Mastering Precalculus: A Comprehensive Foundation for Calculus
Master essential precalculus concepts through a structured, collaborative learning experience. This course covers functions, trigonometry, and analytical geometry, providing a solid foundation for advanced mathematics studies.
What You'll Learn
- Master fundamental concepts of functions and their properties
- Develop strong skills in polynomial and rational functions analysis
- Gain expertise in exponential and logarithmic functions
- Master trigonometric functions and their applications
- Learn to analyze and graph conic sections
AI Mentor Inspiration
Leonard Mathler
An AI tutor specializing in precalculus and mathematical analysis, combining the analytical precision of Leonard Euler with modern teaching methods.
Detailed Schedule
Week 1
Functions and Graphs: Understanding Domain, Range, and Transformations
Master the fundamentals of functions, their properties, and graphical representations.
- Topics:
- Function properties and transformations
- Domain and range analysis
- Inverse functions
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How do transformations affect function graphs?
- What are the key characteristics of inverse functions?
- How do we determine domain and range restrictions?
- Reading Assignments:
- Stewart/Redlin/Watson: Chapters 1-2 (Functions and Graphs)
- Sullivan: Chapters 1-2 (Functions and Their Graphs)
- Practice problems from textbook sections 1.1-1.4
- Video Assignments:
- Watch: 'Introduction to Function Transformations'
- Tutorial: 'Graphing Functions Step by Step'
Week 2
Polynomial and Rational Functions: Analysis and Applications
Explore polynomial and rational functions, focusing on their behavior and characteristics.
- Topics:
- Polynomial functions and their zeros
- Rational functions and asymptotes
- Synthetic division
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How do we determine end behavior of polynomials?
- What techniques help identify polynomial zeros?
- How do we find and interpret asymptotes?
- Reading Assignments:
- Stewart/Redlin/Watson: Chapter 3
- Sullivan: Chapter 3
- Selected practice problems on polynomial division
- Video Assignments:
- Watch: 'Understanding Polynomial Behavior'
- Tutorial: 'Analyzing Rational Functions'
Week 3
Exponential and Logarithmic Functions: Properties and Applications
Master exponential and logarithmic functions and their real-world applications.
- Topics:
- Exponential growth and decay
- Logarithmic properties
- Solving exponential equations
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How do logarithmic properties simplify complex expressions?
- What real-world scenarios model exponential growth?
- How do we solve compound interest problems?
- Reading Assignments:
- Stewart/Redlin/Watson: Chapter 4
- Sullivan: Chapter 4
- Practice problems on logarithmic equations
- Video Assignments:
- Watch: 'Exponential Growth in Nature'
- Tutorial: 'Solving Logarithmic Equations'
Week 4
Trigonometric Functions: Unit Circle and Graphs
Understand trigonometric functions, their properties, and graphical representations.
- Topics:
- Unit circle and radian measure
- Trigonometric graphs
- Basic identities
- Live Session Duration: 90 minutes
- Homework Duration: 180 minutes
- Discussion Points:
- How does the unit circle relate to trigonometric functions?
- What affects the period and amplitude of trig graphs?
- How do we apply basic trigonometric identities?
- Reading Assignments:
- Stewart/Redlin/Watson: Chapter 5
- Sullivan: Chapter 5
- Practice problems on trigonometric graphs
- Video Assignments:
- Watch: 'Understanding the Unit Circle'
- Tutorial: 'Graphing Trigonometric Functions'
Student Experiences
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Learning with Cohorts and AI
Learn Better with Cohorts
Working with peers enhances understanding through collaborative problem-solving and diverse perspectives on mathematical concepts.
AI-Powered Learning
Our AI tutor provides step-by-step problem solutions, identifies learning patterns, and offers personalized practice problems based on your progress.
Frequently Asked Questions
What are the prerequisites for this course?
Students should have completed Algebra II and have a basic understanding of functions and graphing.
How much time should I dedicate to this course weekly?
Plan to spend 8-10 hours per week, including lectures, homework, and group study sessions.
What materials are needed for this course?
A graphing calculator (TI-84 or similar), the required textbook, and access to online resources.
Is this course suitable for self-paced learning?
While the course includes self-study components, participating in scheduled group activities is essential for optimal learning.
How will this prepare me for calculus?
This course builds the essential foundation in functions, trigonometry, and analytical thinking required for success in calculus.
Course Details
- 6 weeks
- Cohort-based learning
- Start anytime
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