College Algebra Syllabus & Core Concepts Study Guide

Course Overview

Introduction to College Algebra

This course, MATH 1111: College Algebra, covers fundamental and advanced algebraic concepts essential for college-level mathematics. The syllabus outlines the main topics, learning outcomes, instructional strategies, and assessment methods. The course is delivered online, utilizing MyMathLab for assignments and tests, and requires a TI-84+ graphing calculator.

Core Topics & Competencies

Review of Algebra

Students will revisit foundational algebraic concepts, including sets, exponents, radicals, polynomials, rational expressions, and complex numbers. Mastery of these basics is crucial for success in subsequent topics.

• Sets and Set Notation: Sets are collections of distinct objects. Set notation uses curly braces, e.g., {1, 2, 3}. Operations include union, intersection, and complement.

• Laws of Exponents: Rules for manipulating exponents, such as $a^m \cdot a^n = a^{m+n}$ and $(a^m)^n = a^{mn}$.

• Simplifying Radicals: Radicals represent roots. Simplification involves factoring and using properties like $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$.

• Polynomials: Expressions with terms of the form $ax^n$. Operations include addition, subtraction, multiplication, and factoring.

• Rational Expressions: Fractions with polynomials in numerator and denominator. Simplification and arithmetic operations are key skills.

• Complex Numbers: Numbers of the form $a + bi$, where $i = \sqrt{-1}$. Operations include addition, subtraction, multiplication, and division.

Equations & Inequalities

This section focuses on solving various types of equations and inequalities, including linear, quadratic, rational, exponential, and logarithmic forms. Application problems are emphasized to connect algebraic methods to real-world scenarios.

• Linear Equations: Equations of the form $ax + b = 0$. Solution: $x = -\frac{b}{a}$.

• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$. Solutions via factoring, completing the square, or quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

• Linear Inequalities: Similar to linear equations, but with inequality signs ($<, >, \leq, \geq$). Solution involves isolating the variable and considering the direction of the inequality.

• Quadratic and Rational Inequalities: Require finding critical points and testing intervals.

• Exponential and Logarithmic Equations: Use properties such as $\log_b(xy) = \log_b x + \log_b y$ and $a^{x} = b \Rightarrow x = \log_a b$.

Functions and Graphs

Understanding functions and their graphical representations is central to algebra. Students learn to plot ordered pairs, define relations and functions, and graph linear, quadratic, exponential, and logarithmic functions.

• Ordered Pairs: Points in the form $(x, y)$ plotted on the Cartesian plane.

• Relations and Functions: A function is a relation where each input has a unique output. Notation: $f(x)$.

• Graphing Linear Functions: $y = mx + b$; $m$ is the slope, $b$ is the y-intercept.

• Graphing Quadratic Functions: $y = ax^2 + bx + c$; the graph is a parabola.

• Graphing Exponential Functions: $y = a^x$; rapid growth or decay.

• Graphing Logarithmic Functions: $y = \log_a x$; inverse of exponential functions.

Systems of Equations & Matrices

Solving systems of equations is essential for modeling and solving real-world problems. The course covers methods for solving systems with two unknowns and introduces matrix techniques.

• Systems of Linear Equations: Two or more equations solved simultaneously. Methods include substitution, elimination, and matrix methods.

• Matrix Representation: Systems can be written as $AX = B$, where $A$ is a matrix of coefficients, $X$ is a column vector of variables, and $B$ is a column vector of constants.

• Application Problems: Real-world scenarios modeled by systems of equations.

Optional Topics

Additional topics may be covered, including variations, absolute value equations, linear programming, conic sections, sequences, series, induction, binomial theorem, permutations, combinations, and probability.

• Variations: Direct, inverse, and joint variation problems.

• Absolute Value Equations/Inequalities: $|x| = a$ has solutions $x = a$ or $x = -a$.

• Conic Sections: Circles, ellipses, parabolas, and hyperbolas.

• Sequences and Series: Arithmetic sequence: $a_n = a_1 + (n-1)d$; Geometric sequence: $a_n = a_1 r^{n-1}$.

