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 students to foundational algebraic concepts and problem-solving techniques essential for further study in mathematics.

Course Description

• Course Title and Number: MTH 65 02 – Beginning Algebra

• Credits: 4

• Instructor: Clayton Willett

• Term: Winter 2026

• Location: Online

This course covers the basic concepts and principles of beginning algebra, including arithmetic operations, equations, inequalities, functions, and polynomials.

Student Learning Outcomes

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

• Evaluate basic functions, make tables, and plot graphs.

• Solve linear and absolute value equations and inequalities.

• Graph linear equations and functions.

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

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

Course Outline

The following outline provides a week-by-week breakdown of the main topics covered in the course:

Week	Main Topics
1	Review: real numbers and variables; Rules for algebra
2	Addition and multiplication properties of equality
3	Linear equations in one variable
4	Formulas and problem solving; Linear inequalities; Linear equations with two variables; Graphing equations using intercepts
5	Slope and slope-intercept of a line; Exam one
6	Point-slope form of a line; Parallel and perpendicular lines
7	Solving systems of linear equations by graphing, substitution, and the Additive Method
8	Adding, subtracting, multiplying, and dividing polynomials
9	Negative exponents; Scientific notation; Polynomials in several variables
10	Special products; Compound inequalities; Absolute value equations and inequalities; Exam two
Finals	Comprehensive final exam

Key Algebra Topics Covered

Variables, Real Numbers, and Mathematical Models

Understanding variables and real numbers is foundational to algebra. Variables represent unknown values, while real numbers include all rational and irrational numbers.

• Variable: A symbol (often a letter) used to represent a number.

• Real Numbers: All numbers on the number line, including integers, fractions, and irrational numbers.

• Mathematical Model: An equation or formula that represents a real-world situation.

• Example: If $x$ is the number of apples, then $2x + 3$ could represent the total cost if each apple costs $2$and there is a $3$ dollar fee.

Linear Equations and Inequalities in One Variable

Linear equations and inequalities are equations of the first degree, meaning the variable is not raised to any power other than one.

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

• Linear Inequality: An inequality such as $ax + b > c$ or $ax + b \leq c$.

• Example: Solve $2x + 5 = 11$.

• Solution: $2x = 6 \Rightarrow x = 3$.

Linear Equations in Two Variables and Graphing

Equations with two variables can be graphed on the coordinate plane, and their solutions are points that satisfy the equation.

• Standard Form: $Ax + By = C$

• Slope-Intercept Form: $y = mx + b$

• Graphing: Plot points that satisfy the equation and draw the line through them.

• Example: Graph $y = 2x + 1$ by plotting points for $x = 0$ and $x = 1$.

Systems of Linear Equations

Systems of equations involve finding values that satisfy two or more equations simultaneously.

• Methods: Graphing, substitution, and elimination (Additive Method).

• Example: Solve the system:

  • $x + y = 5$

  • $x - y = 1$

• Solution: Add equations to get $2x = 6 \Rightarrow x = 3$, then $y = 2$.

Exponents and Polynomials

Polynomials are algebraic expressions involving sums of powers of variables. Exponents indicate repeated multiplication.

• Exponent Rules: $a^m \cdot a^n = a^{m+n}$, $(a^m)^n = a^{mn}$, $a^0 = 1$

• Polynomial: An expression like $2x^2 + 3x - 5$

• Example: Simplify $(x^2)(x^3) = x^{2+3} = x^5$

Factoring Polynomials

Factoring is the process of writing a polynomial as a product of its factors.

• Common Factoring: $ax + ay = a(x + y)$

• Special Products: $(a + b)^2 = a^2 + 2ab + b^2$

• Example: Factor $x^2 + 5x + 6 = (x + 2)(x + 3)$

Rational Expressions and Negative Exponents

Rational expressions are fractions with polynomials in the numerator and denominator. Negative exponents represent reciprocals.

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

• Example: $x^{-2} = \frac{1}{x^2}$

Absolute Value Equations and Inequalities

Absolute value measures the distance from zero. Equations and inequalities involving absolute value require considering both positive and negative cases.

• Definition: $|x| = x$ if $x \geq 0$, $|x| = -x$ if $x < 0$

• Example: Solve $|x - 3| = 5$ gives $x - 3 = 5$ or $x - 3 = -5$

• Solution: $x = 8$ or $x = -2$

Grading and Assessment

• Homework: 20 points (completed on MyMathLab, late penalty 2%/day)

• Quizzes: 20 points (two attempts per quiz, late penalty 2%/day)

• Exams: 60 points (two midterms and one comprehensive final, proctored online)

Course Policies

• Students are expected to complete a minimum of two hours of out-of-class work per credit hour each week.

• Academic honesty is strictly enforced; plagiarism and cheating will result in disciplinary action.

• Reasonable accommodations are available for students with documented disabilities.

• Classroom behavior must be respectful and non-disruptive.

• Cell phones must be turned off during class lectures.

Additional Information

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

• For grievances, accommodations, or non-discrimination policies, refer to the Student Handbook or contact the appropriate college office.