MTH 65 02 – Beginning Algebra: Course Syllabus and Study Guide

Course Overview

This syllabus outlines the structure, policies, and content for MTH 65 02 – Beginning Algebra at Southwestern Oregon Community College. The course is designed to introduce and reinforce foundational algebraic concepts, preparing students for further study in mathematics.

Student Learning Outcomes

• Arithmetic Operations: Execute arithmetic operations with signed numbers, algebraic expressions, and polynomials.

• Functions and Graphs: Evaluate basic functions, make tables, and plot graphs.

• Equations and Inequalities: Solve linear and absolute value equations and inequalities.

• Graphing: Graph linear equations and functions.

• Systems of Equations: Solve systems of linear equations using graphing, substitution, and elimination.

• Exponents and Expressions: Use the properties of exponents and simplify expressions containing exponents (distribute and FOIL).

Course Outline

The following topics are covered, aligning with standard beginning-intermediate algebra curricula:

• Week 1: Review of real numbers and variables; rules for algebra

• Week 2: Addition and multiplication properties of equality

• Week 3: Linear equations in one variable

• Week 4: Formulas, problem solving, linear inequalities, and equations with two variables; graphing using intercepts

• Week 5: Slope and slope-intercept form of a line

• Week 6: Point-slope form, parallel and perpendicular lines

• Week 7: Solving systems of linear equations (graphing, substitution, additive method)

• Week 8: Adding, subtracting, multiplying, and dividing polynomials

• Week 9: Negative exponents, scientific notation, polynomials in several variables

• Week 10: Special products, compound inequalities, absolute value equations and inequalities

• Final Exam: Comprehensive review of all topics

Key Algebraic Concepts

Review of Real Numbers and Variables

• Real Numbers: Include all rational and irrational numbers. Rational numbers can be expressed as fractions, while irrational numbers cannot (e.g., $\sqrt{2}$, $\pi$).

• Variables: Symbols (often letters) used to represent unknown values in expressions and equations.

Properties of Equality

• Addition Property: If $a = b$, then $a + c = b + c$ for any $c$.

• Multiplication Property: If $a = b$, then $a \times c = b \times c$ for any $c$.

Linear Equations and Inequalities

• Linear Equation: An equation of the form $ax + b = c$.

• Solving: Isolate the variable using inverse operations.

• Linear Inequality: Similar to equations but uses $<$, $>$, $\leq$, or $\geq$ instead of $=$.

Graphing Linear Equations

• Intercepts: The points where the graph crosses the axes. Find by setting $x=0$ (y-intercept) and $y=0$ (x-intercept).

• Slope-Intercept Form: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Systems of Linear Equations

• Graphing: Plot both equations and find the intersection point.

• Substitution: Solve one equation for a variable and substitute into the other.

• Additive (Elimination) Method: Add or subtract equations to eliminate a variable.

Polynomials and Exponents

• Polynomial: An expression of the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$.

• Operations: Add, subtract, multiply, and divide polynomials using distributive property and FOIL (First, Outer, Inner, Last) for binomials.

• Negative Exponents: $a^{-n} = \frac{1}{a^n}$

• Scientific Notation: Express numbers as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an integer.

Special Products and Factoring

• Special Products: Recognize patterns such as $(a+b)^2 = a^2 + 2ab + b^2$ and $(a-b)^2 = a^2 - 2ab + b^2$.

• Factoring: Express a polynomial as a product of its factors.

Compound and Absolute Value Inequalities

• Compound Inequality: Combines two inequalities, e.g., $a < x < b$.

• Absolute Value Equations: $|x| = a$ has solutions $x = a$ and $x = -a$.

Course Policies and Guidelines

• Grading: Homework (20%), Quizzes (20%), Exams (60%).

• Homework and Quizzes: Completed on MyMathLab; late work penalized 2% per day.

• Exams: Two midterms and one final, proctored online via Honorlock.

• Academic Honesty: Plagiarism and cheating are strictly prohibited and subject to disciplinary action.

• Accessibility: Students with disabilities should contact the Accessible Education Office for accommodations.

• Classroom Conduct: Professional behavior is expected; disruptive students may be removed from class.

Required Materials

• This is an Inclusive Access course; all materials are provided via MyMathLab and Canvas.

Contact Information

• Instructor: Clayton Willett

• Email: [e-mail]

• Accessible Education Office: [phone]