Welcome to our journey through the core building blocks of algebra. Throughout this course, you’ll strengthen your skills with real numbers, equations, inequalities, functions, and mathematical models. You’ll move from foundational concepts like calculating real numbers and solving linear equations to more advanced topics such as factoring polynomials, solving quadratic and absolute value equations, analyzing functions, and composing them. Each module builds on the last, helping you understand how algebraic relationships connect, how graphs tell a story, and how mathematical models describe real-world situations. By the end, you’ll have a strong, confident grasp of the algebra skills needed for higher‑level math, everyday problem‑solving, and the concepts being introduced in each of your weekly learning modules.
This companion page accompanies the MAT-136 Workshop and Office Hours series. To learn more or join the series live, view the schedule at the bottom of this page. Hope to see you there!
In this module, we will review essential algebra skills that support your understanding of linear equations. You’ll work with real numbers, exponents, scientific notation, and the rectangular coordinate system. You will also practice solving linear equations and applying mathematical models to real‑world situations. By the end of the module, you will be able to:
- Calculate with real numbers
- Solve linear equations using algebraic methods
- Analyze graphs on the rectangular coordinate system
In this module, we will review and practice rational expressions, polynomial expressions, and more advanced algebraic equations. These topics build on the linear concepts from Module One and introduce equations involving powers of xx, absolute values, and quadratic polynomials. By working with these more complex structures, you will strengthen your ability to analyze mathematical models beyond simple linear relationships. By the end of the module, you will be able to:
- Solve linear equations using algebraic methods
- Calculating and factor polynomials
- Solve absolute value equations using algebraic methods
- Calculate rational expressions
- Solve quadratic equations using algebraic methods.
In this week, we will review algebra skills by reviewing how to solve linear inequalities. Building on the equality methods from Modules One and Two, we will review similar algebraic steps to solve and interpret inequality statements. We will also explore foundational function concepts, including how to describe their properties and determine their domain and range. By the end of the module, you will be able to:
- Solve linear inequalities
- Calculate and factor polynomials
- Describe properties of functions
- Find the domain and range of functions
This week, we will build on the function concepts introduced in Module Three by exploring more advanced operations with functions. We will review how to compose two functions and how to transform a function, including shifting its graph. These operations apply specifically to functions and extend assistance with broadening your ability to analyze mathematical relationships beyond equations and expressions. By the end of the module, you will be able to:
- Calculate the composition of two functions
- Analyze linear functions
This week, we will cover linear and absolute value functions and learn to solve systems of linear equations. With absolute value functions, we will focus on finding the vertex and points larger and smaller than the vertex to graph the absolute value function. When solving systems of linear equations, we will review three methods: graphing, substitution, and elimination. During the session, we will discover academic resources for college math basics, and we’ll wrap up with independent practice problems. By the end of the module, you will be able to:
- Analyze linear functions
- Analyze absolute value functions
- Solve systems of linear equations
This week, we will discuss quadratic functions through analysis and graphing. Then we’ll transition to function transformations and how they impact graphs of functions. Finally, we’ll review how to factor polynomials in preparation for next week’s new concepts, including references to helpful video resources. We’ll wrap up the session with independent practice. By the end of this module, you will be able to:
- Analyze quadratic functions
- Graph polynomial functions on a coordinate plane
- Identify transformations of functions
This week, we continue to explore new function types, specifically rational and radical functions. We’ll explore ways to graph rational functions on a coordinate plane and utilize the polynomial factoring skills we reviewed in last week’s session. We’ll introduce the concept of radical functions and demonstrate how to evaluate them. We’ll wrap up the session concepts with a preview of the MAT 136 Module 8 Statistics concepts. Finally, we’ll end with practice problems and solutions. By the end of this module, you will be able to:
- Analyze rational functions
- Analyze radical functions
- Calculate numeric measures to summarize data
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Need More Help?
Join us for the MAT-136, Introduction to Quantitative Analysis Workshop or Office Hours, to ask questions and learn more. Someone from the Academic Support Team will be there to assist you! Click here to see the full workshop and office hours schedule.