Precalculus MATH-2412 Syllabus and Course Structure Study Guide

Course Overview

Introduction to Precalculus

This course, MATH-2412, is designed to prepare students for calculus by covering essential algebraic and trigonometric concepts. The curriculum includes polynomial, rational, exponential, logarithmic, and trigonometric functions, as well as analytic geometry topics such as conic sections and polar coordinates. The course emphasizes both theoretical understanding and practical application of these mathematical concepts.

• Course Title: Pre-Calculus Math (MATH-2412)

• Credits: 4

• Prerequisite: MATH 1316 - Plane Trigonometry

• Textbook: Precalculus, Sullivan, 12th ed, ISBN 9780138279257

• Recommended Calculator: TI-84 family (non-CAS)

Learning Outcomes

State-Defined Learning Outcomes

Students will demonstrate and apply knowledge of the properties of functions, recognize and apply algebraic and transcendental functions, and solve related equations. The course also covers graphing techniques, computation of trigonometric function values, proof of trigonometric identities, and solving triangles.

• Properties of Functions: Understanding domain, range, and behavior of functions.

• Algebraic and Transcendental Functions: Application and solution of equations involving these functions.

• Graphing Techniques: Mastery of plotting and interpreting function graphs.

• Trigonometric Functions: Calculation for key angles in degrees and radians.

• Trigonometric Identities: Proof and application in problem-solving.

• Solving Triangles: Both right and oblique triangles using trigonometric laws.

Texas Core Objectives

• Critical Thinking Skills: Analysis, evaluation, and synthesis of mathematical information.

• Communication Skills: Effective expression of mathematical ideas in written, oral, and visual forms.

• Empirical and Quantitative Skills: Manipulation and analysis of numerical data.

• Teamwork: Collaboration and consideration of diverse perspectives.

• Personal Responsibility: Ethical decision-making and understanding consequences.

• Social Responsibility: Engagement in civic and global communities.

Course Topics and Schedule

Weekly Topic Breakdown

The course is structured to cover the following major topics, each corresponding to chapters in a standard precalculus textbook:

• Week 1: Functions and Their Graphs (Ch. 2)

• Week 2: Transformations, Polynomial Functions (Ch. 2, 4)

• Week 3: Rational Functions, Partial Fraction Decomposition, Inequalities (Ch. 4, 11)

• Week 4: Composite Functions, Inverse Functions, Exponential and Logarithmic Functions (Ch. 5)

• Week 5: Properties of Logarithms, Exponential and Logarithmic Equations (Ch. 5)

• Week 6: Review and Exam 1

• Week 7-8: Trigonometric Functions, Inverse Trig Functions, Trig Equations and Identities (Ch. 6, 7)

• Week 9: Applications of Trigonometric Functions, Law of Sines and Cosines (Ch. 8)

• Week 11-12: Polar Coordinates, Polar Equations, Vectors, Dot Product (Ch. 9)

• Week 13-14: Conic Sections: Circles, Parabola, Ellipse, Hyperbola (Ch. 10)

• Week 15: Sequences, Series, Binomial Theorem (Ch. 12)

• Week 16: Final Exam Review and Final Exam

Sample Course Schedule Table

Week	Topics
1	Functions, Graphs, Properties, Piece-wise Functions
2	Transformations, Polynomial Functions, Real Zeros
3	Rational Functions, Partial Fractions, Inequalities
4	Composite, Inverse, Exponential, Logarithmic Functions
5	Logarithms, Exponential Equations
6	Review, Exam 1
7-8	Trigonometric Functions, Identities, Equations
9	Applications, Law of Sines/Cosines
11-12	Polar Coordinates, Vectors
13-14	Conic Sections
15	Sequences, Series, Binomial Theorem
16	Final Exam

Grading Structure

Assessment Components

Graded work in the course is divided into several categories, each contributing to the final grade. The breakdown is as follows:

Type	Weight	Notes
Assignments in MyLab Math	20%	Homework for each section; best score kept; late penalty applies
Participation + Quiz	15%	Weekly quizzes, in-class activities; lowest 4 dropped
Midterm Exam 1	20%	Based on review; no formula sheets; extra credit for homework completion
Midterm Exam 2	20%	Same as above
Final Exam	25%	Cumulative; can replace lowest midterm score

Grade Scale

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

Key Course Policies

Attendance and Participation

• Regular attendance and active participation are required for success.

• Expect to spend 12-16 hours per week on coursework.

• Late work is generally not accepted for in-class activities, quizzes, or exams.

Homework and Exams

• Homework can be completed after the due date (with penalty) until the exam covering that material.

• Makeup exams are only allowed for extreme circumstances with documentation.

• Extra credit is available for timely completion of homework.

• Final Exam score may replace the lowest midterm score if higher.

• Lowest 4 homework and quiz scores are dropped.

Academic Integrity

• All quizzes and exams must be completed without outside assistance.

• Academic dishonesty results in severe penalties, including possible course failure.

Support and Resources

Student Support Services

• Success Coach: Personalized support for academic and career goals.

• Free Tutoring: Available both in-person and online.

• Student Care Network: Assistance with health, finances, and basic needs.

• Technical Support: Help with eCampus and other college technology.

Summary of Precalculus Topics

Major Chapters Covered

• Ch. 1: Graphs

• Ch. 2: Functions and Their Graphs

• Ch. 3: Linear and Quadratic Functions

• Ch. 4: Polynomial and Rational Functions

• Ch. 5: Exponential and Logarithmic Functions

• Ch. 6: Trigonometric Functions

• Ch. 7: Analytic Trigonometry

• Ch. 8: Applications of Trigonometric Functions

• Ch. 9: Polar Coordinates; Vectors

• Ch. 10: Analytic Geometry

• Ch. 11: Systems of Equations and Inequalities

• Ch. 12: Sequences; Induction; Binomial Theorem

• Ch. 13: Counting and Probability

• Ch. 14: Preview of Calculus: Limits, Derivatives, Integrals

Example: Polynomial Functions

Definition: A polynomial function is an expression of the form $f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0$, where $a_n \neq 0$ and $n$ is a non-negative integer.

• Degree: The highest power of $x$ in the polynomial.

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

• Example: $f(x) = 2x^3 - 5x^2 + x - 7$

Example: Trigonometric Functions

Definition: Trigonometric functions relate angles to ratios of sides in a right triangle. The primary functions are sine, cosine, and tangent.

• Sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

• Cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

• Tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

• Unit Circle: Used to compute values for key angles in both degrees and radians.

Example: Exponential and Logarithmic Functions

Exponential Function: $f(x) = a^x$, where $a > 0$ and $a \neq 1$.

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

• Properties: $\log_a(a^x) = x$ and $a^{\log_a(x)} = x$

• Example: $\log_{10}(100) = 2$

Example: Sequences and Series

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

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

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

Additional info:

• All major precalculus topics are covered as per the course schedule and textbook.

• Students are expected to use MyLab Math for homework and eCampus for course materials.

• Support services are available for academic, technical, and personal needs.