Precalculus Course Outline MA150
Course Code: MA150
Course Title: Precalculus
Credits: 4
Duration: 15 weeks
Prerequisites: Intermediate Algebra or equivalent
Course Description
MA150 Precalculus is designed to provide students with the mathematical foundation required for calculus and other advanced mathematics courses. This comprehensive course covers fundamental concepts including functions, trigonometry, analytic geometry, and algebra that are essential for success in calculus. Through lectures, problem-solving sessions, and interactive exercises, students will develop critical thinking skills and mathematical reasoning abilities necessary for upper-level mathematics and sciences.
Course Objectives
Upon successful completion of MA150 Precalculus, students will be able to:
- Demonstrate a thorough understanding of function concepts including domain, range, operations, and inverses.
- Analyze and graph various types of functions including polynomial, rational, exponential, and logarithmic.
- Apply trigonometric functions, identities, and equations to solve problems.
- Utilize analytic geometry concepts including conic sections, polar coordinates, and parametric equations.
- Implement mathematical models to solve real-world applications.
- Use appropriate technology to visualize functions, solve equations, and analyze data.
Weekly Course Outline
Introduction to functions, domain and range, function notation, composition of functions, inverse functions, and transformations. Graphing techniques for basic functions including linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions.
Polynomial functions, long and synthetic division, the Remainder and Factor Theorems, zeros of polynomial functions, rational functions, asymptotes, and applications. Graphing polynomial and rational functions with emphasis on analyzing key features.
Exponential functions and models, logarithmic functions, properties of logarithms, solving exponential and logarithmic equations. Applications including exponential growth and decay, compound interest, and pH calculations.
Angles and their measure, degrees and radians, arc length, linear and angular speed, unit circle approach, trigonometric functions of any angle, graphs of sine, cosine, tangent functions, amplitude, period, phase shift, and vertical shift. Applications of trigonometric functions.
Trigonometric identities, sum and difference formulas, double-angle and half-angle formulas, product-to-sum and sum-to-product formulas. Inverse trigonometric functions and solving trigonometric equations.
Law of Sines and Law of Cosines, area of a triangle, vectors, vector operations, dot product, complex numbers in trigonometric form, De Moivre's Theorem, and polar coordinates.
Solving systems of linear equations using substitution, elimination, and matrices. Matrix operations, Gaussian elimination, determinants, Cramer's Rule, systems of nonlinear equations, and partial fraction decomposition.
Sequences and series, arithmetic sequences and series, geometric sequences and series, binomial theorem, counting principles, permutations, combinations, probability, and mathematical induction.
Conic sections: parabolas, ellipses, and hyperbolas. Rotation of axes, parametric equations, and polar equations of conics.
Assessment Methods
- Homework Assignments (15%): Weekly problem sets to reinforce concepts covered in class.
- Quizzes (15%): Short weekly quizzes on specific topics to assess comprehension.
- Midterm Examination (25%): Comprehensive examination covering Weeks 1-7 material.
- Final Project (10%): Independent project applying precalculus concepts to real-world problems.
- Final Examination (35%): Cumulative examination covering all topics from the semester.
Required Materials
- Textbook: Precalculus: Mathematics for Calculus (8th Edition) by Stewart, Redlin, and Watson
- Scientific Calculator: TI-84 or equivalent graphing calculator
- Online Resources: Access to Learning Management System for supplementary materials and assignments
- Graph Paper: For manual graphing exercises
Course Policies
- Attendance: Regular attendance is expected. More than three unexcused absences may result in grade reduction.
- Assignment Submission: All assignments must be submitted by the specified deadline. Late submissions will receive a 10% deduction per day.
- Academic Integrity: All work must be your own. Collaboration is encouraged for homework, but quizzes and examinations must be completed independently.
