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PRE-CALCULUS - MATH 1113 (3 Credit Hours)
Description: This course is designed to prepare students for calculus, physics, and related technical subjects. Topics include an intensive study of algebraic and transcendental functions accompanied by analytic geometry and trigonometry.
Prerequisites: Math 1101- Math Modeling or Math 1111 - College Algebra
Course Structure:
- Lesson 1: Equations
- Setting up Equations
- Graphs of Equations and Circles
- Equations of Lines
- Lesson 2: Functions
- Introduction to Functions
- Properties of Functions
- Transformations
- Operations on Functions
- Lesson 3: Polynomial Functions
- Quadratic Functions
- Applications
- Polynomials of Higher Order
- Finding Real Roots of Polynomials
- Lesson 4: Rational Functions
- Domains and x-intercepts
- End Behavior
- Proper and Improper Functions
- Asymptotes
- Graphing
- Lesson 5: Exponential and Logarithmic Functions
- Inverse Functions
- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- Logarithmic and Exponential Functions
- Applications
- Lesson 6: Introduction to Trigonometric Functions
- Angles and Their Measures
- Unit Circle Approach
- Properties of Trigonometric Functions
- Right Angle Trigonometry
- Lesson 7: Graphs of Trigonometric Functions and Inverse Functions
- Graphs of Sine and Cosine Functions
- Graphs of Other Trigonometric Functions
- The Inverse Trigonometric Functions
- Lesson 8: Analytic Trigonometry
- Trigonometric Identities
- Sum and Difference Formulas
- Double-Angle and Half-Angle Formulas
- Product-to-Sum and Sum-to-Product Formulas
- Trigonometric Equations
- Lesson 9: Applications of Trigonometry
- Solving Right Triangles
- The Law of Sine
- The Law of Cosines
- Area of a Triangle and Simple Harmonic Motion
Course Objectives:
After completing this course the student will be able to:
- Identify the characteristics of various functions such as:
- definition of a function domain and range
- average rate of change
- algebraic combinations
- composition
- inverse functions
- Sketch and analyze the graphs of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions.
- Set up and solve word problems using algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions.
- Solve equations using algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions.
- Demonstrate knowledge of the basic trigonometric identities and formulas.
- Demonstrate knowledge of basic properties of logarithmic and exponentials functions.
- Analyze when the use of technology is appropriate and when to apply the technology.
Also Required:
TI-83 or TI-84 Graphing Calculator