: The lesson outlines how the closure property ensures certain operations on integers remain within the set of integers and introduces algebraic properties like identity elements to simplify equations. It emphasizes the significance of zero and one as pivotal elements in maintaining balance and simplicity in algebraic expressions, preparing learners for handling more complex mathematical concepts.

Lesson 3. Positive and Negative Numbers in Equations

This lesson on directed numbers delves into adding, subtracting, multiplying, and dividing both positive and negative numbers, emphasizing the importance of the absolute value and inverse properties. Through practical examples, it shows how these principles apply to equations featuring variables.

Lesson 4. Dissecting Algebra: Rules and Techniques for Simplification

When solving linear inequalities, the solution can be demonstrated using number lines to reflect the inclusion or exclusion of boundaries within solutions. Inequalities differ from equalities and often require graphing to effectively visualize solutions and their ranges, especially when dealing with rational numbers.

Lesson 5. Exponents 101

Negative exponents signal reciprocal operations, transforming base inverses and utilizing straightforward examples to illustrate base and exponent manipulations, even when the base is negative. The lesson methodically shows applying exponents in practical contexts, particularly scientific notation, bridging everyday mathematical applications and classroom theory.

Lesson 6. Polynomials: A Comprehensive Guide

The properties of exponents, such as the product of powers and power of a product, simplify polynomial expressions by adding or multiplying exponents when bases are the same, ensuring clarity in operations involving expanded polynomials and exponents.

Lesson 7. An Introduction to Fractions

Signs in fractions determine positivity or negativity, and operations between fractions depend on aligning signs for addition and subtraction. In multiplication and division, different signs result in a negative product, while similar signs give a positive result.

Lesson 8. Discovering the Art of Factoring: A Deep Dive into Algebraic Problem-Solving

Lesson Summary 4: Break down algebraic expressions by uncovering their prime components and sharing polynomial factoring secrets. Gain mastery in the mathematical dance of rearranging terms and using properties to reveal hidden factors.

Lesson 9. Factor and Conquer: Solving Algebra with Combined Factoring Methods

This section on factoring advances the skill of identifying combinations such as common factors and trinomial squares, vital for decomposing expressions into simpler forms. Logic-driven steps are shown to empower the solution of polynomial equations and decipher real-world applications efficiently.

Lesson 10. Mastering Linear Equations and Inequalities

The coordinate plane is formed by intersecting x- and y-axes, dividing it into four quadrants to graph ordered pairs, with positive/negative numbers indicating direction from the axes. The graph of a line, determined by at least two points, displays the linear relationship, conforming to the established domains (x values) and ranges (y values).

Lesson 11. Quick Methods to Solve Two-Variable Systems

Graphing offers a visual representation of systems of equations, although it can be tricky for large numbers. Intersection of graphed lines can pinpoint solutions, but when lines overlap or are parallel, it indicates dependent systems or inconsistent systems, respectively.

Lesson 12. Mastering Quadratic Solutions

Quadratic equations can be solved using methods like factoring, completing the square, and the quadratic formula, each applicable under different scenarios. Additionally, understanding the property of square roots and the approach to quadratic inequalities enhances your problem-solving toolkit.

In This Course

22 Hours average completion time
2.2 CEUs
12 Lessons
28 Exams & Assignments
76 Discussions
13 Videos
143 Reference Files
11 Articles
Mobile Friendly
Last Updated June 2024

Description

Find out how algebra is simply a natural extension of the math you learned in elementary school. Basic Algebra is designed for all students who need a basic understanding of algebraic operations including simplifying, factoring, solving equations and inequalities, working with fractions or exponents, graphing, and word problems.

In Basic Algebra we will walk step-by-step through a wide variety of explained problems. Learn to perform the steps to solve equations and graph solutions. Understand FOIL (when it isn't wrapping your baked potato). Discover methods for factoring trinomials quickly and easily. Understand slopes and line equations so that you can identify a slope from two points or draw a line with a slope and a point. See how word problems help you translate your math skills to your real world. Explore additional resources for more explanations and practice problems with immediate feedback. Allow the course to lead you from topic to topic, building on what you already know.

Skills You'll Develop

Rational and exponents manipulation
Translating real-world problems into equations
Polynomials and factoring
Understanding algebraic properties
Algebraic problem solving
Graphical analysis and interpretation
Equation and inequality solving
Confidence in mathematical reasoning

More About This Course

Fractions Mastery: Align signs for accurate fraction operations
Linear and Inequalities Mastery: Graph relationships and solve systems
Polynomials Guide: Simplify expressions with exponent properties
Dissecting Algebra: Visualize solutions with graphing techniques
Identity Elements and Axioms: Simplify equations with essential properties
Quadratic Solutions: Tackle quadratics using versatile methods
Understanding Algebra: Grasp foundational algebra concepts effortlessly
Factor and Conquer: Solve equations with combined factoring methods
Positive and Negative Numbers: Master operations with directed numbers
Factoring Art: Uncover prime components of algebraic expressions
Exponents 101: Navigate exponents and scientific notation seamlessly

What You'll Achieve

Define and distinguish between different types of numbers such as natural, whole, integers, rational, and irrational numbers using original definitions and examples.
Identify and apply properties of equality and axioms in algebraic expressions and sentences to demonstrate relationships between variables and constants.
Define the closure property for both addition and multiplication of whole numbers and explain its significance with examples.
Apply the distributive property to simplify algebraic expressions, utilizing multiplication over addition or subtraction, and verify results through calculation.
Identify and apply rules for addition and subtraction of directed numbers to solve algebraic expressions involving both positive and negative integers.
Demonstrate understanding of multiplicative and additive inverse properties by accurately solving equations that include directed numbers.
Define and apply the order of operations to simplify algebraic expressions accurately using PBBEMDAS.
Demonstrate proficiency in using the FOIL method to multiply two binomial expressions, resulting in the correct expression.
Identify the base and exponent in a given mathematical expression and describe their roles in determining the power.
Demonstrate the ability to simplify expressions involving negative exponents by using the reciprocal of the base.
Define a polynomial as a mathematical expression consisting of monomials, where each monomial is either a numeral, a variable, or their product.
Calculate the degree of a polynomial by determining the greatest degree of its terms, adding exponents for each variable present in each term.#
Define the terms numerator and denominator and explain their roles in fractions.