MAC1140 Precalculus Algebra: Syllabus and Core Study Guide

Course Overview

MAC1140 Pre-Calculus Algebra is a foundational college-level mathematics course designed to prepare students for calculus. The course covers a broad range of algebraic and analytic topics, emphasizing functions, graphs, and mathematical modeling. Students will develop skills in manipulating algebraic expressions, solving equations and inequalities, and analyzing various types of functions and their applications.

Course Structure and Main Topics

• Polynomial and Rational Functions

• Exponential and Logarithmic Functions

• Matrices and Systems of Equations

• Conic Sections and Analytic Geometry

• Sequences, Series, and the Binomial Theorem

Module 1: Polynomial and Rational Functions

Key Concepts

• Absolute Value Inequalities: Solve inequalities involving absolute values using algebraic manipulation and graphical interpretation.

• Function Behavior: Identify intervals where functions increase, decrease, or remain constant. Locate relative maxima and minima using graphs.

• Symmetry and Function Types: Test for symmetry (even, odd, neither) and recognize piecewise functions.

• Transformations: Apply vertical/horizontal shifts, reflections, and stretching/shrinking to graph functions.

• Polynomial Functions: Identify, graph, and analyze polynomial functions, including end behavior, zeros, and turning points.

• Division and Theorems: Use long and synthetic division, the Remainder Theorem, and the Factor Theorem.

• Finding Zeros: Apply the Rational Zero Theorem, Linear Factorization Theorem, and Descartes's Rule of Signs.

• Rational Functions: Identify and graph rational functions, including asymptotes (vertical, horizontal, slant) and transformations.

• Inequalities: Solve polynomial and rational inequalities and apply them to real-world problems.

Module 2: Exponential and Logarithmic Functions

Key Concepts

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

• Logarithmic Functions: Convert between logarithmic and exponential forms, evaluate logarithms, and use properties (product, quotient, power).

• Graphing and Domains: Graph logarithmic functions and determine their domains.

• Solving Equations: Solve exponential and logarithmic equations using properties and the one-to-one property.

• Applications: Model exponential growth and decay, use logistic growth models, and select appropriate models for data.

Module 3: Matrices, Determinants, and Systems of Equations

Key Concepts

• Partial Fraction Decomposition: Decompose rational expressions with distinct and repeated linear or quadratic factors.

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

• Matrix Algebra: Add, subtract, and multiply matrices; perform scalar multiplication; solve matrix equations; and model applications.

• Determinants and Cramer's Rule: Evaluate determinants (second and third order) and use Cramer's Rule to solve systems of equations.

Module 4: Conic Sections, Sequences, and Series

Key Concepts

• Conic Sections: Graph and write equations for ellipses, hyperbolas, and parabolas (centered at the origin and not at the origin). Solve applied problems and identify conics without completing the square.

• Sequences and Series: Find terms of sequences using general and recursive formulas, use factorial and summation notation, and analyze arithmetic and geometric sequences.

• Formulas: Use formulas for the general term and sum of arithmetic and geometric sequences, including infinite geometric series.

Assessment and Grading

Assessment	Percent of Final Grade
Proctored Chapter Tests	60%
Discussions	4%
Homework	21%
Proctored Final Exam	15%

Grading Scale:

Grade	Percentage
A	90 - 100%
B	80 - 89.9%
C	70 - 79.9%
D	60 - 69.9%
F	0 - 59.9%

Required Materials

• Textbook: Algebra and Trigonometry, 6th Edition (Pearson)

• Technology: Reliable computer, internet, webcam, microphone, whiteboard, and MyMathLab access

Academic Integrity and Participation

• All work must be your own; academic dishonesty results in severe penalties.

• Regular participation and timely completion of assignments are required for success.

• Attendance is verified by completing an academic activity in the first week.

Support and Resources

• Math Lab and Academic Success Center for tutoring and study support

• Online tutoring via Brainfuse

• Technical support and accessibility resources available through Broward College

Summary Table: Main Topics and Learning Outcomes

Module	Main Topics	Key Learning Outcomes
1	Polynomial & Rational Functions	Graphing, solving, transformations, inequalities
2	Exponential & Logarithmic Functions	Evaluation, graphing, equations, modeling
3	Matrices & Systems	Matrix operations, solving systems, determinants
4	Conic Sections, Sequences & Series	Graphing conics, sequence formulas, series sums

Additional info: This syllabus provides a comprehensive overview of the MAC1140 Precalculus Algebra course, including all major topics and expectations. For detailed explanations, examples, and practice problems, refer to the required textbook and course materials.