# MATH 1033 Intermediate Algebra

**CATALOG DESCRIPTION:**

Topics included graphing linear functions, quadratic functions, absolute value functions, radical functions and rational functions, with a focus on simplifying, adding and multiplying these functions as well as methods to solve equations involving these types of functions. Other topics include inequalities, functional equations, factoring polynomials, applied problems, systems of equations, quadratic formula, completing the square and complex numbers. (Prerequisite: Placement through Daytona State College placement test or MAT0024 with grade of “B” or better.). Lab Fee $5. FA, SP, SU.

**This course also helps develop the general education
skills of (1) critical thinking; (4) computation; and (6) computer literacy.**

CREDIT HOURS: 4 semester hours

DEGREE: A.A. or A.A.S.

CONTACT HOURS: 60 hours lecture and 15 Hours in Academic Support Center

INSTRUCTION METHODS: Lecture

MAJOR LEARNING OUTCOMES:

After successful completion of this course, the student will be able to:

1. Simplify rational expressions and complex fractions. **
(1, 4, 6)**

2. Add, subtract, multiply, and divide rational expressions.

**(1, 4, 6)**

3. Solve rational equations.

**(1, 4, 6)**

4. Solve applied problems that lead to rational equations.

**(1, 4, 6)**

5. Graph linear equations.

**(1, 4, 6)**

6. Identify relations that are functions.

**(1, 4, 6)**

7. Recognize domain and range of relations.

**(1, 4, 6)**

8. Use functional notation and evaluate functions at specific domain values.

**(1, 4, 6)**

9. Find the slope of a line and use slope to determine if lines are parallel or perpendicular.

**(1, 4, 6)**

10. Use ideas of slope and intercepts to name equations for described lines.

**(1, 4, 6)**

11. Solve systems of linear equations using substitution and elimination methods.

**(1, 4, 6)**

12. Solve applied problems using systems of equations in two variables.

**(1, 4, 6)**

13. Solve inequalities and compound inequalities.

**(1, 4, 6)**

14. Solve first degree equations and inequalities that contain absolute value terms.

**(1, 4, 6)**

15. Solve literal equations and formulas for specified variables.

**(1, 4, 6)**

16. Use interval notation to describe solution sets of inequalities.

**(1, 4, 6)**

17. Use rational exponents and related properties to simplify radical expressions.

**(1, 4, 6)**

18. Solve equations involving radicals.

**(1, 4, 6)**

19. Rationalize the denominator and otherwise put radical expressions in simplified form.

**(1, 4, 6)**

20. Be familiar with the field of complex numbers and how they are related with the reals, rational, irrationals, and integers.

**(1, 4, 6)**

21. Perform basic operations of addition, subtraction, multiplication, division, and exponentiation with complex numbers.

**(1, 4, 6)**

22. Solve quadratic equations using the zero-product property.

**(1, 4, 6)**

23 Solve quadratic equations using the square root property and the method of completing the square.

**(1, 4, 6)**

24. Solve quadratic equations using the quadratic formula.

**(1, 4, 6)**

25. Solve quadratic inequalities.

**(1, 4, 6)**

26. Solve applied problems that involve quadratic equations.

**(1, 4, 6)**

27. Apply the Pythagorean Theorem to solve right triangle application problems.

**(1, 4, 6)**

COURSE OUTLINE:

I. Operations Using Rational Expressions

A. Simplifying Rational Expressions Including Multiplication and Division

B. Finding Least Common Multiples

C. Addition of Rational Expressions

D. Subtraction of Rational Expressions

E. Simplifying Complex Rational Expressions

II. Rational Equations

A. Solving Rational Equations

B. Applications of Rational Equations

C. Solving Rational Literal Equations (Formulas)

III. Functions

A. Definition and Identifying Functions

B. Domain and Range of Functions

C. Slope

D. Graphing Linear Functions

E. Using Slope-Intercept Form to Determine Linear Equations

IV. Systems of Linear Equations

A. Solution by Graphing

B. Elimination and Substitution Methods

C. Applied Problems that Involve 2 variable systems

V. Rational Exponents and Radicals

A. Introduction to Radicals

B. Rational Exponents and Their Properties

C. Simplifying Radical Expressions

D. Addition, Multiplication and Division of Radical Expressions

E. Rationalizing the Denominator

F. Equations with Radicals

G. Pythagorean Theorem and Related Applied Problems

VI. Complex Numbers and Quadratic Equation

A. Complex Numbers

B. Square Root Property and Completing the Square

C. The Quadratic Formula

VII. Inequalities

A. Linear Inequalities and Interval Notation

B. Set Operations and Compound Inequalities

C. Equations and Inequalities Involving Absolute Value

D. Quadratic Inequalities