Enhanced College Algebra: Syllabus and Course Structure Study Guide

Course Overview

Course Description

This course, Enhanced College Algebra (MATH 152E), covers foundational and advanced topics in algebra, including equations, inequalities, functions, exponentials, logarithms, and sequences. It fulfills the Level 1 core-mathematics requirement for general education and emphasizes quantitative reasoning and critical thinking skills.

• Field and Order Axioms: Fundamental properties governing algebraic operations and the ordering of numbers.

• Equations and Inequalities: Methods for solving linear, quadratic, and absolute value equations and inequalities.

• Relations and Functions: Introduction to functions, their properties, and graphical representations.

• Exponentials, Roots, Logarithms: Study of exponential and logarithmic functions, including their properties and applications.

• Sequences: Exploration of arithmetic and geometric sequences.

Required Materials

• Textbook: College Algebra, Sullivan, 12th edition, Pearson.

• Online Access: Pearson MyLab Math is required for homework and assignments.

• Calculator: Non-graphing, scientific calculator with logarithmic and exponential functions for exams.

Student Learning Outcomes

• Quantitative Reasoning: Apply mathematical concepts to solve numerical problems in various contexts.

• Critical Thinking: Evaluate assumptions, assess information, and solve problems using logical reasoning.

Grading and Evaluation

Grading Distribution

Component	Percentage
Homework	25%
Attendance / Participation	10%
Exams (3 midterms)	45%
Final Exam	20%
Total	100%

Grading Scale

Grade	Percentage Range
A	90% – 100%
B	80% – 89%
C	70% – 79%
D	60% – 69%
E	0% – 59%

Note: Final grades are rounded to the nearest integer.

Course Calendar and Topics

Weekly Content Overview

Week	Dates	Topics	Key Concepts
1	Aug 17 – 21	§1.1, §R.5, §1.2	Linear equations, factoring, quadratic equations
2	Aug 24 – 28	§1.2, §1.6, §2.1	Absolute value equations/inequalities, distance and midpoint formulas
3	Aug 31 – Sept 4	§2.2, §2.3	Graphs of equations, lines
4	Sept 7 – 11	Review, Exam 1	Assessment of SLO 4, 10
5	Sept 14 – 18	§3.1, §3.2	Functions, graphs of functions
6	Sept 21 – 25	§3.4, §3.5	Library of functions, piecewise functions, graphing transformations
7	Sept 28 – Oct 2	§4.1, §4.3	Linear and quadratic properties, functions and models
8	Oct 5 – 9	§4.3, §4.4, review, Exam 2	Assessment of SLO 4, 10
9	Oct 12 – 16	§5.1, §5.2, §5.3	Polynomial functions and graphs, rational functions
10	Oct 19 – 23	§5.4, §5.5, §8.1	Graphs of rational functions, polynomial/rational inequalities, systems of linear equations
11	Oct 26 – 30	§8.1, §6.1, §6.2	Composite functions, one-to-one and inverse functions
12	Nov 2 – 6	§6.2, review, Exam 3	Assessment of SLO 4, 10
13	Nov 9 – 13	§6.3, §6.4, §6.5	Exponential and logarithmic functions, log properties
14	Nov 16 – 20	§6.5, §6.6	Logarithmic and exponential equations
15	Nov 23 – 27	§6.8	Exponential growth and decay
16	Nov 30 – Dec 4	§6.8, review	Exponential growth and decay, review
Exam Week	Dec 7 - 11	Final Exam	Comprehensive assessment

Key Algebra Topics Covered

Review of Algebra

Students will revisit fundamental algebraic concepts, including operations with real numbers, factoring, and solving linear and quadratic equations.

• Linear Equations: Equations of the form $ax + b = 0$.

• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$.

• Factoring: Expressing polynomials as products of simpler polynomials.

• Example: Solve $2x + 3 = 7$; $x^2 - 5x + 6 = 0$.

Equations & Inequalities

This section covers solving equations and inequalities, including those involving absolute values.

• Absolute Value Equations: $|x| = a$ implies $x = a$ or $x = -a$.

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

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

• Example: Solve $|x - 3| = 5$.

Graphs of Equations

Students learn to graph equations and analyze the properties of lines and other functions.

• Graphing Linear Equations: $y = mx + b$

• Example: Graph $y = 2x + 1$.

Functions

Introduction to functions, their notation, and graphical representation.

• Function Notation: $f(x)$

• Piecewise Functions: Functions defined by different expressions over different intervals.

• Graphing Transformations: Shifts, stretches, and reflections of function graphs.

• Example: $f(x) = |x|$, $g(x) = x^2$

Polynomial Functions

Study of polynomial functions, their properties, and graphs.

• General Form: $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_0$

• Example: $f(x) = x^3 - 2x^2 + x - 5$

Rational Functions

Analysis of rational functions, including their graphs and inequalities.

• Rational Function: $f(x) = \frac{P(x)}{Q(x)}$ where $Q(x) \neq 0$

• Example: $f(x) = \frac{1}{x-2}$

Exponential & Logarithmic Functions

Exploration of exponential and logarithmic functions, their properties, and applications such as growth and decay.

• Exponential Function: $f(x) = a^x$

• Logarithmic Function: $f(x) = \log_a(x)$

• Exponential Growth/Decay: $y = y_0 e^{kt}$

• Example: Solve $2^x = 8$; $\log_2(8) = x$

Systems of Equations & Matrices

Solving systems of linear equations using algebraic methods and introduction to matrices.

• System of Equations: Two or more equations solved together.

• Example: Solve $\begin{cases} x + y = 3 \\ 2x - y = 0 \end{cases}$

Sequences, Series, & Induction

Introduction to sequences and series, including arithmetic and geometric progressions.

• Arithmetic Sequence: $a_n = a_1 + (n-1)d$

• Geometric Sequence: $a_n = a_1 r^{n-1}$

• Example: Find the 5th term of $a_n = 2 + 3(n-1)$

Course Policies and Resources

• Attendance: Required; excessive absence may affect grades.

• Academic Honesty: Students must adhere to university standards; generative AI use is prohibited.

• ADA Accommodations: Available for students with documented disabilities.

• Support Resources: Tutoring, advising, technology, health, and financial resources are available.

Exam and Homework Policies

• Homework: Completed online; multiple attempts allowed; due by last day of classes.

• Exams: Three midterms and a comprehensive final; one notecard allowed per exam; retake opportunity for Exam 1.

Transferable Skills

• Critical Thinking: Evaluating assumptions and solving problems.

• Quantitative Reasoning: Analyzing and solving numerical problems.

Emergency and Weather Procedures

• Weather Plans: Follow university guidance for schedule adjustments.

• Emergency Procedures: Know exit routes and protocols; notify instructor of special needs.

Summary Table: Main College Algebra Topics

Chapter	Main Topics
0	Review of Algebra
1	Equations & Inequalities
2	Graphs of Equations
3	Functions
4	Polynomial Functions
5	Rational Functions
6	Exponential & Logarithmic Functions
7	Systems of Equations & Matrices
8	Conic Sections
9	Sequences, Series, & Induction
10	Combinatorics & Probability

Additional info: The syllabus provides a comprehensive structure for College Algebra, aligning with standard topics and learning outcomes. The weekly calendar ensures coverage of all major algebraic concepts, preparing students for both academic and professional success.