I. General Information

1. Course Title:
Precalculus

2. Course Prefix & Number:
MATH 1472

3. Course Credits and Contact Hours:

Credits: 5

Lecture Hours: 5

Lab Hours: 0

4. Course Description:

The purpose of this course is to provide students with the essential mathematical background needed for the study of Calculus. Topics covered in this course include solving equations, polynomial and rational functions, radical functions, exponential and logarithmic functions, trigonometric functions and their inverses, trigonometric identities, applications, polar coordinates and graphs, sequences and series, and conic sections if time allows.

5. Placement Tests Required:

Accuplacer (specify test):

College Level Math Exam

Score:

63

6. Prerequisite Courses:

8. Prerequisite (Entry) Skills:
Students entering this course should have a cursory understanding of solving equations and inequalities, functions and graphs, polynomial functions, rational functions, inverse functions, exponential functions, logarithmic functions, problems solving, and the use of a graphing calculator.

9. Co-requisite Courses:

There are no corequisites for this course.

II. Transfer and Articulation

1. Course Equivalency - similar course from other regional institutions:

Bemidji State University, 1470 Precalculus, 5 credits
St. Cloud State University, MATH 115, 5 credits

III. Course Purpose

1. Program-Applicable Courses – This course fulfills a requirement for the following program(s):

2. MN Transfer Curriculum (General Education) Courses - This course fulfills the following goal area(s) of the MN Transfer Curriculum:
Goal 4 – Mathematical/Logical Reasoning

IV. Learning Outcomes

1. College-Wide Outcomes

College-Wide Outcomes/Competencies	Students will be able to:
Analyze and follow a sequence of operations	Solve complex problems by following a sequence of operations.
Apply abstract ideas to concrete situations	Solve problems that apply the topic to real world situations.
Utilize appropriate technology	Use the graphing calculator as developed for the study of functions and parametric/polar graphing.

2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of the course:

• Identify graphs of functions and recognize transformations;
• Perform operations and compositions with functions;
• Solve linear and quadratic equations and inequalities;
• Find the zeros of a polynomial function and solve polynomial equations;
• Solve exponential and logarithmic equations;
• Solve problems using right triangle trigonometry;
• Solve problems using law of sines and law of cosines;
• Apply properties of trigonometric functions;
• Recognize and use trigonometric identities;
• Find inverses of trigonometic functions;
• Use polar coordinates and graphs;
• Recognize and generate sequences and series;
• Identify and work with conic sections.

V. Topical Outline

Listed below are major areas of content typically covered in this course.

1. Lecture Sessions

Listed below are major areas of content typically covered in this course. 

1. FUNCTIONS, GRAPHS, AND MODELS
• Using Graphing Utilities
• Functions
• Functions: Graphs and Properties
• Functions: Graphs and Transformations
• Operations on Functions; Compositions
• Inverse Functions
2. MODELING WITH LINEAR AND QUADRATIC FUNCTIONS
• Linear Functions
• Linear Equations and Models
• Quadratic Functions
• Complex Numbers
• Quadratic Equations and Models
• Additional Equation Solving Techniques
• Solving Inequalities
3. POLYNOMIAL AND RATIONAL FUNCTIONS
• Polynomial Functions And Models
• Polynomial Division
• Real Zeros and Polynomial Inequalities
• Complex Zeros and Rational Zeros of Polynomials
• Rational Functions and Inequalities
4. MODELING WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS
• Exponential Functions
• Exponential Models
• Logarithmic Functions
• Logarithmic Models
• Exponential and Logarithmic Equations
5. TRIGONOMETRIC FUNCTIONS
• Angles and Their Measure
• Trigonometric Functions: A Unit Circle Approach
• Solving Right Triangles
• Properties of Trigonometric Functions
• More General Trigonometric Functions and and Models
• Inverse Trigonometric Functions
6. TRIGONOMETRIC IDENTITIES AND CONDITIONAL EQUATIONS
• Basic Identities and Their Use
• Sum, Difference, and Cofunction Identities
• Double-Angle and Half-Angle Identities
• Product-Sum and Sum-Product Identities
• Trigonometric Equations
7. ADDITIONAL TOPICS IN TRIGONOMETRY
• Law of Sines
• Law of Cosines
• Vectors in the Plane
• Polar Coordinates and Graphs
• Complex Numbers and De Moivre's Theorem
8. SEQUENCES AND SERIES
• Sequences and Series
• Mathematical Induction
• Arithmetic and Geometric Sequence 
9. ADDITIONAL TOPICS IN ANALYTIC GEOMETRY (if time allows)
• Conic Sections; Parabola
• Ellipse
• Hyperbola
• Translation and Rotation of Axes
• Systems of Nonlinear Equations