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# Intermediate Algebra: Lumen Learning (Editable Text)

## Content Overview

 Course Materials YES NO Lumen OHM Questions? X Editable Text? X Video Support? X - embedded in text Written Assessments/ Test? X Workbook? X

### Text

Intermediate Algebra by Lumen Learning is a derivative work based on Developmental Math: An Open Program, provided by Monterey Institute of Technology and Education. The text for this course is a "digital textbook" of a current, curated collection of OER resources with embedded video examples created by James Sousa (mathispower4u.com). The course covers one semester of Intermediate algebra for college students in developmental math. The course is also fully integrated in our online homework platform, Lumen OHM. The course is laid out over 15 modules including a review.

## Topic Overview

The specific learning outcomes covered in this course include:

### Module 0: Review

• A review of the order of operations with real numbers, and arithmetic with fractions

### Module 1: Real Numbers and Algebraic Expressions

• Classify real numbers, use properties of real numbers
• Solve linear equations that contain fractions, absolute value, and require the distributive property
• Classify solutions to linear equations
• Solve applications of linear equations including distance, rate, and time, area, volume, and perimeter, and temperature conversion

### Module 2: Linear Inequalities

• Represent inequalities with intervals, and on a number line
• Solve linear inequalities including compound inequalities, and absolute value inequalities
• Classify solutions to inequalities

### Module 3: Graph Linear Equations and Inequalities

• Writing equations of lines given points, words, and graphs
• Graph linear equations and inequalities using tables, intercepts, and slope/ intercept formats

### Module 4: Functions and Function Notation

• Define a function using a table, words, and an algebraic expression
• Identify a function given a graph, identify whether a function is one-to-one from it's graph
• Define the domain and range of linear, quadratic, and square root functions

### Module 5: Linear Functions

• Define and calculate slope, write the equation of a linear function given slope, or two points, or a scenario
• Transform linear functions using compressions, reflections,  and stretches
• Model applications with linear functions
• Define and graph piecewise linear functions

### Module 6: Linear Systems

• Define and classify solutions to linear systems of two and three equations
• Use elimination and substitution to solve linear systems of two equations
• Write and solve a system of two or three equations given a scenario
• Solve systems of three equations using substitution
• Solve and graph systems of two inequalities, solve applications with two inequalities

### Module 7: Exponents

• Use exponent rules to simplify expressions
• Write numbers using scientific notation, solve applications expressed with scientific notation

### Module 8: Polynomials and Polynomial Functions

• Identify polynomials, and perform algebraic operations on polynomials
• Learn methods for multiplying and dividing polynomials
• Recognize characteristics of polynomial functions and their graphs

### Module 9: Factoring

• Factor trinomials using a variety of methods including greatest common factor, and grouping
• Factor special cases of polynomials including those with squares, cubes, and fractional exponents
• Methods for solving polynomial equations including factoring and the zero product principle

### Module 10: Rational Expressions and Equations

• Define and simplify rational expressions
• Perform algebraic operations on rational expressions
• Solve rational equations including variation
• Define and use proportions to solve problems

### Module 11: Roots and Rational Exponents

• Define and evaluate roots, rewrite roots as rational exponents
• Perform algebraic operations on radical expressions
• Rationalize a denominator
• Solve radical equations and applications including kinetic energy, and volume

### Module 12: Quadratic Equations and Complex Numbers

• Solve quadratic equations using factoring, completing the square and the quadratic formula
• Define imaginary and complex numbers
• Perform algebraic operations on complex numbers
• Classify solutions to quadratic equations using the discriminant

### Module 13: Exponential, and Logarithmic Functions

• Define, evaluate, and graph exponential functions with various bases
• Define composite and inverse functions
• Define logarithmic functions in terms of an inverse
• Evaluate and graph logarithmic functions with various bases

### Module 14: Exponential and Logarithmic Equations

• Define and use properties of logarithms to solve logarithmic equations
• Use properties of logarithms to solve exponential equations
• Solve applied exponential and logarithmic equations
Length: One semester Delivery: This course has been taught face to face, and in an emporium

## Online Content

Algorithmic practice and assessment problem sets delivered by Lumen OHM include a formative assessment covering the whole module, a set of practice problems for each page of text and a summative assessment covering the whole module.

## Online Assessment Features

Many questions in the Lumen OHM libraries are randomized, algorithmic questions. Students get immediate feedback after they submit an answer. Question types include:
• Entering an integer, fraction, decimal
• Graphing
• Reading information from a graph
• Multiple choice