College Algebra with Corequisite Support – Course Syllabus and Study Guide

Course Overview

Introduction to College Algebra with Corequisite Support

This course, MAT 037/137, is designed to provide students with a comprehensive understanding of College Algebra, supported by additional instruction and practice. The course is structured to help students master algebraic concepts and develop problem-solving skills necessary for success in mathematics and related fields.

• MAT 037: Developmental support for College Algebra

• MAT 137: College Algebra (credit-bearing course)

Students will engage in both asynchronous online learning and synchronous sessions via Zoom, with a focus on algebraic expressions, equations, functions, and their applications.

Course Structure and Format

Course Dates and Format

• Dates: August 25 – December 3, 2025

• Format: Asynchronous online course with scheduled Zoom meetings (Mon/Wed 6:30–8:45pm, Tue/Thu 5:00–7:00pm)

• Expected Time Commitment: Approximately 15 hours per week (5 hours lecture + 10 hours study and assignments)

Learning Outcomes

MAT 037 Learning Outcomes

By the end of MAT 037, students will be able to:

• Perform basic operations with polynomial, rational, radical, logarithmic, and exponential expressions.

• Solve linear, quadratic, and rational equations.

• Solve systems of linear equations.

• Use function notation and basic terminology associated with functions.

• Graph linear functions.

MAT 137 Learning Outcomes

By the end of MAT 137, students will be able to:

• Solve linear, quadratic, polynomial, rational, logarithmic, and exponential equations.

• Graph and analyze linear, quadratic, higher-degree polynomial, piecewise, rational, logarithmic, and exponential functions.

• Perform algebraic operations on functions.

• Construct and apply appropriate mathematical models to solve problems from business, social science, life, and health sciences.

• Solve systems of equations and inequalities using algebraic techniques, graphing, and matrices.

Key Topics and Concepts

1. Algebraic Expressions and Operations

Algebraic expressions involve variables, constants, and operations such as addition, subtraction, multiplication, division, and exponentiation.

• Polynomial Expressions: Expressions involving terms with non-negative integer exponents.

• Rational Expressions: Ratios of two polynomials.

• Radical Expressions: Expressions containing roots (e.g., square roots).

• Logarithmic and Exponential Expressions: Involving logarithms and exponents.

Example: Simplify $2x^2 + 3x - 5 + 4x^2 - x + 7$.

Solution: Combine like terms: $(2x^2 + 4x^2) + (3x - x) + (-5 + 7) = 6x^2 + 2x + 2$.

2. Equations and Inequalities

Solving equations and inequalities is fundamental in algebra. Types include linear, quadratic, rational, and absolute value equations and inequalities.

• Linear Equation: $ax + b = 0$

• Quadratic Equation: $ax^2 + bx + c = 0$

• Rational Equation: Involves fractions with polynomials in numerator and denominator.

• Solving Inequalities: Similar to equations, but solutions are intervals.

Example: Solve $2x - 5 = 9$.

Solution: $2x = 14 \implies x = 7$.

3. Functions and Their Properties

A function is a relation that assigns exactly one output to each input. Key properties include domain, range, and types of functions (linear, quadratic, polynomial, rational, exponential, logarithmic).

• Function Notation: $f(x)$

• Domain: Set of all possible input values.

• Range: Set of all possible output values.

Example: If $f(x) = 2x + 3$, find $f(4)$.

Solution: $f(4) = 2(4) + 3 = 11$.

4. Graphing Functions

Graphing is a visual representation of functions. Key concepts include intercepts, slope, and transformations.

• Linear Function: $y = mx + b$

• Quadratic Function: $y = ax^2 + bx + c$

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

Example: Graph $y = 2x + 1$.

Solution: The graph is a straight line with slope 2 and y-intercept 1.

5. Systems of Equations

Systems of equations involve finding values that satisfy multiple equations simultaneously. Methods include substitution, elimination, and matrix methods.

• System of Linear Equations:

  • $\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$

• Solution Methods: Substitution, elimination, matrices.

Example: Solve $\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$.

Solution: Add equations: $x + y + 2x - y = 5 + 1 \implies 3x = 6 \implies x = 2$. Substitute: $2 + y = 5 \implies y = 3$.

6. Matrices and Their Applications

Matrices are rectangular arrays of numbers used to solve systems of equations and represent data.

• Matrix Notation: $A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

• Matrix Operations: Addition, subtraction, multiplication.

• Application: Solving systems of equations using matrix methods (e.g., Gaussian elimination).

7. Sequences and Series

Sequences are ordered lists of numbers; series are sums of sequences.

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

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

• Sum of Arithmetic Series: $S_n = \frac{n}{2}(a_1 + a_n)$

• Sum of Geometric Series: $S_n = a_1 \frac{1 - r^n}{1 - r}$ (for $r \neq 1$)

Example: Find the 5th term of the sequence $2, 5, 8, 11, ...$

Solution: $a_5 = 2 + (5-1)\times3 = 14$

Course Materials and Resources

• Textbook: College Algebra + Corequisite Support (8th edition) by Blitzer, Pearson Education.

• Calculator: TI-83, TI-83+, or TI-84+ (other calculators require instructor approval).

• Online Platform: MyLab Math for assignments and practice.

• Binder and Lecture Notes: Recommended for organizing course materials.

Grading Policies and Expectations

• Assignments: MyLab Math assignments and introductory tasks (15% of course grade).

• Quizzes and Exams: Regular quizzes, a midterm, and a final exam.

• Participation: Active participation in discussions and completion of all assignments is expected.

Support and Success Strategies

• Lesson Pages and Note-taking: Each module includes step-by-step lesson pages and video resources.

• Discussions: Engage with classmates in discussion forums for feedback and support.

• Practice Homework: Complete MyLab Math assignments after each section.

• Quizzes: Assess understanding after each module.

• Technical Support: Available through the college’s help desk and online resources.

Academic Policies and Student Conduct

• Academic Integrity: Adherence to college policies on honesty and plagiarism is required.

• Acceptable Use of Technology: Use technology responsibly and ethically.

• Disability Accommodations: Support is available for students with documented needs.

• Communication: Regularly check email and course announcements.

Grading Scale (Sample Table)

The grading scale determines letter grades based on percentage scores. (Additional info: Table values are inferred as the original table is not visible.)

Percentage	Letter Grade
90–100%	A
80–89%	B
70–79%	C
60–69%	D
Below 60%	F

Summary

This syllabus provides a roadmap for success in College Algebra with Corequisite Support. Students are expected to engage actively, utilize available resources, and adhere to academic policies to achieve their learning goals.