**Elementary Algebra**

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**This course includes:**

**916**

### dynamic, multi-version questions

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### Elementary Algebra Course Outline

### What are the foundations of algebra?

Concepts Covered:

- What are the basic properties of whole numbers?
- How is the language of algebra used?
- How are integers added and subtracted?
- What are the steps to multiply and divide integers?
- What is the best way to visualize fractions?
- How do you add and subtract fractions?
- How are problems with decimals solved?
- What makes an integer a real number?
- What are the properties of real numbers?
- How are units converted to different systems of measurement?

### How are linear equations and inequalities solved?

Concepts Covered:

- What steps must be followed to solve equations by using the subtraction and addition properties of equality?
- How are equations solved by using the division and multiplication properties of equality?
- How are equations with variables and constants on both sides solved?
- What general strategy is used to solve linear equations?
- How are equations with fractions or decimals solved?
- How is a formula solved for a specific variable?
- What steps must be taken to solve linear inequalities?

### How are math models used to help solve everyday problems?

Concepts Covered:

- What problem-solving strategies can be used to solve word problems?
- How are percent problems solved?
- What are mixture problems?
- How is the Pythagorean Theorem applied to triangles and rectangles?
- How are uniform motion applications solved?
- What steps must be taken to solve applications with linear inequalities?

### What are uses of different types of graphs?

Concepts Covered:

- How is the rectangular coordinate system used?
- What are the steps to graph linear equations in two variables?
- How is a line graphed by using intercepts?
- Why is understanding the slope of a line important?
- How is the slope-intercept form of a line identified and used?
- How is the equation of a line found?
- What do the graphs of linear inequalities look like?

### How are systems of linear equations solved?

Concepts Covered:

- How are systems of equations solved by graphing?
- How are systems of equations solved by substitution?
- How are systems of equations solved by elimination?
- How are applications with systems of equations solved?
- How are mixture applications with systems of equations solved?
- How are systems of linear inequalities graphed?

### What are polynomials, and how are they used?

Concepts Covered:

- What steps must be followed to add and subtract polynomials?
- What are the multiplication properties of exponents?
- How are polynomials multiplied?
- What are the special products patterns of polynomials?
- How are monomials divided?
- How are polynomials multiplied?
- What are the rules of integer exponents and scientific notation?

### How is factoring used to solved certain types of equations?

Concepts Covered:

- How is the greatest common factor of two or more expressions found, and how does factor by grouping work?
- How do you factor quadratic trinomials with leading coefficient 1?
- How do you factor quadratic trinomials with leading coefficient other than 1?
- How are special products factored?
- What is the general strategy for factoring polynomials?
- How are quadratic equations solved?

### What types of problems are rational expressions and equations used to solve?

Concepts Covered:

- How are rational expressions simplified?
- How are rational expressions multiplied and divided?
- How are rational expressions with a common denominator added and subtracted?
- How are rational expressions with unlike denominators added and subtracted?
- What steps must be followed to simplify complex rational expressions?
- How are rational equations solved?
- How are proportions and similar figure applications solved?
- What are uniform motion and work applications, and how are they solved?
- What are direct and inverse variation problems, and how are they solved?

### What are the defining properties of roots and radicals?

Concepts Covered:

- How do you simplify and use square roots?
- What different properties can be used to simplify square roots?
- How are square roots added and subtracted?
- How are square roots multiplied?
- How are square roots divided?
- What steps must be followed to solve equations with square roots?
- What are higher roots, and how are they handled in expressions?
- What are rational exponents?

### How are quadratic equations applied to various situations?

Concepts Covered:

- How are quadratic equations solved by using the square root property?
- How are quadratic equations solved by completing the square?
- How are quadratic equations solved by using the quadratic formula?
- How are applications modeled by quadratic equations solved?
- How do you graph quadratic equations?

Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

**About the authors:**

## Senior Contributing Authors

**Lynn Marecek,** Santa Ana College

**MaryAnne Anthony-Smith,** Formerly of Santa Ana College

## Assessment Question Author

**Donna Densmore**Mathematics Instructor

Bossier Parish Community College