Intermediate Algebra (College Algebra) – Course Syllabus and Study Guide

General Information

This syllabus outlines the structure, objectives, and requirements for a college-level Intermediate Algebra course, which is equivalent to College Algebra. The course is designed to provide students with foundational algebraic skills necessary for further study in mathematics and related fields.

Course Details

• Section Number: 08003

• Meeting Times and Location: ONLINE

• Credits: 4 (elective credit only)

• Term: FALL 2023

Instructor Information

• Instructor: Monika Rydzewski

• Office Hours: Wednesday 2:00pm-2:40pm, online

• Email: [e-mail]

Course Description

This course covers essential algebraic concepts including sets, relations, functions, polynomial operations, factoring, rational expressions, equations (linear, quadratic, radical, rational), systems of equations, inequalities, exponents, radicals, graphs of linear equations, and applications. The course prepares students for further study in mathematics and related disciplines.

• Prerequisites: MAT 0022, MAT 0028 with a 'S' grade, or appropriate placement score.

Course Objectives

Upon completion of the course, students should be able to:

1. Factoring

   • Factor polynomials completely.

   • Factor polynomials with common factors.

2. Algebraic Fractions and Rational Exponents

   • Determine values for which an algebraic fraction is undefined.

   • Perform operations and express in simplest form.

   • Solve rational equations.

   • Solve problems involving variation.

3. Radicals and Rational Exponents

   • Express in simplest radical or rational exponent form.

   • Perform operations.

   • Rationalize denominators.

   • Solve radical equations.

4. Complex Numbers

   • Define complex numbers.

   • Perform operations with complex numbers.

5. Quadratic Equations

   • Solve by factoring, taking roots, completing the square, and using the quadratic formula.

   • Use the discriminant to determine the nature of the roots.

6. Linear Equations and Inequalities in Two Variables

   • Graph the solution sets.

   • Find the equation given various criteria.

   • Express the equation in various forms.

7. Systems of Linear Equations and Inequalities in Two Variables

   • Solve systems of equations graphically and algebraically.

   • Solve systems of inequalities graphically.

8. Introduction to Functions

   • Define function.

   • Express functions numerically, symbolically, and graphically.

9. Applications of all the above topics.

Key Concepts and Formulas

Factoring

• Greatest Common Factor (GCF): The largest factor shared by all terms in a polynomial.

• Factoring Trinomials: Expressing $ax^2 + bx + c$ as $(mx + n)(px + q)$.

• Difference of Squares: $a^2 - b^2 = (a - b)(a + b)$

• Perfect Square Trinomials: $a^2  2ab + b^2 = (a + b)^2$

Algebraic Fractions and Rational Exponents

• Undefined Fractions: A rational expression is undefined when its denominator equals zero.

• Operations: Addition, subtraction, multiplication, and division of rational expressions.

• Rational Exponents: $a^{m/n} = \sqrt[n]{a^m}$

Radicals and Rational Exponents

• Simplifying Radicals: $\sqrt{a^2} = |a|$

• Rationalizing Denominators: Multiplying numerator and denominator by a suitable radical to eliminate radicals from the denominator.

• Solving Radical Equations: Isolate the radical and raise both sides to the appropriate power.

Complex Numbers

• Definition: A complex number is of the form $a + bi$, where $i = \sqrt{-1}$.

• Operations: Addition, subtraction, multiplication, and division of complex numbers.

Quadratic Equations

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Discriminant: $D = b^2 - 4ac$ determines the nature of the roots.

Linear Equations and Inequalities in Two Variables

• Slope-Intercept Form: $y = mx + b$

• Standard Form: $Ax + By = C$

• Graphing: Plotting points and drawing the line or region representing the solution set.

Systems of Linear Equations and Inequalities

• Solving Systems: By substitution, elimination, or graphing.

• Graphical Solution: The intersection point(s) of the lines or regions.

Functions

• Definition: A function is a relation in which each input has exactly one output.

• Representations: Tables, graphs, equations, and mappings.

Course Materials

• Textbook: Intermediate Algebra w/MML (custom HCC edition or 8th edition) by Martin-Gay

• Calculator: Scientific calculator encouraged but not required.

Graded Assignments

• Tests: Mid-term and final exams, proctored online, each worth 200 points.

• Quizzes: Weekly online quizzes with multiple attempts allowed.

• Homework: Online homework sets for each section, completed using MyMathLab.

Grading Procedures

Grades are calculated as a percentage of total points earned. Letter grades are assigned as follows:

Percentage	Letter Grade
90%-100%	A
80%-89%	B
70%-79%	C
60%-69%	D
Below 60%	F

Course Policies

• Attendance: Regular participation in online activities is required.

• Make-Up Policy: Make-up work is allowed only under documented circumstances and must be arranged in advance.

College Policies

• Academic Integrity: Cheating, plagiarism, and unauthorized collaboration are prohibited.

• Important Dates: Deadlines for adding, dropping, and withdrawing from the course are specified by the college calendar.

• Title IX: Prohibits discrimination based on sex, gender, or related factors.

• Disability Services: Accommodations are available for students with documented disabilities.

Realities of Taking an Online Course

Self-Discipline

• Online courses require strong time management and self-motivation.

• Students must keep up with assignments, quizzes, and exams independently.

Meeting Deadlines

• Assignments and quizzes have strict deadlines; late work is generally not accepted.

Technical Requirements

• Computer with at least 2 GHz processor and 1 GB+ RAM.

• High-speed internet connection.

• Webcam and microphone for proctored exams.

• Required software: web browser, PDF reader, Microsoft Office, etc.

Computer Skills Prerequisites

• Basic computer navigation, file management, and internet skills.

• Email and word processing proficiency.

Technical Help

• Technical support is available through the college's help desk and online resources.

Additional info:

• This syllabus provides a comprehensive overview of the course structure and expectations for College Algebra students. For detailed content on each algebraic topic, refer to the course textbook and assigned materials.