College Algebra Syllabus and Course Structure Overview

Course Overview

This syllabus outlines the structure, policies, and content coverage for College Algebra (MATH 1314). The course provides an in-depth study of algebraic concepts, including polynomial, rational, radical, exponential, and logarithmic functions, as well as systems of equations, matrices, sequences, series, probability, and conic sections. The course is designed to develop mathematical reasoning, problem-solving skills, and quantitative literacy essential for further study in mathematics and related fields.

Course Topics and Structure

Major Topics Covered

• Equations & Inequalities

• Graphs of Equations

• Functions (including domain, range, operations, compositions, and inverses)

• Polynomial Functions

• Rational Functions

• Exponential & Logarithmic Functions

• Systems of Equations & Matrices

• Conic Sections (may be included)

• Sequences, Series, & Probability (may be included)

Learning Outcomes

• Apply graphing techniques to various types of equations and functions.

• Demonstrate and apply knowledge of properties of functions, including domain, range, operations, compositions, and inverses.

• Evaluate all roots of higher degree polynomial and rational functions.

• Recognize and apply polynomial, rational, radical, exponential, and logarithmic functions and solve related equations.

• Recognize, solve, and apply systems of linear equations using matrices.

Course Modules and Key Assignments

The course is divided into twelve modules (M1–M12), each focusing on a major topic in college algebra. Each module includes mastery assessments, practice assignments, and checks for understanding. Below is a summary of the module topics and their focus:

Module	Main Topic	Key Skills/Assignments
M1	Functions	Identifying functions, function notation, intervals of increase/decrease, evaluating functions
M2	Linear Equations	Working with different forms, calculating slope, graphing, parallel/perpendicular lines
M3	Symmetry & Graph Transformations	Identifying even/odd functions, applying transformations
M4	Combining & Composing Functions	Algebraic operations, function composition
M5	Quadratic Functions	Standard and vertex forms, properties, applications
M6	Finding Roots	Synthetic division, factoring, constructing polynomials
M7	Polynomial & Rational Equations	Graphing, Intermediate Value Theorem, transforming and graphing rational equations
M8	Inverse Functions	Identifying invertibility, finding and graphing inverses
M9	Exponential Functions	Solving, graphing, and applying exponential functions
M10	Logarithms	Converting, solving, graphing, and applying logarithmic equations
M11	Matrix Algebra	Algebraic operations on matrices
M12	Gaussian Matrix Methods & Inverse Matrices	Gauss-Jordan method, solving systems with matrices

Grading Structure

Grades are determined by mastery assessments (80%) and checks for understanding (20%). Each module's mastery assessment is weighted equally. The grading scale is as follows:

Grade	Percent	Description	Grade Points
A	90-100	Excellent/Superior Performance	4
B	80-89	Above Required Performance	3
C	70-79	Minimum Required Performance	2
D	60-69	Below Required Performance	1
F	Below 60	Failure	0

Key Mathematical Concepts and Skills

Functions

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

• Notation: $f(x)$ denotes the value of function f at input x.

• Domain and Range: The set of all possible input values (domain) and output values (range).

• Operations: Functions can be added, subtracted, multiplied, divided, and composed.

• Inverse Functions: If $f(g(x)) = x$ for all $x$ in the domain of $g$, then $g$ is the inverse of $f$.

Equations and Graphs

• Linear Equations: Equations of the form $y = mx + b$ (slope-intercept form), $Ax + By = C$ (standard form).

• Slope: $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Graphing: Plotting points, identifying intercepts, and analyzing symmetry and transformations.

Polynomial and Rational Functions

• Quadratic Functions: $f(x) = ax^2 + bx + c$ (standard form), $f(x) = a(x-h)^2 + k$ (vertex form).

• Factoring: Expressing polynomials as products of lower-degree polynomials.

• Roots/Zeros: Solutions to $f(x) = 0$.

• Rational Functions: Functions of the form $f(x) = \frac{P(x)}{Q(x)}$, where $P$ and $Q$ are polynomials and $Q(x) \neq 0$.

Exponential and Logarithmic Functions

• Exponential Functions: $f(x) = a \cdot b^x$, where $a \neq 0$, $b > 0$, $b \neq 1$.

• Logarithmic Functions: $f(x) = \log_b(x)$, the inverse of the exponential function $b^x$.

• Properties:

  • $\log_b(MN) = \log_b(M) + \log_b(N)$

  • $\log_b\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N)$

  • $\log_b(M^k) = k \log_b(M)$

Systems of Equations and Matrices

• Matrix Operations: Addition, subtraction, multiplication, and finding inverses.

• Solving Systems: Using Gaussian and Gauss-Jordan elimination methods.

• Matrix Equation: $AX = B$, where $A$ is a matrix of coefficients, $X$ is a column matrix of variables, and $B$ is a column matrix of constants.

Course Policies and Resources

• Required Materials: College Algebra and Trigonometry (Lial et al., 7th Edition), scientific or graphing calculator, reliable computer, webcam, and internet access.

• Software: Pearson MyLab Math (access provided after syllabus quiz completion).

• Proctoring: Respondus Lockdown Browser required for assessments.

• Academic Integrity: All work must be original; use of AI-generated solutions is prohibited.

• Support Services: Tutoring, counseling, library, and technical support are available to all students.

Summary Table: Module Topics and Key Skills

Module	Topic	Key Skills
M1	Functions	Identifying, evaluating, and graphing functions
M2	Linear Equations	Forms, slope, graphing, parallel/perpendicular lines
M3	Symmetry & Transformations	Even/odd functions, graph transformations
M4	Combining & Composing Functions	Operations, composition
M5	Quadratic Functions	Standard/vertex forms, properties, applications
M6	Finding Roots	Synthetic division, factoring, constructing polynomials
M7	Polynomial & Rational Equations	Graphing, Intermediate Value Theorem, rational equations
M8	Inverse Functions	Invertibility, finding and graphing inverses
M9	Exponential Functions	Solving, graphing, applications
M10	Logarithms	Solving, graphing, properties, applications
M11	Matrix Algebra	Matrix operations
M12	Gaussian Matrix Methods	Gauss-Jordan method, solving systems

Additional Info

• Students are expected to participate actively, adhere to deadlines, and maintain academic integrity throughout the course.

• All assessments are proctored and require a dedicated calculator and one page of personal notes.

• Support services are available for academic, technical, and personal needs.