Precalculus Course Syllabus and Study Guide Overview

Course Overview

Introduction to Precalculus (M125)

This course is designed to prepare students for higher-level mathematics and computer science courses, including calculus. It covers a range of foundational topics essential for success in subsequent courses such as M126 (Trigonometric Functions), M215, or M119. The course emphasizes quantitative reasoning and mathematical communication.

• Course Code: M125 (Precalculus)

• Prerequisites: Grade of C- or better in Math M107 or equivalent, or a math placement score of level 4 or above.

• Textbook: Precalculus Essentials, 6th Edition by Robert Blitzer (Chapters 1-3 covered)

• Calculator: TI-83 or TI-84 (TI-Inspire and calculator apps not allowed)

Main Topics Covered

1. Equations and Inequalities

This topic introduces students to solving various types of equations and inequalities, which are foundational skills in precalculus.

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

• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$; solved by factoring, completing the square, or using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Inequalities: Linear and quadratic inequalities, solved using algebraic manipulation and sign charts.

• Applications: Word problems involving equations and inequalities.

2. Functions and Their Graphs

Functions are central to precalculus, providing a framework for modeling relationships between variables.

• Definition of a Function: A relation where each input has exactly one output.

• Function Notation: $f(x)$ denotes the output of function $f$ for input $x$.

• Types of Functions: Linear, quadratic, polynomial, rational, exponential, logarithmic, and inverse functions.

• Graphing: Plotting functions, identifying intercepts, domain, and range.

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

Example: The graph of $f(x) = (x-2)^2 + 3$ is a parabola shifted right by 2 units and up by 3 units.

3. Polynomial and Rational Functions

These functions extend the concept of linear and quadratic functions to higher degrees and ratios of polynomials.

• Polynomial Functions: Functions of the form $f(x) = a_nx^n + \ldots + a_1x + a_0$.

• Zeros of Polynomials: Values of $x$ where $f(x) = 0$.

• Rational Functions: Functions of the form $f(x) = \frac{P(x)}{Q(x)}$, where $P$ and $Q$ are polynomials and $Q(x) \neq 0$.

• Asymptotes: Vertical and horizontal asymptotes describe the behavior of rational functions as $x$ approaches certain values or infinity.

4. Exponential and Logarithmic Functions

These functions are essential for modeling growth and decay, and for solving equations involving exponents and logarithms.

• Exponential Functions: $f(x) = a \cdot b^x$, where $a \neq 0$, $b > 0$, $b \neq 1$.

• Logarithmic Functions: $f(x) = \log_b(x)$, the inverse of the exponential function.

• Properties: Laws of exponents and logarithms, such as $\log_b(xy) = \log_b(x) + \log_b(y)$.

• Applications: Compound interest, population growth, radioactive decay.

Example: The solution to $2^x = 8$ is $x = 3$ because $2^3 = 8$.

5. Quantitative Reasoning and Mathematical Communication

Students are expected to interpret, analyze, and communicate quantitative information effectively.

• Interpretation: Understanding mathematical forms (equations, graphs, tables, words).

• Translation: Converting between different mathematical representations.

• Calculation: Performing accurate mathematical computations.

• Communication: Explaining quantitative evidence in support of arguments for various audiences.

Assignments and Grading

Assignment Types and Weights

The course uses a variety of assignments to assess understanding and application of precalculus concepts.

Assignment Type	Weight
Homework	20%
Quizzes	20%
Written Assignments	10%
Exams (Midterms & Final)	50%

Grading Scale

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

Course Policies and Support

Attendance and Participation

• Students are required to watch all video lectures and complete assignments on time.

• Active participation is essential for success in the course.

Late / Make-up Policy

• Missed quizzes and tests require prior notification and a legitimate reason for make-up.

• Documentation may be required for excused absences.

Academic Integrity

• Use of generative AI tools for assignments is prohibited unless explicitly allowed.

• All work must be original and completed individually unless otherwise specified.

Student Support Services

• Free Tutoring: Both in-person and online options are available.

• Student Counseling Center: Confidential support for academic and personal issues, including stress and ADHD.

• Technical Support: University IT services and online resources are available for technical issues.

Important Dates

Event	Date
Labor Day	September 1st
Last day to withdraw with automatic W	September 28th
Last day to withdraw with W or F	October 17th
Final Exam	October 17th

Additional info: The course schedule includes regular homework, quizzes, written assignments, and exams, with due dates provided in the course summary. Students are encouraged to use all available resources, including tutoring and counseling, to support their learning and well-being.