Precalculus Syllabus and Study Guide: Course Structure, Topics, and Learning Outcomes

Course Overview

Introduction to Precalculus

This course provides a comprehensive foundation in precalculus, preparing students for further study in calculus and related fields. Topics include linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions, as well as systems of equations and analytic geometry.

• Course Code: MAC1147 (GM) Precalculus

• Department: Mathematics & Statistics, College of Arts and Sciences

• Textbook: Precalculus by Sullivan, Pearson, 12th edition

• Delivery: Standard, with class handouts and online assignments

Learning Outcomes

Core Competencies

Upon completion, students will be able to:

• Solve polynomial and rational inequalities

• Analyze, model, and create graphs of polynomial functions

• Analyze rational, exponential, and logarithmic functions and their graphs

• Analyze conic sections and their graphs

• Solve systems of equations using matrix methods

• Evaluate sums of arithmetic and geometric sequences

• Solve equations involving exponents with the Binomial Theorem

• Solve application problems using mathematical techniques

• Analyze trigonometric functions and their graphs

• Verify and use trigonometric identities

• Solve trigonometric equations

Course Topics

Major Chapters and Content Areas

• Chapter 1: Linear & Quadratic Functions

• Chapter 2: Functions & Their Graphs

• Chapter 3: Polynomial & Rational Functions

• Chapter 4: Exponential & Logarithmic Functions

• Chapter 5: Trigonometric Functions

• Chapter 6: Analytic Trigonometry

• Section 11.1: Systems of Linear Equations

Key Concepts and Definitions

Functions and Their Properties

• Function: A relation in which each input has exactly one output.

• Domain and Range: The set of possible input and output values for a function.

• Linear Function: $f(x) = mx + b$

• Quadratic Function: $f(x) = ax^2 + bx + c$

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

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

• Exponential Function: $f(x) = a^x$

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

• Trigonometric Functions: $\sin(x), \cos(x), \tan(x)$ and their reciprocals

Systems of Equations and Matrices

• System of Linear Equations: A set of equations with multiple variables solved simultaneously.

• Matrix Methods: Techniques such as Gaussian elimination and matrix inversion for solving systems.

• Example: Solve $\begin{cases} 2x + 3y = 5 \\ x - y = 2 \end{cases}$ using matrices.

Conic Sections

• Conic Sections: Curves obtained by intersecting a plane with a cone: circles, ellipses, parabolas, and hyperbolas.

• General Equation: $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$

Sequences and Series

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

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

• Binomial Theorem: $(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k$

Course Structure and Assessment

Grading Breakdown

Component	Percentage
Tests	45%
Quizzes	12%
Online Homework	20%
Attendance & Participation	3%
Final Exam	20%

Assignment Types

• Online Homework: Regular assignments via Access Pearson

• Quizzes: Weekly, based on current topics

• Tests: Four major tests and a comprehensive final exam

• Class Participation: Attendance and engagement

Course Policies and Resources

Attendance and Success Tips

• Regular attendance is required and monitored

• Active participation and timely submission of assignments are essential

• Utilize tutoring services and academic resources for support

Academic Integrity

• Strict adherence to university policies on academic honesty

• No unauthorized collaboration or use of prohibited resources

Accessibility and Support

• Accommodations available for students with disabilities

• Support services include tutoring, counseling, and academic advising

Course Schedule

Weekly Topics and Assignments

• Chapters and sections are covered sequentially, with regular reviews and assessments

• Spring break and holidays are observed as per university calendar

• Final exam is comprehensive, covering all major topics

Additional Info

• Students are encouraged to communicate regularly with the instructor

• Preparation and organization are key to success in this course