• Mathematical Induction: Proof technique for statements involving integers.

• Binomial Theorem: $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$.

• Permutations and Combinations: Counting methods. Permutations: $n!$; Combinations: $\binom{n}{r} = \frac{n!}{r!(n-r)!}$.

• Probability: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Instructional Strategies & Assessment

Learning Methods

Instruction includes collaborative learning, problem-solving, modeling, discussion, practice exercises, and testing. Students use MyMathLab for assignments and tests, with support options such as videos and interactive help.

• Readiness Quizzes: Assess skills before each chapter; scores below 70% require tutoring.

• Homework: Unlimited attempts; must score at least 60% to take chapter tests.

• Tests: Timed, with up to three attempts; highest score counts.

• Final Exam: Comprehensive, online.

Grading Policy

Grades are determined by weighted categories. A minimum grade of "C" is required for progression and graduation.

Category	Weight
Tests	40%
Homework	30%
Participation	10%
Final Exam	20%

Grade Scale:

Letter Grade	Percentage
A	90-100%
B	80-89%
C	70-79%
D	60-69%
F	59% and below

Course Schedule (Sample Weeks)

Weekly Content Progression

The course is structured by weeks, each focusing on specific sections and assignments. Below is a sample schedule:

Week	Competencies	Content	Assignments
1	1	Syllabus Quiz, Chapter 1 Readiness, Sections 1.1, 1.2	Selected assignments in MyLab
5	1-2	Sections 9.1, Chapter 1 Test, Chapter 2 Readiness Quiz	Selected assignments in MyLab
8	2-3	Sections 2.5, Chapter 2 Test, Chapter 3 Readiness Quiz	Selected assignments in MyLab
11	3-4	Sections 3.5, Chapter 3 Test, Chapter 4 Readiness Quiz	Selected assignments in MyLab
14	5	Sections 4.6, Chapter 4 Test, Chapter 5 Readiness Quiz	Selected assignments in MyLab
17	1-5	Sections 5.5, 5.6, Chapter 5 Test, Final Exam	Selected assignments in MyLab

Additional info: The schedule covers all main College Algebra topics, including optional advanced topics as time permits.

Resources & Support

Required Materials

• Textbook: Algebra and Trigonometry: Graphs and Models, Bittinger, Marvin, 7th Edition (Pearson).

• MyMathLab Access: Required for all assignments and tests.

• Calculator: TI-84+ Graphing Calculator or equivalent.

Academic Support

• Tutoring: Available online and on campus through Academic Support Centers.

• Library Services: Access to resources and research support.

• Accessibility Services: Accommodations for students with disabilities.

Ethics & Academic Integrity

Policies

• Academic Misconduct: Cheating, plagiarism, fabrication, and copyright infringement are strictly prohibited.

• Ethical Use of AI: AI tools are not allowed unless explicitly permitted by the instructor.

• Work Ethics: Evaluated in occupational courses; not in this general education course.

Important Dates & Deadlines

Sample Term Dates

• Classes Begin: August 17

• Last Day to Add/Drop: August 19

• Midterm: October 8

• Last Day to Withdraw: October 30

• Final Exam: December 8-9

Summary Table: College Algebra Main Topics

Chapter	Main Topics
1	Review of Algebra: Sets, Exponents, Radicals, Polynomials, Rational Expressions, Complex Numbers
2	Equations & Inequalities: Linear, Quadratic, Rational, Exponential, Logarithmic Equations & Inequalities
3	Graphs of Equations & Functions: Linear, Quadratic, Exponential, Logarithmic Functions
4	Polynomial & Rational Functions: Operations, Graphs, Applications
5	Systems of Equations & Matrices: Solving Systems, Matrix Methods
Optional	Conic Sections, Sequences, Series, Induction, Binomial Theorem, Combinatorics, Probability

Additional info: This guide summarizes the syllabus and core concepts for College Algebra, providing a structured overview for exam preparation and course navigation.