Elementary Algebra
Welcome to Elementary Algebra, a foundational one-semester course meticulously designed for students embarking on their first-level algebra journey. Structured across 71 class sessions, each lasting 1.5 hours, this course is specifically tailored for learners with diverse backgrounds and learning styles who seek to build a solid mathematical foundation and gain confidence before advancing to college-level mathematics.
Building directly upon prealgebra, the course presents material in small, logical steps, ensuring accessibility for college students needing developmental math, high school students, and adult learners returning to education. Our instructional approach emphasizes a proven cycle: assessing readiness, breaking down complex procedures into clear, step-by-step instructions, reinforcing learning through immediate practice, and connecting abstract algebra to engaging, real-world applications.
Throughout the course, learners will progress through ten comprehensive modules. You will start by reinforcing mathematical foundations, including arithmetic review and the real number system, before mastering the skills to solve linear equations and inequalities. The curriculum then seamlessly integrates math models and geometry, enabling you to translate everyday word problems into algebraic equations. As you advance, you will dive into graphing on the coordinate plane, solving systems of linear equations, and performing operations with polynomials. The final stages of the course focus on advanced foundational topics, including factoring, rational expressions, roots and radicals, and a thorough exploration of quadratic equations using methods like completing the square and the quadratic formula.
By the end of this course, you will have developed robust problem-solving skills, enhanced your mathematical literacy, and mastered the ability to apply algebraic reasoning to practical scenarios. Through interactive features like pre-module diagnostic quizzes, step-by-step algorithm guides, and real-world writing exercises, Elementary Algebra 2e ensures you are fully prepared and confident to succeed in Intermediate Algebra and beyond.
Adaptive
Varies by mastery
2 domains
How the course works
A session is a short study-and-practice checkpoint, not a fixed class meeting. The course can move faster when material is already familiar and slow down when a topic needs more practice.
Study a focused page
Read a small prerequisite-ordered set that gives the context for the next practice step.
Check understanding
Answer linked questions so the system can tell what is already strong and what needs review.
Keep moving
Unlock the next set after the current material is understood, with review scheduled as needed.
Who this course is for
This course is designed for students taking a one-semester elementary algebra course. It is specifically tailored for learners with diverse backgrounds and learning styles who need to build a solid mathematical foundation. Because the content builds directly on Prealgebra and is presented in small, logical steps, it is ideal for students who need to build confidence in their math skills before moving on to more advanced college-level mathematics.
Objectives
- Simplify numerical expressions and evaluate algebraic expressions using the properties of the real number system and the order of operations.
- Solve linear equations and inequalities in one variable using algebraic properties, and graph the solution sets of inequalities on a number line.
- Translate real-world scenarios, including geometric, percentage, and simple interest problems, into algebraic equations and solve them.
- Graph linear equations in two variables on the rectangular coordinate system and determine the equation of a line given various parameters such as slope and intercepts.
- Formulate and solve systems of linear equations in two variables using graphing, substitution, and elimination methods to address applied problems.
- Perform arithmetic operations (addition, subtraction, multiplication, and division) on polynomials and apply the properties of exponents, including negative exponents and scientific notation.
- Factor polynomials using various techniques, such as identifying the greatest common factor, factoring trinomials, and recognizing special products.
- Simplify, add, subtract, multiply, and divide rational expressions, and solve rational equations, including those involving complex fractions.
- Simplify radical expressions and perform operations with square roots to solve radical equations.
- Solve quadratic equations using multiple methods, including factoring, the square root property, completing the square, and the quadratic formula, and graph quadratic equations.
Syllabus
Solve Equations Using the Subtraction and Addition Properties of Equality
Solve Equations using the Division and Multiplication Properties of Equality
Solve Equations with Variables and Constants on Both Sides
Use a General Strategy to Solve Linear Equations
Solve Equations with Fractions or Decimals
Solve a Formula for a Specific Variable
Solve Linear Inequalities
Use a Problem-Solving Strategy
Solve Percent Applications
Solve Mixture Applications
Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem
Solve Uniform Motion Applications
Solve Applications with Linear Inequalities
Use the Rectangular Coordinate System
Graph Linear Equations in Two Variables
Graph with Intercepts
Understand Slope of a Line
Use the Slope-Intercept Form of an Equation of a Line
Find the Equation of a Line
Graphs of Linear Inequalities
Solve Systems of Equations by Graphing
Solving Systems of Equations by Substitution
Solve Systems of Equations by Elimination
Solve Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations
Graphing Systems of Linear Inequalities
Add and Subtract Polynomials
Use Multiplication Properties of Exponents
Multiply Polynomials
Special Products
Divide Monomials
Divide Polynomials
Integer Exponents and Scientific Notation
Greatest Common Factor and Factor by Grouping
Factor Trinomials of the Form x2+bx+c
Factor Trinomials of the Form ax2+bx+c
Factor Special Products
General Strategy for Factoring Polynomials
Quadratic Equations
Simplify Rational Expressions
Multiply and Divide Rational Expressions
Add and Subtract Rational Expressions with a Common Denominator
Add and Subtract Rational Expressions with Unlike Denominators
Simplify Complex Rational Expressions
Solve Rational Equations
Solve Proportion and Similar Figure Applications
Solve Uniform Motion and Work Applications
Use Direct and Inverse Variation
Simplify and Use Square Roots
Simplify Square Roots
Add and Subtract Square Roots
Multiply Square Roots
Divide Square Roots
Solve Equations with Square Roots
Higher Roots
Rational Exponents
Solve Quadratic Equations Using the Square Root Property
Solve Quadratic Equations by Completing the Square
Solve Quadratic Equations Using the Quadratic Formula
Solve Applications Modeled by Quadratic Equations
Graphing Quadratic Equations in Two Variables
References
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