Course Description
From Basics to Brilliance: Dive into the World of Algebra
In today's fast-paced and ever-evolving world, mathematical competency is no longer a luxury – it's a necessity. From managing household budgets to interpreting data-centric news, the importance of a solid foundation in mathematics, particularly Algebra, cannot be overemphasized. Whether you are a student setting the stage for advanced studies or an adult learner seeking to sharpen your analytical acumen, the transition from arithmetic to algebra opens doors to a world of abstract thinking and logical reasoning.
Why Algebra?
During our initial learning years, we all become familiar with the basics of arithmetic - adding, subtracting, multiplying, and dividing numbers. As we grow, the patterns of numbers beckon us to explore further, to understand not just the 'how' but also the 'why' behind mathematical operations. Enter Algebra, a branch of mathematics that goes beyond the specifics of numbers, introducing us to the exciting world of variables, constants, and their interplay. By delving into algebra, you unravel the mysteries of relationships between varying quantities, setting the stage for more advanced mathematical studies like calculus and trigonometry.
Course Overview
Our "Beginner to Intermediate Algebra" online course is tailored to guide learners through this intriguing transition. Modern data has consistently highlighted the importance of algebraic knowledge in diverse sectors, from technology to finance. Hence, understanding the crux of algebraic operations – be it simplifying expressions, factoring complex numbers, or decoding word problems – can enhance problem-solving abilities and set you apart in professional and academic realms.
Curriculum Breakdown:
Lesson 1: Introduction to Algebra
Unravel the world of algebra by understanding its key terms and the underlying motivation for its study. Engage in assignments that set the stage for upcoming modules.
Lesson 2: Journey Through Real Numbers
Dive into the vast ocean of real numbers. Get acquainted with their properties, classifications, and significance in the algebraic world.
Lesson 3: Mastering Algebraic Operations
From addition to division, explore how operations are transformed when we introduce variables into the mix.
Lesson 4: The Magic of Functions
Discover how functions encapsulate relationships between numbers and learn to interpret, represent, and utilize them effectively.
Lesson 5: Linear Equations & Their Graphs
Delve into the world of lines, slopes, and intercepts. Understand the foundational blocks of algebraic equations.
Lesson 6: Exploring Linear Inequalities
Not everything is equal. Learn the nuances of inequalities and their graphical representations.
Lesson 7: Systems of Equations – Dual Interplay
When equations come in pairs or sets, there's a system. Decode methods to solve and interpret them.
Lesson 8: Systematic Inequalities
Venture into a more advanced realm where inequalities come together to form systems, providing richer insights.
Lesson 9: Word Problems – Algebra in Action
Witness the practical application of algebra as you tackle real-world problems using mathematical tools.
Lesson 10 & 12: Diving Deep into Polynomial Functions
Understand the power and versatility of polynomials across two intensive modules, from basics to advanced applications.
Lesson 11: Exponential & Logarithmic Functions
Grasp the concepts of growth and decay, exploring natural logarithms and their applications.
Lesson 13: Geometry Meets Algebra
Experience the confluence of shapes and equations, enhancing spatial reasoning.
Lesson 14: Probability and Statistics - Predicting the World
Conclude the course by applying algebra to predict outcomes and analyze data, laying a foundation for statistical studies.
In essence, this course is not merely about learning algebra but about fostering a way of thinking. Algebra trains the mind to handle abstract concepts, solve problems, and make informed decisions. So, whether you are kickstarting your mathematical journey or rekindling an old passion, this course promises clarity, competence, and confidence. Dive in and let the numbers lead the way!
- Completely Online
- Self-Paced
- 6 Months to Complete
- 24/7 Availability
- Start Anytime
- PC & Mac Compatible
- Android & iOS Friendly
- Accredited CEUs
Learning Outcomes
- Create a function using variables to determine the final cost of an item given an unspecified base price and a sales tax rate of 10%
- Demonstrate an understanding of algebra by defining and providing examples of operations, variables, functions, and graphs
- Demonstrate understanding of the properties of real numbers by correctly applying commutativity, associativity, distributivity, identity, and inverse in problem solving.
- Identify and describe the main subsets of the set of real numbers, including natural, whole, integer, rational, and irrational numbers.
- Demonstrate the ability to manipulate algebraic equalities by performing equivalent operations on both sides while maintaining equality.
- Identify and apply the order of operations to evaluate algebraic expressions containing variables and parentheses.
- Define and explain the concepts of domain and range of a function by providing examples and non-examples using algebraic expressions and graphical representations
- Identify whether a given relation is a function or not by applying the vertical line test on its graph and justify the reasoning behind the result
- Demonstrate the ability to solve linear equations and determine solutions graphically by identifying points of intersection.
- Identify and describe the slope and y-intercept of a linear function given its equation in the form y = mx + b.
- Define and graph the solution set for a given linear inequality in the form ax + b > c
- Demonstrate the manipulation of linear inequalities by applying appropriate rules to solve and graph solutions
- Recognize and describe equations in multiple dimensions by identifying expressions that represent planes in three-dimensional graphs.
- Demonstrate mastery of lesson content at levels of 70% or higher.
Assessment Guide
| Assessment | Points |
|---|---|
| Introduction | 1 points |
| Lesson 1 – Algebra Terms and Motivation | 10 points |
| Lesson 2 – The Set of Real Numbers | 10 points |
| Lesson 3 – Algebraic Operations | 11 points |
| Lesson 3 Exercises | 7 points |
| Lesson 4 - Functions | 10 points |
| Lesson 4 Exercises | 8 points |
| Lesson 5 – Linear Equations | 10 points |
| Lesson 5 Exercises | 9 points |
| Lesson 6 – Linear Inequalities | 11 points |
| Lesson 6 Exercises | 3 points |
| Lesson 7 – Systems of Linear Equations | 10 points |
| Lesson 8 – Systems of Linear Inequalities | 10 points |
| Lesson 9 – Solving Word Problems I | 10 points |
| Lesson 9 Exercises | 4 points |
| Lesson 10 – Polynomial Functions | 10 points |
| Lesson 10 Exercises | 8 points |
| Lesson 11 – Exponential and Logarithmic Functions | 10 points |
| Lesson 12 – Polynomial Functions II | 9 points |
| Lesson 12 Exercises | 3 points |
| Lesson 13 – Application of Algebra to Geometry | 9 points |
| Lesson 13 Exercises | 4 points |
| Lesson 14 – Application of Algebra to Statistics and Probability | 9 points |
| The Final Exam | 47 points |
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