College Algebra Syllabus and Core Topics Overview

College Algebra Syllabus Overview

Course Description

This course covers the foundational concepts of algebra, including properties of real numbers, equations and inequalities, functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations, and complex numbers. The course is designed to meet the General Education requirement for Mathematics.

Course Learning Outcomes and Objectives

Equations and Inequalities

• Linear Equations: Solve linear equations in one variable, including those with fractions and rational expressions. Recognize identities, conditional, and inconsistent equations.

• Complex Numbers: Perform addition, subtraction, multiplication, and division of complex numbers. Work with square roots of negative numbers.

• Quadratic Equations: Solve quadratic equations by factoring, square root method, completing the square, and quadratic formula. Use the discriminant to determine the nature of solutions and select efficient solving methods.

• Other Types of Equations: Solve polynomial, radical, rational exponent, quadratic-in-form, and absolute value equations.

• Linear and Absolute Value Inequalities: Use set-builder and interval notation, graph solution sets, solve linear and compound inequalities, and solve inequalities involving absolute values.

Functions and Graphs

• Basics of Functions: Find domain and range, determine if a relation is a function, evaluate functions, and graph by plotting points. Use the vertical line test and extract information from graphs.

• Function Behavior: Identify intervals of increase, decrease, or constancy. Locate relative maxima and minima, recognize even/odd functions and symmetries, and work with piecewise functions. Find and simplify the difference quotient.

• Linear Functions and Slope: Compute slope, write point-slope and general equations of lines, graph horizontal and vertical lines, and use intercepts for graphing.

• Parallel and Perpendicular Lines: Find slopes and equations for parallel and perpendicular lines.

• Transformations of Functions: Recognize and graph common functions using vertical/horizontal shifts, reflections, and stretching/shrinking.

• Combinations and Compositions: Combine functions arithmetically, form composite functions, and determine domains.

• Inverse Functions: Verify and find inverses, use the horizontal line test, and graph functions with their inverses.

• Distance, Midpoint, and Circles: Use distance and midpoint formulas, write equations of circles in standard form, and convert general to standard form.

Polynomial and Rational Functions

• Quadratic Functions: Recognize and graph parabolas, determine minimum/maximum values, and solve optimization problems.

• Polynomial Functions: Identify polynomial functions, analyze graphs, determine end behavior, find zeros using factoring, and understand multiplicity and turning points.

• Dividing Polynomials: Use long and synthetic division, apply the Remainder and Factor Theorems.

• Zeros of Polynomials: Use the Rational Zero Theorem, find zeros, solve equations, and construct polynomials with given zeros (including conjugate roots).

• Rational Functions: Find domains, identify and graph vertical, horizontal, and slant asymptotes, and use arrow notation.

• Polynomial and Rational Inequalities: Solve inequalities involving polynomials and rational expressions.

Exponential and Logarithmic Functions

• Exponential Functions: Evaluate and graph exponential functions, including base e. Apply compound interest formulas.

• Logarithmic Functions: Convert between logarithmic and exponential forms, evaluate logarithms, use properties, graph logarithmic functions, and determine domains. Work with common and natural logarithms.

• Properties of Logarithms: Apply product, quotient, and power rules. Expand and condense expressions, and use the change of base formula.

• Exponential and Logarithmic Equations: Solve equations using like bases, logarithms, and the one-to-one property.

Systems of Equations and Inequalities

• Linear Systems (Two Variables): Determine solutions, solve by substitution and addition, and identify systems with no or infinite solutions.

• Linear Systems (Three Variables): Verify and solve systems in three variables.

• Partial Fractions (if time permits): Decompose rational expressions with distinct/repeated linear or quadratic factors.

Matrices and Determinants (if time permits)

• Matrix Solutions: Write augmented matrices, perform row operations, and use Gaussian and Gauss-Jordan elimination to solve systems.

Assessment and Grading Policy

• Exams: 90% of the final grade

• Homework: 10% of the final grade

Grading Scale

Grade	Percentage Range	Grade Point Value
A	93-100%	4.0
A-	90-92%	3.7
B+	87-89%	3.3
B	83-86%	3.0
B-	80-82%	2.7
C+	77-79%	2.3
C	70-76%	2.0
D	60-69%	1.0
F	0-59%	0.0

Key Formulas and Concepts (Selected)

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

• Distance Formula: $d = \sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2 }$

• Midpoint Formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

• Standard Form of a Circle: $(x - h)^2 + (y - k)^2 = r^2$

• Exponential Function: $f(x) = a \cdot b^x$

• Logarithmic Function: $y = \log_b x \iff x = b^y$

• Compound Interest Formula: $A = P \left( 1 + \frac{r}{n} \right)^{nt}$

Additional Information

• ADA and DEI Statements: The course provides reasonable accommodations for students with disabilities and is committed to diversity, equity, and inclusion.

• Classroom Etiquette: Students are expected to maintain respectful behavior, avoid disruptions, and adhere to college policies regarding electronic devices and conduct.

• Withdrawals: Students must officially withdraw to avoid receiving an "F". Deadlines are provided in college publications.

Additional info: This syllabus outlines the main topics and learning objectives for a standard College Algebra course, matching the typical curriculum found in college-level algebra textbooks. The formulas and concepts listed are representative of the core material students are expected to master.