Precalculus Syllabus and Course Information – Key Concepts and Study Guide

Precalculus Syllabus and Course Information

Course Overview

This course is designed for students intending to study mathematics, science, or engineering. It covers essential precalculus topics including functions, equations, inequalities, graphs, and applications. The course prepares students for calculus by developing algebraic skills and understanding of mathematical models.

Learning Objectives

• Domain, Range, and Symmetry: Define the domain, range, and symmetry of a function given its formula or graph.

• Function Composition: Develop the sum, product, and composition of two functions.

• Attributes of Rational Functions: Develop the attributes and graph of a rational function.

• Polynomial and Rational Equations: Solve polynomial and rational equations and inequalities.

• Graphing: Analyze the graph of a polynomial and rational function.

• Exponential and Logarithmic Functions: Analyze the attributes of exponential and logarithmic functions.

• Systems of Equations: Solve systems of equations using substitution and matrices.

• Binomial Theorem: Write the terms of a sequence using the Binomial Theorem.

Prerequisites

• MAT-108 (Intermediate Algebra) or equivalent background verified by placement testing.

Required Materials

• Textbook: Precalculus, 12th Edition by Michael Sullivan.

• Calculator: A scientific calculator that performs exponential and logarithmic calculations.

Major Topics and Weekly Schedule

The following topics are covered throughout the semester, organized by week:

Week	Topics	Important Dates
8/18	Course Introduction, Algebra Essentials, Polynomial Equations, Rational Expressions, Solving Equations, Interval Notation, Solving Inequalities
8/25	Distance and Midpoint Formulas, Graphs of Equations in Two Variables, Symmetry, Linear Equations
9/1	Functions, Graphs of Functions	No Class Monday, September 1 (Labor Day)
9/8	Library of Functions, Piecewise-Defined Functions, Graphing Techniques	Exam 1 Wednesday, September 16 (covers Chapters 1 and 2)
9/15	Quadratic Functions, Polynomial Functions, Rational Functions, Inequalities
9/22	Polynomial and Rational Inequalities, Synthetic Division, Rational Zeros, Exponential and Rational Inequalities
9/29	Exponential Functions, Inverse Functions	Exam 2 Wednesday, October 15 (covers Chapters 3 and 4)
10/20	Logarithmic and Exponential Equations, Financial Models, Exponential Growth and Decay Models
10/27	Systems of Equations, Matrices, Sequences	Exam 3 Wednesday, November 5 (covers Chapter 5)
11/10	Conics, Ellipses, Hyperbolas
11/17	Systems of Linear Equations, Substitution, Matrices, Inequalities, Sequences
11/24	Review for Exam 4	No Class Monday, November 24 (Thanksgiving Break)
12/1	Binomial Theorem, Final Exam Review	Exam 4 Wednesday, December 3 (covers Chapters 10 and 11)
12/8	Final Exam	Last Class Day Monday, December 8

Key Concepts and Definitions

• Function: A relation in which each input has exactly one output. Functions can be represented by equations, graphs, or tables.

• Domain and Range: The domain is the set of all possible input values; the range is the set of all possible output values.

• Polynomial: An expression consisting of variables and coefficients, involving only non-negative integer powers of variables.

• Rational Function: A function that is the ratio of two polynomials.

• Exponential Function: A function of the form $f(x) = a^x$, where $a > 0$ and $a \neq 1$.

• Logarithmic Function: The inverse of an exponential function, $f(x) = \log_a(x)$.

• System of Equations: A set of equations with the same variables, solved simultaneously.

• Matrix: A rectangular array of numbers used to represent systems of equations and perform operations.

• Binomial Theorem: Describes the algebraic expansion of powers of a binomial: $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$

Examples and Applications

• Example (Polynomial Equation): Solve $x^2 - 5x + 6 = 0$. Factoring gives $(x-2)(x-3)=0$, so $x=2$ or $x=3$.

• Example (Exponential Growth): The population $P$ after $t$ years is $P = P_0 e^{rt}$, where $P_0$ is the initial population and $r$ is the growth rate.

• Example (System of Equations): Solve $\begin{cases} x + y = 5 \\ x - y = 1 \end{cases}$. Adding equations: $2x = 6 \Rightarrow x = 3$, then $y = 2$.

Grading Policy

• Sixty-minute examinations: 400 points total (100 points each)

• Final examination: 200 points

• Grade scale: A (540–600), B (480–539), C (420–479), D (360–419), F (0–359)

Attendance and Make-Up Policy

• Attendance is expected but not directly graded.

• Missed exams must be made up promptly; see syllabus for details.

Academic Integrity

• Cheating and plagiarism are strictly prohibited and will result in disciplinary action.

Support Services

• Blackboard: Online course materials and assignments.

• MyCCAC Portal: Registration, grades, financial aid, and communication.

• CCAC Email: Official communication regarding the course.

• Learning Support: Free tutoring available remotely.

• Office of Disability Resources: Accommodations for students with disabilities.

Assigned Problems (Sample Table)

The syllabus provides a list of assigned problems from the textbook for each section. These problems are intended to reinforce key concepts and problem-solving skills.

Section/Page Number	Assigned Problems
A.1 p.11–A.11	55–56, 69–76, 85–106
A.3 p.A42–A53	30–39, 44–47, 54–59, 75–81, 102
1.1 p.31–32	19–38, 45–68 (intercepts only), 57–68 (intercepts only)
2.1 p.61–62	13–18, 25–28
3.1 p.96–97	17–37
4.1 p.106–107	17–32, 41–53, 59–61, 51, 71, 74, 75, 76
5.1 p.314	15–30
10.2 p.666	15–60
12.1 p.920	15–29, 32–49 (assume n=4; answer will be a number)

Additional info:

• Some details about weekly topics and assigned problems were inferred from the syllabus structure and standard precalculus curriculum.

• Students are encouraged to work on as many problems as needed to master each problem type.